Introduction to the Light-Emitting Diode: Real Applications for Industrial Engineers 3031307151, 9783031307157

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Synthesis Lectures on Materials and Optics

Hisashi Masui

Introduction to the Light-Emitting Diode Real Applications for Industrial Engineers

Synthesis Lectures on Materials and Optics

This series publishes concise books on topics that include advanced and state-of-the-art methods to understand and develop materials for optics. Leading experts on the subject present and discuss both classical and new wave theory, techniques, and interdisciplinary applications in the field. Optical materials play an integral role in the development of numerous advances in areas from communications to sensors to photonics and more, and this series discusses a broad range of topics and principles in condensed matter physics, materials science, chemistry, and electrical engineering.

Hisashi Masui

Introduction to the Light-Emitting Diode Real Applications for Industrial Engineers

Hisashi Masui San Jose, CA, USA

ISSN 2691-1930 ISSN 2691-1949 (electronic) Synthesis Lectures on Materials and Optics ISBN 978-3-031-30715-7 ISBN 978-3-031-30716-4 (eBook) https://doi.org/10.1007/978-3-031-30716-4 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Dedicated to All My Teachers, to My Dear Wife, and to My Dearest Parents

Foreword

The practical information you find in this book, you will not find in standard LED textbooks. Dr. Hisashi Masui possesses deep knowledge of device packaging from a standpoint of a graduate student, postdoctoral scholar, and also a leading industry engineer who has worked in the LED Industry both in the US and internationally. Mr. Masui arrived at the University of California, Santa Barbara as a visiting researcher through an industrial member company supporting my research. Mr. Masui joined the MOCVD research group and pursued his Ph.D. through the Solid-State Lighting & Energy Electronics Center (SSLEEC) at UC Santa Barbara. In the Center we partnered with over a dozen leading LED companies, during which time Mr. Masui’s expertise in device packaging technology was developed. The emphasis at UCSB was on the academiaindustry collaborations to develop solid-state lighting. SSLEEC maintains the spirit of collaboration, and Dr. Masui carries with him the same spirit throughout his career. After graduate school, Dr. Masui returned to work professionally at several leading LED manufacturing companies. Through his explanations, he offers the reader practical LED-centric knowledge difficult to access on traditional textbooks. Be sure to check out the first half of the book (Chaps. 1–3) to learn about the LED industry from an insider perspective. The second half (Chaps. 4–5) will expose readers to the technical details which semiconductor professionals learn. The appendices contain the basic solid-state physics familiar to most semiconductor engineers and will be useful as a reference for those with non-semiconductor backgrounds. Winter 2022

Steven P. DenBaars University of California Santa Barbara, CA, USA Shuji Nakamura University of California Santa Barbara, CA, USA

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Preface

While working as an experimental scientist at a renowned LED company, I gradually realized two facts. One, not all engineers at the company had LED or solid-state lighting (SSL) backgrounds. Two, there were a lot more people working beyond R&D, in manufacturing and marketing/sales who might not be so interested in LED physics or semiconductor materials science. There are plentiful LED textbooks written by leading researchers and professors of the field, but those advanced textbooks were not quite satisfactory to engineers new to the company. They seemed wanting to learn something else. Under such circumstances, I was asked by my immediate manager to gather a small class to teach LED basics. You might think the class started on discussing the pn junction; instead we began with how LED products were characterized and why particular methods of characterization were used, what quantities engineers and customers were interested in knowing, and where in the vast field of science those quantities originated from. After a few years my class became a full coverage of LED engineering, from semiconductor physics all the way to product manufacturing. I then came to believe that the class contents were valuable enough to write down. Years before being familiar with the LED, my first encounter with solid-state luminescence was at my college back in the 1980s. A physics professor, Prof. Tokihisa Nakamura, demonstrated an inorganic electroluminescence (EL) device privately, in the dark after school. The glowing sheet in dim green looked mysterious and fascinating. When I started my first graduate school study, I begged my advisor, Prof. Manabu Takeuchi of materials science, to initiate an organic EL project. It was in 1989, only a year and half after Eastman Kodak’s original paper on an organic EL device. I encountered the LED as a professional in 1991. As I finished my master’s thesis, I obtained my first job at Stanley Electric where I was assigned an LED project on epitaxy technology, despite my wish of joining its EL team. Stanley Electric was a well-established public company famous for its LED products. The research group I joined was investigating liquid-phase epitaxy of ZnSe for blue-LED application (this was before GaN emergence—it was a lucky opportunity because I put my hands on a material and growth technique other than GaN and MOCVD), and soon after I branched off to MOCVD to grow ZnSe. In 1994 I was transferred as a visiting scholar to University ix

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of California Santa Barbara (UCSB) where I studied GaN epitaxy under Prof. Steven P. DenBaars with his postdoc researchers and graduate students. Young Prof. DenBaars was a renowned researcher in MOCVD technology and had moved from Hewlett-Packard. At his lab GaN publications written in English were apparently insufficient for those eager MOCVD researchers to collect technical information, while Japanese patents were extra sources of technical knowledges. I became busy extracting all growth conditions from Japanese patents to carry out MOCVD GaN growth with the UCSB researchers. If you recall, the mid-1990s was a hot time of GaN technology, with newly-explored GaN devices like lasers and white LEDs in addition to fundamental growth and materials discoveries. World conferences on nitride semiconductors were full of learnings and fun (often afterhours activities also). Upon completion of the 2-year joint project, I went back to Stanley Electric and worked in a GaN MOCVD group. I also had a chance to work in a product packaging and characterization department at Stanley Electric. I became attracted by the LED, due largely to its established solid-state physics aspects. At the same time I gradually built up my feeling of lack of knowledge to be a senior professional. It was indeed a thirst and urge for scientific knowledge. I wanted to concentrate on the interest of mine; unfortunately Tokyo was too busy, with too many attractions that would drag me out to the downtown. That was not what I needed. In 2002, I passed exams and entered UCSB’s graduate school and started my study as a fulltime graduate student under Prof. DenBaars. Next to him already was Prof. Shuji Nakamura, the 2014 Nobel laureate. Prof. Nakamura had been known as one of the industrial pioneer engineers who contributed to industrialization of InGaN LEDs. Prof. Nakamura told me in person some of his breakthroughs made during his industrial career. While taking advanced optoelectronics and MOCVD classes, my assigned research subject was LED packaging technology, which I later extended into LED characterization. Prof. DenBaars put me in charge of a newly allocated packaging lab, to which I started gathering packaging equipment and characterization instruments. A few years later it appeared like a small assembly and inspection line that you would find in a startup company, supporting packaging and characterization of LED devices from MOCVD reactors of both Profs. DenBaars and Nakamura. I can emphasize the importance of supplier relations here: In order to customize newly purchased lab instruments, and to receive long-term services on them, maintaining good supplier relations does pay off. With 5 years and a few more months, I obtained a degree in materials science. After spending a short period as a postdoc, I was hired at Soraa, which was a local startup company started by a few UCSB professors a year earlier. Santa Barbara (and neighboring City of Goleta) was an interesting area where a startup environment had grown. Meaning, professors had experiences of starting companies, small warehouse spaces were always available somewhere in the area, students and postdocs were seeking jobs without relocating, local engineers and techs were mobile to switch to a new company, and so on. Yet Santa Barbara is a small city for a company to grow big. Soraa was trying to be larger with its novel technology. Silicon Valley is resourceful and accommodates more

Preface

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people. I was transferred to Soraa’s brand-new Silicon Valley office to which the company’s headquarter functions were also moving. My colleagues and I worked on packaging technologies and phosphor integration combined with characterization to industrialize the novel technology out of UCSB. Given the young company’s energy and the time of SSL excitement, we focused on high-end lighting products. All of a sudden, a few years later a group of employees including myself got laid off. Being laid off was not a pleasant experience, but it turned out to be a chance to a new exposure. Soon after I joined Bridgelux, another LED company in the great Silicon Valley area. Bridgelux aimed at general lighting products where cost-effective solutions were sought. I was solely in charge of a new phosphor integration process to implement. About when I made the first demo unit of a cost-effective lighting solution, one of the ex-UCSB friends of mine introduced me to a position at Lumileds. Lumileds had lots of optoelectronics history from its HewlettPackard time and was under Royal Philips back then. Lumileds was also full of resources. I was first put in charge of a new concept LED chip. A few months later I demonstrated a unique approach to the concept by hand-making an LED device, and in coming years brought that approach to new-product implementation (NPI), where I had opportunities to see and learn manufacturing engineering closely. This exposure to manufacturing made me believe that industrial R&D engineers need to know manufacturing to a certain extent, in addition to various aspects of LED physics and color science. Over these years of my career, “LED” has been always the keyword of my profession, yet every company tried to accomplish something different. Thus working at various LED companies gave me skills of taking various concepts and approaches to tackle a problem. At every place I worked, there were always many teachers who taught me something that I had not learned previously. I wish to thank all my teachers. As a result of my professional experiences as described above, I came to believe that it was my task to put the learnings in a form of concise book. Therefore, this book has been written for industrial engineers predominantly. This book describes what you need to know to get started at an LED company. Not only that, during your future years in the industry, this book will support you for deeper learning in LEDs, from R&D to manufacturing, wherever your career is headed. Even more, if you are in academia, I hope this book tells you how attractive the world of LED industry is. We have so many interesting problems to solve, or at least to resolve (in fact, one of the great things I learned in industry is that any problem can be resolved, if not solved). And we have many people working in various branches, from deep R&D, system designing, manufacturing, all the way to sales and marketing and field engineering. Everybody wants to know more about LED technology, but about various aspects of it in various ways of thinking. That is the reason why this book has come about. While there are many textbooks on LEDs that you can purchase, this book uniquely focuses on industrial engineering, on subjects that industrial engineers confront at their work. I have to admit, nevertheless, that upon writing about industrial aspects of technology things get slightly difficult, because of companies’ intellectual properties and confidentiality. This has been a challenge of this book.

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Nonetheless, a wide range of engineers in the LED industry should benefit from this book, as the scope spans from the LED physics essence, LED device structure, product ingredients, manufacturing methods, applications, to customer communications from a viewpoint of industrial engineers. After providing a brief chapter of Introduction, the book starts with a discussion on Characterization of LED devices for a reason that this is the first burden that new engineers owe. Chapter 2 describes what quantities the industry is interested in and how they are measured. This chapter provides you knowledge of language and terminology that the LED industry uses. The subsequent Chap. 3 discusses various types of LED devices and how they are fabricated. This somewhat deep knowledge in LEDs will definitely take you further in the industry. You will find various “layers” in the LED: For many people the LED means LED lighting devices or light engines, for others it implies LED light bulbs or lighting fixture, while physics students may envision a pn junction or semiconductor chips. This chapter reveals what is inside an LED product, in order to establish connections between a semiconductor chip and a lighting fixture. Chapter 4 provides a deep dive into physics of each technology in the LED. This chapter should inform you what scientists and engineers of each field are concerned with the most, to help understanding and conversation with them. Because of the deep-dive nature, semiconductor physics of the undergraduate level may be a prerequisite to survive this chapter. Finally, related topics of optics are laid out in Chap. 5. These topics cannot be missed when LED science and engineering are considered. San Jose, CA, USA Winter 2022

Hisashi Masui

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Definition and the Range of LED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 LED in Lighting History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Safety Precautions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 4 5

2 Characterization Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Purpose of Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Characterization Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Data Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Efficiency Breakdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Effect of Encapsulation on Light Output . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Optical Characterization, Geometry Involved . . . . . . . . . . . . . . . . . . . . . . . 2.7 Electrical Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Testing and Characterization in Wafer and Tile Forms . . . . . . . . . . . . . . . 2.9 Thermal Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Reliability Tests and Stressing Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 2.11 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 7 8 14 23 27 28 33 35 36 40 43 43

3 Device Architecture and Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 LED Chip (Die) and Market Segmentation of Products . . . . . . . . . . . . . . 3.2 Chip Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 LED Wafer Fabrication via Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Functional Device Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Down-Converter (Phosphor) Integration and Packaging . . . . . . . . . . . . . . 3.6 UV-Pump White LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Stack-Up Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45 45 49 53 60 67 78 79 83 83

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Contents

4 Semiconductor Crystals and Device Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Semiconductor Materials for LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Luminescence Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 In Semiconductor Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 In Device Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Crystal Defects in GaN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Phosphor Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Material Types for LED Application . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Luminescence Characteristics of Phosphors . . . . . . . . . . . . . . . . . . 4.4 Silicone Encapsulant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 LED as a Diode: Electrical Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Diode Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Real LED Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85 85 91 91 96 99 101 101 103 105 108 108 110 114 115

5 Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Light as EM Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 TIR Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Reflectance and Transmittance Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Geometrical Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Fourier Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Fourier Transform by Wave Diffraction and Interference . . . . . . . 5.5.2 The Use of a Lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Electron Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117 117 122 122 125 130 131 135 139 140 141

Appendix A: Eight-Page Introduction to Semiconductor Basics . . . . . . . . . . . . . .

143

Appendix B: Hole Generation and Transport in Mg-Doped GaN . . . . . . . . . . . . .

153

Appendix C: Origin of the Turn-On Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

157

Appendix D: Wave-Particle Duality and the Wavefunction . . . . . . . . . . . . . . . . . .

163

Appendix E: Crystal Momentum and the E–k Diagram . . . . . . . . . . . . . . . . . . . . .

165

Appendix F: Entropy and Thermal Carrier Distribution . . . . . . . . . . . . . . . . . . . .

169

Appendix G: Density of States and Quantum Effect . . . . . . . . . . . . . . . . . . . . . . . .

173

Appendix H: Phonons and Their Role in Electronic Transitions . . . . . . . . . . . . . .

177

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Appendix I: Spontaneous and Piezoelectric Polarization Fields in III-Nitrides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

179

Appendix J: The ABC Model for Recombination Dynamics . . . . . . . . . . . . . . . . .

183

Appendix K: The Exciton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

193

Appendix L: Organic LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

195

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

197

Acronyms

1D, 2D, 3D AC ADB AFS ALD AR AS AVI BAM BEOL BF BKM BOM BOSE BRDF BTDF CBCP CCD ccp CCT CHMSL CIE CMP COA COB CPC CRI CRT CSP

One-dimensional, Two-dimensional, Three-dimensional Alternating current Adaptive driving beam Advanced front-lighting system Atomic layer deposition Augmented reality, Anti-reflective Aperture stop Automated visual inspection BaMgAlO Back end of line Bright field Best known method Bill of materials Ba ortho-silicate Eu Bidirectional reflectance distribution function Bidirectional transmittance distribution function Center beam candlepower Charge-coupled device Cubic close-packed Correlated color temperature Center high-mount stop lamp Commission Internationale de l’Eclairage (International Commission on Illumination) Chemical-mechanical polishing Color over angle Chip on board Compound parabolic collector/concentrator Color-rendering index Cathode ray tube Chip-scale package xvii

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CTE CW D65 DAP DC DF DH DMA DMM DOE DOS DRBFM DRL DSP DUT EBL EL EM EPD EQE ESD EXE FA FC FMEA FOM FOV FS FT FWHM GGI GRIN GRR hcp HEMT HMD HT HTOL ID IESNA IP

Acronyms

Coefficient of thermal expansion Continuous wave, Cool white Daylight illuminant (a CIE illuminant standard) Donor-acceptor pair Direct current Dark field Double hetero Dynamic mechanical analysis Digital multimeter U.S. Department of Energy, Design of experiments Density of states Design review based on failure mode Daytime running lamp Double-side polished Device under test Electron blocking layer Electroluminescence Electromagnetic Electrophoretic deposition External quantum efficiency Electrostatic discharge Light-extraction efficiency Failure analysis Flip chip Failure mode and effect analysis Figure of merit Field of view Field stop Fourier transform Full width at half maximum Gold-gold interconnect Graded index Gage repeatability and reproducibility Hexagonal close-packed High-electron-mobility transistor Head-mount display High temperature High temperature operation life Invention disclosure, Identification/identifier The Illuminating Engineering Society of North America Intellectual property

Acronyms

IQE IR ITO I–V JEDEC L0, L1, L2, etc. LCD LCL LD LED LEO LES, LEA LLO LM-80 LOP LPE LT LuAG MCPCB MIL-STD MOCVD MQW NA NIST NPI NRR NW ODR PCB PDMS PEC PET PIG PL PMT POR p&p PSA PSS PVC QCSF

xix

Internal quantum efficiency Infrared Indium tin oxide Current-voltage Joint Electron Device Engineering Council Level 0, Level 1, Level 2, etc Liquid-crystal display Lower control limit Laser diode Light-emitting diode Lateral epitaxial overgrowth Light-emitting surface, Light-emitting area Laser liftoff Lumen-maintenance 80 (a lumen-maintenance standard) Light output Liquid-phase epitaxy Low temperature Lutetium aluminum garnet Metal-core printed circuit board U.S. Military standard Metalorganic chemical vapor deposition Multiple quantum well Numerical aperture National Institute of Standards and Technology New product introduction/implementation Nonradiative recombination Neutral white Omni-directional reflector Printed circuit board Polydimethylsiloxane Photoelectrochemical Polyethylene terephthalate Phosphor in glass Photoluminescence Photomultiplier tube Plan of record Pick and place Pressure-sensitive adhesive Patterned sapphire substrate Polyvinyl chloride Quantum confined Stark effect

xx

QD QFN QW R&D RDL RGB RH RI RIE RSS RT Rth , Rth SAC SCASN SEM SKU SLD SLS SMD SMU SQW SRH SSP TCS TD TDD TEM TFFC TIM TIR TMCL TMSK TSV TTV TVS UBM UCL UPH UID UV Vf , Vf

Acronyms

Quantum dot Quad-flat no-leads Quantum well Research and development Redistribution layer Red, green, and blue Relative humidity Refractive index Reactive ion etch Root sum squared Room temperature Thermal resistance Sn-Ag-Cu solder SrCaAlSiN Scanning electron microscopy Stock keeping unit Super luminescent diode Strained-layer superlattice Surface-mount device Source-measure unit Single quantum well Shockley-Reed-Hall Single-side polished Test-color sample Threading dislocation Threading dislocation density Transverse electromagnetic, Transmission electron microscopy Thin-film flip chip Thermal interfacial material Total internal reflection Temperature cycle Temperature shock Thru-silicon via Total thickness variation Transient-voltage suppressor Under-bump metallization Upper control limit Units per hour Unintentionally doped Ultraviolet Forward voltage

Acronyms

VOC VPE VR VTF WHTOL WL WPE WW XRD YAG

xxi

Volatile organic compound Vapor phase epitaxy Virtual reality Vertical thin film Wet high-temperature operation life Wavelength Wall-plug efficiency Warm white X-ray diffraction Yttrium aluminum garnet

1

Introduction

1.1

Definition and the Range of LED

LEDs are widespread in our lives today. Not only do we hear the name everyday and see them everywhere, but many people actually work on them, researching, manufacturing, and selling. At the same time many companies and individuals buy and use/consume LEDs. Because of these various aspects of people interacting with LEDs, the term “LED” has different meanings to different people. While LEDs illuminate offices and houses, physics researchers like university professors and graduate students may be thinking of mm-sized grains of semiconductor and their band diagrams of the pn junction. For device and module packaging engineers, LEDs are to emit light and heat that they want to handle neatly. Optical designers may not care much about electricity while they are dealing with the novel miniature but powerful light engines. Shop owners and employees regard LEDs as little electronic parts that happen to emit light, or emerging light-bulb products that customers recently tend to ask for. A company representative may consider LEDs as his sources of profit that he only sees on financial reports. An LED company manufactures and sells LED chips, while another LED company fabricates the LED lighting luminaire and sells it. End consumers look at modern light bulbs and flash lights that they think a little too expensive as LEDs. An electrician may think LEDs are large lighting fixtures and fancy luminaires that he needs to install in a new building. A car enthusiast may believe the LED makes the coolestlooking headlamps on his high-end car, without noticing traffic lights and street lights are also LEDs. Cellphone photographers may be surprised with knowing their camera flash is an LED. For LED professionals, these above are just various stages of LED products and prevailing applications. The LED can today mean anything from a semiconductor chip to lighting fixture in various application fields. That is why, it will not be so surprising to hear that many LED engineers have not seen a bare LED chip.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4_1

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2

1 Introduction

“LED” is originally an acronym for the light-emitting diode and has become a common noun.1 It is pronounced “el-ee-dee” in most cases, while a small number of people tend to pronounce “lez” in plural. It was more than 100 years ago that the diode was originally an electrical rectifying device of a vacuum tube. Vacuum tubes have been replaced by the solid-state technology (namely the semiconductor technology); thus the diode means solely a semiconductor-based rectifying device today. The LED is a type of diode that emits light which is visible to humans in most cases, yet in physics light often implies the electromagnetic (EM) wave. Therefore for its wider meaning, a solid-state diode that emits an EM wave can be called an LED. From a viewpoint of electrical devices, an LED is a DC device that is operated at low voltages (∼1.5–4 V). This electrical device has been integrated into various lighting devices and can draw enormous wattage when multiple LED chips are operated together. Within the scope of this book the meaning of the LED spans from a modern semiconductor device that emits visible light to lighting products that use LED chips. In the language of LED industry, that is L0 and L1 (see Chap. 3), with a little extent to L2. Another keyword in this book is the solid-state lighting (SSL). UV and IR LEDs are only of interest along the natural course of our LED discussions. Organic semiconductors are generally discussed entirely separately, thus excluded from upcoming discussions. In a spirit of “Introduction for Industrial Engineers,” the major focus of this book is not only to explain details of LED products but also to describe how LED products are made. Academic interests in physics of semiconductor devices are set as a secondary focus of this book.

1.2

LED in Lighting History

The LED is a hot field today. Why? Because lighting is a big human interest and a need by human nature, thus has become a part of modern industry. In ancient times, lighting was accomplished via flame from wood, candle (wax, solid kerosene), oil (liquid kerosene), then gas in the 19th century. The 20th century saw step-changes in lighting based on vacuum technology: Incandescent filament bulbs, discharge bulbs like the fluorescent tube lamps, and arc lamps. Mankind became able to create artificial light bright like the Sun. Accordingly, many lighting companies thrived during the century and some of them are still in existence today. When the lighting industry encountered the white LED at the end of the century, many found opportunities in it for the approaching 21st century. Today it is considered that the second half of the 20th century was a historical turnover from the vacuum technology to the solid-state technology. Transistors took over vacuum tubes in the 1960–1970s. LCDs took over CRTs in the 1990s. And the LED is the next generation player in lighting, taking over from the vacuum-based light bulbs.

1 This is similar to “laser” which is no longer spelled in capitals. Furthermore, a verb “lase” has been

derived and used in discussions.

1.2

LED in Lighting History

3

Another large industry counting on SSL technology was the automotive. Headlights equipped on earliest cars utilized oil and gas flames, and stops and turns of a vehicle were signaled by the operator’s hand. Electric light bulbs became popular for both headlights and taillamps in the 1910s as on-vehicle generators improved. High-CCT discharge lamps appeared around 2000, when white LEDs were extending into high-power applications. White LEDs were first employed for auxiliary front lighting of high-end passenger vehicles, and the first LED headlamp was finally launched in 2006. Red LED taillamps were employed in center high-mount stop lamps (CHMSLs) that the US law required in 1985. LED stop lamps first appeared in Europe in 1992 and began to be seen in the US on commercial trucks by the mid-90s. Once local traffic regulations had certified LED lamps, they spread quickly to various types of automobiles because of LEDs’ high brightness, fast response, mechanical robustness, and design flexibility. Headlight applications are different from general lighting, as they are strictly controlled by local traffic regulations. By contrast, CCT and color rendering requirements are not so demanding. Automotive applications were founded on precedent outdoor-application engineering of transportation signaling (e.g., railroad crossing lights) and signage, which aggressively moved from mechanical message boards (e.g., split-flap displays and rollsigns) to multi-color LED message boards (using discrete emitters) during the 1980s–90s. Emergence of blue and green nitride LEDs enabled full-color outdoor displays, e.g., dynamic digital out-of-home (DOOH) advertising billboards. A unique but major application that the white LED found was the camera flash. In photography artificial lighting had been sought and it was first attained via flash powders late in the 19th century. Flash powders were burning metal powders. In the 1930s press photographers shifted to portable flash bulbs; that was metal burned in a small glass bulb and thus one-time use per bulb. During the 1960s–80s electronic flashes wiped out flash bulbs. Electronic flashes utilize Xe discharge, hence are bulky and providing only one (or a small range of) CCT. As built-in cameras became popular in mobile phones, the LED happened to be the only possible solution. LEDs are compact, fast response, and readily provide various CCTs. The LED itself had its own history before meeting the lighting industry. Following the great period of scientific discoveries in solid-state luminescence during the first half of the previous century [1], light emission from semiconductor materials was engineered and industrialized in a small scale during the 1950–1970s. Applications were limited to indoor like circuit-status indicators, because LEDs were small but dim compared to other existing light sources. Those semiconductors were indirect-bandgap materials. Once researchers got access to direct-bandgap materials and bandgap engineering, the 1980s became a decade of brightness improvements that enabled outdoor applications (signboards and automotive stop-lamps). These modern LEDs made the first large step to lighting applications. The second, and final large step was the invention of endurant blue LEDs leading to the downconversion white LEDs in the 1990s. General lighting was already a large market, hence lighting companies began to invest in LED lighting technology. About 25 years later, the LED industry thrives today in spite of worldwide trade complications.

4

1 Introduction

LED manufacturing became an international operation during the 2000s. In early years of LED industrialization, R&D and manufacturing were largely focused on the synthesis of semiconductor materials that heavily depended on epitaxy equipment development, and were conducted by American companies (followed by Japanese companies during the 1980s-90s. Refer to Sects. 3.1 and 4.1), where manufacturing cost reduction was one of main targets for market penetration. Both for intellectual-property confidentiality and for advanced facilities (e.g., cleanroom engineering), manufacturing stayed within the country where R&D was performed. Triggered by the market demand for high-power LEDs around 2000 (preceded by the emergence of the phosphor-converted white LED in 1996), the international operation took off, especially in low-power product options due to the cost-down competition. Asian countries had experienced electronics and automotive industries since the 1970s; as a result, infrastructure was secured and the labor force was grown. These Asian countries received the back end of line (assembly)2 first, then followed by the middle of line (device fab), and finally the front end of line (epitaxy) became common towards the end of the 2000s. This movement enabled a worldwide supply of cost-effective LED chips and created opportunities for startup companies without possession of expensive epitaxy facilities. During the 2010s, the effort of product cost reduction introduced the fabless business model by hiring Asian contract manufacturers (CMs), which was successful in some cases. CMs had limited manufacturing capacities and tended to prioritize high-margin orders, which counteracted the cost-down effort. Today, LED manufacturing is dynamically seeking an optimized operation, while the world economy has been unpredictable.

1.3

Safety Precautions

Before start working on LEDs, one must understand how LEDs may threaten people’s lives and health. Light emitted from LEDs is not immediately harmful to human eye or skin; nevertheless, there are a few exceptions. EM waves in the UV-C range (the shortest wavelength range of UV, 100–280 nm) destroy biocells, and there exist LEDs that emit UVC. They need to be shielded completely when operated to eliminate any harm. Other UVs, UV-A and UV-B, can burn human skin quite badly, like sun tanning. Violet and short-WL blue have similar effects to some degree. All UV can degrade plastic resin, thus shielding equipment may require frequent quality inspection. The rest of visible wavelengths and IR wavelengths (800 nm and beyond) are not of biological harm. Even if a wavelength is not harmful, concentrated energy of EM waves can burn human tissues. The laser is an immediate example as light emission from a laser is a straight beam and does not spread, thus energy density does not dilute even in a far distance. As for LEDs, emitted light spread in space as the distance from the LED increases. Therefore a chance of burned eye or skin by an LED is rare, unless in a very vicinity of an LED where the energy density of emitted light is high. As a reference of energy density, solar radiation energy on 2 See Sect. 3.5 for nomenclature.

Reference

5

earth’s surface is approximately 1 mW/mm2 on a bright day. The reader must know how bright the daylight is to the eye. LED light emission easily exceeds this solar level. For example, a 1-mm2 blue chip can easily exceed 500 mW of light emission (for those who wonder, the luminous efficacy of the sunlight is about 100 lm/W). Or, if one uses a little magnifying glass to focus sunlight onto a piece of paper, he can create a burn mark of ∼1 mm2 in a moment. Energy of light can be this strong, therefore exposure of concentrated light to human tissues should be avoided. LED products contain various chemical elements, and some of which may be toxic. Completed LED chips hardly contain any toxic elements. During epitaxy, GaAs substrates may be used, where As is a toxic element. GaAs substrates may remain in IR LED products. MOCVD uses potentially toxic and flammable chemicals and device processing in cleanrooms utilizes chemicals potentially hazardous, but they do not reside in end products. In a few lighting products quantum-dot (QD) phosphors may be used. QDs contain Cd which is a toxic element. These toxic elements require attention when the LED products get disposed after use. As far as handling those products, there is little danger. Old LED products may have used Pb-containing solder; as of today Pb has been removed from the entire industry.

Reference 1. Shchekin O, Craford MG (2017) History of solid-state light sources. In: Karlicek R, Sun CC, Zissis G, Ma R (eds) Handbook of advanced lighting technology. Springer, Switzerland, p 41-70

2

Characterization Techniques

2.1

Purpose of Characterization

Characterization of LED devices is required for two main reasons. One is to understand properties of LED devices and products in detail for further improvements in R&D. The other is to control production quality. The latter is often called “testing.” In this book we do not make rigorous distinction between these two words; use them rather interchangeably. Characterization is repeatedly performed and data is analyzed by R&D engineers and process engineers for the above purposes. Another important function of characterization is to publish product properties in a form of datasheets, so customers can design their products appropriately with LEDs and communicate with the LED manufacturer and its application engineers when necessary. Presentation of data in datasheets is carefully examined upon publishing, since datasheets may be interpreted by customers from their own viewpoints. Datasheets are also frequently analyzed by competitor companies. Such effort of analyzing competitors’ products is called “bench-marking” or “competitive analysis” and is an important operation in a company to assess its products against the competition. In those efforts of bench-marking, terminology used in datasheets is occasionally different between companies. Test conditions are independently defined between companies, hence making the bench-marking difficult and puzzling for customers who try to compare LED products from two or more manufacturers. But this is the reality. Datasheets often contain binning information. Binning was originally a manufacturing and sales technique of grouping produced devices of a product type in terms of device properties (Vf , LOP, WL, color, etc) into predetermined “bins.” Since the binning technique affects production yields, and therefore production costs and end sales pricing, binning has become an important strategic parameter in modern manufacturing. Binning is also called “sorting.” LEDs are commonly subjected to optical, electrical, and thermal characterizations. Another important area of characterization is reliability tests, where devices are subjected to © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4_2

7

8

2 Characterization Techniques

continuous operation and/or stressing for an extended amount of time and monitored their property changes over time. Test methods and conditions are defined by the LED manufacturer, by a customer, or by an industry organization (e.g., IESNA LM-80), depending on product’s application field.

2.2

Characterization Apparatus

When characterization is performed on discrete LEDs (independently packaged LED devices, not epitaxial wafers or LED-mounted tiles or lead frames), the most fundamental property to be characterized is the total amount of light that the LED generates, often called the light output (LOP) for short. It is very natural for LED engineers to be interested in how much light is coming out of an LED under a given operating condition. The instrument used for this purpose is an integrating sphere connected with an optical fiber to a spectrometer,1 as illustrated in Fig. 2.1. A DUT (device under test) can be placed either in the middle of an integrating sphere (the 4π method) or at an interior wall of a sphere (the 2π method), depending on DUT’s spatial light distribution and physical dimensions. Integrating sphere manufacturers produce both types of spheres. One of the highly-recognized and widely-used spectrometers in the industry is Instrument Systems’ CAS140 series. It comes with a dedicated software (SpecWin) and system calibration combined with an integrating sphere including a connecting optical fiber. Another wellknown brand is Ocean Insight (formerly Ocean Optics) which produces handy palmtop-size spectrometers of various types at affordable prices. In most cases they require adequate calibration combined with optical fibers at use points to obtain absolute quantities of measurements, or measured raw values would have no NIST traceability (see later in the present section). On selecting an integrating sphere, the 2π method typically offers faster operation in swapping DUTs. When DUTs are large (like light bulbs), the 4π method is preferred because it becomes difficult to mount on a sphere wall. Ideally the sphere white interior is perfectly enclosed, yet in reality openings like a sample port and a fiber end has to be made. A rule of thumb is that the total opening area is kept less than 5% of the total sphere interior surface. As LED properties are affected by temperature, the DUT is typically mounted on a temperature-controllable stage. For integrating sphere theory and technology, handbooks are published by integrating sphere manufacturers [6]. Before powering up a DUT, a use-point calibration called self-absorption correction may be performed. As IES LM-79 (refer to Sect. 2.10) describes and recommends, this is for better accuracy because a DUT absorbs its own light reflected back from the sphere interior. 1 While modern spectrometers use semiconductor array detectors (e.g., CCD), the traditional way

of measuring a spectrum is a monochromator combined with a photo multiplier tube (PMT). This method is today used for phosphor characterization (e.g., Horiba PTI fluorometer) as it is effective for low-intensity light. Sweeping a range of wavelengths rather takes time, thus the array detectors took over LED measurements.

2.2

Characterization Apparatus

9

Fig. 2.1 Schematic diagram showing an integrating sphere measurement combined with a spectrometer. An LED device placed in the sphere (shown is the 2π method) is connected to a power supply and driven in either the pulsed, single-pulse, or DC mode. Emitted light is fully captured by the sphere and a part of it is sent to the spectrometer via the optical fiber. Direct light from the LED to the fiber end is concealed by a baffle plate (not shown in this figure. See Fig. 5.6). Located inside the spectrometer are a grating and a CCD array which is typically cooled to suppress thermal noise. Each pixel of the CCD array receives photons of one assigned wavelength dispersed by the grating. The entire optical hardware needs to be calibrated to the NIST standards. The software converts data collected by the spectrometer to conceivable formats, e.g., spectral plots and computed quantities. When the entire hardware is properly calibrated, the spectrum is prepared to provide the radiant flux value as the area under the spectral curve. The spectrum unit [W/nm] is obtained as shown using the photon counts n, wavelength λ, unit charge q, and the number 1240. See Sect. 2.3

Self-absorption correction is carried out as follows. An integrating sphere is equipped with an auxiliary lamp in its interior (not drawn in Fig. 2.1) whose spectrum is measured twice: Once without a DUT and another with the DUT, provided that the test system (without a DUT) has been calibrated to a traceable standard (see below about NIST traceability). Spectral ratio between the two represents the absorption spectrum of the DUT and is used to compensate raw spectral readouts to account for light absorption by the DUT. Self-absorption correction is DUT-dependent, thus it is required for every measurement set of each DUT type.

10

2 Characterization Techniques

Fig. 2.2 Illustrative presentation of the three operation modes. The pulsed operation is repeatedly turning on the device momentarily (tens of µs, typically) at a constant current. Duration of one current pulse is called the pulse width. The distance of two pulses is called the pulse period (commonly in the range of ms); the inverse of this is the pulsed frequency [Hz]. The ratio of the width to the period is called the duty cycle or duty factor [%]. The spectrometer collects light for a given duration (“integration” or “exposure” time) to capture multiple (tens to hundreds) pulses to obtain sufficient optical signal strength. The measured radiant flux value should be divided by the duty cycle to present the correct flux value for the device being turned on. The pulsed operation is used to suppress heat generation during the measurement and preferred in R&D. The single-pulse operation is to minimize the test duration for high throughput in product manufacturing. The device is turned on at a constant current for a minimal length of time for the spectrometer to capture sufficient amount of light. Typically the integration time starts after a slight delay to avoid interference between the device being on and the spectrometer responding. For this reason, the pulse rise time is not questioned. Vf is also measured during a pulse. Due to the length of the pulse, the device sometimes generate a noticeable amount of heat, which may affect test results, especially on AlInGaP devices. The DC operation is intended to establish thermal equilibrium during a test at a designated constant current. This is the closest to actual use conditions, although thermal parameters (Rth , etc.) play major roles in test results

A DUT is powered by an external power supply, either pulsed or DC (Fig. 2.2), via constant current rather than constant voltage. The pulsed measurement (Fig. 2.3) is to suppress heat generation within the DUT and operating conditions are defined such that heat generation during a measurement can be negligible. For example, 10-µs pulse width with a 1% duty cycle is often found in literatures. Integration time of the spectrometer is set to collect a sufficient amount of light, which may be as short as a subsecond or as long as several seconds—at least long enough to capture many pulses to reduce possible measurement errors. The pulsed method is preferred in R&D, though one measurement takes rather long (several seconds to tens of seconds). In manufacturing process engineers do not appreciate the long measurement time, and hence have implemented a similar method called the single-

2.2

Characterization Apparatus

11

Fig. 2.3 An example of fundamental pulsed circuits. Voltages (V and V R ) can be measured using an oscilloscope or triggered digital multimeters (DMMs). Device current is V R /R. Device voltage is V − V R . An oscilloscope is fundamentally a time-resolving voltmeter, and thus has a high input impedance (1 M). Many of them have an option of 50  input which is used to measure current directly (e.g., photodiode output) where I = V /50

pulse or monopulse measurement. In the single-pulse measurement a DUT is turned on for a few tens of milliseconds and the spectrometer is triggered to take a measurement within the duration of the electrical pulse. In this way a measurement can be performed within less than a second. The downside is that heat generation is not controlled well. The effect of heat can be compensated by accumulated data and knowledge in each testing in manufacturing. Another method is the DC measurement. A DC measurement is done by operating a DUT at a constant current for long enough time and an LOP measurement is taken when DUT temperature has stabilized. A DUT does generate heat, but this method is the closest to the real usage case of the LED in the field. A DC measurement takes a lot of time, as does any measurement at a raised temperature, therefore it is a common practice to characterize LEDs at room temperature (so that many measurements can be taken without varying temperature) and generate a “k factor” (transfer function) after performing a smaller number of pulsed or DC measurements at a desired temperature. In datasheets it is common to publish 25 ◦ C data along with thermal derating characteristics above 25 ◦ C. In this way, an LED manufacture can inform customers whose use-point temperature may be unknown to the manufacturer. To enable necessary measurements at desired temperatures, integrating-sphere instruments in R&D are equipped with temperature-controllable sample stages (see to Sect. 2.9). The range of LED drive currents can be wide hence an engineering team needs to make a wise choice in employing a power supply for their measurements. The precision source-meter unit (SMU) product family (source-and-measure instruments) from Keithley Instruments and other electronic instrument manufacturers is accurate and versatile. Millisecond pulses can readily be generated and even shorter pulses of microseconds may be achieved by certain

12

2 Characterization Techniques

SMU models, in addition to DC capability. For more flexible pulsed measurements, widely accepted was a pulse supply by Hewlett-Packard/Agilent Model 8114A. This model has been discontinued unfortunately; possible successors of it are highly functionalized and often far too expensive for most LED test purposes. Vektrex’s SpikeSafe Performance product family is a high-power pulse converter, being coupled with an external bulkhead DC power supply to generate high-wattage current pulses. This product family offers multi-channel instruments that become convenient when multiple LED devices are operated in reliability tests. One can find various pulsed-measurement instruments for laser diodes commercially available. These LD instruments often define the below-threshold state of a laser diode being the off state [12]; for LEDs this “off state” does not guarantee a DUT being completely turned off and the DUT may still be glowing. Precautions should be taken on employing a LD pulse supply. Comprehensively, it is common (and essential in high-current measurements) to determine Vf using the 4-wire sensing technique, referred to as Kelvin sensing, to avoid nonnegligible voltage errors (cause by wire resistance and contact resistance) of tenths of a volt at high current. Characterization engineers and technicians are occasionally requested to make measurements outside tool’s designed capability, e.g., too low or high drive currents, too low LOP, etc. by other engineers or managers. The tool may still operate out of the designated range yet the engineers should inspect every obtained data set for any possible malfunction of the tool and tolerance and errors in the data. For example, in a measurement at a low pulsed current, one must confirm whether the current level is accurate and precise, whether LOP intensity is sufficiently above spectrometer’s detection limit over the entire spectral range, and so on. Knowing noise levels of instruments is essential in such low-signal measurements, and having a “toolbox” to mitigate severe noise influence is helpful. For instance, the toolbox may contain applying a longer integration time, using data averaging over multiple measurements to make resulting data more robust, and sampling a narrower spectral range to reduce contribution of background noises. Post-measurement data manipulation (e.g., truncating a spectrum by eliminating noise-floor ranges) may improve the data quality as well. For routine measurements, it is necessary to define a proper LED submount, referred to as a “test vehicle,” to make DUT handling easy and integrating-sphere mounting secure and reproducible. Largely used in the LED industry, but not universal, is the starboard (Fig. 2.4). A company may design and fabricate its own test vehicle(s). Once a test vehicle is defined, a sphere mount including electrical contacts (the “fixture”) is designed accordingly. The fixture commonly contains a temperature-controlling mechanism. Another universal test vehicle often seen in a lab is the TO can (TO header). “TO” stands for transistor outline, and they are widely used in electronics for discrete devices, and thus convenient for chip-level characterization. Their various shapes and sizes are distinguished via numbers—TO-18 and TO-46 may be most common ones in LED labs. Deep-UV LEDs employ TO cans as product packages because a TO can can be hermetically sealed with a UV-transparent window.

2.2

Characterization Apparatus

13

Fig. 2.4 An example of a starboard used in a commercial product: Shown here is a LUXEON Star in 2002 (rated 1 W; equivalently 350 mA. LUXEON is a brand that Lumileds introduced in 1999) that was the first appearance of a starboard package in the industry. The starboard is a type of printed-circuit board (PCB), where the core material is either metal or FR4, of a hexagonal shape approximately 2 cm across. An LED device is typically placed in the middle of it and the circuit pattern has been arbitrary prepared for the purpose. Black-finish surface (called the solder mask) and Au solder pads are sometimes preferred when surface appearance needs to be maintained over time (e.g., in reliability tests). In this product solder has been applied to the contact pads for customer’s convenience upon electrical wire soldering. Image courtesy of Lumileds

An important aspect of operating optical characterization apparatus is the calibration. Since collected data may be shared with external groups or customers, the data must possess “accuracy” (obtaining absolute true values). At the same time since the apparatus is used repeatedly for many years, it needs to possess “precision” (obtaining the same value repeatedly). The accuracy of an apparatus is expressed via NIST traceability. An integrating sphere combined with a spectrometer should be calibrated annually or biannually using NIST-traceable light sources (either LEDs or incandescent light bulbs, though certified light sources are expensive) to be considered accurate. It is better (and often required) to get the apparatus calibrated regularly; annual calibration is common. When a need arises to compare multiple integrating-sphere tools, one may perform a series of measurements often referred to as a “round robin,” where several devices are measured using tools in question and readouts compared. Mutual calibration between multiple integrating-sphere tools is more difficult than one would imagine, even if they are all NIST traceable. The variation between tools should be strictly minimized within predefined control limits, or it is not so uncommon to find several % of discrepancies in readouts between tools. Sometimes an uncalibrated power supply or an uncalibrated temperature controller causes significant errors. Optical apparatus is required to be precise over time as already mentioned. Daily monitoring of readouts using several devices is commonly performed for this purpose, and is helpful when a suspicion has arisen in data reproducibility. The statistical technique “gage repeatability and reproducibility” (gage R&R or GRR) is used to evaluate precision in a systematic way. Repeatability refers to repeated measurements by an operator and reproducibility is about those by multiple operators. GRR can reveal unexpected effects. One operator may demonstrate outstanding repeatability, which may be difficult for other operators to follow, or

14

2 Characterization Techniques

deteriorated repeatability, which may be difficult for the manager to correct. Operators’ performance may vary due to their mental states, e.g., Monday morning versus Friday evening. When trying to compare data sets against these of a customer or external facility, confidentiality may prevent both parties disclosing tool details and test conditions fully, making mutual data understanding difficult. The best a characterization engineer can do is to have thorough discussions prior to characterization, rather than after.

2.3

Data Interpretation

As today’s commercial software has become advanced and user-friendly (calculating all necessary numbers for the operator) the measurement system has become a black box to many LED engineers. The importance is emphasized here of understanding the underlying science and how those optical quantities are obtained in the software. Inside the spectrometer are a grating and a CCD array detector (Fig. 2.5). Incident light is dispersed by wavelength when it hits the grating surface, then light of each wavelength falls on destination pixels of the detector array. The detector converts a photon into an electron which is measured as an electrical current for a given duration (called integration time or exposure time). Thus, the spectrometer is an instrument that measures the photon counts (the number of photons) at each wavelength, provided that the system has been calibrated as a whole to the NIST standards. Once this measurement is done, the software converts the

Fig. 2.5 Illustration of spectrometer’s interior (reproduction from Instrument Systems’ catalog). Incident light is guided to a grating that separates wavelengths, then pixels of the array detector receive assigned wavelengths to count the number of photons arriving during the integration time. The detector is often Peltier-cooled to reduce background thermal noise

2.3

Data Interpretation

15

Fig. 2.6 An example of the LED spectrum (from Lumileds’ LUXEON FX2 product datasheet, 2020). The spectral shape is a common one among white LEDs using blue chips combined with YAG phosphors. This spectrum chart has been prepared using a normalized scale on the ordinate and the radiant flux (total optical energy) is described elsewhere in the datasheet. “Normalized power” in the axis label means the energy density [W/nm] normalized to its peak value within the spectrum. Image courtesy of Lumileds

photon-count data (as a function of wavelength) into other forms of numerical data. First, what software does is to create a data set commonly referred to as a “spectrum,” which can be a graphical chart of energy distribution of light plotted over the wavelength range (Fig. 2.6). The mathematical process of this first step goes as follows. At a wavelength, the total energy of collected photons (per second) is obtained as a product of the number of photons (already measured) and the energy of one photon E ph . The latter is calculated as E ph [eV] =

1240 , λ [nm]

(2.1)

where 1240 is a number to be memorized to convert between the wavelength and the photon energy (refer to Appendix D.). Light exhibits both wave and particle nature, called the duality,2 which is where this 1240 factor comes from, and we will jump between the two quantities for the rest of the book without mentioning. Repeat the Eq. (2.1) calculation at all wavelengths (it would be a nice and easy exercise for the reader on a spreadsheet) and plot the results as a function of the wavelength. That is the spectrum shown on datasheets. One caveat is that the spectrum is plotted in units of W/nm, which only means that the 2 Refer to Appendix D.

16

2 Characterization Techniques

total wattage in the spectrum (hence optical energy) is calculated by integrating over the wavelength. For practical reasons when making measurements, it is convenient to choose on the software a spectral step of 1 nm, or the energy at each wavelength must be normalized by the wavelength step width upon further calculation. The 1-nm resolution is generally sufficient in LED measurements. The radiant flux3 is the total optical energy measured in units of W and readily calculated from a spectrum by integrating over the spectral range, as already mentioned. When a spectral data set is integrated on a spreadsheet, it is just a summation: add up all cells to obtain a sum of energies at all wavelengths. If it was a pulsed measurement the duty cycle would need to be taken into account properly. In doing this calculation, we encounter an interesting mathematical notion: The expectation value. Using the spectrum I (λ) and the photon counts n ph as a function of wavelength λ, the expectation value u of our spectrum analysis is expressed as radiant flux number of photons  I (λ) dλ =  n ph (λ) dλ

u=

(2.2)

in units of W, or it may be easier to see in units of eV by dividing by electron’s charge (1.6 × 10−19 [J/eV]). The expectation value in our case is the average photon energy, which can be readily converted to a wavelength using Eq. (2.1). Then this wavelength is called the centroid wavelength: A very important notion in spectrum analysis. The centroid wavelength can be considered as a representing wavelength of a spectrum. Now we move into photometry and colorimetry. While the unit system that we have so far dealt with is radiometry (involving only physical quantities like energy and wavelength), photometry involves the human eye perception and is a parallel establishment to radiometry. Colorimetry is another establishment and describes how the human eye recognizes colors. In photometry, the counterpart to radiant flux in radiometry is luminous flux, measured in units of lm (lumens). The luminous flux (often incorrectly called the “lumen” for short reflecting its unit name) L is calculated as  L = 683 I (λ) V (λ) dλ (2.3) where I (λ) is the spectrum discussed above and V (λ) is the relative luminous efficiency function or luminosity function,4 which is the spectral human-eye sensitivity, defined by 3 The radiant flux is sometimes improperly abbreviated as the radiance for short. However, radiance

is defined in radiometry to be a counterpart of luminance in photometry. See Sect. 2.6. 4 A similar function, the scotopic luminosity function, is used for dim environment and it is not

commonly used in LED applications.

2.3

Data Interpretation

17

Fig. 2.7 The tristimulus functions (the color-matching functions) x(λ), ¯ y¯ (λ), and z¯ (λ). The origin of these functions is the spectral response of the three types of “cones” (photoreceptor cells) in the human eye. The three curves have been drawn in such a way that the areas under the curves become equal. The V (λ) (the peak value is unity) in Eq. (2.3) has been defined to be the same as y¯ (λ). ISO/CIE 11664-3 : 2019

the French organization CIE based on lab experiments about 100 years ago. V (λ) has been tabulated and published, and is included in Fig. 2.7. Executing Eq. (2.3) on a spreadsheet is simple. A measured spectrum is multiplied by the eye sensitivity at each wavelength, then the product is summed over the entire wavelength range. The luminous flux tells how bright a light source would appear to the eye. The constant 683 is a historical fudge factor to convert from the ancient unit “candela” (where a candle had been defined as a standard) to the modern photometric unit (see Sect. 2.6). Thus the fudge factor 683 resulted in the modern photometry unit system [15]. Colorimetry starts with three eye-related functions called the color-matching or tristimulus functions: x(λ), ¯ y¯ (λ), and z¯ (λ) plotted in Fig. 2.7. They come from eye’s photoreceptor cells called “cones” that are responsible for color perception. Their spectral responses are predominantly in red, green, and blue, respectively. V (λ) and y¯ (λ) were found to be very similar, and therefore have been defined as equal functions. Now let us assume that we have a spectrum from a measurement. We calculate a value X using a similar equation to Eq. (2.3) but here weighted by x(λ) ¯ instead of V (λ) (and it does not call for the 683),  X= I (λ) x(λ) ¯ dλ. (2.4) By repeating the same operations with y¯ (λ) and with z¯ (λ) we obtain two more values Y and Z , respectively. To understand how the eye will recognize a color, ratios between these three values will be sufficient. Therefore normalization is to be applied as

18

2 Characterization Techniques

x=

X , (X + Y + Z )

(2.5)

and similarly y and z are obtained. Because of the normalization, z = 1 − (x + y) and only x and y need to be plotted in a 2D chart. This is the x–y color chart known as the CIE 1931 color space (Fig. 2.8). In the 1931 space a white point is found at (0.33, 0.33), implying the three cones are responding equally to the incident light. When a spectrum has fallen at

Fig. 2.8 The chromaticity diagram of the CIE 1931 color space, namely the x–y color chart. The closed curve indicates the area of human color perception. Large x values appear reddish and large y values appear greenish, as implied from Fig. 2.7. Along the perimeter wavelengths of saturated colors, i.e., dominant wavelengths, are distributed. A combination of blue + yellow (Fig. 2.12) attains a white appearance as drawn via the lever rule on the line section connecting blue and yellow points (indicated by two arrows). Similar color construction can be performed using three (or more) colors where a mixed color can fall on within a connecting triangular area called a color gamut. (0.33, 0.33) is considered to be white, known as CIE Illuminant E. The Planckian locus is indicated by the broken line. In the enlarged part of the figure several CCT contours are shown

2.3

Data Interpretation

19

(x0 , y0 ), the dominant wavelength of the spectrum is found graphically by drawing a line from the white point (0.33, 0.33) through (x0 , y0 ) extending to the perimeter of the chart where wavelength numbers have been distributed. The ratio of the line segment between the white point and (x0 , y0 ) to that between the white point and the intersection at perimeter is called the color purity. A saturated color (vivid color) means a color with high color purity. Within the color space a curve extending from the red area towards the white area has been drawn. This is the blackbody curve (also called the Planckian locus) which describes how the emission of a blackbody varies as its temperature is varied. Hence, a temperature can be assigned to a color point on the locus. This assigned temperature is called the color temperature. CIE-defined illuminants, e.g., the daylight reference D65 , do not fall exactly on the Planckian locus due to earth’s atmospheric absorption of solar radiation. To clarify a potential confusion: the dominant wavelength is determined by human eye perception, not by physics of light. A two-peak spectrum for instance is perceived as singlecolor light and this perceived color is expressed by a dominant wavelength. While it is not meaningful to find a dominant wavelength for a white light, color LEDs find benefits of using the dominant wavelength in applications. For example, AlInGaP red LEDs are sensitive to environmental temperature in their emission spectra and human perception of their color is the determinative factor at the end use point where the dominant wavelength acts as a comprehensive parameter. For the same reason, the luminous flux of AlInGaP LEDs is more commonly stated at the end use point than the radiant flux. A caveat, especially important in R&D, is that the eye sensitivity changes drastically in red and purple/blue WL ranges and the luminous flux changes accordingly when a spectrum changes even slightly. In such a case it may be misleading to refer to the luminous flux changes for LOP evaluation; in contrast, the radiant flux will guide the engineer correctly. The dominant wavelength is predominantly used for color binning of chips. The centroid wavelength, on the other hand, has a rigid mathematical foundation as we have seen earlier in Eq. (2.2). It can be considered as a representative wavelength of a spectrum apart from human perception, and it is meaningful and useful to calculate a centroid wavelength of a white spectrum. The peak wavelength is often used on color LEDs to describe the spectral peak location, although it is not mathematically endorsed. The peak wavelength is only a wavelength where radiation energy of the spectrum is concentrated the most. The popularity of the peak wavelength comes from its graphical appealing character as it can be readily found in a spectrum. For example, a change in the peak wavelength of a set of spectra can be easily captured. Derived from the 1931 color space is the 1976 color space using u  and v  coordinates. These two color spaces are widely used in industry; it will depend on the application which color space is preferred. Transposing from the (x, y) coordinate system to the (u  , v  ) system is simply a mathematical calculation given as u =

4x , −2x + 12y + 3

(2.6)

20

2 Characterization Techniques

v =

9y . −2x + 12y + 3

(2.7)

Graphically speaking, Eqs. (2.6) and (2.7) are only stretching and contracting the chart in a complex way, therefore the color information is maintained. The 1976 color space consequently has less transparency to how the human eye functions, yet it has its own advantages in color science, as it is described as a “more uniform” color space. Artificial white light sources (fluorescent and LED lamps) are unlikely to fall right on the Planckian locus but are likely in its vicinity. After the 1931 space was published, and fluorescent lamps became prevalent during 1940–1970, there were research efforts made to assign color temperatures to those artificial light sources. The correlated color temperature (CCT) was defined as the blackbody temperature nearest to the color point of the light source in question. The “nearest” was only meaningful in a uniform color space (the 1931 space was not suited). As a result, in the 1976 space CCT contours intersect the Planckian locus almost perpendicularly, thus CCT would be easily determined graphically. The MacAdam ellipse indicates a small area on a color chart within which the human eye perception does not distinguish any color differences. Because the 1976 space is more uniform, MacAdam ellipses [8] appear rounder and nearer sizes over the entire chart than them appearing on the 1931 space. The MacAdam ellipse is utilized in color binning of products by various steps: 1-step ellipses being the most rigorous (tight color control) and 3-step being the least. The choice of the step depends on color control maturity in production to minimize yield loss while satisfying the application’s needs. An extra benefit that the LED industry receives from the u  –v  chart is the fact that the blue and yellow is tied by a vertical line (constant u  ) in the chart. This means that the color point of white LEDs consisting of a blue chip and a yellow phosphor only moves up and down (only v  changes), simplifying crude data analysis. Automotive front lighting application is an example (Fig. 2.9). Up to this point, we have defined many quantities from a spectrum using rather simple and explicit mathematical operations. What was done was a data reduction, therefore it is not possible to back-calculate the spectrum from color coordinates, CCT, or any of these quantities; one would encounter an infinite number of spectrum options. The spectrum contains the richest information, and it is a good idea to store all measured spectral data even when data reduction has been done. Calculated numbers should be reported in appropriate decimal points. For example, reporting a wavelength number in tenth or hundredth points in nanometers is not very useful in many LED cases. The common rules of significant figures are of course applicable. To characterize color of light further, there is a widely-used set of numbers that involves some implicit and nontrivial mathematical operations.5 That is the color-rendering index (CRI) [3]. CRI numbers R1 to R8 for a light source are obtained from corresponding test color samples (TCS1 through TCS8) by comparing against an appropriate illuminant (a blackbody for CCT lower than 5000K; a daylight above 5000K) in a uniform color space. Ra is obtained by averaging over R1 to R8 . Ra was somewhat mistakingly called the CRI 5 Walking through these unintuitive mathematical operations would not provide us much insight.

2.3

Data Interpretation

21

Fig. 2.9 The chromaticity diagram of the CIE 1976 color space, namely the u  –v  color chart. Large u  values appear reddish and small v  values appear bluish. The Planckian locus and dominant wavelengths are also included in the figure. Note blue and yellow have similar u  values. The lever rule for color balancing and blending no longer works intuitively in the u  –v  space. In the enlarged part of the figure several CCT contours are shown

number, yet they are synonymous today (since a 1995 publication). TCS1 through TCS8 are unsaturated color of various hues and TCS9 to TCS12 are more saturated colors. Among these R9 (TCS9 is a saturated red) has been of strong interest in LED industry. This is because primitive white LEDs were a lack of red. During efforts of improving color rendering and attaining warm-white LEDs, red phosphors started to be developed and added to white LEDs, where R9 acted as an explicit index of improvements. Approximate appearance of those color samples are presented in Fig. 2.10. One occasionally encounters negative CRI values reported by software, especially on strongly tinted LEDs. Those negative values do not mean much beyond implying very poor color rendering. As the CRI method was defined before the LED illumination emergence, it is considered not fully sufficient to express quality of new lighting technologies. Therefore, new methods have been proposed for in academic and industrial use, where interest in color rendition is not exactly concurred between the two parties. Among these, one that has lately gained popularity and industrial use is the TM-30 method, proposed by Illumination Engineering Society (IES) [9]. TM-30 (ANSI/IES TM-30-20, updated and published in 2020) is careful

22

2 Characterization Techniques

Fig. 2.10 CRI test color samples from TCS01 to TCS14. Note that vivid colors of TCS09 to TCS12 are not included to compute Ra

about the selection of a reference light source, to which a sample light source is compared against, and also about changes in hue of the color samples with respect to the reference light. TM-30 starts by defining 99 color samples called Color Evaluations Samples (CES) in Fig. 2.11 and is characterized by three key metrics: Fidelity Index (R f ), Gamut Index (Rg ), and Vector Graphic (Fig. 2.11). R f is a similar idea to Ra but over the 99 color samples. A color-point change of each color sample between the reference and sample light sources is tracked and used in calculating Rg , which indicates the degree of color saturation (“colorfulness” or “chroma”) caused by the sample light source. Color samples have been selected such that their color points surround the white point (i.e., reference light sources). When the area in the color space surrounded by the sample color points of a sample light is greater than that of a reference light (that is Rg > 100), that means that the sample light source causes more color saturation (more vivid appearance) of illuminated objects. This is because a color space exhibits color saturation towards its periphery. When

Fig. 2.11 Approximate appearance of TM-30’s 99 color samples (left) and an example of the vector graphic (right) where the result of a test light source is indicated by a red curve being compared to a circular reference light source (black curve). Wider portions of the red curve than the black curve indicate more saturated colors and narrower portions show less saturated colors. Images adapted from [9, 13]

2.4

Efficiency Breakdown

23

Rg < 100, illuminated objects appear pale. During this Rg computation the 99 color samples are grouped with like colors into 16. The vector graphic is to express Rg graphically. A reference light is expressed by a circle in a color space, against which a polygonal area (16 data points from Rg computation) by a sample light is superimposed. In this way it is readily understood which color appears more vivid and which is more pale.

2.4

Efficiency Breakdown

Our main interest in LED analysis using radiometry and photometry is the efficiency. LED engineers like to quantify how LEDs are low energy consumption and high-efficiency light sources. The wall-plug efficiency ηwp indicates how efficient in energy consumption an LED is. It is the radiant flux (total optical output power, energy per second) Wopt per unit electrical input power Wele : Wopt . (2.8) ηwp = Wele This indicates what percentage of electrical input is converted into optical radiation energy. The rest of electrical input becomes heat which is considered wasted energy. To express how bright the LED is, Eq. (2.8) is expanded into a form using the luminous flux L from photometry Wopt L · Wele L Wopt = ξlm , L

ηwp =

(2.9)

where ξlm (in units of lm/W) is called the luminous efficacy. It tells how much luminous flux (how many lumens) the LED creates from 1 W of electrical input. The wall-plug efficiency and luminous efficacy are convenient numbers to advertise how energy-efficient an LED is, neatly useful in sales and marketing. Meanwhile, engineers need to go back to the lab and improve the LED further. But how? Engineers need to know a more detailed view of the efficiency. For instance, which components in the LED are working well and which are not, in order to allocate their next efforts. For this reason we formulate a detailed efficiency breakdown. A popular model case is a blue LED with single-phosphor system, where the LED generates blue light that is partially absorbed by the phosphor and re-emitted as yellow light, generating white light as a whole, as illustrated in Fig. 2.12. We take the luminous efficacy term from Eq. (2.9) and expand it as Wblue Wopt L · · Wele Wblue Wopt = ηblue · ηconv · ξrad .

ξlm =

(2.10)

24

2 Characterization Techniques

Fig. 2.12 A simple model of a white LED consisting of a blue chip and a yellow-emitting phosphor. Part of blue light gets converted to yellow light by the phosphor, while the rest of blue exits unconverted

The last term in Eq. (2.10), ξrad , is the luminous efficacy of radiation (occasionally referred to as the lumen equivalent) in units of lm/W and is purely determined by the spectral shape. It tells how bright a spectrum appears to the eye (how many lumens) when optical radiation power is 1 W. Manipulating the spectral shape for this purpose is called the spectral engineering. The aim of the spectral engineering is to include more efficient wavelengths into a spectrum while achieving a target white light. Not only UV and IR, but also purple and deep red are unfavored in this respect. Warm-white light contains rich red and tends to be lower in ξrad than cool white for this reason. The middle term ηconv is the conversion efficiency (dimensionless or %). Conversion efficiency is a measure for how much energy has been lost upon down-conversion. The caveat is that ηconv is unity when no down-conversion occurs (although, no down-conversion contradicts our model that white light is obtained by a downconverting system). The product of the two terms (ηconv · ηrad ) is sometimes inappropriately called the conversion efficiency [lm/W] as efficiency is generally a dimensionless number. The ηconv · ηrad product may, however, be a more intuitive quantity: how many lumens are generated from 1 W of blue pump light input. The first term ηblue is the wall-plug efficiency of the pump LED. Determining radiant flux of the pump LED can be controversial and requires attention. We discuss this topic in the next section and move on in the efficiency breakdown. For the first two terms in Eq. (2.10) we first expand the second term ηconv as n white · E white n blue · E blue n white λblue = · n blue λwhite = ηdevice · ηdefic .

ηconv =

(2.11)

Equation (2.11) is to examine how well the down-conversion mechanism has functioned. The blue radiant flux Wblue can be written as a product of photon count n blue (the number of blue photons per second) and the centroid photon energy E blue from the expectation value calculation, Eq. (2.2). White radiant flux can be written in the same way using photon count n white and the centroid photon energy E white . Then these two photon count numbers are compared (ηdevice in %) and the centroid energies (wavelengths as λblue and λwhite ) are

2.4

Efficiency Breakdown

25

compared (ηdefic in %), as displayed in Eq. (2.11). The former, the quantum efficiency of the device ηdevice , tells what percentage of the input photons has been successfully exited the device package; the rest have been lost somewhere in the system as heat. The latter, the quantum deficit ηdefic , tells how much energy of a photon, on average, has been preserved upon down-conversion; the rest is lost as heat. The energy loss from quantum deficit has a name: the Stokes loss. R&D engineers concerned with phosphors are particularly interested in the terms in Eq. (2.11). When phosphors started being combined with blue LEDs, phosphor engineers were embarrassed by the low phosphor efficiency numbers that LED engineers reported based on their LED experiments. LED engineers measured and compared device efficiency before and after phosphor integration (i.e., blue device and white device, respectively), and the result indicated the phosphor material was mediocre. Phosphor engineers argued that this particular phosphor was known to be highly efficient, as proven by their own elaborate measurements. This event was how LED engineers acquired a notion of package efficiency ηpackage = ηdevice /ηtrue where ηtrue is a direct function of phosphor’s “stand-alone” quantum efficiency ηphosphor and the amount of blue-to-yellow conversion that is graphically explained in Fig. 2.13. The LED package itself thus plays a great role in device efficiency, which can be written as ηconv = ηdevice · ηdefic = ηtrue · ηpackage · ηdefic .

(2.12)

Today, a common experimental method to study device efficiency is to determine phosphor efficiency ηtrue outside the LED package (e.g., via conventional monochromatic-light excitation) and to dump any unexplained losses observed in a phosphor-integrated LED into the package efficiency “bucket.” If one prefers, he could break down ηpackage further into finer efficiency components, e.g., metal-reflector efficiency, bonding-wire efficiency, chipreabsorption efficiency, etc. However, those efficiencies would not be universal as package types and shapes vary, hence no one has officially attempted to decompose ηpackage further. Regardless, the introduction of ηpackage illustrates that the LED efficiency equation was not given a priori; rather LED engineers learned and developed it the hard way. The same expansion can be applied to the first term of Eq. (2.10), ηblue , by treating blueLED efficiency as conversion from electrons to photons. The number of electrons n electron is counted via electrical current I ([A] = [C/s], total charge per second) divided by the unit charge q = 1.6 × 10−19 [C]. An electron’s equivalent of the photon energy is the electronic potential. In our case the forward voltage of the device, V f , is the corresponding quantity, in units of electronvolts [eV]. Therefore it is written as

26

2 Characterization Techniques

Fig. 2.13 Pictorial presentation of photon losses in a package. As photons propagate in a package (towards the right of the figure) a portion is lost upon down conversion and another portion is absorbed by the package materials. Note that it is not readily possible to quantify absorbed yellow and blue photons (c and d in the figure, respectively) separately in experiments. In embedded equations the input number of blue photons is normalized to unity. n blue,absorbed is the number of blue photons absorbed by the phosphor and n yellow is the number of photons that the phosphor emitted. Reference [5] provides a thorough discussion on conversion analysis

n blue · E blue [W] I · qV f q n blue E blue [eV] = n electron Vf = ηexternal · ηohmic .

ηblue =

(2.13)

The first term of the last line, ηexternal , is called the external quantum efficiency (EQE). It describes how many electrons out of 100 have ended up being photons escaping from the LED chip into free space (in other words, captured by the detector). ηexternal can be written in a simpler form: ηexternal = Wblue /(I · E blue ) where E blue is in units of eV. ηohmic describes an efficiency related to the ohmic loss (energy loss related to electrical resistance), which is due to any voltage drop caused by current flow including bulk resistances of semiconductors and metals, interfacial properties like Schottky barriers, and so on. The reason for ηexternal being called “external” is the fact that not all photons generated in an LED chip exit the chip into free space where our measurement takes place. The probability

2.5

Effect of Encapsulation on Light Output

27

Fig. 2.14 Summary of efficiency breakdown presented in the text body. While the presented breakdown method is comprehensive, details in definition and terminology may not be universally agreed upon in the LED industry and academia. This is because these developments and evolution of efficiency analysis were accomplished by multiple research institutes carrying out LED research independently where various names and acronyms were assigned to equivalent or similar notion. Today it is impractical to make an effort to rename and come to a complete agreement. The reader is suggested to be flexible and state his definitions to avoid ambiguity in discussion

for generated photons inside the chip to exit is called the light extraction efficiency (EXE). EQE can be written as a product of EXE and internal quantum efficiency (IQE), which is the ratio between the number of injected electrons and generated photons inside the chip. IQE cannot be measured directly. IQE is one of primary concerns of epi engineers, while EXE is a major concern of device engineers and packaging engineers. We conducted the basic idea of efficiency breakdown using a rather simple model case (Fig. 2.14). In reality multiple phosphors may be used simultaneously (where cascade downconversion is probable) and more elaborate efficiency breakdown may be considered accordingly on a case-by-case basis.

2.5

Effect of Encapsulation on Light Output

In the previous section we mentioned that determining the pump radiant flux requires attention. In characterizing the conversion efficiency, a set of two measurements is needed: before (i.e., the blue pump) and after (i.e., the resulting white) phosphor integration. However, it is known that silicone encapsulation changes LOP of a packaged blue device and the degree of LOP enhancement varies depending on chip LOP and shape of silicone encapsulation

28

2 Characterization Techniques

[2, 14]. For this reason, it has been proposed that an experimentally-determined calibration factor should be taken into account [11] when calculating the conversion efficiency. When a “before phosphor” measurement is performed, the blue LED is encapsulated in a clear resin or glass dome lens. This is believed to be the way to properly determine the blue flux that phosphor receives in a white device. In early white LEDs, a phosphor was in a powder form and was integrated onto a blue LED chip as a phosphor-silicone mixture. In this way, the phosphor powder was fixed in place by thermally curing the silicone. Today many white LED products have the same or similar structure. Using silicone in contact with the LED chip changes light extraction (see Chap. 5), resulting in increased radiant flux coming out of the LED chip compared to the bare chip measured in air. It may not be straightforward to remove encapsulant from an already-encapsulated blue device6 and make a white LED consequently using the very same blue chip, so a sister chip may be used to evaluate a calibration factor. The spherical shape (hemispherical for 2π-emitting packages) is preferred because it provides the lowest probability of TIR within it by achieving normal (or close to normal) light incidence at the silicone-air interface. Larger hemispheres have more chances to suppress TIR; a rule of thumb is either 2.5, 4, or 10 times larger than the chip, depending on experimental limitations and often on whom one talks to [7].

2.6

Optical Characterization, Geometry Involved

All our discussions earlier in this chapter were based on the integrating sphere measurement where all photons from a DUT are collectively measured using an integrating sphere. In many applications however, LEDs are combined with external optics, namely lenses, which collect and steer light in a desired way. In this section we consider geometrical characterizations of emitted light from an LED. Application engineers are interested in how much light from an LED can be collected by their optics and becomes useful in their optical systems. Light not collected by the optics is wasted (stray light). Therefore, we wish to establish definitions and terminology to communicate how emitted light is distributed in space in terms of the direction of light propagation. Rudimentary lenses are circular and sufficiently larger than an LED. Light emitted from an LED toward a lens makes a conical geometry around their optical axis as illustrated in Fig. 2.15. The luminous intensity (in units of candela [cd]) is defined as the luminous flux going into a unit solid angle of steradian [sr]. Hence a light beam with a constant luminous intensity is a diverging beam. A 1-sr cone has approximately 65° of the apex angle. In measurements a small detector of a known size is placed away from a DUT to attain a small 6 There are chemical solutions available commercially to dissolve and remove LED encapsulants.

Those chemicals are very common in failure analysis and reverse engineering to disassemble target devices and products.

2.6

Optical Characterization, Geometry Involved

29

Fig. 2.15 When an LED device is placed in front of a lens, only a certain fraction of emitted light reaches the lens, and the rest (typically light emitted towards side directions) is not useful (stray light). The solid angle that the LED at the apex and the lens perimeter form is the collection angle of the lens, and it is conical when the lens is circular. The collection angle is naturally dependent on the distance between the LED and the lens. To a first approximation, an LED at the apex is treated as an ideal point light source to construct a sketch like shown here

solid angle (for sufficient angular resolution), and the detector readout is normalized in terms of solid angle to report in units of cd. While luminous intensity is of great interest to application engineers, LED engineers know that luminous intensity can be increased without much effort by simply using a large chip. LED engineers’ interest rather resides in how much luminous intensity they can generate from a small chip. It is therefore fair to normalize the luminous intensity by the area of the light source. That is the luminance, the luminous intensity divided by the light emitting surface (LES), measured in units of cd/m2 or “nits.” Luminance is the first quantity that LED engineers consider, when asked for luminous intensity by application engineers. For application engineers, the luminance is a secondary interest (implying LES is less of interest). When luminance is greater for the same desired luminous intensity (i.e., LES is smaller), application engineers are happier because their whole optical system may become smaller and lighter, which is good for designability and manufacturing cost. Determination of luminance is straightforward when the surface from which light is emitted uniformly is known. When LES cannot be defined explicitly or light is emitted nonuniformly over an LES, one would have to resort on an imaging technique. A common tool is the telescopic imaging camera that maintains a small NA of its optics. Microscopes are not suitable because of their large NA. One drawback of the telescopic imaging is the fact that cameras use RGB color filters to obtain color information, rather than spectrometry. Therefore the camera needs to be calibrated to a certain color point, and light sources away from the calibrated color point require careful inspection (and correction if necessary) of retrieved data from the imaging tool and its software. It can become harmfully misleading to rely too much on photometry and colorimetry numbers obtained from a color-filtered measurement system. An external lens also brings in optical distortion (see Chap. 5). To add a few notes, since radiometry and photometry are parallelized unit systems, there are radiometric quantities and units corresponding to the luminous intensity and luminance. They are the radiant intensity [W/sr] and radiance [W/(sr · m2 )], respectively. Another unit encountered frequently is lm/m2 or lx (lux), which is the illuminance. Illuminance

30

2 Characterization Techniques

Table 2.1 Radiometric and photometric quantities [10]. This book uses other symbols than those listed as “common symbol” in this table for the sake of local discussion clarity Radiometric quantity (common symbol) [units] Photometric quantity (common symbol) [units] Radiant flux (φe ) [W]

Luminous flux (φv ) [lm]

Radiant intensity (Ie ) [W/sr]

Luminous intensity (Iv ) [cd]

Radiance (L e ) [W/(sr·m2 )]

Luminance (L v ) [nit]

Irradiance (E e ) [W/m2 ]

Illuminance (E v ) [lx]

is a measure of lumens impinging on a unit surface, indicating how brightly a surface is illuminated. Table 2.1 summarizes these quantities and their units. It is noticed that a term “radiant” is used for radiometric quantities and “luminous” is for photometric quantities. The intensity is a quantity defined as the flux per unit solid angle. With use of external optics in mind, it is important for LED engineers to understand in which direction light is emitted from an LED. An instrument that characterizes the radiation pattern of light emission is the goniometer (Fig. 2.16). A goniometer operates by setting a DUT and a small detector (or an end of an optical fiber connected to a spectrometer) far apart, where the DUT rotates with respect to the optical axis of the goniometer. The DUT-

Fig. 2.16 a Goniophotometer produced by Instrument Systems, sizing approximately 1-m wide. It can be called a spectrogoniometer when combined with a spectrometer, rather than a photo detector. Inside the tool a DUT is placed at the origin of a 2-axis rotational stage. The detector (one end of an optical fiber) is fixed at the other end of the tool. By closing the lid the dark environment is readily obtained for experimental ease. Image courtesy of Instrument Systems. b Principle of operation. The polar angle θ is varied between −90 and +90° in increments of angle corresponding to , the solid angle that the DUT and the detector make. The azimuthal angle φ is varied stepwise, e.g., 0, 45, 90, and 135°. The detector readout is the irradiance in units of W/m2 and because of the geometry the measured quantity is expressed in the radiant intensity [W/sr]

2.6

Optical Characterization, Geometry Involved

31

detector distance r can be chosen to be 32 cm, so that r 2 = 0.1 [m2 ] in equations for ease of calculation. The detector solid angle is made very small, in the range of 10−3 sr for angular resolution. The polar angle θ is swept incrementally at a fixed azimuthal angle φ. From the readout (either radiant or luminous flux incident on the detector) at each inclination angle from the axis, one can construct a radiation pattern chart by plotting flux as a function of the polar angle. The color-over-angle (COA, using CCT, x–y, or u  –v  ) chart is constructed in the same manner. The radiation pattern where luminous intensity falls off as the cosine of the angle from the surface normal is the Lambertian distribution. In other words, the luminance is constant over the polar angle because the apparent LES reduces as cosine with the angle and two cosine components cancel each other. The Lambertian distribution is often used in calculations because the cosine is a simple mathematical function. In applications narrower (more forward directed) radiation patterns are desired simply because more light can be coupled to the external optics. Although the goniometer is a useful instrument, an on-axis (device surface normal) measurement sometimes suffices the interest of characterization. Such a simplified tool of a detector fixed at the optical axis with no mechanical movement becomes handy to save time on characterization and on tool maintenance. There one may encounter several less common terms. The lux-per-lumen [lx/lm] is a metric to indicate how well light is directed along the optical axis. The lux comes from illuminance of an on-axis surface (i.e., the detector), and the lumen is a luminous flux value from an integrating sphere measurement. The center-beam-candlepower (CBCP) is the on-axis luminous intensity [cd]. All these are far-field characterization.7 Near-field characterization (light intensity and color distribution across the LES of a light source) is more an R&D and application development interest, and is performed via imaging methods. Although in many cases a light source is regarded as a point light source, a real light source has a finite extent that can be treated using a quantity called the etendue. Etendue is a concept that relates two (or more) optical surfaces (Fig. 2.17a), e.g., a light source and an illuminated surface which may be a lens. It commonly appears in illumination designs using non-focusing optics, like projectors. The etendue value E1 of the surface area on the left of Fig. 2.17a is defined as E1 = 1 S1 . (2.14) S1 is the surface area and 1 is a solid angle to the other surface (to elaborate, S1 = S10 · n where n is the unit vector parallel to the optical axis when the surface-normal vector S10 is not parallel to the optical axis). Because the notion is symmetric, another etendue (for the surface area on the right) is E2 = 2 S2 . (2.15) In general, the area of a portion of a spherical surface is calculated as a product of the radius of the sphere and a solid angle. Then it follows that E1 = E2 as

7 Far-field implies characteristics of light emission projected over a distance. Near-field is at the light

source.

32

2 Characterization Techniques

Fig. 2.17 a The concept of etendue is shown schematically. S1 and S2 are two surface areas and 1 and 2 are solid angles for them to the other areas. Implicitly assumed here is that the two surfaces are perpendicular to the optical axis that connects their centers. d is the distance between the two surfaces along the optical axis. b A cross-sectional expression of the concept of etendue. A and B are line segments representing surface areas. θ and φ are angles to the other line segments. d is the distance. If A is an LES and B is a focusing lens, δ is an angle variance that incoming light rays to the top of B would have. And if d is lens’ focal length, then Ray 1 past B propagates parallel to the optical axis, but Ray 2 past B approaches and crosses the optical axis and Ray 3 past B goes away from the optical axis. Thus the beam past a collimation lens is not exactly collimated but diverges slightly

1 S1 =

S2 S1 = S2 2 d2

(2.16)

where d is the distance between the two surfaces, given that the solid angles are small so that a flat area ≈ a spherical area of the same perimeter. Etendue therefore expresses a mutual relation of two surface areas using their product divided by their distance. It is indeed defined to be equal for two surfaces in question (this fact is expressed as “etendue is conserved,” unless a diffuser or a similar optical element randomly disturbing optical rays is in the path). Figure 2.17b is a 2D equivalent of the above discussion. It is readily understood that A = φd and B = θ d given that the solid angles are small, thus 2D-equivalent etendue is AB/d. Etendue conveniently describes the variance of incident/exiting angles of light rays into/off a surface area. In Fig. 2.17b the angle variance into Surface B, δ, is geometrically obtained as

2.7

Electrical Characterization

33

  2 θ B A cos ∼ δ d 2 + 2 2 Ad . δ∼ 2 d 2 + B4

(2.17) (2.18)

For a lens, the greater the angle variance of incident light, the greater the exiting light angle variance. In the case of collimating light using a lens of Surface B (e.g., a telecentric microscope, see Chap. 5), a collimated beam with a small cross section (small B) has greater beam divergence (due to an angle variance of incident light) than a beam with a large cross section (large B). A smaller etendue than at a light source is unattainable; therefore, high luminance (i.e., small area) sources are commonly desired. Some textbooks define etendue as E1 = Aπ(N A)2 , where the numerical aperture N A = sin θ2 . sin θ2 corresponds to the radius of Surface B (if Surface B is a flat circle). It may then be written as E1 ≈ AB/d 2 for a small θ , to maintain the symmetry between E1 and E2 . As a reminder, NA is not necessarily defined at the focal point (refer to Sect. 5.4). At the end of this section, some thoughts are provided on luminous flux versus luminous intensity. The former is, as its name affirms, a measure of flux, or the flow of a substance. The amount of flow, which is typically well-confined within a closed boundary parallel to the flow like water flow in a garden hose, is not a function of distance along the flow direction. From this picture we can say the flux is a convenient measure for collimated light, and less convenient for diverging light. Light emitted from an LED diverges as every light ray propagates straight into its own direction. For this reason the luminous intensity is a better suited notion for LED light emission. The luminous intensity is not a function of distance (or more appropriately, radius) for undisturbed diverging light. Therefore for integrating spheres of various sizes, the size of the sphere plays fundamentally no role in the readout. This is because the integrating sphere is an apparatus that measures the luminous intensity (thus not a function of sphere diameter) and the total (spatially integrated) luminous flux is calculated as the luminous intensity [cd] times the solid angle of the sphere (4π [sr]). Many textbooks formulate this inversely, with the luminous intensity as the luminous flux divided by 4π, but this is rather a counterintuitive way of describing the luminous intensity in the case of diverging light.

2.7

Electrical Characterization

The most fundamental and informative electrical characterization of an LED is the currentvoltage (I –V ) characteristic, which reveals how healthy the device is. Figure 2.18a shows a schematic I –V curve8 with several conventional definitions indicated. For a single junction device (an LED or a cluster of LEDs connected only in parallel), the operation voltage ranges 8 It is customary to plot I as a function of V, while a consensus of plotting is that the abscissa (horizontal axis) has the controlled (input) variable while the ordinate (vertical axis) displays the

34

2 Characterization Techniques

Fig. 2.18 a A schematic I –V curve of a diode. Under forward bias (positive applied voltage) a turnon voltage is found by the tangential intersection on the voltage axis. A symbol V f is used for forward voltage as a variable for short as well as a value at a designated current. A symbol I f is similarly used for forward current as a variable and as a value. Reverse bias (negative applied voltage) is barely of interest in LED production and application except as an indication of defectiveness (leakiness) of a device or product. Symbols Vr and Ir are used for the reverse to replace V f and I f , respectively. The breakdown (this is a proper function of a diode, not a diode breaking down permanently) is rarely observed in a lab or production. For example, AlInGaP LEDs show a breakdown in the 15–30 V range. InGaN LEDs hardly show a breakdown within a practical range of reverse voltage. b An I –V curve around the origin with examples of test points indicated. These test points are momentarily addressed (rather than sweeping) during a test step in production to sort and yield out defective devices

from about 1.5 to 4 V, whereas the current range can be very wide, spanning from tens of nA up to a few A. Test equipment needs to be appropriately selected for the intended ranges of measurements. Commercially-available precision source-and-measure units are versatile instruments, optionally equipped with voltage and current programmable sweep functions. An LED is operated at a forward voltage V f beyond the turn-on voltage where current flows through the LED. The dynamic resistance (differential resistance) is defined above the turn-on as a slope of the I –V curve ( V / I ). It is predominantly a measure of bulk resistances of semiconductors and metals in the LED device. The turn-on voltage Vtur non reflects interfacial properties in the LED device, including the pn junction and metal-semiconductor interfaces. Below the turn-on the LED behaves like an open circuit and virtually no current flows. When an LED is defective causing noticeable current flow below the turn-on, the LED is said to be “leaky.” On the reverse voltage side, little to no current may flow. LEDs are not purposely operated in this region, yet this reverse current can be utilized in testing as a metric of defectiveness. In R&D it is typical to obtain a full range of the I –V curve by sweeping either V or I across the range of interest (e.g., −4 to +4 V with 0.01-V increments). The DUT temperature needs to be well-managed and a sweep needs to be done quickly, or the DUT may heat up response (output) from the system. The current is the controlled variable on the LED but it is plotted as the ordinate.

2.8 Testing and Characterization in Wafer and Tile Forms

35

at high current, resulting in a distorted I –V curve. An I –V curve bending inward (towards lower voltage) may be an indication of semiconductor materials heating up, while bending outward (towards higher voltage) may be caused by metals heating up. Leakage current (small current flow that is not expected in a healthy pn junction) is often examined down to the nA range. I –V characteristics are sometimes expressed as J –V characteristics where J is the current density (current divided by current-flowing active area [A/cm2 ]). J –V plots are common when the area of device (∼LES) is varied in a series of experiments. The idea of current density is that a unit area of semiconductor receives an equal load from a current flow when the total area of semiconductor (thus LES) changes. This is a fair assessment from the semiconductor’s point of view. In manufacturing, situations are different as the testing throughput is a great concern. Rather than sweeping, I and V are measured at predefined points (shown in Fig. 2.18b) to judge whether values are within the predetermined specifications. If any of measured data points has fallen out of the specification range, the device is judged defective. Typically the µA–A range is a sufficient capability for a test instrument. As for datasheets, a rated operation current is specified due to the current-driven nature of LEDs and forward voltage is a resulting property given a range of it as a product specification. Other classes of electrical characterization and testing include the electrostatic discharge (ESD) which is a destructive test to assess whether a device can withstand high voltage surges. The human body model is commonly used under various standards and test methods (MIL-STD-883 Method 3015, JEDEC Standard JS-001, ICE 61000-4-2). To protect LED products from ESD, a transient voltage suppressor (TVS) is implemented at L1 (Level 1, see Chap. 3) as shown in Fig. 2.19 or L2 to release voltage surges through it.

2.8

Testing and Characterization in Wafer and Tile Forms

During the manufacturing process, devices may still be physically connected together in a wafer or tile form, before they are separated into discrete chip/devices (called “singulation”). All devices are tested at various stages of production in order to reject defective devices in as early a stage as possible (“yielding off”). No further processes occur on rejected devices. This is a production technique to avoid adding meaningless production costs. Test data is also used to bin for production control purposes like kitting, which is different from product binning for sales purposes (refer to Sect. 3.4). In-line testing is done by automated machines that place probing needles or a probe card onto devices and apply single-pulse measurements. An optical fiber end or an open port of an integrating sphere is placed near the DUT as a wafer or tile cannot be enclosed in a sphere while being needle-probed. Recorded data are compared against predefined process control limits. When an off-control-limit point is detected, the corresponding device is “inked” (traditionally rejected devices were marked by ink; today it is done electronically via wafer/tile lot identification and device address on a wafer/tile) and excluded from further processes.

36

2 Characterization Techniques

Fig.2.19 A built-in TVS on an LED L1 package (LUXEON Rebel ES, 3 mm × 4.5 mm) manufactured by Lumileds. The small dark-looking block is the TVS. On the right is a schematic I –V curve of a device equipped with a TVS. Large reverse current is passed through the TVS at relatively low voltage in order to release harmful ESD reverse voltage. The inset shows a circuit diagram where a reverse diode has been inserted as a proxy for a TVS. In practice a type of Zener diode is used as the TVS. The Zener diode is a pn-junction device that utilizes the diode breakdown phenomenon to define a voltage in a circuit. Photograph courtesy of Lumileds

Testing can be implemented at many production steps for elaborate failure and cost analysis of a production line; however, testing itself adds time and cost. An appropriate production line needs to be designed with a proper number of in-line test steps. Accumulated yield data is utilized to constantly improve underperforming processes and modify the production line to attain ever higher yield over the life of the product. In R&D, wafer characterization is routinely used for fast feedback in experiments, rather than processing devices all the way to packaging. EL and electrical characteristics can be collected on processed wafers on a probe station using needle-probe manipulators. Even unprocessed epi wafers can be subjected to quick EL characterization using indium dots as metal contacts,9 in addition to common photoluminescence mapping.

2.9

Thermal Characterization

Optical and electrical properties of materials composing an LED change with temperature; so does the LED performance. Temperature of an operating LED is determined by various factors: drive conditions (current, voltage, pulsed or continuous, etc.) and the environment 9 Metallic In tends to contaminate needle tips by adhering to them and is mildly toxic, hence to be

used with caution. It is a nondestructive test because In can be removed readily by dipping the wafer in an acid like HCl.

2.9 Thermal Characterization

37

(ambient temperature, heat sink, etc.). Therefore, it somewhat depends on the LED itself, as it is unintentionally a heat generator. It is important for LED engineers to understand temperature-dependent characteristics of LED devices. Another aspect of temperature characterization is the need to communicate with customers via datasheets. In most cases a manufacturer’s application engineers do not know how their LED products are used by customers, or customers are unwilling to fully disclose how LEDs get integrated in their optical systems. For this reason, the most common solution is for manufacturers to publish temperature characteristics of their products in datasheets. Temperature characteristics are measured in the following way. With current and temperature as independent variables, a DUT is mounted on a temperature-controlled stage and set at the room temperature, that is 25 ◦ C. Using the pulsed measurement method, current is swept across a relevant range and device characteristics (LOP, Vf , etc.) are collected as a function of current. Next the temperature stage is set at another temperature (for example 55 ◦ C) and the same measurements are repeated to acquire another set of device characteristics. Repeat this measurement at various temperatures of interest to complete a current and temperature mapping of device characteristics. An important assumption in this temperature characterization is that the pulsed drive of a DUT generates only a negligible amount of heat in the LED thus the LED temperature stays equal to the stage temperature all times. Data is presented as in Fig. 2.20. Full curves of radiant flux and Vf are presented as a function of current at representative temperature(s), accompanied by temperature derating curves at the rated current. Another critical property of an LED device is the thermal resistance Rth .10 Rth is measured using a DC measurement in addition to the pulsed measurements performed above. The DUT is now operated continuously at the rated current while the stage temperature is maintained at the temperature of interest, for example 85 ◦ C. Chip temperature will no longer be equal to the stage temperature due to the heat generation in the LED device. Rth is a quantity that describes this temperature difference between the LED chip (defined as junction temperature T j ) and the stage as a temperature reference point. Rth depends not only on the chip but also on the whole package. Thus Rth is product specific. A thermal circuit model is given in Fig. 2.21. Rth is calculated as temperature difference between the chip and reference point generated heat in the device T j − Ts (2.19) = (I · V f ) − Wopt

Rth [◦ C/W] or [K/W] =

where Ts is the stage temperature. Vf , radiant flux, and the junction temperature need to be known during the DC measurement. Junction temperature cannot be measured directly because the chip is too small. Instead, it is probed using Vf (or alternatively the spectral peak wavelength). The same Vf value can be located in the pulsed measurement mapping 10 The thermal resistance is often called simply Rth (ar-tee-aitch). It is also written as “Rth,” though

“th” should be subscripts like Rth .

38

2 Characterization Techniques

Fig. 2.20 Temperature characteristics of LUXEON FX2 Cool White products, shown in Lumileds’ datasheet (2020). LOP (top right) and Vf (bottom left) characteristics are shown in the full current range (100–1500 mA) at 25 and 85 ◦ C (85 ◦ C is a representative temperature for automotive applications). Temperature derating curves (top left and bottom right) are provided from −40 to +150 ◦ C at the rated current 1000 mA. Images courtesy of Lumileds

(via interpolating if necessary) at the same current, from which junction temperature is deduced. Taking a temperature reference point at the sample stage (the “case”) is a realistic representation of practical application systems where the heat sink or L2 board acts as a temperature stage. However, this reference point is outside the LED product and an arbitrary thermal-interface material (TIM, e.g., heat-conductive grease) used between the device and stage/case gets unavoidably included in the measured Rth value. LED manufacturers are typically not responsible for the TIM that customers use, therefore when a manufacturer measures Rth of its products, a reference point is taken within a product (board or submount) so that an external TIM is not involved. In either case the temperature reference point must be declared to avoid errors and confusion. Manufacturers also try to provide deeper considerations on their products for customer’s thorough understanding—an example is shown in Fig. 2.22.

2.9 Thermal Characterization

39

Fig. 2.21 Shown is a basic thermal circuit model that commonly appears in datasheets. The heat source is a DC-operating device at V [V] and I [A]. An appreciable amount of input electrical energy leaves the system as light, thus I × V is multiplied by WPE to subtract the optical power. The rest of electrical energy turns into heat and raise the device temperature, typically represented by the junction temperature T j , because of the thermal resistance preventing heat to be dissipated instantaneously. Consequently T j = Rth × [I × V × (W P E − 1)] + Ts . For more advanced thermal models, multiple heat sources (e.g., phosphor) and multi-component Rth are considered. In electrical-circuit equivalents, temperature at a point corresponds to the voltage (potential) and a flow of heat corresponds to the current. Fixed case temperature corresponds to the ground potential. Photographs are showing temperature reference points. On the left is a L1 device where a tip of a thermocouple is attached to a side of the product submount on the case (starboard). On the right is a COB device where a thermocouple is attached to a prepared sensor pad on its board. Photographs courtesy of Lumileds

Often in R&D, phosphor temperature T p is also of interest. Phosphor temperature can be conveniently measured using an IR imaging camera [1]. For elaborate studies of thermal characteristics the MicReD T3Ster is a revolutionary instrument11 to characterize thermal behavior of packaged devices. The T3Ster instrument monitors the junction temperature during a DUT cools down from a sudden power off after a steady-state operation. How junction temperature drops depends on package’s thermal conditions. An obtained transient curve of junction temperature is mathematically converted into another functional curve called the structure function that is modeled by a 1D RC (resistance-capacitance) network 11 T3Ster (Thermal Transient Tester) was developed in 2000 by Hungarian engineers of a spinoff

company Microelectronics Research and Development (MicReD). MicReD became a part of Flomerics (UK, 2005) which became a part of Mentor Graphics (USA, 2008). Since 2017, Mentor Graphics is a Siemens group company.

40

2 Characterization Techniques

Fig. 2.22 A more elaborate thermal circuit model is proposed along with the “LUXEON Neo 0.5mm2 ” product structure in its application brief (2022). Even in elaborate analyses only heat conduction is considered, and convection and radiation thermal paths are omitted due to their minor contribution. In incandescent light bulbs, the latter two can be great heat dissipation paths. Image courtesy of Lumileds

(Fig. 2.23) [4]. The structure function is graphed in a chart as cumulative Cth (capacitance of heat) against cumulative Rth (resistance to heat flow), where a plateau corresponds to a discrete Rth component and a step corresponds to a discrete Cth component. The very last large step is typically a heatsink as it should have a large heat capacity. By analogy to an electrical RC circuit associated with an inherent time constant, a thermal circuit also has inherent lagging in cooling to a ground potential (i.e., ambient temperature). In reality, however, since the model is 1D and the real packaged device is a 3D object, a structure function turns out be smeared and nontrivial to analyze. Therefore in experiments, two measurements are compared, e.g., one with TIM (e.g., heat-conductive grease) and another without TIM, to identify where the end of a package (i.e., right before the TIM and heatsink) is, as indicated in Fig. 2.23, and to determine Rth of the package itself. During temperature characterization and also reliability tests, maximum temperature should not exceed the melting temperature of solders used. SAC is around 220 ◦ C and AuSn is about 280 ◦ C.

2.10

Reliability Tests and Stressing Experiments

Reliability (how well a product maintains its initial properties over time) of a product is very important information for a customer, therefore manufacturers are expected to provide reliability information of their products. Reliability tests are carried out in a climate chamber where temperature and humidity, as well as air/gas compositions when necessary, are controlled. Products or devices are inserted in a climate chamber and operated for extended durations, typically thousands of hours, with intended interruptions for measurements outside the chamber. Seven days is equal to 168 h, 30 days is 720 h, and 365 days is 8,760 h,

2.10

Reliability Tests and Stressing Experiments

41

Fig. 2.23 Structure functions and a thermal circuit model of the thermal transient tester knowns as T3Ster (pronounced “tri-ster”). An ideal structure function based on the model is shown as a purple curve. Experimentally obtained structure functions are shown as red (with TIM) and blue (without TIM) curves. Where the two curves diverge is identified to be the entry (heat source side) of the TIM layer. Note a structure function curve ends in a large vertical step which corresponds to a heatsink. Image “T3Ster Master - Cumulative Structure Functions” created by MenterMAD, license CC BY-SA 4.0. https://commons.wikimedia.org/wiki/File:T3Ster_Master_-_Cumulative_Structure_Functions. png

plus time for intermittent measurements. Obviously, because of this enormous time consumption, reliability tests are better begun sooner than later. An adequate number of one product/device type are tested together to acquire data statistics; it may be tens of samples, or it can be hundreds of samples. In addition, it is time-saving to run various test conditions (e.g., various drive currents, various ambient temperatures, etc.) in parallel. Thus a set of reliability tests tends to consume many products/devices. The consequence of the long duration and a number of samples (not to mention the occasional mishaps) is that organizing reliability tests is a labor intensive work. Sample-mounting boards are custom-designed to accommodate products/devices of interest. Small-scale reliability tests may be done in an R&D lab using a minimal amount of resources e.g., a hot plate or small oven and a power supply for quick learnings. Multiple devices may be connected in series to test as many devices at a time while a constant current through them is maintained by an SMU. To increase the compliance voltage in order to accommodate more devices in series, a low-cost power supply may be stacked with the SMU since positive and negative terminals of a power

42

2 Characterization Techniques

supply are typically off the ground terminal so that two power supplies can be stacked like batteries. The reliability test is like a lifetime test of products/devices, to learn how they may fail (what components inside an LED device may fail) under given conditions within a given time. Eventually the objective is to publish how long the product/device will operate and maintain its initial properties at rated conditions. This aim of the reliability test has been extended into a notion of the stressing test. Advanced stressing tests today serve two purposes: We want to understand in a shorter time when products/devices fail (rather than waiting for thousands of hours) and we want to find out in a shorter time how products/devices fail (called “failure modes”). The former is the accelerated test, where harsher conditions (higher drive current, higher ambient temperature and/or humidity, etc.) are applied to accelerate degradation of device properties (but not to introduce a new failure mode). The accelerated test provides not only faster learnings but also cost savings. Defining accelerated test conditions requires some upfront learnings. By comparing accelerated test results to non-accelerated test results, an acceleration factor can be determined to estimate device lifetimes in consequent accelerated tests. For example, doubled drive current might cause two times faster degradation on a particular product, whereas it might induce a factor of ten of acceleration on another product. Now the latter is often called the hammer test, where extreme conditions are applied to induce device failures, ideally almost immediately. In this way one can find weakest components inside an LED device without spending much time. Test methods vary depending on what is looked for. For example, pulsed operation of extremely large current can be applied to induce electrical failure. The sample may be irradiated with high-power blue laser beam to induce optical failure, e.g., silicone browning. Every test has unique conditions depending on the type of products/devices, and sometimes test conditions are determined by collaboration between the manufacturer and a designated customer. A common classification of tests (where acronyms are used a lot) includes the high-temperature operation life (HTOL) and wet HTOL (WHTOL). 85 ◦ C + 85% RH (relative humidity) has appeared to be widely adopted in WHTOL but not universal. In addition many other tests have been invented. They include the temperature cycle (TMCL), temperature shock (TMSK), electrostatic discharge (ESD), storage lifetime, corrosive gas environment, and so on. Some of these tests, e.g. corrosive gas tests, may be carried out without devices powered up. Illumination applications share industry standards, such as LM-80. LM-80 is a method for measuring lumen maintenance (change of luminous flux over time) of component-level LED light sources (excluding complete lighting systems). A 30% reduction of the initial luminous flux value (referred to as L70) is the reference point. LM-80 data may be followed by TM-21, which is a method of projecting useful lifetime of the LED components. A few more standards around LM-80 are as follows. LM-79 is a guide of precautions for measuring LED lighting products. LM-82 covers temperature characterization. LM-84 describes changes in LED properties over time. All above are methods approved by The Illuminating Engineering Society of North America (IESNA).

References

43

Failed units are subjected to failure analysis (FA) to elucidate failure mechanisms. Computational modeling work is also helpful to visualize thermomechanical behavior and induced stress of various components within a device. Data analysis techniques and tools including Six Sigma, failure mode and effect analysis (FMEA), and related ones are widely utilized.

2.11

Further Reading

• Leschhorn G, Young R (2017) Handbook of LED and SSL metrology. Instrument Systems, Munich

References 1. Chen KJ, Lin C, Chen HC et al (2013) Effect of the thermal characteristics of phosphor for the conformal and remote structures in white light-emitting diodes. IEEE Photonics J 5:8200508 2. David A, Hurni CA, Aldaz RI et al (2014) High light extraction efficiency in bulk-GaN based volumetric violet light-emitting diodes. Appl Lett Phys 105:231111 3. Houser K, Mossman M, Smet K et al (2016) Tutorial: Color rendering and its applications in lighting. LEUKOS 12(1-2): 7-26. https://doi.org/10.1080/15502724.2014.989802 4. Joint Electron Device Engineering Council (JEDEC) (2010) Transient dual interface test method for the measurement of the thermal resistance junction to case of semiconductor devices with heat flow through a single path. JESD51-14 5. Krames MR, Shchekin OB, Mueller-Mach R et al (2007) Status and future of high-power lightemitting diodes for solid-state lighting. J Display Technol 3:160-175 6. Labsphere (2017) Technical guide integrating sphere theory and applications. PB-16011-000 Rev.00 7. Masui H, Fellows NN, Sato H et al (2007) Direct evaluation of reflector effects on radiant flux from InGaN-based light-emitting diodes. Appl Optics 46, 5974-5978 8. Ohno Y, Blattner P (2014) Chromaticity differences specification for light sources. CIE TN 001:2014 9. Royer MP (2022) Tutorial: Background and guidance for using the ANSI/IES TM-30 method for evaluating light source color rendition. LEUKOS 18(2): 191-231. https://doi.org/10.1080/ 15502724.2020.1860771 10. Spiro IJ (1980) Radiometry and photometry. Optical Engineering 19:SR-008 11. Sun C-C, Chang Y-Y, Yang T-H et al (2014) Packaging efficiency in phosphor-converted white LEDs and its impact to the limit of luminous efficacy. J Solid State Lighting 1:19 12. Tektronix (2019) Keithley 2520 pulsed laser diode test system datasheet. 09/19 EA 1KW-61621-0 13. U. S. Department of Energy (2015) Solid-state lighting technology fact sheet: Evaluating color rendition using IES TM-30-15. PNNL-SA-114005. https://www.energy.gov/sites/prod/ files/2016/04/f30/tm-30_fact-sheet.pdf 14. Zheng Y, Stough M (2008) White LED with high package extraction efficiency, Final Report. DOE Award Number: DE-FC26-06NT42935. https://www.osti.gov/servlets/purl/963890 15. Zong Y (2016) From candle to candela. Nature Phys 12:614

3

Device Architecture and Fabrication

3.1

LED Chip (Die) and Market Segmentation of Products

The LED is a semiconductor device that converts electricity into visible light. Three types of semiconductor materials are primarily used today for optoelectronic devices: AlGaAs, AlInGaP, and InGaN. They are high-efficiency materials based on their material nature of direct bandgap, and for this reason these three materials are also used in laser diode (LD) applications e.g., the compact disc (CD), digital video disc (DVD), and Blu-ray Disc (BD), respectively. These materials are summarized in Table 3.1. When the industry exploited LEDs for a wider range of applications in the 1980s, they emitted only dim light and were predominantly used for indoor applications like appliance indicators. The leading semiconductor material among other indirect-bandgap materials was AlGaAs. AlGaAs latticematches to the GaAs substrate in the entire Al-Ga composition range and its direct bandgap is maintained for Al compositions less than 45%, corresponding to 624 nm as the shortest achievable emission wavelength. AlGaAs with high Al composition was prone to oxidization, limiting popular emission wavelengths to 640–660 nm. Chips (die, dies, dice, etc. — They are referred to and spelled in a few ways) were small, as small as 250 μm (10 mils) long on a side, since semiconductor materials were expensive. Effort was made not to waste the materials: For example, in dicing-saw singulation the saw kerfs (sacrificial streets for the saw blade to incise-and-remove the wafer material) were made as narrow as possible. Scribe-and-break singulation was also examined for potentially “zero” kerf, yet the yield was lower because of edge chipping of the brittle material and “twin” chips caused by incomplete breaking. The bullet lamp package shown in Fig. 3.1 was a popular method to manage the light beam. Because of this popularity, the lamp designing was competitive and proprietary between LED manufacturers. The universal metric of LOP was the brightness in units of millicandela (mcd). Those small chips were typically rated around only 20 mA, for one reason being rudimental heat sinking via the lead frame of the bullet package. As surfacemount devices (SMDs, sometimes called “chip LEDs” in comparison to the bullet package. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4_3

45

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3 Device Architecture and Fabrication

Table 3.1 Main semiconductor materials for today’s LED use Semiconductor material

Color range

A laser application

Epitaxial method

Decade of major development

AlGaAs

Red–IR

CD

LPE

1980s

AlInGaP

Green–red

DVD

MOCVD

1980–90s

InGaN

UV–green

Blu-ray

MOCVD

1990s

See Fig. 3.1) were developed, LED devices were able to accommodate solder-reflow processes onto circuit boards with other discrete components, thus expanded productivity. As LED manufacturers improved brightness in following years, the AlGaAs LEDs started being used in outdoor applications including multi-color sign boards (with GaP:N green LEDs) and automotive auxiliary stop lamps. The LED industry was recognized as a large growing industry. In parallel to the growing market acceptance, an R&D achievement around 1990 was the use of a new material system AlInGaP. AlInGaP materials enabled further wavelength tunability from red into the yellow range. The tunability was a strong advantage for lawregulated outdoor applications (e.g., traffic lights) that required careful control of light color (hence emission wavelengths). It was around 2000 that the market began to demand brighter LEDs. To attain high brightness the chip size became larger, as large as 1 mm2 , which was typically rated 350 mA (∼20 mA × area factor 16). These large-chip LEDs were called high-power LEDs. As the input electrical power increased, heat dissipation became an apparent issue, causing LED efficiency deterioration with increased chip temperature. Packaging technology was consequently evolved to reduce thermal resistance of high-power LED packages, in addition to improving LED chip efficiency to reduce heat generation. For green and blue wavelength ranges, commercial LEDs were GaP:N and SiC (∼10 mcd), respectively, until early in the 1990s. Both materials possessed indirect bandgaps, hence were considered not worth pursuing further improvements. Late in 1993 a sudden announcement was made that an InGaN-based high-brightness blue LED was being commercialized, and green followed soon after. The commercialized product used a small chip in a bullet package providing 1000 mcd. Other LED manufacturers acknowledged the InGaN technology and followed to develop blue and green LED products based on the InGaN material system, with great efforts made to protect intellectual properties (i.e., patent filing and law suits). As with AlInGaP LEDs described in the previous paragraph, InGaN LEDs also employed large-chip architecture over the years. Outdoor color displays were a demonstrative application of high-brightness RGB LEDs. On the other hand the general illumination application puzzled LED engineers for a while; since white light from RGB LEDs did not perform well in this application. Today we have learned the color science and understand that it was because of poor color rendering (in addition to electrical complexity). Another factor was that most LED engineers at one time believed that the three primary

3.1

LED Chip (Die) and Market Segmentation of Products

47

Fig. 3.1 Left: White LED in a bullet lamp package (by Cree) of most common 5-mm diameter. An LED chip and phosphor is placed in a small cup of the Ag-plated lead frame (also refer to Fig. 2.12). Optical-grade epoxy resin is the encapsulant molded into the bullet shape. Two Au bond wires are seen indicating a lateral chip is used. In manufacturing ∼25 units are connected in one large lead frame, and at the end leads are cut and separated into discrete lamps. Longer of the two metal leads is the positive polarity by convention. Another common size is a 3-mm package, sometimes denoted as T1 while T1-3/4 for the 5-mm package where 1 indicates 1/8 of an inch. Package designs are a subject of intellectual properties and thus bullet-package components are not available off the shelf. Right: IR chip-LED manufactured by Stanley Electric. These rectangle SMD packages are called by their dimensions: Shown here is the 3015 package indicating 3.0 mm × 1.5 mm of outer dimensions. The black cube located in the middle of the package is the semiconductor chip (AlGaAs) glued using Ag epoxy. After wire bonding, epoxy encapsulant (this particular product has employed slightly translucent resin for light-distribution pattern purposes) is molded on and the whole PCB is sawn into discrete devices as shown

colors were necessary to synthesize white light. The first commercial white LED in 1996 by Nichia Chemical (a phosphor company originally) surprised the industry by utilizing two complementary colors (blue and yellow) neatly encapsulated in a bullet package. Today the consequence of chip size evolution is the market segmentation of high-, mid-, and low-power LEDs in general illumination applications. Example products are shown in Fig. 3.2. High-power LEDs are approximately 1 W of electrical input or higher. 350 mA into an InGaN LED requires approximately 3 V, thus 1 W has become a dividing line. Lowpower LEDs are those using conventional small chips of ∼20 mA drive. Mid-power LEDs are somewhat in between, although this border between low- and mid-power LEDs has become unclear in recent years. Segmentation is a type of marketing classification that in turn has set cost and engineering standards (similar to passenger-car marketing). This means that, while fundamental science is the same for all segments, required technology and engineering vary.

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Fig. 3.2 High-power LED (left) of a 3535 package (3.5 mm × 3.5 mm footprint). The substrate is alumina for heat dissipation and a dome lens is built in to increase LOP. It is not uncommon to employ multiple high-power chips in a package to increase LOP. Mid-power LEDs (the group in the middle) is a low-cost option. Packages are lead frames with white reflector housing molded on. Often multiple low-power chips are used in a package. Dispensed phosphor integration is common without a built-in lens, thus the yellow-orange appearance results. Low-power LEDs (the group on the right) is the lowest cost option. Structurally it is very similar to the mid-power ones, but most cases one chip per package. Also the SMD in Fig. 3.1 belongs to this segment

High-power LEDs require the use of costly ceramic packages for enhanced heat sinking, whereas mid- and low-power LEDs opt for lead frames, quad flat no-leads (QFN) packages, or FR4-based PCBs to be cost effective. Other classes of illumination products include the chip-on-board (COB) devices shown in Fig. 3.3a. They use inexpensive small dies, with a

Fig. 3.3 a COB products of various sizes manufactured by Lumileds. In the 2010s when product development was the most competitive, manufacturers proposed all various sizes of products without industry standards being established. Largest COBs (LES > 30 mm in diameter) consume more than 100 W of input power whereas small ones (LES ∼ several mm) are in the range of a few watts. A common notation used is for example 1203: the first two digits indicate the number of chips connected in series (thus the operation voltage is approximately 3 [V] times of it) and the last two imply the number of strings (parallel lines of series-connected chips). Photograph courtesy of Lumileds. b The Miro series manufactured by Alanod is a well-known Al-core substrates for COBs. The cross-sectional drawing (reproduction from Alanod’s catalog) shows its layering structure. Highly engineered layers allow environmentally-protected high-reflectivity being maintained over time

3.2

Chip Architecture

49

number of them connected via wire bond in a package, that generate a nontrivial amount of heat requiring decent heat sinking. Aluminum substrates coated with highly-engineered reflective layers, illustrated in Fig. 3.3b, are commonly used in COB products. For the past several years LEDs have been integrated with other electronics into modules. Hence the notion of “levels” was born: Level 0 (L0), L1, L2, and so on. L0 indicates the free-standing LED chip. The chip mounted on a submount (e.g., a piece of ceramic plate) is called L1. The chip-scale package (CSP) implies a L0 package where a blue-emitting chip is integrated with phosphor to be a white-emitting chip with no submount. CSP provides customers an opportunity of mounting it in their optical systems in their desired way. The majority of high-power and mid-power products are L1, as they are already mounted on a submount or a reflector cup, regardless of phosphor integration. L2 is the module, where various electronic components including LEDs are mounted on a larger circuit board. L2+ and L3 includes lighting fixtures where L2 devices go in and integrated systems beyond. Apart from the modern high-brightness LEDs, older-technology (i.e., indirect-material) color LEDs are still in limited use as indoor indicators, e.g., home appliances and toys. These LEDs utilize indirect bandgap materials that were largely developed before AlGaAs emergence. The green to red range is their territory: 555 nm by GaP, 565 nm by N-doped GaP, 700 nm by ZnO-doped GaP. Adding As shrinks GaP’s bandgap (refer to Fig. 4.1), thus resulting in slightly longer wavelengths. Hewlett-Packard and Monsanto were two major players, in case the reader wishes to seek publications. The commercial value of LED chips is of general interest though rarely commented in literature. Craford mentioned in his 1997 article that a price of 10-20 cents per chip was viable [15]. Making a ballpark estimate from this, a 4” wafer has an area of 7000 mm2 with a few mm of edge exclusion and 16 small chips (since the article was written before the high-power era) per mm2 gives approximately 100 000 chips per wafer; thus the cost of a commercially viable epi wafer would have been in the range of $10 000, or perhaps lower by taking into account device fab and singulation + sorting costs.

3.2

Chip Architecture

A variety of chip architectures have been invented and commercialized to date to enhance device performance, predominantly the efficiency. At the same time saving production cost is extremely important for a manufacturer to stay competitive in the market. Therefore today, various chip architectures are in use to balance performance and cost on an applicationby-application basis. To take a glance at them, a chronological review of chip technology probably provides the best understanding. Semiconductor terminology will be thoroughly explained in Sect. 4.1. Early III-V material systems (lattice-matching systems, often called traditional III-V materials in contrast to the newer III-nitride materials which are lattice-mismatched systems) were able to utilize electrically-conductive substrates (e.g., p-type GaAs). An LED

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Fig. 3.4 Schematics (not to scale) showing popular chip architectures, approximately in the order of development and commercialization. a Vertical chip with one wire bond. A metal contact has also been prepared on the bottom of the chip so that conductive glue (e.g., Ag epoxy) makes a good electrical contact to the chip. The arrow indicates the direction of current flow. b Lateral chip with two wire bonds per chip. Mesa structure is required because the epi substrate is insulating. For this reason, die-attach glues do not have to be electrically conductive. Clear silicone is often employed for die attach, despite its low thermal conductivity. c FC is a flipped lateral chip to eliminate wire bonds and to enhance heat dissipation into the submount. FC becomes possible when the substrate is highly transparent to the emission wavelengths. In practice FC is used in high-power large chips where current spreading becomes a major issue, thus a via structure (Fig. 3.10) is typically employed with. For such distributed metal contacts, gold-gold interconnect (GGI) is the die-attach (DA) method, or a redistribution layer (RDL, Fig. 3.11) is added. d TFFC is a FC with the epi substrate having been removed. The remaining semiconductor film is only several microns thick, hence mechanical support of the epi layer is crucial. TFFC is always fabricated on a submount, thus GGI is a default DA method and no RDL is applied. e VTF does not require a mesa structure, thus the active region is fully remained. Although it requires wire bonding, the overall fabrication process becomes simpler than TFFC

chip was fabricated in such a way that negative and positive electrodes were prepared on top and bottom of the chip, respectively (or vice versa when an n-type substrate was used). Electrode metallization was conducted at the wafer level using photolithography and thin-film deposition techniques. The metallized wafer was cut into chips using a spinning diamondblade dicing saw. Singulated chips were glued on a lead frame using electrically-conductive heat-curable glue (e.g., Ag epoxy) and an Au wire bond connected the top electrode to another electrical post of the lead frame. Since current flows vertically in the chip in this architecture, it later became called the vertical chip in contrast to the newer lateral chip (Fig. 3.4). Among a few substrate options for III-nitride LEDs, the most common choice was sapphire. Industrial sapphire wafers are a pure oxide material (optically clear and transparent) and inherently electrically insulating; hence the vertical chip architecture was discarded.

3.2

Chip Architecture

51

Instead of metalizing the bottom contact on the back of the substrate, a small area of deposited semiconductor material was removed from the top by an etching technique until the firstdeposited layer on the substrate was exposed to the surface, to which the bottom contact was metallized. In the resulting architecture the chip required two wire bonds on top of the chip and current flowed sideways, thus this architecture was referred to as the lateral chip. Lateral-chip geometry is often referred to as a mesa structure. Mesa structure was a result of removing a part of semiconductor material that would otherwise emit light, and was thus considered to be expensive. Therefore the effort was to minimize the mesa-etched area. Another important technique to note here is that there is a thin layer of ITO (indium-tinoxide, having replaced the very thin Au deposited layer that was used in early InGaN chips) over the top area for lateral current spreading. This is because the top p-type GaN layer has low electrical conductivity. Without a current spreading layer current would flow straight down solely along the electric field and light would be generated only underneath the p-type metal bonding pad. Since the sapphire substrate is transparent, these lateral chips for lowand mid-power LEDs optionally employ an omni-directional reflector (ODR) deposited on the bottom of their transparent substrates in order to redirect emitted light back towards the top of the chip. An ODR is a nonmetallic DBR-based reflector designed to function for a wide range of light incident angles of the emitted blue wavelengths. Late in the 1990s, when the industry pursued high-power devices, dissipation of the large amount of heat generated in a large chip became a great hurdle to overcome. The sapphire substrate had reasonable but not ideal thermal conductivity, and consequently engineers changed the chip architecture by flipping the chip upside down (although, definition of top and bottom of the chip is subjective). The sapphire substrate was then facing up in a package, and LOP was entirely through the substrate as sapphire was perfectly transparent. This architecture is called the flip chip (FC). Both n- and p-type contacts were rigidly attached onto two separate electrodes prepared on the heat-sinking submount so that heat dissipation was maximized, while light output could be enhanced by inserting an extra reflective metal (e.g., Ag) right underneath LES as a part of the p-type metal contact stack. Then a question was raised: Is the piece of sapphire sitting on top needed? Ample study was performed on light extraction, whether sapphire would help to enhance light extraction in FC, and if so, what would be the optimum thickness. This discussion was later dismissed by the discovery of light-extraction benefit by surface roughening in 2004. After removing the sapphire substrate from a FC via the laser liftoff (LLO) technique, the exposed n-type GaN surface was photoelectrochemically (PEC) etched resulting in a rough surface. The roughened surface functioned nicely to break the total internal reflection (TIR) occurring in the planar semiconductor layers and enhanced light extraction. Thus, the industry concluded that the sapphire substrate was to be removed followed by PEC roughening (with added cost, of course). This architecture is called the thin-film FC (TFFC). TFFC added production cost, but the bonus was that TFFC was a preferred 1-sided emitter, whereas FC was a volumetric 5-sided emitter. Application engineers found advantages of TFFC in light coupling into their optics.

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Yet all InGaN chips had the disadvantage of being mesa structured. With the FC and LLO technique, mesa structure became unnecessary by making the n-type contact on top (the exposed n-type layer) of the chip via wire bonding. This architecture is called the vertical thin-film (VTF). To assist lateral current spreading in the n-type layer, metal fingers or mesh may be patterned on the exposed surface protruding from the bonding pad. An extra benefit of VTF is, when VTF devices are prepared on a submount of a semiconductor wafer (e.g., Si) with a reflective metal layer (e.g., Ag) in between, a conventional chip fabrication facility can produce 1-side emitter chips (i.e., L0) that a customer can easily handle and attach using common DA and wire-bonding equipment. The only drawback of this metal contact was that it shaded the LEA. Thus a version of VTF, the embedded-contact VTF (ECVTF), introduced n-vias in the chip to connect to the patterned n-contact metal prepared on the submount rather than using a wire bond. EC-VTF architecture appeared very similar to (virtually the same as) large-area TFFC (See Fig. 3.10). All these elaborate optical and electrical improvements happen at a cost. Therefore, each application determines which architecture is adequate and affordable. Now we shift gears to AlInGaP LEDs. AlInGaP LED structures are grown on the GaAs substrate, which is optically absorbing. Effort was made to replace GaAs with a transparent substrate after growing a complete LED structure [5]. The LED structure on GaAs was attached onto a GaP wafer via a wafer fusion (also called wafer bonding) technique, then the original GaAs substrate was detached using wet-etch methods. The rest of chip fabrication was carried out just as the same into vertical chips. The next challenge was the light extraction. III-V materials have relatively high refractive indices and large part of generated light was trapped in rather symmetric cubic chips. Using a dicing saw method with shaped-tip saw blades, less-symmetric chip shapes were created. This technology is the chip shaping1 : A few examples are shown in Fig. 3.5. After a big wave of chip shaping in the industry around 2000, applications demanded higher power and consequently AlInGaP LEDs experienced similar development that InGaN LEDs received, like VTF (but not TFFC due to fabrication difficulties). Figure 3.6 shows an example of VTF products using a semiconductor wafer submount and assembled via a conventional facility. Reference [12] provides a comprehensive overview of chip evolution reviewed above. Each chip architecture requires an appropriate die attach method. Table 3.2 lists common methods of die attach/contacting methods. Au forms a destructive intermetallic with Al [2], which requires attention whenever Al is near Au. Chips are typically guaranteed a thermal budget for reflowing up to three times. A recommended temperature profile of reflowing is disclosed in a product datasheet. To evaluate quality of attach, a wire bond is subjected to wire-pull and ball-shear tests. The die shear test is for all die attach methods. X-ray imaging is used to inspect voids in reflowed solder. 1 Chip shaping was unsuitable for sapphire wafers since sapphire was not a sawable material due

to its inherent mechanical properties; instead it cracked and shattered. No shaping techniques other than saw blades were industrialized in chip shaping. Chip shaping was nevertheless effective on InGaN-on-SiC LEDs, given an intellectual property name “ATON”.

3.3

LED Wafer Fabrication via Epitaxy

53

Fig. 3.5 Examples of chip shaping: a Truncated inverted pyramidal shape of Lumileds’ large-chip AlInGaP LED (circa 1999, photograph under operation, courtesy of Lumileds), b Cree’s conventionalsize InGaN LED prepared on SiC substrate, branded as MegaBright (circa 2001, photograph under operation), and c 3535-packaged InGaN FC LED prepared on SiC, commercialized by Cree as XLamp XT-E circa 2011. The chip sitting in a clear dome has a truncated pyramidal shape with deep crossed grooves, and is conformally coated by a yellow phosphor (courtesy of CreeLED, Inc.). Chip shapes were made only into epi substrates, in order not to waste epi materials

Fig. 3.6 A Lumileds product using an AlInGaP VTF chip. Au wires make the top contact with a finger pattern of contact metal. Underneath the epi layer, a dark-looking substrate is seen. Two electrodes have been prepared on the backside of the product using metallized thru-vias for reflow attach. Photograph courtesy of Lumileds

3.3

LED Wafer Fabrication via Epitaxy

LED chips are made from a functional wafer referred to as the “epi wafer.” Epitaxy is verbally abbreviated as “epi,” or fully articulated as “epitaxial growth.” Epitaxy is a technique of forming layers of semiconductor materials on a single-crystal wafer (substrate), where crystallographic information (crystal structure, lattice constant, etc.) is inherited from the substrate to the layers formed. The LED is a pn junction device, so that the goal of LED epi is to deposit high-quality p- and n-type layers on a substrate, with other functional layers that are part of the modern LED design. For example, a designated light-emitting layer (“active layer” or “active region”) is sandwiched between the n and p layers, as schematically shown in Fig. 3.7.

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Table 3.2 Common die attach/contacting methods Method

Mechanism

Applications

Characteristics

Ag epoxy

Fluid dispense + thermal cure

Vertical chip

Electrically conductive, low temperature process (150–180 ◦ C), tarnishes over time Electrically insulating, transparent or white appearance, low temperature process (150–180 ◦ C)

Silicone

Wire bonding

Lateral chip, COB

Heat + ultrasonic + force

GGI

SAC

AuSn

Vertical chip, lateral chip, VTF

TFFC, EC-VTF

Eutectic reflow

FC

FC, VTF

Electrical contacting only (no DA function), relatively slow process, low thermal stress, large mechanical impact/stress Expensive, accurate die position control, clean (no organic substance), attach tool typically available at chip manufacturers only High temperature (∼260 ◦ C), contaminated by organic substances (e.g., solder flux) Expensive, highest temperature (∼300 ◦ C or above), solder flux often used to reduce voiding

This type of layering is called the double-hetero (DH) structure since both interfaces of the active layer are formed with pairs of slightly different (= hetero) materials. The layers sandwiching the active layer are called cladding layers. The DH structure provides better recombination efficiency than a pn homojunction because carriers can stagnate within the active layer. In the InGaN LED case, an InGaN active layer is sandwiched by n- and p-type GaN layers. More advanced structures have more complex layering designs with additional functional layers.

3.3

LED Wafer Fabrication via Epitaxy

55

Fig. 3.7 An example of double-hetero (DH) structure. a Schematic of epitaxial layering. A light emitting layer is grown on an n-type layer and followed by a p-type layer. b Schematic band diagram under a flat-band condition. The light-emitting layer has smaller bandgap and creates a benefit of pooling carriers (carrier confinement). Also, emitted photons transmit through the larger-bandgap nand p-type cladding layers. Solid and open circles indicate electrons and holes, respectively

There are numerous techniques to perform epitaxy. Today the most common in LED industry is the metalorganic chemical vapor deposition (MOCVD),2 which is a type of vapor-phase epitaxy (VPE). MOCVD [14] uses toxic gases and flammable precursors, so is rather an expensive technique requiring safety equipment and detoxifying exhaust systems. It has nevertheless been industrialized profitably during the last three decades because of LED technology and market acceptance. VPE has a common advantage of obtaining atomically abrupt interfaces between various layers by switching gaseous precursors. The liquid-phase epitaxy (LPE) process was largely developed earlier than MOCVD for AlGaAs and related LEDs. LPE forms comparatively dull interfaces because of its use of molten precursors. MOCVD is driven by the chemical reaction of precursors promoted by heat, and higher temperature helps to synthesize semiconductor materials of higher quality by desorbing unwanted byproducts like alkyls. AlInGaP LED structures are attained predominantly by alternating gaseous precursors at a growth temperature in the range of 650–800 ◦ C . In contrast, the InGaN LED structure requires growth temperature varied vastly during a growth between 500 and 1200 ◦ C in addition to gaseous precursor switching. InGaN composition is extremely sensitive not only to the gas mixing ratios but also to the growth temperature. Any nonuniform temperature profile on growing wafers leads to an emission wavelength spread of resulting devices, hence low eventual production yields. Gas-flow dynamics in the reactor chamber are important for the same reason, and because vapor-phase convection changes with growth temperature, gas-flow dynamics are even more abstruse. Enormous amounts 2 We use the most common name MOCVD in this book, while other names like OMCVD, MOVPE,

etc. can be found in literatures. These various names imply the same growth technique in practice, though one can argue the strict definitions indicated by each name, e.g., epitaxy versus deposition. Especially when it comes to intellectual property concerns, wording may become critical to highlight and differentiate a key technology.

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of resources have been put into these challenges of equipment hardware to manage growth conditions and to maintain the equipment reliable over time. The wealth of accumulated theoretical and empirical knowledge is kept confidential as an LED manufacturer’s trade secrets. The AlInGaN system is quite a mischievous material for MOCVD engineers. Some details of the complexity around InGaN MOCVD growth3 are given below [8]. To form multiple layers on a substrate, material compositions and dopant concentrations (amounts of intentional impurity elements) need to be controlled at each layer by varying both precursor gas mixture and substrate temperature consecutively in a growth run. Generally speaking growth temperature reflects the atomic bond strength between the cation and anion of the growing material. Binary GaN is grown at around 1000 ◦ C, while AlGaN requires as high as 1200 ◦ C. InGaN calls for various temperatures in the range of approximately 600–900 ◦ C depending on its composition, which determines the resulting emission color. This tremendous difference in growth temperature between AlGaN and InGaN is the reason for preventing the use of quaternary AlInGaN in a structure. Shown in Fig. 3.8 is a simple yet representative structure of InGaN LEDs. The structure is realized by the following procedure. After inserting sapphire substrates into an MOCVD reactor, they experience high-temperature (HT) thermal cleaning followed by a GaN (or AlN) nucleation layer (also called a LT-buffer layer) deposited at lower temperature around 500 ◦ C.4 The nucleation layer is thin and functions to accommodate the 16% lattice mismatch between sapphire and forthcoming HT GaN. Substrate temperature is then raised to around 1000 ◦ C and a HT GaN layer is grown for about 4–5 μm thick without intentional doping (often referred to as unintentionally doped, UID, being lightly n-type because of GaN’s nature 3 MOCVD is typically operated under reduced reactor pressure for various reasons. However, atmo-

spheric MOCVD is more common for III-nitride growth. In its infancy when reduced pressure of GaN MOCVD was not questioned, a researcher found a broken vacuum pump on his MOCVD machine but decided to proceed in growth experiments rather than fixing the pump because of lack of domestic hands. He obtained a better GaN crystal out of atmospheric growth. By 2000 when GaN growth technology had been shared worldwide, researchers elucidated how the growth pressure affected GaN growth and proved that atmospheric growth did have advantages in coalescence control in the early stage of growth. Several growth techniques were then developed based on coalescence controlling with photolithographically defined SiO2 growth masks or partially-etched substrates. These growth techniques are referred to as lateral epitaxial overgrowth (LEO) and other names. In these LEO GaN materials, threading dislocation densities were reduced by several orders of magnitude. 4 The low-temperature (LT) nucleation layer was originally invented using AlN because of its lattice constant being between those of sapphire and GaN, which somewhat buffers the lattice constant difference. For this reason the nucleation layer had been called the buffer layer, although today a buffer layer tends to imply a HT GaN layer as mention in the present section. The effect of a LT buffer layer was discovered by accident. It was reportedly described that a reactor heater broke one day but the operating researcher did not notice the broken heater. He included the failed substrate in the reactor after fixing the heater and continued on the growth experiment. Resulting was a clearerlooking film grown on the failed substrate. After publication of the LT AlN buffer layer, LT GaN was also found to function just the same as a LT AlN nucleation layer to grow high-quality layer on top of it.

3.3

LED Wafer Fabrication via Epitaxy

57

Fig.3.8 A simple example of InGaN MQW LED structure. a Schematic of epitaxial layering. Electrically functional layers are the Si-doped GaN and above. b Schematic band diagram under a flat-band condition (majority of complexity has been omitted for the sake of visual simplicity). The electron blocking layer (EBL) is inserted on the p-type side of the active region to keep more mobile electrons (solid circles) from spilling out from the active region. Injection of holes (open circles) into the active region is usually compromised

of creating N vacancies). This thickness is required to establish good quality GaN, as shown in the following mechanism [6, 11]. The HT GaN layer initiates as three-dimensional islands around the polycrystalline nuclei of the nucleation layer. Soon after, the GaN islands start coalescing as they grow larger. At the coalescence front generated are threading dislocations due to the fact that two independent islands are not exactly crystallographically aligned (called “mosaicity.” See Fig. 4.7). With repeating coalescence as the layer growing thicker, threading dislocations encounter and cancel with each other to disappear at a probability. After 4–5 μm the HT GaN has reached its final quality of threading dislocation density (TDD) being around 1×108 cm−2 (one per 1 μm2 ). For this purpose, the HT GaN layer is occasionally called the buffer layer or the coalescence layer. Si doping is introduced toward the end of this HT GaN layer to make its top section sufficiently n-type for a contact metal. This single GaN layer prepared on sapphire is sometimes called a “template” in R&D. Once the n-type GaN layer is formed, the substrate is cooled to a desired temperature for InGaN active layer growth. The InGaN active layer is made very thin (a few nm) to suppress QCSE (see Chap. 4). The structure is referred to as the quantum well (QW), a special case of DH, because of its thickness introducing quantized effects, i.e., discrete energy levels in the active layer. To add more volume of light-emitting material in an LED structure the thin InGaN layer may be repeated multiple times sandwiched by larger bandgap layers (“barrier layers”), referred to as the multiple QW (MQW) structure while the former is called the single QW (SQW) structure. Because of InGaN’s tendency of decomposing, N2 carrier gas is used to apply N overpressure in the reactor and a slow deposition rate is carefully maintained so that high-quality InGaN will result. To complete an LED structure two p-type layers are deposited at higher temperatures. This temperature increase makes the InGaN growth

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even more troublesome by exposing the grown InGaN layer to temperatures exceeding its decomposition temperature. Nevertheless, Mg-doped AlGaN, which has a larger bandgap than GaN and serves as an electron-blocking layer (EBL) to prevent electrons from spilling over into the p-type layer, is grown on the InGaN active layer. The EBL is followed by a final GaN layer which is heavily doped with Mg to be a p-type contacting layer. A shorter growth time is preferred to minimize InGaN exposure to the high temperatures, yet a reasonable thickness of p-type material is needed to avoid the pn-junction punch-through. The p-type thickness is typically agreed on being around 200 nm. Impurity doping is in general considered to be merely a perturbation to the crystal until it starts affecting the host lattice (the Mg-doped p-type GaN layer is such a case with the doping concentration is close to 1%). Dopants are generally 100% thermally ionized at ambient temperature to provide carriers, but p-type GaN is a different story. Mg is the only industrialized element to obtain p-type GaN.5 A Mg atom in GaN captures a hydrogen atom from MOCVD carrier gas and ammonia (the precursor for nitrogen atoms), deactivating itself as a dopant. To expel H atoms from Mg-doped GaN, the industry applies thermal annealing to completed epi wafers in N2 , for example at 700 ◦ C for 20 min. The Mg acceptor energy level is located ∼0.2 eV deep in the GaN bandgap and ambient thermal energy (26 meV) is insufficient to ionize them fully, so that hole concentration is 1% or so of doping concentration. In addition, to GaN’s nature of being n-type counteracts to the acceptor. Carrier mobility is low due partly to its own high doping concentration. Altogether, good current spreading in a p-type GaN layer is unlikely. Epi engineers play clever growth tricks to overcome the difficulties described above. Yet the unbreakable boundary condition has been the fact that the InGaN LED structure needs the n-type layer to be first on the substrate. Occasionally a question raised whether an InGaN LED growth can be started from a p-type layer. The answer is “it is unrealistic” for a few reasons. GaN is naturally n-type, TDs need to be reduced by growing thick on sapphire, and H needs to be expelled easily from p-type layers through the grown layers. Also, there is a chance of contaminating the active layer by the p-type dopant (i.e., the Mg memory effect in the reactor) when a p-type layer is grown prior to the active layer. On a separate note, epi wafers are visibly bowed due to the lattice-mismatched system where the epi layers are put under strong compressive strain by sapphire. These progresses in MOCVD technology were made not only by LED manufacturers but also by equipment manufactures. Aixtron (Germany) and Emcore (later became Veeco, U.S.A.) led the industrial market with their own unique technologies, while other manufactures e.g., Thomas Swan (U.K.) and Nippon Sanso (Japan) contributed also by their irreplaceable technologies. As LED-dedicated high-performance MOCVD machines became commercially available, and epi growth and device fab technologies were shared with LED 5 Other elements were examined in early times. Beryllium had a good reputation for obtaining p-type

but was highly toxic, and unsuited to industrialization. Zn made a very deep acceptor but was in turn used as a recombination center in InGaN codoped with Si (thus donor-acceptor-pair for luminescence) in an early commercial blue LED when InGaN growth techniques were immature [7].

3.3

LED Wafer Fabrication via Epitaxy

59

manufactures worldwide upon expiration of early IP, the LED industry encountered a turning point where the number of epi and chip manufactures in the world step-increased. Worldwide expansion of chip business increased cost competitiveness, especially in general lighting applications. To close this section we discuss epi substrate options. GaAs is widely used in power electronics and high-speed electronics, e.g., high-electron mobility transistors (HEMTs). Hence the LED industry is well-supported also. AlGaAs and AlInGaP are lattice-matching systems to GaAs, therefore high-quality (low defect density) materials are obtained. (100) GaAs is used for LED device growth. A slight offcut (an equivalent word “miscut” is misleading since a slight off-angle from an exact crystallographic plane is intentionally introduced) may be utilized to control epi surface morphology and/or atomic ordering. For InGaN LEDs GaN substrates have been long sought after as the InGaN LED has been researched, yet commercialization is limited, produced mostly using the hydride VPE (HVPE) technique. GaN boule growth requires extreme synthesis conditions (high temperature + high pressure = a bomb!) and governments’ safety regulations ban experiments and production in/near populated cities. Sapphire became popular with the invention of the nucleation layer. The cplane sapphire wafer (with an intentional offcut) dominates InGaN LED growth today. Other crystallographic planes are used for nonpolar and semipolar GaN research. Sapphire is often presented as a hexagonal crystal but it is triclinic, thus the c-plane possesses only a threefold rotational symmetry whereas c-plane GaN has a six-fold symmetry. Another important fact is that c-plane GaN grows on c-plane sapphire by rotated 30◦ , resulting in a smaller 16% lattice mismatch. That the a axis of GaN is now parallel to the m axis of sapphire (See Fig. 4.6). Both single-side polished (SSP) and double-side polished (DSP) wafers are readily obtained commercially. The patterned sapphire substrate (PSS) was invented for improving light extraction [20]. Wet etching of planar wafers using hot acid creates μm-size 3D topography on a surface. Optimized MOCVD growth achieves a planar surface of the GaN film on a PSS but the GaN-sapphire interface is no longer planar so that TIR is suppressed. The word “sapphire” reminds one of a gemstone with deep-blue appearance. According to gemology, our transparent pure aluminum-oxide crystal should be called “corundum.” When a corundum crystal contains Cr as an impurity, it is called “ruby,” with a deep-red appearance. Some white LED spectra in datasheets show a small sharp peak at 694 nm. This red peak is the renowned ruby line (actually two fine discrete lines) caused by Cr in sapphire substrates and alumina submount. Sapphire has been industrialized as sapphire windows (e.g., wrist watches in the past and mobile phones today) to provide ample wafer supply at an affordable price. Sapphire became cost competitive as LED industry grew where the epi wafer size advanced from 2-inch to today’s 4- and 6-inch,6 leaving Si wafer’s costeffective claim behind. The Si wafer was considered and experimented as a cost-effective option against sapphire; however the mid-2010s sapphire won the lm/$ race. Si has how6 It has been common to call wafer sizes in inches rather than millimeters, and 150 mm wafers are

often called 6” wafers verbally. 6” (151.2mm) is apparently larger than 150 mm, potentially causing issues in wafer processing and handling systems designed for 150-mm wafers.

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ever regained attention last few years for emerging micro-array LED applications where Si-electronics integration is sought. (111) Si is used for GaN growth because of its six-fold surface rotational symmetry. SiC once competed against sapphire, armed with its thermal and electrical advantages. SiC has polytypes (various atomic layer stacking sequences). 4H and 6H are used for GaN growth because of their hexagonal structures. SiC is a transparent material with 3.0–3.2 eV of bandgap, while the appearance has a slight tint that darkens when doped for electrical conduction. SiC wafers are manufactured by a limited number of companies due partly to strong intellectual properties, preventing ample supply as epi substrates, and remain costly. Today SiC has found its home in GaN electronics.

3.4

Functional Device Fabrication

Epi wafers go through the device fabrication process (“wafer fab” or “device fab”) to be electrically functionalized. This device processing consists of three process stages: Making the epi wafer electrically accessible, singulating into discrete chips, and sorting the chips. Prior to these, InGaN epi wafers receive thermal annealing in a N2 ambient to activate Mg as the p-type dopant. Any H-containing environment is avoided after this activation process. For AlInGaP epi wafers, depending on product types, they may be subjected to wafer bonding (see Sect. 4.1) before starting device fabrication. The first stage, metal contact formation, is straightforward for vertical and lateral structures. Common photolithography techniques are used to put down necessary photoresist mask patterns and common vacuum thin-film deposition techniques deposit p- and n-type contact metals. An epi wafer for vertical chips receives metal deposition on both surfaces for top and bottom contacts. Lateral chip architecture (Fig. 3.9) requires an etching to form a mesa structure. Reactive ion etch (RIE), a dry-etching method, is used to expose a part of the n-type GaN layer prior to depositing a metal, e.g, Al. Unique to the InGaN LED is a transparent ITO layer deposited on the p-type GaN surface to realize lateral current spreading [9], followed by a small Au bonding pad. The FC may be obtained by flipping a lateral chip and solder-bonding on a submount, e.g., a PCB. Light is emitted through sapphire, therefore the p-type area is preferably coated with a reflecting metal, e.g., Ag. On selecting a p-type GaN contact metal, an important requirement for the metal is to possess a large work function to make an ohmic contact (low contact resistance) to the p-type GaN. ITO (although is not a metal) fulfills this requirement with reflective Ag overcoating. Au is another large work-function metal but absorbs blue light, and was used as a thin semitransparent p-type contact layer before ITO emerged. Another noble metal Pt is a compromised option of reflectivity and work function. Because the FC provides enhanced heat dissipation, it is attractive and suitable as high-power large chips [19]. Current spreading in the n-type layer of mesa structure (Fig. 3.9) becomes rather insufficient in a large chip. To circumvent current crowding, which causes local heating and LOP loss, the mesa structure is modified to the n-via structure (Fig. 3.10) where small areas

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Fig. 3.9 Schematic illustration (not to scale) of an InGaN LED lateral chip with mesa structure. The Si-doped n-type layer is exposed via RIE in a small area (approximately 100 μm across) where a negative contact metal stack is deposited. The entire p-type GaN area becomes LES which is covered by ITO (except near chip edges for singulation purposes). A small Au bonding pad follows the ITO deposition. Au ball bonding is exclusively used to attach wires. Chip shape and dimensions vary, while total thickness is typically around 100 μm

Fig. 3.10 TFFC structure shown in cross section [13]. The n-type contact metal structure (n via) and a p-type contact metal are distributed across the LES to suppress current crowding. Light is not generated at n vias, thus n vias have the minimum size that photolithography can reliably create (see Sect. 3.7). The number of vias and their distribution pattern are determined by electrical properties of the epi layers. A commercial TFFC LED produced by Lumileds is shown in the photograph. Dark circles are the n vias. Photograph courtesy of Lumileds

of the epi layer are dry-etched into the n-type layer. A contact metal is deposited into these vias to reach the n-type layer with a dielectric insulating layer in place. Dielectric layers (SiO2 , SiNx , etc. via a sputtering method) serve as electrical insulation and passivation of sensitive semiconductor surfaces e.g., etched sidewalls.

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A consequence of the n-via structure is the scattered n-contact areas surrounded by the blanket p-contact. This geography introduces die attach challenges. Gold-gold interconnect (GGI) attach is typically employed, despite its expense, for precise attach without bonding metal smearing. It is, however, more convenient for conventional solder attach to be used. The redistribution layer (RDL, Fig. 3.11) is an additional pair of dielectric and metal layers for this purpose. An RDL repositions the metal contacts to two distinct metal pads on each corner of a chip with a sufficient gap between them so that solder reflow can be applied. This is good for customers who wish to perform their own die attach but do not have access to GGI. Thin-film chip fabrication technology serves as a baseline for the recent industry interest in pixelated emitters. Instead of making scattered n-vias, a deep grid of n-contact can be formed. In order to eliminate optical cross talk (an off-pixel getting illuminated by a neighboring on-pixel), the n-contact grid reaches the emitter surface (called a trench structure, Fig. 3.12) and acts as a light wall between pixels. Contact metal stacks in products are designed (choice of metals, order of layering, thicknesses, etc.) to achieve desired device properties, including reliability. It is often called an under-bump metallization (UBM), borrowed originally from the Si technology terminology. Each metal has designated functions based on characteristic properties of the metal. Table 3.3 is a list of commonly used metals in the device fab and packaging. Gold (Au) is used to finish a metal stack owing its inertness and die-attach capability. A thick (>1 μm) Au bonding pad is common to accommodate mechanical impact of wire bonding. Au is also used almost exclusively as the bonding wire. Silver (Ag) is an attractive metal yet weak adhesion and electromigration are considered to be serious disadvantages. High reflectivity is deteriorated in ambient air because Ag is prone to tarnishing. Titanium (Ti) and tungsten (W) are hard metals and often used to encase Ag layers to prevent electromigration. Ti is an oxygen scavenger; hence, it is used to protect neighboring metals from being oxidized. Aluminum (Al) is a versatile inexpensive metal and has uniform reflectivity across the visible range extending into UV but is not as reflective as Ag. Nickel (Ni) is used in a metal stack to block intermixing. A renowned example is Al and Au [2]. Al and Au should not come in contact in a device or they will form an intermetallic (a type of alloy) at raised temperature causing mechanical and electrical failure due to volume shrinkage and brittleness of the intermetallic. Convenient alloys are utilized on purpose: Eutectic bonding uses the Au-Sn alloy, whereas a lower-temperature solder is Sn-Ag-Cu (SAC), a type of Pb-free solder. It is inevitable for a high-performance chip architecture to go through many photolithographic and thin-film-deposition process steps, causing increased production cost. Creating various topography by etching and layer-deposition on an epi wafer could induce poor coverages of consecutive layer deposition at corners, ridges, edges, steps, and trenches, leading to increased chances of mechanical failure, i.e., voiding, cracking, and delaminating, and ultimately electrical failure. Physical vapor deposition (PVD)7 techniques are used for metal 7 In contrast to chemical vapor deposition (CVD), PVD does not rely on chemical reactions of source

species. Thermal and electron-beam (e-beam) evaporation (evap) methods use molten precursors

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63

Fig. 3.11 a Schematic cross section showing a FC with a RDL. The hatched area is a multilayer nmetal. The cross-hatched area is a multilayer p-metal. The second dielectric layer provides insulation in order to redistribute n and p metal areas. The final solder pads (UBMs) commonly utilize a plating technique for fast deposition rates. b Plan view of the p-metal area. It covers almost the entire epi area. Holes are to clear n vias. c Plan view of the n-metal area. This layer connects the distributed n vias. This n-metal layer is followed by the second dielectric layer then UBM formation. The photograph shows the bonding pad side of a L0 product from Lumileds. Topography of metal and dielectric layers can be seen under two solder pads and in between. The gap between pads is typically around 200 μm to prevent solder bridging the two pads. Photograph courtesy of Lumileds

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3 Device Architecture and Fabrication

Fig. 3.12 Cross section of a chip having a trench structure (before sapphire removal). Note that the n-contact grid isolates the n-layer of each pixel by reaching the sapphire substrate. Sapphire is consequently removed by LLO after submount attach

and dielectric layer formation: Vacuum evaporation is a line-of-sight deposition technique whereas sputtering allows a certain degree of deposition on shaded surfaces. One of the latest technology methods being gradually adapted in large-scale manufacturing is the atomic layer deposition (ALD). ALD allows us to deposit conformally-coating layers with ultra-accurate thickness control, even in high aspect-ratio trenches. Overall, great care is paid to ensure corner/step coverages be as intended in device designs, with these thin-film deposition techniques in mind. Device engineers continuously make efforts to improve device designs to be cost-competitive by reducing process steps without compromising device performance and reliability. Metallized wafers are subjected to the second stage: singulation. Traditionally, the diamond-blade dicing saw was the accepted industrial method to singulate GaAs and GaP wafers. Sapphire wafers were different and appeared to shatter upon blade sawing. Sapphire wafers are manufactured thick in order to compete against wafer bow during the MOCVD growth: 2-inch wafers were approximately 0.5 mm thick, and the 6-inch ones are as thick as 1 mm or even thicker. InGaN LED epi wafers need to be back-thinned prior to singulation using common grinding and lapping/polishing techniques8 for improved production yields (source). Sputtering methods use an energized ion species (e.g., Ar+ ) to bombard a solid precursor (target). A target can be a compound material, e.g., SiO2 . 8 Even in the manured glass polishing industry, there seems no absolute distinction between these three techniques and they are often called interchangeably. Approximately speaking, grinding uses fixed abrasive and the abrasive (e.g., grinding wheel) and workpiece come in contact intermittently. Lapping uses either fixed (lapping films like very fine sandpapers with water as heat-removing lubricant) or loose (diamond-powder liquid suspension) abrasive and is performed on a solid platform (e.g., metal-based rotating stage) where a workpiece maintains continuous contact with the abrasive. Polishing is a finest step using either solid or pliable (e.g., synthetic fabric) platform with loose abrasive that may involve chemical action from the suspension liquid. Chemical-mechanical polishing (CMP) is a type of polishing with enhanced chemical action, performed on a pliable platform of polymer.

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Table 3.3 Commonly used metals in LED fabrication Symbol

Properties

Ag

Highest reflectivity in the visible Reflector in FC, mid- and low-power spectrum range, highest electrical and package interior thermal conductivity, large coefficient of thermal expansion (CTE). Prone to electromigration, weak adhesion, prone to tarnishing especially in sulfur-containing environment

Use

Al

Reasonable reflectivity in visible and Contact layer to n-type layers, ribbon UV ranges, good electrical and thermal bonding conductivity. Soft, large CTE. Low cost, versatile

Au

Good reflector for red and IR but absorbs blue, good electrical and thermal conductivity. Inert, soft, large work function. Expensive

Contact layer to p-type GaN layer, metallization finish, wire bond pads, GGI bumps, AuSn eutectic bond

Cu

Absorbs blue to green, second best electrical and thermal conductivity. Large CTE, good mechanical strength, prone to oxidization, weak adhesion to SiO2 . Low cost, fast deposition via plating

Initiation layer (seed layer) for plating, PCB circuitry, SAC solder, CuW heat sinks

Ni

Magnetic, chemically stable. Fast deposition via plating

Separation layer between dissimilar metals

Ti

Oxygen scavenger. Good adhesion, helps W from diffusing

Ag guard/barrier layer, in between W and SiO2 as TiNx welding layer

W

Low electrical conductivity, hard, high melting temperature. Fills holes and voids

Ag guard layer, CuW heat sinks

upon singulation and for final chip dimensions. Diamond-tip mechanical scribing9 (scoring) was chosen for singulation in early commercial products. In several years the LED industry became more competitive in production cost, and diamond scribing began to be considered expensive due to tip wear and limited scribing speed. Laser scribing techniques were then developed as a faster method. Laser scribing has several names based on their principles: Ablation dicing, stealth dicing, and other derived techniques. Since these techniques use 9 This is very similar to traditional glass cutting, which also requires the smooth surface of a wafer

being cut. Glass cutting is performed by one-stroke scoring followed by breaking. The sapphire wafer used multiple-stroke scoring. The c-plane sapphire possesses only three-fold symmetry, thus the scribe direction can affect singulation quality and yield, in addition to the difference between the a and m axes.

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short-WL UV lasers, wafer surface needs to be made optically smooth for the laser beam to penetrate. Laser scribing leaves rough traces on chip sidewalls that help light extraction compared to rather smooth sidewalls from diamond scribing. Singulation is completed by mechanical breaking. Three long blades apply pressure along a scribed line (three-point breaking) to separate chips. Sapphire is not a docile material when it comes to singulation. Wafers will not break in a straight line nor perfectly vertically, rather the break lines wiggle. Sidewalls of singulated chips will be curved surfaces. This wiggled breaking is referred to as “walk-off.” Photolithographic masks of wafer fab need to be designed to accommodate walk-off by introducing sufficient but minimal spaces between chips for maximized production yields per wafer. The thinner the wafer the smaller the walk-off dimensions, thus wafers are processed as thin as possible (∼100 μm), as long as spontaneous breaking is prevented. To fabricate the thin-film devices (TFFC and VTF), substrate removal is necessary at L1. It needs to be done after die attach because bare epi layers are not rigid enough to be handled by themselves. Once chips are attached on a submount, followed by an underfill of the hollow space between the chip and submount to brace the epi layer, LLO is applied to pop off the sapphire from the rigidly-supported epi layer. Sapphire surface needs to be clean and smooth for the LLO laser beam (193 or 248 nm) to penetrate and decompose a very slight portion of GaN at sapphire interface. LLO is followed by cleaning of any residue remaining after GaN is decomposed into Ga (melting point = 30 ◦ C) and N2 . Singulation processes are carried out on semiconductor-grade adhesive tapes10 laminated onto industry-standard metal ring frames (Fig. 3.13). PVC-backed pressure-sensitiveadhesive (PSA) tapes are used in wafer breaking owning their stretchable property, whereas more rigid PET- and polyolefin-backed UV-curable-adhesive tapes are used for dicing and back-thinning. Tape transfer is performed as necessary depending on the nature and sequential order of device fab processes. Various process tapes are commercially available today. PVC is a low-cost option combined with acrylic-based PSA and is used in the tape-stretch process to create spaces between singulated chips for forthcoming pick-and-place (p&p). UV-curable adhesive is employed on PET or polyolefin liner and serves to step-reduce tackiness after UV exposure. Reduced tackiness assures chip/wafer removal and high-yield tape transfer. Silicone-based adhesive may be a replacement for acrylic PSA in temperaturedemanding processes. Other tape properties are liner thickness, adhesive thickness and softness, tackiness, single- or double-sided, thermal or optical release functions (loss of tackiness for wafer release), etc. Singulated chips are handled using ring frames towards the forthcoming sorting process.

10 When LED industry was at its infancy, the PVC tape (called “blue tape” because of its appearance)

was universal for processing and handling chips. As the industry grew and became international operation, the blue tape failed to hold chips upon transportation or to release chips at a destination due to hardened adhesive over time. Tape manufacturers developed UV-curable tape products. They were designed to provide high initial tackiness which could reduce upon UV (∼365 nm) exposure. In this way, chips are well secured during storage and transportation and get released when necessary.

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Down-Converter (Phosphor) Integration and Packaging

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Fig. 3.13 Industry-standard metal ring frame (tape frame). Sizes vary to support 4 to 12 inch wafers and shown is an 8” one

Singulated chips on a ring frame are sent to the third stage: sorting, or almost equivalently, binning. Factory production is a collection of efforts to produce identical products in large quantities, yet not everything is carried out perfectly ideally. To accommodate production variances buried in resulting devices, sorting is implemented. Sorting is a process of grouping like-devices in terms of their properties (LOP, Vf, WL, etc.) in order to guide the later production processes. In the present case, blue chips are tested at appropriate steps during the production. Failed chips (i.e., out of pre-defined control limits) are inked11 and excluded from the later process steps (“yielding off”), so that unnecessary processes (i.e., phosphor integration and packaging on failed blue chips) will not be executed. Passed devices are grouped either physically (moved to separate bins or bin tapes) or electronically (recorded with device identification and test results). Binning conditions (e.g., how many bins are between the upper and lower control limits) are pre-determined based not only on technical capabilities but also application and sales strategies. When multiple chips are used as a set in a device (like in COBs), chips are taken from multiple bins to build a set (rather than taking like-chips from one bin) so that the resulting device property is averaged out to be the same. For example, two chips connected in series do not have to be from one Vf bin, but can instead be from a high and low Vf bin, respectively. This technique is called “kitting.” Kitting is a wise technique to reduce unconsumed bins.

3.5

Down-Converter (Phosphor) Integration and Packaging

Phosphors (not phosphorous) are a class of highly engineered materials that realize downconversion from high-energy photons to low-energy photons. Because of this role, “downconverter” is another name used in LED industry. Luminescence of this type is called photoluminescence (PL) or fluorescence. Historically, lookalike luminescence generated by 11 It has been a common practice to mark failed devices or components using ink, therefore it is said

“inked.” It is still a valid term in today’s electronically-operated manufacturing.

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phosphorous compounds was called “phosphorescence,” leading to the name “phosphor,” despite the fact that a modern phosphor may not contain the element phosphorous in it. Phosphor materials are produced mostly in a powder form for LED applications. Early white LEDs consisted of a phosphor powder mixed with clear silicone elastomer integrated onto a blue chip via a dispense method. Mixing with silicone made it more convenient to handle phosphor powders and to control the hue of resulting white. This dispense or “goopin-cup” technique is still used today in low/mid-power and COB devices because of its ease of multiple phosphor blending and cost effectiveness. In COBs sedimentation techniques were sought to densify the powder in silicone to enhance heat transfer. Sedimentation can simply be achieved by waiting for a prolonged time after dispense to allow particles to settle down, or centrifugal methods can assist to speed up the sedimenting process. One of difficulties is the particle-mass dependence; a phosphor blend tends to settle in layers by mass densities and particle sizes. Synchronized with chip’s trend towards higher power around 2000, other phosphor integration methods were developed to enable densification of powders and conformal coating of phosphor layers over chips. Densification improves heat dissipation, enabling cooler device operation and reducing material degradation risks. Also, densification reduces CTE of a down-converter layer, reducing risks of phosphor layer delamination due to heat cycles during device operation. Spraying is a relatively simple method to achieve large-area phosphor integration using a solvent-diluted phosphor-silicone liquid suspension. Conformal coating may be attained, yet densification is weak because particles only sit on top of each other. Other challenges include inhomogeneous suspension, large material waste, and nozzle clogging. A phosphor-blend suspension in a reservoir requires continuous agitation to remain a homogeneous mixture. As a suspension is being consumed, phosphor blend ratios gradually shift due to heavier particles being sprayed first by gravity. For these reasons reservoir sizes are somewhat limited, and frequent suspension recharges are needed owing to a large waste at the use point, where high air-pressure spray blows off most of the powders rather than allowing them to land on the workpiece. Small-diameter nozzles get quickly clogged by fluid left when a spray head sits idle, as solvents evaporate leaving viscous silicone behind. A high solvent content in a suspension enables a conformal coating due to the fact that powders (with a low content of silicone) immediately dry out upon landing on heated workpiece/devices. A low solvent content results in more wetted layers on devices (due to a high content of silicone) enabling sufficient coverages on vertical surfaces and areas out of line-of-sight. Toluene is a common solvent. Any solvent is somewhat toxic and thus a spray tool should be enclosed and equipped with ventilation. Precast sheets also allow for large-area integration via lamination [3]. Those phosphor-loaded silicone sheets may be prepared on release liner films and color-tested prior to integration. In this way color targeting becomes accurate and precise. During lamination, heat and pressure are applied to achieve conformal coverage. Phosphor sheets stretch at corners and edges of devices, hence conformality worsens with great topography. Blade coating (and screen/stencil printing) can handle highly powder-loaded mixture (slurry) in which sedimentation would not occur.

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Down-Converter (Phosphor) Integration and Packaging

69

Challenges are to fill any topography (e.g., chip and wire bond) without generating voids and to control accurate and precise blade height for color targeting purposes. Rework is possible: Rework is a redo of integration when the previous integration has failed in preliminary wet (= silicone uncured) color testing, by washing off the wet phosphor layer with a solvent. Slurry may be used repeatedly over multiple workpieces to minimize waste. A fully coated tile may lose geographical landmarks, leading to singulation difficulties. Electrophoretic deposition (EPD) uses a bath of electrolyte in which phosphor particles are electrically charged and suspended [16]. Two plate electrodes in the bath establish a uniform electric field across the bath and phosphor particles are forced by the field to attach and densify on one of the electrodes, which is a chip-populated tile whose surface has been made electrically conductive [4]. In order to secure deposited particles on a workpiece, a binder material can either be included in the solution or infused into a deposited layer after drying the electrolyte off the workpiece. As charged particles land only where an electric field is, a 2D phosphor pattern can be created by forming an electrode pattern on a workpiece prior to phosphor deposition [18]. Deposition of phosphor blends has been done but remains challenging as various phosphor materials electrically charge differently so that response to an electric field is different. Sintered ceramic emerged around 2008 enabling the highest possible thermal conductivity of a down-converter [1]. It is a solid plate made from a powder sintered at a very high temperature (1000 ◦ C), close to its melting temperature. During sintering all organic substances are burned, leaving a pure inorganic material, which is highly thermally conductive and resistant to any degradation. A sintered plate is sawn into small pieces of platelets which are then integrated via gluing; here, the organic glue (e.g., silicone) may be the main degradation concern. It is not readily possible to blend multiple phosphors as sintering temperature of phosphor materials varies. Phosphor blending can be achieved by a similar approach: “Phosphor in glass” (PIG) is phosphor powders bound by clear glass and shaped into a plate at much lower glass-melting temperature. Integration is done in a similar way to a sintered ceramic plate. These plates are color-targeted prior to integration like the preform films, yet integration is done individually so that kitting can be applied for color control improvement. Remote phosphor is an integration technique where phosphors are not in contact with chips. A phosphor precast plate in silicone resin can be placed away from pump blue chips in a package so that phosphors do not suffer from the rising chip temperature and stay cooler. A phosphor precast is often designed to be a part of luminaire housing (Fig. 3.14) so that mechanical strength is required. The amount of phosphor consumption tends to increase. Table 3.4 and Fig. 3.15 summarize these phosphor integration techniques described above. Most LED manufacturers obtain phosphor, silicone, and other packaging ingredients from suppliers. As for phosphors, many material families were researched during the previous century for fluorescent lamp applications, but those materials were primarily designed for deep-UV excitation. Up until early in the 2010s, phosphor manufacturers put great efforts in phosphor engineering in concert with requests and demands from LED manufacturers. Those efforts decelerated towards the mid 2010s as the efficiency race transformed to the

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Fig. 3.14 A prize-winning Philips LED light bulb employed remote phosphor (left). Yellow-looking phosphor plates were a part of lamp housing. These revolutionary white LED light bulbs began to arrive in the consumer market circa 2009, and this 60-W incandescent-equivalent light bulb won the Bright Tomorrow Lighting Prize competition by the United States Department of Energy in 2011. In a later commercial version (right, under operation) a bulky metal heatsink was exposed to dissipate heat from LED chips and built-in electronics to ambient air. An LED light bulb has to rely for heat sinking on thermal conduction and convection, whereas an incandescent light bulb largely dissipates heat via thermal radiation

lumen-per-dollar race. Proprietary phosphor technology has been a key differentiator for LED manufacturers: LED companies make their own blends from vast selections of phosphor products to match their application needs. Phosphor materials span various chemistry. Ce-doped YAG (Yttrium-aluminum-garnet) is a relatively old phosphor [17]. YAG absorbs blue light (but not UV light) to cause spectrally-wide yellow luminescence and its commercial availability makes it almost universally used in white LEDs. Red luminescence had been one of major concerns in the LED industry, and is today typically obtained from SCASN (SrCaAlSiN) among other options after overcoming nontrivial intellectual-property hurdles. The green spectral region can be covered by LuAG (Lutetium-aluminum-garnet) while β-SiAlON was researched extensively during the 2000s. When blue luminescence is desired, BAM (BaMgAlO) can be excited by shallow-UV. Silicates including BOSE (Ba ortho-silicate Eu) are versatile material families covering the entire range of color, yet their downsides are insufficient environmental stability and thermal quenching. Phosphor materials commonly use rare-earth elements whose supply chains can be jeopardized by international trade politics. Phosphors in some cases include license fees leading to increased product prices. Epoxy resin was exclusively used in early bullet and SMD LEDs, and is only used today in those traditional products due to its susceptibility to blue light. Silicones (not silicon) are a class of polymers whose chemical backbone consists of Si, O, H, and C. Silicone is either mixed with phosphor powders or molded into lens shapes on packages. High clarity (i.e., high optical transmission) is desired, and high refractive index is often sought to enhance light extraction by densifying its chemical structure, which also helps to suppress

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Table 3.4 Phosphor integration methods Converter integration method

Phosphor fluid/slurry

Dispense (goop-in-cup)

Low powder loading in silicone Limited phosphor loading due to the dispense nature, thus poor thermal conductivity. Least expensive, low material waste, easy to tune color, and rework possible Densely packed phosphor layer, sedimenting takes long time or utilize a centrifugal method, blended powders tend to be layered upon sedimenting

Dispense + sedimentation

Properties

Spray

Diluted fluid of silicone and Conformal layer possible, solvent (potentially toxic) with resulting layers moderately continuous agitation densely packed, color consistency maintenance difficult especially in blended powders. Large material waste, spray needle easy to clog requiring frequent cleaning

Blade coating, screen printing, stencil printing

High powder loading in silicone

Densely packed layers attainable. Low material waste

EPD

Powders in electrolyte

Relatively dense conformal layer, a binder material is necessary in a solution or by post-deposition infusion. Rework possible. Maintaining a homogeneous electrolyte over a deposition period is difficult

Precast sheet

High powder loading in partially-cured silicone

Prior hue test possible on phosphor sheets enabling kitting. Relatively dense conformal layer

Sintered ceramic plate and phosphor in glass

–

Prior hue test possible enabling kitting. High thermal conductivity, attach performed singly using glue thus lower integration throughput

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Fig. 3.15 Phosphor integration methods: a Dispense (goop-in-cup), b Spray, c Precast film lamination, d Blade coating, e Sintered platelet attach, f EPD, and g Remote phosphor

gas permeation from environment (i.e., moisture, corrosive gases, sulfuric molecules, etc.). Adding phenyl groups to its chemistry densifies its structure; at the same time, it makes the silicone prone to yellowing (increased optical absorption especially in the blue region) induced by thermooptical stress attacking the chemical bonds. Other properties considered are viscosity and hardness (comprehensively “rheology”), shelf life (storage) and pot life (at a use point), temperature profiles for curing, shrinkage upon curing, cure mechanism (Pt-catalyzed or condensation), and so on. The silicone industry itself is vast and products possessing aforementioned properties are unique. LED R&D engineers occasionally attempt to alter silicone properties for experiment purposes, e.g., varying viscosity by adding solvents or fumed silica, etc. Silicone chemistry is also a strong subject of the intellectual property.

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Table 3.5 Common materials for submount and package. In addition to thermal conductivity, CTE is an important parameter for packaging materials to reduce mechanical failure in long-term device operation Material

Thermal conductivity (W/(Km))

CTE (ppm/K)

Ceramic AlN

180

3.6

Ceramic alumina (Al2 O3 )

28

8.4

FR4 (glass-reinforced epoxy laminate)

0.9 (lateral) / 0.3 (vertical)

13 / 70

Aluminum

200

23.5

Copper

395

17.1

Copper-tungsten (CuW)

180–220

6.5–8.5

Kovar (low CTE Ni-Co-Fe alloy)

17

5

Alloy 42 (low CTE Ni-Fe alloy) 12–15

4–6

For device packages, there are an unlimited number of product examples found in the market today. Each of them has certain advantages depending on their applications. In general illumination, low- and mid-power packages are the low cost options largely used in indoor lighting apparatus e.g., light bulbs and troffers. These packages have borrowed conventional electronics technologies including the lead frame, QFN, and FR4 (a type of glass-reinforced epoxy) printed circuit boards (PCB). Several submount materials are listed in Table 3.5. Lowcost blue-InGaN lateral chips are populated in these packages via p&p using appropriate DA glue, followed by conventional ball wire-bonding. Al-wire and thinner (0.7 mil) Au-wire bonding endeavors of cost down did not succeeded predominantly due to reliability risks. A single package can accommodate multiple chips to increase LOP, and the goop-in-cup method is employed for phosphor integration. The COB is a large-scale multi-chip package, providing up to ten thousand lumens per device. They are largely used in high-bay lighting e.g., factory buildings and warehouses. A dedicated Al-based submount (Fig. 3.3b) is used with a reflecting polymer dam to hold dispensed phosphor fluid in place. Within the area surrounded by the dam, low-cost blue-InGaN chips are distributed as an array via p&p and they are connected via wire bonding. High-performance chips are no longer used due to competitive cost-down. A ring-shape dam is then dispensed and cured in a way to surround the chip array and to conceal electrical traces of the submount. Dispense phosphor integration is a convenient method to support various CCT and CRI of product lines. Products with Ra ∼ 80 are standard grades and those with Ra ∼ 90 are generally considered premium grades. The high-power LED is for outdoor lighting and decorative landscape illumination with multiple color options in addition to white. The high-power LED was started more or less as an enlarged mid-power LED, where a metal slug was added in the center of the package

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for enhanced heat dissipation, as exhibited in Fig. 3.16. As packaging technology advanced and the market demanded higher power in smaller footprint, more costly materials, e.g., the metal-core PCB (MCPCB) and alumina (white appearance) and AlN (higher heat conductivity at a cost but gray appearance) ceramic tiles, began to be developed and employed. Highperformance large-area chips (1 mm2 and larger) are used. Converter integration is chosen to assist heat dissipation rather than a simpler dispense method, (Table 3.4), and a dome lens may be formed on top via injection/transfer molding12 for enhanced light extraction. In the general illumination field, the conventional technology for “quality of light” (e.g., efficiency and color rendering) has matured. The most recent trends are going towards effective use of light (shine light where and when needed), use-point color tuning (create appropriate color where and when needed) and human mental/psychological effects from light, so-called the human-centric lighting [10]. LED engineers are again entering a new field, just as they did when exploring illumination and color science upon white LED emergence 26 years ago. Lighting systems are becoming more heavily integrated with controlling electronics, shifting towards “Smart Lighting.” Horticulture mostly follows the above technologies of general illumination with designated spectral engineering. In highly-densified vertical farming, heat dissipation of LED light sources, in addition to large electrical power consumption and air conditioning of the room, becomes a great system-level challenge. Automotive applications are concerned with road safety and are regulated strictly by local law. Therefore packaging is performance- and reliability-oriented and premium materials tend to be used including ceramic submount and AuSn attach. As high luminous flux is desired for headlights while color requirements are minimal, cool white via blue-yellow mixing is sufficient and almost universally used. As high-current operation is common and necessary in headlights (typical car batteries are no higher than 12 V), Al ribbon bonding is used at L2 when necessary. Heat sinking is maximized at L0 and L1: Sintered ceramic plates are preferred and employed despite their higher cost. External optics are always implemented in headlights and daytime running lights (DRLs) as law requires strict control of light beam distribution on the road surface. To provide better coupling to the optics, LEDs employ reflective side coating (TiO2 powder13 + silicone via dispense or compression molding) around the chip at L1 to confine light forward. The dome lens is not employed as it makes the apparent source size larger (LES appears larger to external optics through a built-in lens), which is not favored by external optics. With the recent growing interest in the advanced front-lighting system (AFS) 12 Molding is a process of shaping materials (typically polymers) using heat and pressure. In com-

pression molding, the packaging/encapsulation material (e.g., pellets of a polymer) is placed in the mold chase cavity with a workpiece (e.g., a chip-populated tile), and the top chase “compresses” the material to flow and fill the cavity. In transfer molding, the material in a transfer pot (a charge) is “transferred” to the workpiece in the chase cavity by a plunger. The material left in the transfer paths (called runners or sprues) is considered to be a waste. In both molding techniques, the material amount per run is precisely controlled so that there will be little voids or excess. Injection molding is a traditional technique where the material is “injected” into a chase cavity from a reservoir (hopper). The above categorization is nominal; there are technical overlaps in advanced molding technology. 13 TiO is known to be photocatalytic. 2

3.5

Down-Converter (Phosphor) Integration and Packaging

75

Fig. 3.16 Lumileds’ pioneering high-power LED series, LUXEON 1-Watt Emitter (red on the left and blue on the right, circa 2005). The red emitter employed the truncated inverted pyramidal chip shown in Fig. 3.5. The white product (not shown here) offered 45 lm of luminous flux at 350 mA corresponding to 38 lm/W of efficacy. LUXEON 1-Watt series employed a lead frame structure with a metal slug built in its package. A hollow dome lens was attached not in contact with the chip (thus not for light extraction benefit); it provided mechanical protection, according to the cutaway drawing. The lead frame structure became obsolete when revolutionary small-footprint ceramic architecture emerged; LUXEON Rebel (Fig. 2.19) was the Lumileds’ product introduced in 2007. Cutaway drawing courtesy of Lumileds

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Fig. 3.17 Flexible strips of automotive-grade LED lighting unit introduced by Lumileds in 2019, LUXEON 3D LED. Image courtesy of Lumileds

and adaptive driving beam (ADB), an ultimate architecture is believed to be a cluster of micro LEDs (μLEDs) fabricated on a functional Si substrate — a monolithic architecture. Since dimensions of each micro LED are vastly different from conventional LED chips, approaching the size of phosphor grains, suitable packaging technologies are under investigation today. Red and amber LEDs are used in taillamps. Reliability requirements are still high but regulation is not as strict as headlights. Recent trends in taillamps are towards flexibility to establish a unique, distinguishable visual impression of a vehicle. A more 3D-like appearance of an entire taillamp component is recently favored over conventional 2D-like appearance of taillamp units. A product example is shown in Fig. 3.17. These flexible LED lighting units rely on advanced packaging technology to satisfy automotive-grade reliability performance. Another trend is the decorative illumination. Examples include the front grille illuminated to highlight automaker’s brand logo and the ground surface illuminated when a door is opened in a dark. Generally speaking, automotive products are required to maintain a supply for many years, tens of years. For a good inventory management, new products are cleverly designed (for example, a new L1 product using an inherited footprint) to straightforwardly replace/upgrade predecessor products. Display applications are experiencing a major phase change expanding into wearable devices such as wristwatch displays. Early display applications were low- and mid-power white LEDs used in small LCDs replacing compactfluorescent-lamp (CFL) backlighting during the 2000s, when mobile phones (smartphones) employed high-resolution color displays. Side-emitting (side-view) SMD packages were developed for direct light-coupling into waveguide plates using reflow assembly process. Personal computer (PC) displays joined this trend, and LED-backlit LCDs continued to dominate the small-display market by continuous cost reduction. A competition began late in the 2000s when OLED-equipped smartphones were commercialized. White-LEDs were disadvantageous because the emission spectrum did not match LCD’s RGB color filter spectra. During the 2010s, LCD home televisions employing RGB discrete LEDs (thus better color matching) entered consumer stores. A color display actively creates various colors (rather than illuminating objects); Therefore the notion of color gamut differentiates the display application from the general illumination (where color rendering is more of interest). White

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Down-Converter (Phosphor) Integration and Packaging

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light for illumination is characterized via CRI: A rich spectrum (containing all wavelengths) of a single white is a winner because a human eye sees reflected color of various objects. A color display is required to exhibit saturated colors, a display light source must contain three (or more) independent sharp spectral lines, typically RGB. Any color can be synthesized by mixing the three colors and adjusting mutual LOP intensity, and there is no notion of CRI. The area on a color chart spanned by the saturated colors is the color gamut: A large gamut is attained by increasingly saturated-color light sources, namely RGB LEDs. A recent trend that emerged during the last few year in the industry is to employ mini LED chips for direct-view wearable devices . Mini LEDs (∼100 μm in dimensions) tend to employ FC architecture because of lack of room for wire bonding pads. The future generation of display applications will be RGB micro LEDs (∼10 μm in dimensions) for augmented reality and virtual reality (AR and VR). Handling tens of thousands of micro LED chips per device is a great engineering challenge. Industrializable packaging technologies are under investigation in this respect. Speaking of the micro LED, a new application field of micro LEDs reported early in 2022 was the optical interconnect of low energy consumption. The high-speed modulation type applications have been utilizing LDs and SLDs; in near future, micro LEDs may be seen in short-distance optical communication devices. Camera flash is another application where the LED thrives. Duration of each operation is as short as a few hundreds of ms. Even in torch mode hours of operation is unlikely. Thus, heat dissipation is a minor concern and requirements in reliability and product lifetime are not as demanding as other applications. Instead, allocation of physical space in a mobile phone unit is extremely competitive and minimal space is assigned to the flash component. As a result the CSP appears an attractive solution providing sufficient luminous flux, while side light needs to be suppressed by reflective side coating to couple to external optics efficiently. As mobile-phone photography is getting more and more popular, flash performance is improving. Two-color tuning (between warm white and cool white) has been commercialized. More functional flash products are sought for high-quality photography. To the end of product manufacturing discussions, all fabrication processes from wafer singulation till product completion are collectively referred to as the back end of line (BEOL), or simply the back end. The front end of line is from the epitaxy to the wafer fab, though definitions vary. Some people refer to the middle of line, meaning the device wafer fab. The manufacturing process depends on product types. An illumination product may be produced in the following order in its back end.

1. Populating chips on a lead frame via die attach (e.g., glue dispense) and electrical connection (e.g., wire bonding), or maybe FCs on a metal-patterned tile via SAC reflow 2. Phosphor integration via slurry dispense or spray coating, followed by thermal cure of the phosphor layer 3. Light up and color tests to yield off out-of-spec devices 4. Dome lens formation via a compression or transfer mold technique using clear silicone

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5. Blade-saw singulation of the tile or the lead frame prepared on a ring frame with process tape laminated 6. Automated visual inspection (AVI) for singulated tile piece and dome shape quality 7. Final test and binning using a bowl-feed binning machine 8. Packing in a tape-and-reel for shipment.

BEOL consumes various processing materials. While constructing a feasible sequence of process steps (“process flow”) and continuously improving process efficiency and yield are enjoyable engineering parts of BEOL, what makes BEOL successful really depends on commercial supplies of various high-quality process materials e.g., silicone, adhesive tapes, submount materials, solder, white coating pigments, etc. It is interesting to realize, that these product ingredients and process consumables tend to come from long-standing high-tech companies, especially old chemical companies that have participated the semiconductor industry. It is valuable to explore suppliers and maintain collaborative environment to keep BEOL viable.

3.6

UV-Pump White LEDs

While blue-pump white LEDs dominate the market as we have been discussing so far, UVpump white LEDs have long been of interest for more flexibility in color-tuning, primarily by applying a three (or more) primary-color phosphor blend. Including a slight amount of UV light in a spectrum adds another welcomed effect of fluorescence from illuminated objects. For example, a piece of bright white fabric or a sheet of white paper often contains fluorescing pigments. These objects will appear more natural (as illuminated by sunlight) when illuminated by a UV-pump white LED. A major drawback is the total efficiency. UV-pump increases the Stokes loss. InGaN UV LEDs are commonly lower efficiency than InGaN blue LEDs. In addition, higher energy photons promote silicone damage, as discussed in Sect. 4.4. As a result, UV-pump LEDs have been limitedly used in high-end illumination products. Including violet light instead is a good compromise by reducing an extra risk of silicone damaging — Fig. 3.18 is a spectrum example of those commercial products where a violet light content (∼410 nm) is revealed. A blue LEDs may be built using a blue phosphor on a pump UV LED, but such a device is not beneficial for the above reasons. Nevertheless, this concept opens up a technique in white-LED construction that blue LED chips can be used in place of blue phosphor in a UV-pump white LED. Blue-pump amber LEDs are commercialized for increased color stability compared to AlInGaP.

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Stack-Up Tolerance

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Fig. 3.18 Lumileds’ LUXEON CoB with CrispWhite Technology is a product of a violet-enhanced spectrum (peak around 410 nm). Phosphors are likely excited both by blue and by violet. Image courtesy of Lumileds

3.7

Stack-Up Tolerance

Errors and tolerances are everyday realities in manufacturing due to uncertainty in manufacturing processes. This is nevertheless insufficiently emphasized in R&D designing processes of photolithography, packaging, assembly, etc. Here, an exercise of photolithography and tile singulation is discussed for tolerance analysis. Let us consider an imaginary tile-singulation process where (1) photolithography, (2) die attach, (3) and dicing steps are applied consecutively to a good number of tiles. At each step, measurements are made to evaluate the process parameters and to collect statistical data of the process quality. Each accumulated data set will form a data distribution which will be a normal distribution (Gaussian distribution) or can be approximated by a normal distribution. A normal distribution is characterized by a quantity, the standard deviation σ , indicating how wide or narrow the distribution is. In this example, singulated devices are characterized by the chip position, defined as the distance between a chip edge and a singulated-tile edge (Fig. 3.19b). Accumulated chip position data will form a normal distribution. The chip location is an important property of the device for a customer to ensure the chip will be aligned to the optical aperture of external optics upon customer’s system assembly. We wish to find a numerical relationship between this device property and manufacturing process parameters.

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Fig. 3.19 Cross-sectional schematics representing a dies attached on a tile and b a singulated tile piece. The pitch of photolith pattern is a  while the first row distance to the fiducial is a. Saw-machine stepping index is a  and the first row alignment is c in order to cut between chips right in the middle. The chip size b = 1 mm. The blade thickness is 100 μm. On the singulated tile piece the chip position d can be calculated on a piece of paper as d = (a − 100) − (c + b). In reality, however, neither a, b, nor c is a single number but each has a process-specific distribution around the target value to which the normal-distribution analysis is applied

In Step 1, a photolith mask was aligned to a tile using a global fiducial having prepared on the tile (Fig. 3.19a). Consequently, metal was deposited to make a metal contact pattern on the tile. The mask pattern pitch a  was 2100 μm. The mask alignment a generated an error distribution due to an achievable alignment precision over many tiles. A measured data distribution indicated σa = 30 μm around every 2100 μm pitch with respect to the global fiducial (Fig. 3.20). In Step 2, chips with side length b = 1 mm were attached to each metal pad using pattern recognition. Die attach aligning to each pad generated an error distribution due to attach uncertainty over many chips. A measured data distribution indicated σb = 50 μm with respect to the metal pad underneath. Note this DA error caused by pattern recognition precision and DA mechanical uncertainty is independent (“orthogonal”) from the Step-1 error. In Step 3, tiles were saw-singulated using a 100-μm-thick blade. Sawing step index a  was 2100 μm, aligning to the global fiducial, c. Assume the kerfs were 100-μm wide for the sake of calculation simplicity, and this singulation generated an error distribution σc = 10 μm around the every 2100 μm pitch due to saw-machine’s mechanical precision, in addition to an error caused by alignment of the first saw line to the global fiducial, c. Note this singulation error is due to mechanical precision of the dicing saw and not dependent on either mask alignment or die attach. The designed chip position d is calculated to be 500 μm. Because of the process errors above, however, the chip position values were not exactly 500 μm but distributed around 500 μm. The standard deviation of the combined process to determine the distribution of accumulated d, σt , can be predicted by the following equation:  (3.1) σt = σa 2 + σb 2 + σc 2 .

3.7

Stack-Up Tolerance

81

Fig. 3.20 A normal distribution at a = 2100 μm with σ = 30 μm. As a large amount of process data is accumulated, data distribution approaches a normal distribution. For this reason the mathematical function of the normal distribution is used to analyze accumulated data. 68% of distribution around the center value defines the standard deviation σ . ±3σ indicates accepting almost all distribution (99.7%). A more “precise” process will require either (1) choosing LCL and/or UCL closer to the center/target value (rejecting tails of the distribution) and/or (2) modifying the process to make the distribution tighter (making σ smaller). A more “accurate” process requires another improvement of the process so that the center value is brought closer to the target value until the center value equals the target value. The measurement bin size (grouping size of the abscissa) is arbitrary and adjusted within the measurement capability to exhibit a representing distribution of the process

This calculation is called the root sum squared (RSS). It has a form of the vector length (though σ is always a positive quantity by definition); thus the tolerance analysis forms a multi-dimensional space. A required condition for this analysis to be valid is the orthogonality: Error generation mechanisms must be mutually unrelated. Now the process engineer in charge would have to make a decision. It is a property of the normal distribution that the range of ±1σ contains 68% of total distribution, and that of ±3σ contains 99.7%, as indicated in Fig. 3.20. Looking at the error distribution of Step-1 mask alignment, if the process engineer chose the upper control limit (UCL) and lower control limit (LCL) to be ±1σ (accepting deposited metal contacts of a  between 2070 and 2130 μm and the rest getting inked), Step 1 would become more precise but only 68% of deposited metal contacts would be utilized in the next DA step. This seems a bit wasteful. The process engineer could decide the UCL and LCL to be ±3σ (2010 and 2190 μm), then 99.7% (almost all deposited metal contacts on the tiles) would be utilized in the next step. The control limits need to be determined by balancing process precision (i.e., tolerance specifications) and yield.

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Equation (3.1) calculates σt = 59 μm thus 3σ being 177 μm. A customer specification may be d being ±160 μm around 500 μm. The process engineer could choose to narrow the control limits from the 3σ values, but that would worsen the production yield. The engineer would do better to improve one of the three process steps, such as mask alignment. If σa is reduced to 15 μm, σt becomes 53 μm and the engineer can ship more than 99.7% of the products to the customer. Another type of errors is the center value of the a error distribution being, for example, 2090 μm rather than being 2100 μm. This is an inaccurate process; the process engineer should go and check if the mask aligner was calibrated properly. If another measurement was made on the final products and the center value of the d distribution was 490 μm, process engineers should go and check whether dicing saw was properly calibrated, DA pattern recognition functioned properly, and chips were larger than 1.000 mm. More elaborate analysis takes more considerations into account. In this exercise, the blade thickness will have a distribution over many blades, and kerf width will form its own distribution apart from the blade thickness distribution due perhaps to dicing tape rigidity. The blade thickness and kerf width are however not orthogonal as the kerf width depends on the blade thickness. It would be appropriate to include the kerf width as a parameter rather than the blade thickness. A customer specification may include additional chip-position tolerances in the perpendicular direction and rotational orientation on the tile piece. Thus, the present exercise can be treated as multiple higher-dimensional problems. Improving precision of each fabrication or measurement machinery may force the process itself to slow down, resulting in a reduced UPH (units per hour) of the process. In designing a production line, UPH of all process steps ideally become equal (balanced throughput) or the line suffers from a bottleneck process step. For this reason a production line may implement multiple p&p tools working in parallel with a single curing oven, for example, to balance out UPH of the two process steps. For batch process (a duration-limited process) like oven curing, one can adjust UPH by adjusting oven loading, whereas for a continuous process (a one-ata-time rate-limited process, e.g., p&p, dicing, testing), it is a little more difficult to adjust UPH when producing a large amount of products, and will require multiple machines (more capital investment and factory floor space) to expand process capacity. These production parameters (control limits, UPH, yield, etc.) are continuously monitored in manufacturing and improved as a whole in conjunction with sales and marketing inputs of production plans. Upon considering multiple photolith steps discussed in Sect. 3.4, repetitive mask alignment generates errors at each mask alignment and all errors add up. Assume an alignment step raises σ = 2 μm. Four similar consecutive mask-alignment steps will make it doubled according to Eq. (3.1) and attaining fine dimension features becomes more difficult. Not to mention that 3D topography adds more errors in photolith processes. Therefore reducing the number of photolith steps is not only to save production cost but also to improve process precision. Process engineers also encounter a quantity called and written as Cpk. This is the process capability index C pk which is one of quantities proposed to analyze capability of a process. The basic idea of the analysis is to determine given a set of process/product specs (upper and

References

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lower specification limits), how well the normal distribution of the process fits to the span of the specification limits in terms of the ±3σ span. When a ±3σ span equals the specification span, Cpk is defined as unity. When a distribution is much tighter than a specification limits (i.e., a better process) Cpk increases. In the process capability analysis terminology, a simple case is where the center value of the distribution matches the target value (a centered process) and capability of a process is expressed with an index C p : U SL − LSL . Cˆ p = 6σˆ

(3.2)

ˆ is often added to denote future events (prediction). USL and LSL are upper and lower specification limits (equivalent to the control limits applied to an accumulated data set of past events). Cpk is a modified index of C p for noncentered processes and indicates fundamentally the same notion.

3.8

Further Reading

• Stringfellow GB, Craford MG (eds) (1997) High brightness light emitting diodes. Academic Press, Cambridge, Massachusetts • Nakamura S, Pearton S, Fasol G (2000) The blue laser diode: The complete story, 2nd edn. Springer Berlin, Heidelberg

References 1. Bechtel H, Schmidt P, Busselt W et al (2008) Lumiramic: a new phosphor technology for high performance solid state light sources. In: Ferguson IT, Taguchi T, Ashdown IE, et al (eds) Eighth International Conference on Solid State Lighting, San Diego, August 2008, vol 7058:70580E, SPIE. https://doi.org/10.1117/12.794941 2. Blish II RC, Li S, Kinoshita H et al (2007) Gold-aluminum intermetallic formation kinetics. IEEE Trans Device Mater Reliab 7:51-63 3. Chandra H (2014) Laminating encapsulant film contacting phosphor over LEDs. US Patent 8,736,036 B2, 27 May 2014 4. Collins III WD, Krames MR, Verhoeckx GJ et al (2003) Using electrophoresis to produce a conformally coated phosphor-converted light emitting semiconductor. US Patent 6,576,488 B2, 10 June 2003 5. Kish FA, Steranka FM, DeFevere DC et al (1994) Very high-efficiency semiconductor waferbonded transparent-substrate (Alx Ga1−x )0.5 In0.5 P/GaP light-emitting diodes. Appl Phys Lett 64:2839 6. Morkoç H (1999) Nitride semiconductors and devices, Chap 4. Springer Berlin, Heidelberg 7. Nakamura S, Mukai T, Senoh M (1994) High-brightness InGaN/AlGaN double-heterostructure blue-green-light-emitting diodes. J Appl Phys 76:8189 8. Nakamura S, Pearton S, Fasol G (2000) The blue laser diode: The complete story. Springer Berlin, Heidelberg

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9. Narukawa Y, Narita J, Sakamoto T et al (2006) Ultra-high efficiency white light emitting diodes. Japan J Appl Phys 45:L1084 10. Pattison PM, Tsao JY, Brainard GC et al (2018) LEDs for photons, physiology and food. Nature 563:493 11. Ponce FA (2000) Crystal defects and device performance in LEDs and LDs. In: Nakamura S, Chichibu SF (eds) Introduction to Nitride Semiconductor Blue Lasers and Light Emitting Diodes. Taylor&Francis, London 12. Shchekin O, Craford MG (2017) History of solid-state light sources. In: Karlicek R, Sun CC, Zissis G, Ma R (eds) Handbook of advanced lighting technology. Springer, Switzerland, p 41-70 13. Shchekin OB, Epler JE, Trottier TA et al (2006) High performance thin-film flip-chip InGaN-GaN light-emitting diodes. Appl Phys Lett 89:071109 14. Stringfellow G (1999) Organometallic vapor-phase epitaxy: Theory and practice, 2nd edn. Academic Press, Cambridge, Massachusetts 15. Stringfellow GB, Craford MG (eds) (1997) High brightness light emitting diodes. Academic Press, Cambridge, Massachusetts 16. Talbot JB, McKittrick J (2016) Review — Electrophoretic deposition of phosphors for solid-state lighting. ECS J Solid State Sci Technol, 5:R3107 17. Tien TY, Gibbons EF, DeLosh RG et al (1973) Ce3+ Activated Y3 Al5 O12 and some of its solid solutions. J Electrochem Soc 120:278 18. Vampola KJ, Pacella N, Patel A (2021) Phosphor deposition system for LEDs. US Patent 10,923,635 B2, 16 Feb 2021 19. Wierer JJ, Steigerwald DA, Krames MR et al (2001) High-power AlGaInN flip-chip lightemitting diodes. Appl Phys Lett 78:3379 20. Yamada M, Mitani T, Narukawa Y et al (2002) InGaN-based near-ultraviolet and blue-lightemitting diodes with high external quantum efficiency using a patterned sapphire substrate and a mesh electrode. Japan J Appl Phys 41:L1431

4

Semiconductor Crystals and Device Physics

4.1

Semiconductor Materials for LEDs

History tells us that the semiconductor industry was born during the 1950s with Ge and Si, the Group IV materials. Both materials crystallize in the diamond structure, which is one of the two close-packed structures: cubic close-packed (ccp) structure. In the periodic table (Fig. 4.1), C is found above Si. C takes various crystallographic forms, but when crystallized in the diamond structure (this is a diamond) it can be considered as a semiconductor, though semiconductor diamond has not been industrialized to date. While Ge phased out during the early years, Si paved the main road to the integrated circuit (IC) partially because of its native oxide SiO2 , which is a great electrical insulator. For our interest, Si is used in spectrometers as a photodetector. Si has a bandgap of 1.1 eV; thus common spectrometers function up to 1100 nm. Beyond that (into deeper IR) other types of detectors need to be used. One of those is the Ge photodiode, owing to its smaller bandgap (0.67 eV). To extend functionality of semiconductor devices beyond the Group IV materials, researchers investigated compound semiconductors, especially the III-V materials. In the periodic table, next to Si are Al and P, and Ga and As to Ge. In the III-V systems GaAs (1.42-eV bandgap) played a dominant role, and it was found that mixing elements (Al, Ga, and In from Group III and P and As from Group V) in a semiconductor material was feasible. These materials crystalize in the same structure as Si and Ge, but it is now called the zincblende structure as two constituents (III and V) participate. Along with this compound semiconductor exploration, material synthesis technology made a great progress. Epitaxy is a technique where layers of functional semiconductor materials are deposited on thin single-crystal substrate sequentially to obtain a device structure. Semiconductor materials “grow” in such a way that the crystallographic characteristics are transmitted from the substrate, so that high material quality is maintained throughout the epitaxial layers. A prior technique to epitaxy was the diffusion method, where impurities were thermally diffused

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4_4

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Fig. 4.1 Excerpt from the periodic table. In general, the higher in the table the smaller the atomic size and makes stronger atomic bonds leading to a larger bandgap. A Group IV element can be a semiconductor by itself, whereas a combination of III and V or II and VI elements can be a semiconductor. These compound semiconductors have various degrees of ionic character (in addition to the fundamental covalent bond character) in their atomic bonds that tend to increase the bandgap. That is, there is a trend that II-VI semiconductors have larger bandgaps than III-V semiconductors

(or implanted) into host semiconductors to form a junction (for this reason old textbooks analyzed nonabrupt pn junctions). It was almost impossible to make functionalized multiplelayer structures via diffusion techniques. III-V epitaxy thus founded a new field of bandgap engineering leading to a dramatic leap in the semiconductor technology. AlGaAs. The first epitaxy method widely developed was liquid-phase epitaxy (LPE), where AlGaAs materials were investigated. The LED industry was led by Hewlett-Packard and Stanley Electric. This ternary material maintains its direct bandgap up to 45% of Al (55% of Ga), covering 1.42 (873 nm) to 1.98 eV (624 nm). Thanks to nature, its lattice constant varies little with Al/Ga composition, suiting epitaxial growth onto commercially available GaAs substrates. During the 1980s AlGaAs LEDs replaced the GaP:ZnO red LED which had been commercialized since the late 1960s, and extended their use into outdoor applications including signboards and automotive auxiliary lamps, though it was nontrivial for a new technology to be certified for legally-regulated applications. Multi-color signboards were manufactured by combining with indirect-bandgap GaP:N green LEDs. This LED proliferation was largely due to the fact that AlGaAs LEDs demonstrated higher efficacy than red-filtered incandescent lamps. Designing double-hetero (DH) structures was a major subject of industrial research. The active layer thickness was determined by minority-carrier diffusion lengths, and thus thicker

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Semiconductor Materials for LEDs

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p-type active layers1 were chosen (a few µm thick, which was considered to be “thin” back then) owing to the electron’s longer diffusion length. Cladding layers contained more Al to make confinement barriers sufficiently high, although p-type doping into a high-Al layer was difficult, limiting the electron confinement barrier height. Thus p-layer conductivity and barrier height had to be a tradeoff. Current crowding around the top contact was a universal problem because carriers drifted straight down along the electric field and lateral spread away from the contact metal had to rely on carrier diffusion. Current spreading in the p-layer was therefore enhanced by making the layer thick (>15 µm). Contacting metal (Au) contained Zn for the p-layer and Ge for the n-layer, and was annealed to make alloyed regions (thus providing extra doping in the AlGaAs) to achieve better ohmic contact characteristics.2 Light extraction was also identified to be an issue, as the GaAs substrate absorbed emitted light. A solution was to remove the GaAs substrate entirely by wet etching. A thick (∼125 µm, which was readily possible because LPE provided fast growth rates) n-type AlGaAs layer was grown on the substrate prior to the device structure to be a structural support upon substrate removal. AlGaAs is a brittle material, thus for wire bonding, 2–3 µm thick bonding “pads” (Au or Al) were needed to avoid cratering in the chip caused by mechanical impact of wire bonding. High-Al AlGaAs materials are prone to oxidization, making devices fail in WHTOL. LPE had a natural purification benefit of eliminating oxygen so that high quality materials were obtained. In contrast, LEDs via MOCVD were dimmer because of contained oxygen atoms acting as NRR centers. Another industrialized ternary material was InGaAs, for IR emitters and high-speed electronic devices. AlInGaP. There were great demands to realize shorter-wavelength LEDs using a direct bandgap material (GaP:N was an indirect-bandgap green emitter), and the material targeted was AlInGaP. Today AlInGaP remains as one of the two main semiconductor material systems used for LEDs. The advantage was the flexibility of the quaternary system to match its lattice constant to the GaAs substrate while maintaining a degree of freedom in tuning the active-layer bandgap. The difficulty was the incorporation of Al into InGaP which had been grown via LPE for high-speed electronics applications. This was because AlP was a much more stable compound than InP in a melt (a liquid of molten ingredients) and Al alone did not travel into a growing layer. The LED industry started moving to the vapor-phase epitaxy (VPE) around 1990 as MOCVD had been successfully demonstrated to incorporate Al. While still lattice-matching to GaAs, the shortest achievable emission wavelength was determined to be approximately 540 nm and the longest was 656 nm. AlInGaP loses the emission efficiency in shorter WL ranges as it becomes an indirect bandgap material (only InP has a direct bandgap among the three binary constituents). This is a fundamental disadvantage; hence AlInGaP was not seriously pursued as a green emitter. Al incorporation

1 As the diffusion length of electrons in the p-type was experimentally determined greater than that

of holes in the n-type, the p-type active layer can be made thicker (for more active volume) than the n-type one. 2 Highly doped materials are sometimes denoted as p+ and n+ .

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in AlInGaAs had been reported to increase susceptibility to oxidation of the material, but it was found insignificant in MOCVD AlInGaP materials. AlInGaP LEDs were developed in two chronological stages. The first stage was the conventional small-chip applications where materials and growth knowledges were gained. MOCVD equipment and precursor chemicals were improved to fulfill optoelectronics requirements. In the 1980s, the AlInGaP material system and its QW structures were intensely investigated for DVD laser diode (LD) purposes where MOCVD was still considered to be an expensive production method. At the beginning of the 1990s, Hewlett-Packard (its Optoelectronics Division later became Lumileds) and Toshiba (who had had AlInGaP LD research background) were independently exploring AlInGaP LEDs. DH structures were believed to be more production-compatible than the QW structures owing to MOCVD’s thickness and composition uniformity capabilities. AlInGaP must lattice-match to the substrate for high-efficiency light emission. Within this restriction, direct-indirect crossover was explored for active layer use. During this exploration, atomic ordering in an alloy was discovered. Alloy ordering is a short-range periodic structure (a superlattice along {111}) of two constituent (AlP/GaP and InP), in order for the alloy to reduce local strain. This was somewhat a similar phenomenon to the In segregation seen in InGaN. Alloy ordering was considered to be a threat because an ordered active material emitted a longer wavelength than the corresponding disordered (randomly mixed) alloy, thus going against the effort of achieving shorter wavelengths. In chip designing, the two major issues were the same as in AlGaAs: Current spreading and light extraction. Cladding layers were ideally AlInP (cladding layers can be indirect bandgap) for the maximum confinement-barrier heights, although p-type doping into a high-Al alloy was difficult, leading to a tradeoff in Al content, similar to AlGaAs. Light extraction was another serious concern as III-phosphide’s refractive index was large and the GaAs substrate was light-absorbing. This was first circumvented by growing thick n-type and p-type transparent “window” layers (e.g., GaP or AlGaAs) for emitted light to acquire a chance to travel to a chip sidewall before hitting the absorbing substrate. Thick layers were beneficial to current spreading as well. The drawback was the long epitaxy time. Growing a multi-layer DBR immediately on a GaAs substrate was an alternative option to avoid the substrate absorption, yet the ultimate solution was to remove the GaAs substrate entirely. Epi wafers without absorbing substrates were achieved by the technique of wafer fusion (wafer bonding). After removing the GaAs substrate, the epi layer was brought in contact with a GaP wafer, then a pressure-and-heat process achieved atomic bonding between the two. Mechanical and electrical characteristics of the bonded interface were proven to be sufficient as commercial products. With the onset of high-power applications around 2000, AlInGaP LEDs gradually entered into the second stage: Development of high-power large chips. A MQW LED was demonstrated in 1999. MQW devices attained brighter light emission due to increased carrier density and reduced self-absorption by the reduced active-layer volume. MQW structures potentially enabled narrower spectra and shorter emission wavelengths due to the quantum confinement effects. Thin-film technologies and light-extraction techniques evolved along with the InGaN LED devices. As of

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89

today InGaN red LEDs have not commercialized because of epitaxial difficulties in growing high-In alloys and significant color shifts induced by drive current changes. Emission wavelengths of AlInGaP LEDs are fundamentally sensitive to device temperature, nevertheless, it remains as a main red-emitting material. InGaN. Well before 1990 researchers desired to complete RGB3 and started searching for blue-emitting materials with a hope that the LED would conquer the entire visible wavelength range by the end of the century. SiC blue LEDs were successfully commercialized by Cree in 1989. They had low brightness (∼10 mcd) of pale blue emission because of the indirect bandgap. Going into the 1990s the competition was between direct-bandgap ZnSe- (II-VI) and GaN- (III-V) based materials using VPE methods. By 1994 GaN research groups were able to present evidence of excellence over ZnSe including an announcement of a commercial 1000-mcd blue LED product by Nichia Chemical. ZnO (II-VI) was investigated for a brief period as another blue-emitting material. It was concluded that the II-VI materials were frail enough that energy of emitted photons would break atomic bonds of the LED crystal leaving defects behind, despite the fact that 3M had reported lasing using a ZnSe-based structure in 1991. Sumitomo Electric also challenged the GaN-based LEDs by commercializing ZnSebased phosphor-free white LEDs in 1999 [4]. III-nitride materials crystalize in the wurtzite structure, which belongs to the second type of close-packed structures, the hexagonal close-packed (hcp) structure. The crystallographic symmetry is lower leading the material system to exhibit various different optical behaviors from zincblende materials. Today the AlInGaN system is the main LED material responsible for blue and green spectral regions with the complementary AlInGaP red. As discussed in Chap. 3 growth temperature between AlGaN and InGaN is vastly different, hence the AlInGaN system is used only as ternary materials in LEDs. As a consequence, an InGaN LED structure lacks the ability to fully lattice match to a substrate and the entire structure remains under stress. AlGaN is typically used only for the EBL in visible-WL LED structures (AlGaN has more use in UV LEDs nevertheless). An AlGaN layer grown on GaN is prone to cracking due to tensile strain caused by its smaller lattice constant than GaN. AlGaN is also difficult to make p-type. Hence the EBL is grown thin. On the other hand, InGaN determines the emission wavelength. It is the heart of the III-nitride LEDs. Nonetheless, InN remained a mysterious material for a long time. The bandgap had been believed to be 1.9 eV (653 nm) even after the InGaN LED emergence. It was not until 2005 researchers learned the true 0.7-eV (1.8 µm) bandgap. This discovery was achieved by synthesizing purer InN, as well as by the ability to measure up to such long wavelengths, out of the Si-detector range. Indium is a large atom compared to Ga, hence it is difficult to 3 To our surprise it had not been a common knowledge that a pair of complementary colors could

appear white to the human eye. LED engineers believed for a long time that the three primary colors (RGB) were needed to synthesize white light until seeing the first white LED commercial product (using a blue LED and yellow-emitting phosphor) of Nichia Chemical in 1996. Nichia Chemical had been a phosphor manufacturer for TV applications and this down-conversion technique prevailed because it was more practical in producing white LEDs than combining RGB. It was not until 2004 a blue-excitable red phosphor was industrialized.

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incorporate freely into the rigid GaN network, while N always tries to escape as N2 gas. A consequence of these atomic properties is a miscibility gap of the InGaN alloy. That is, a certain range of In composition becomes thermodynamically unstable at a given temperature, and the whole alloy separates into two thermodynamically-stable alloy phases with two different In compositions (spinodal decomposition). In InGaN MOCVD, immiscible phases at RT can be synthesized at growth temperature by controlling chemical-reaction dynamics of the constituents. Then quick reduction of reactor temperature “freezes” the miscible InGaN before it phase-separates during cooling down. In a real LED structure, however, HT AlGaN/GaN p-type layers need to be grown afterwards—this is very unfortunate because InGaN will be given abundant time to settle in another stable phase(s) during HT AlGaN/GaN growth. Thus LED growth is a complex multi-dimensional problem that epi engineers have been fighting against for years. Even a miscible InGaN alloy is known to be microscopically inhomogeneous. There are microscopic regions with higher In concentration than their surroundings as In atoms tend to cluster together to reduce local strain, which is a similar driving force to the ordering occurring in AlInGaP. This phenomenon is called the In segregation. Indium segregation is a very important mechanism for the InGaN LED to function at high efficiency. These microscopic In-segregated regions in the active layer have smaller bandgaps than surroundings and work as potential wells, or “pockets,” to attract carriers. Many carriers come across these pockets, fall in, and meet the opposite type of carriers to recombine with quite high probability, before running into any nonradiative recombination centers like threading dislocations and other types of crystal defects. This unique In-segregation mechanism maximizes radiative recombination efficiency at In compositions for blue emission, while for purple and UV emission, lower In compositions allow for microscopically homogeneous InGaN alloy—thus, the benefits from In segregation disappear. Green and even longer-WL LEDs require higher In compositions—because In clustering is due to local strain relief, strain fields around threading dislocations (TDs) interact with In incorporation. Epi engineers recognize this interaction and use it as a control knob for In incorporation. The active layer of green LEDs suffers from other effects which will be covered in the upcoming section. Some properties of semiconductor materials exhibit general trends. The higher in the periodic table, the smaller the lattice constant (because atoms are smaller) and the larger the bandgap (due to stronger atomic interaction). Group IV crystals rely purely on covalent atomic bonds, while atomic bonds of III-V crystals contain some degree of ionic character (attraction between electrical charges of constituent elements), which becomes stronger (more ionic) in II-VI crystals. Greater bandgaps result from the ionic character. When a semiconductor crystal is heated, its bandgap shrinks as a result of atomic distances being greater (= thermal expansion) leading to less atomic interaction. Refractive index tends to be larger for a smaller-bandgap material (lower in the periodic table), because constituting atoms have more charges on average from which refractive index originates. Regarding the nomenclature, it used to be common and preferred to write the Group-III elements in order of the periodic table, e.g., AlGaInP, and add suffixes to indicate alloy

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compositions, e.g., (Alx Ga1−x ) y In1−y P, where Al and Ga are grouped because of lattice constant considerations. When the composition is obvious in a context, e.g., AlGaInP latticematched to GaAs, or is not of strong interest in a discussion, some suffixes are omitted, e.g., (AlGa)InP where y = 0.5 may be assumed. On the contrary, InGaAs was a natural notation in a sense of adding In to GaAs, rather than GaInAs. Over time, these compound semiconductor materials started being called via phonetically comfortable “words” thus AlInGaP and InGaN have resulted to date. It seems no strict rules exist today even in scientific publications, except Group-III elements come first followed by Group-V elements.

4.2

Luminescence Mechanism

4.2.1

In Semiconductor Materials

EL color is determined by the bandgap of the semiconductor material that is the active layer in an LED device structure. In a simple carrier recombination model, electrons and holes (a hole is a lack of a valence electron in atomic bonds) are injected into a thin active layer from negative (n-) type and positive (p-) type layers, respectively, and meet with the opposite type of carriers to recombine within the active layer. In the energy scale electrons are in the conduction band and holes are in the valence band. When a pair of them recombines across the bandgap, a photon with energy (determining color of light) approximately equal to the bandgap energy is emitted as a result of the pair having annihilated. The emitted photon energy in units of eV appears numerically similar to the turn-on voltage in units of V. These radiative recombination processes are depicted in Fig. 4.2a. A radiative recombination can also occur via a shallow impurity energy level (e.g., a donor or acceptor level, or both) as shown in Fig. 4.2b. These radiative recombinations are called near-band-edge luminescence. On the other hand, there are cases where a photon is not emitted when pair annihilation has occurred. Electron-hole pairs recombining via a chemical impurity, via a crystal defect, via surface states, and so forth, are referred to as non-radiative recombination (NRR) as indicated in Fig. 4.2c, d. Therefore, it is essential to maintain high material quality (no crystal defects and no unintentional impurities) to attain radiative recombination. It is important to note that a surface of a crystal is considered to be a defect (a termination of periodic structure of atoms) in terms of luminescence. It is impossible to eliminate surfaces from a device structure as device dimensions are finite, yet it is possible to suppress negative impacts of crystal surfaces by passivating those surfaces using dielectric layers. To go beyond the simple recombination model using a band diagram above, one has to know how the band structure is constructed. The conduction band and valence band are collections of atomic orbitals of all constituting atoms. Atomic orbitals have to spread in energy when the same type of atoms are placed close together (Pauli’s exclusion principle). These spread atomic orbitals are collectively called an energy band, e.g., a conduction band.

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Fig. 4.2 Schematic explanation of carrier recombination. Black and white circles represent electrons and holes, respectively. The vertical scale is in the electron energy, where E C and E V being the conduction and valence band edges, respectively. a Band-to-band recombination. A photon corresponding to the bandgap energy is emitted. b When shallow impurity levels are involved. Recombination between donor and acceptor levels, E D and E A , is called DA-pair luminescence. These processes contribute luminescence because impurity levels are close to a band edge. At very low temperature these near-band-edge luminescence can be resolved in a spectrum. c Recombination via a mid-gap state E M . This process is considered to be NRR in most cases, although parasitic yellow luminescence (e.g., a broad peak around 550 nm in a GaN luminescence spectrum) is sometimes observed and attributed to mid-gap states. Such mid-gap luminescence from blue-emitting InGaN QWs has been little reported to date. The SRH statistics analyzes recombination via mid-gap states thoroughly. d NRR via surface states. Any surface of a semiconductor material is considered to be a crystal defect due to termination of a periodic atomic array and creates many energy states through which an electron can roll down

In a close-packed structure where each atom has four neighboring atoms, two neighboring atoms share two electrons to form an atomic bond between them. An atom shares two s-orbital electrons and six p-orbital electrons with the four neighbors. The result is the sp 3 hybrid orbital, constructing the tetrahedral unit of the close-packed structure. Within the limit of LED interest (that implies the interest in the band structure is only near the bandgap, i.e., at the  point (see page 94) in a direct-bandgap material), it is known that the conduction band edge consists of s-orbitals predominantly, while the valence band edge consists of p-orbitals mainly. The s-orbitals are spherical thus the conduction band edge is regarded spatially isotropic. The p-orbitals can be split into three components (Fig. 4.3): px , p y , and pz . Each can accommodate two electrons of opposite spins. These p-orbitals look elongated in the x, y, and z directions, respectively. When the crystal is cubic, as with the diamond and zincblende structures, px , p y , and pz are energetically equivalent ( px , p y , and pz are “degenerate”). With the three components combined, as they are equivalent in energy, the valance band edge appears spherical like the conduction band edge. When numerous electrons in the conduction band fall into empty sites in the valence band, (i.e., electron-hole recombination, as already discussed above), resulting photons are also collectively isotropic, hence emitted light is unpolarized. Intuitively speaking, a spherical electron cloud changes

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Fig. 4.3 Atomic orbitals of an atom. The s-orbital is spatially spherical. The p-orbitals are elongated in x, y, and z directions and when they have the same energy in a crystal they are mixed to form a spherical orbital. These four orbitals form the sp 3 hybrid orbital in a close-packed structure

into another spherical cloud upon electronic transition, where no deformation of the electron cloud occurs. In short, unpolarized light is generated by a cubic semiconductor because of its band structure. In wurtzite structure, the z direction (defined as perpendicular to the basal plane, see Fig. 4.6) is unique while the x and y directions (both in the basal plane) are equivalent. In InGaN the pz resides slightly lower in energy than px and p y because of InGaN’s crystal structure, which is slightly elongated in z from the ideal close-packed geometry, leading to weaker atomic interaction in the z direction than the x and y directions. When electronic transition occurs from the conduction band (isotropic) to the valence band the electron arrives to the closer px or p y (at 50% probability to each) rather than the farther pz . That is, a spherical electron cloud changes into a disk-shape cloud where electron charges are no longer spatially isotropic, and the result is an oriented electric field. With numerous electronic transitions the electric fields are found lying in the x–y plane. Light propagates perpendicular to the field, along the z-axis (for the present case) and epi growth direction towards the device surface. For an observer on the x axis, however, the electric field appears in the y direction but not in the z direction. Therefore, the emitted light appears polarized (see Chap. 5). Fermi’s golden rule describes the electronic transition in more detail. Polarized light emission can also be attained in a strained cubic material where x, y, and/or z may be no longer equivalent. Strain can be introduced into an active layer by slight lattice mismatch via controlling alloy compositions (pseudomorphic growth).4 For instance, a crystal lattice elongates in the growth direction when squeezed in the growth plane (compressive strain), trying to maintain its volume unchanged. When a lattice elongates, constituting atoms become farther apart and the corresponding p orbital moves to a lower energy due to reduced atomic interaction. 4 Thin films are better under compressive stress than tensile stress because the latter leads a film

to crack. This is typical in AlGaN layers grown on GaN. The critical thickness is a characteristic quantity to a particular system. Within a critical thickness a heteroepitaxial layer can be grown pseudomorphically and beyond the critical thickness the layer spontaneously introduces defects to release strain. Strained-layer superlattices are often included within/near the HT-GaN buffer layer of an InGaN LED structure to manage strain in forthcoming layers, e.g., AlGaN EBL. The Stoney formula is a commonly seen in stress analysis of thin films.

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The electric fields from electronic transitions will more likely be parallel to the growth plane, like the InGaN example just discussed above. Carriers in a semiconductor do not reside exactly at band edges. They have thermal energy from ambient and distribute themselves in energy reflecting the thermal energy.5 This thermal carrier distribution is described using the Fermi-Dirac statistics, and in many cases it reduces to a mathematically simpler formulation of the Boltzmann statistics. Radiative recombination occurs between thermally distributed electrons and holes. Thus the emitted photon spectrum has a finite broadness with the high-energy tail reflecting the thermal carrier distribution (and the density-of-states, DOS, of the energy bands)6 and the lowenergy tail typically indicating the DOS of the alloy fluctuation around the band edges. When temperature of an LED device is changed, several things will happen to its spectrum. The high-energy tail stretches out and the spectrum broadens because carriers distribute wider in energy. The peak wavelength red-shifts because the bandgap shrinks. This temperatureinduced change of bandgap is more pronounced in AInGaP LEDs than in InGaN LEDs. When current injection is increased, the peak wavelength blue-shifts because of band filling (more carriers filling the band to an upper energy) though increased current may cause the device to heat up. The complete band structure of a semiconductor material is described by the E–k diagram (Fig. 4.4). Here k symbolizes the electron wave number of the Bloch wave; describing how the electron wavefunction belongs to the whole crystal,7 in contrast to what we discussed above the local electron orbitals. The band structure tells that relationship between electronic energy and momentum (k) varies by the direction in a crystal. This is because of interaction between a free electron and the atomic array. Atomic arrangements are different in different directions in a crystal. One direction may look sparse and well-ordered, while another direction may appear very crowded and not-so-well-ordered. When an electronic wave nests well with a periodic atomic array, the electron’s energy lowers. When an electronic wave becomes repelled by atomic charges, the electron’s energy rises. The origin (k = 0) is called the  point where all local electronic orbitals are in the same phase of the wavefunction across the crystal. Any carriers away from the exact band edge ( point) with extra energy must have a non-zero (but very small) k. The X point is located at the surface of the so-called first Brillouin zone along the direction. The L point is that along the direction. Two electrons in the conduction band, while waiting for transition opportunities, may interact to repel each other such a way that one electron jumps up in the empty conduction band to (+E, +k) by kicking the other electron to the valence band (−E, −k) where a hole resides. In this case there will be no photon generated. This nonradiative process is known as the Auger recombination. Auger recombination plays a detrimental role when carrier density in

5 Refer to Appendix F. 6 Refer to Appendix G. 7 Refer to Appendix E.

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Fig. 4.4 An example of E–k diagrams of direct and indirect bandgap materials. A local minimum of a conduction band is called a “valley.” Note that the lowest valley in GaAs (direct bandgap) is located at  aligned with the maximum of the valence band, whereas that of AlAs (indirect bandgap) is located off the  towards X. By alloying GaAs and AlAs, energies of the  and X valleys change and become equal at 55% Ga in AlGaAs. That is the direct-indirect crossover. Note that the valence-band structures are very similar between the two because these two materials share a common anion

the active layer has increased (spread wider in E and k). It is the dominant mechanism for the current droop (emission efficiency drops as drive current is increased8 ) in InGaN LEDs [6, 15]. Although almost extinct, there are a few types of LEDs using indirect bandgap materials, e.g., SiC (blue) and N-doped GaP (green). Indirect bandgap materials have their conduction band minima off the  point.9 Upon recombination electrons need to compensate their finite k to recombine with holes at the  point. It is true that a localized electron at a dopant atom acquires greater momentum uncertainty (the uncertainty principle) promoting the radiative recombination slightly, yet this momentum compensation requires the crystal lattice to vibrate locally (phonon) upon radiative recombination. Consequently radiative recombination becomes less probable and thus slower than for a direct bandgap case, and resulting light emission is dim.

8 The term “droop” gained popularity in 2001 to indicate this phenomenon. It is also called the

efficiency droop. 9 Refer to Appendix H.

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4.2.2

4 Semiconductor Crystals and Device Physics

In Device Structures

We discussed in the previous section that InGaN alloy inhomogeneity (In segregation) contributes to efficient radiative recombination. In the LED structure however, carriers confront other complications, and as a consequence all commercial InGaN LEDs have adopted the quantum-well (QW) structure. A QW structure has a thin (a few nm) InGaN active layer sandwiched by larger bandgap InGaN or GaN. This is because the wurtzite structure is a hexagonal crystal structure that possesses electrical polarity along the c-axis (parallel to the z direction) due to anion-cation spatial asymmetry. The electrical polarization creates an electric field parallel to the z direction10 that forces electrons and holes to move towards opposite sides of the thin layer. In a QW it appears as in the schematic band diagram11 given in Fig. 4.5a and this phenomenon is called the quantum confined Stark effect (QCSE). If the InGaN active layer was thicker, electrons and holes would be so far apart they would barely have a chance to recombine. A few nm is thin enough to realize efficient recombination, and at the same time it is sufficiently thin to observe quantized effects, e.g., quantized energy levels, which is why it is called the QW. Wurtzite III-nitride materials have electrical polarization under an unstrained state (because a nitride crystal lattice is slightly elongated along the c-axis from the ideal close-packed geometry) which is called the spontaneous polarization. And since the polarization is a result of lattice deformation, any strain caused by external stress will induce extra polarization (Fig. 4.6b). This is called the piezoelectric polarization. The electric field in a QW is generated by the sum of these two polarizations (on top of the built-in electric field of the pn-junction depletion layer). Green LEDs require higher In compositions in the active layer, which then experiences greater stress applied from the barrier layers and the entire LED structure because of their larger lattice constants.12 Therefore QCSE is more severe in green LEDs. This is why green LEDs typically have lower efficiency than blue LEDs. AlInGaP is a zincblende material and LED structures are grown on a (100) plane where electrical polarization is not observed. What is worse, applying a forward bias to an InGaN QW LED increases the electric field in the QWs (Fig. 4.5b). Injected carriers then suffer from stronger QCSE, even if there are field-screening effects created by carriers’ own charges. Increased carrier density increases the Auger recombination as already discussed. To mitigate the QCSE, the number of QWs in a device can be increased to split up the applied bias spatially and to moderate carrier accumulation. This is the multi-QW (MQW) structure, differentiated from the single-QW 10 Refer to Appendix I. 11 During the 2000s, computer simulation of band diagrams advanced and became widely available

by commercial products and academic free software, which enabled ready access to fine details of complex band diagrams of InGaN QW LEDs whenever necessary. 12 In mechanics, stress is an applied force per unit area. Strain is a resulting displacement normalized to the original dimension; thus it is a relative displacement. The ratio between these is a quantity called Young’s modulus which is material specific. For a very hard material, strain is very small (little change in its shape) when a large external stress is applied. Poisson’s ratio is another material-specific quantity that indicates the ratio between lateral strain and vertical strain.

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Fig. 4.5 Illustration of QCSE in an InGaN/GaN QW a at equilibrium (carriers have been drawn in for the sake of visual convenience) and b under forward bias. Because of piezoelectric fields created by in-plane compressive strain in InGaN, electric fields in QWs point opposite to the built-in field. For this reason, electrons and hole are squeezed in triangular wells and separated farther apart when forward bias is applied, resulting in reduced chances of pair annihilation. Note that quantized energy levels in QWs get squeezed up in triangular wells when positive bias is applied, leading to spectral blue shifts with bias voltage

Fig. 4.6 a A hexagonal prism representing a GaN crystal with three representative crystallographic planes indicated. Nonpolar planes are those parallel to the c axis and semipolar planes are those inclined with respect to the c-axis. For the c-plane, orientating to the +c-axis is the Ga-face (the top face of the hexagonal prism) and to the −c-axis is the N-face (the bottom face). They exhibit different chemical behaviors. The c-axis does not possess an inversion symmetry. For this reason opposite electric charges appear on +c and −c planes when the prism is elongated or contracted parallel to the c-axis. b An elongated hexagonal prism is sketched due to in-plane compressive stress, representing InGaN grown on c-plane GaN

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(SQW). Carriers still have difficulties to distribute themselves evenly across the QWs by overcoming every potential barrier between two wells, and rather tend to pile up at/near the first well layer leading to Auger recombination, while farther layers deplete carriers. For this reason there will be an optimum number of QWs, which will depend on the operational current density of the aimed device application. A universal MQW design for all applications is infeasible. Green LEDs typically exhibit drastic peak blue-shifts as forward bias is increased due to the quantized energy levels moving higher in the triangular (as internal electric fields are so strong) potential wells, in addition to localized-state (due to In segregation) filling and band filling. As seen so far, the QCSE is unfavorable in an LED structure, and AlInGaP LEDs do not suffer from the QCSE as there is only the built-in field in the active region. Efforts have been made to eliminate the QCSE in the InGaN LED structure entirely. A lattice-matched quaternary system can reduce strain in a controlled manner in every layer of a structure, yet has not made much progress because of the growth difficulties. Growth orientations other than the polar c-plane orientation have been investigated since the mid-2000s. As shown in Fig. 4.6a, perpendicular orientations from the c-plane are called nonpolar planes/orientations as they do not induce electrical polarization in the growth direction. Other inclined crystallographic planes started consequently referred to as semipolar planes. Growth on these orientations is another possibility and LED structures on various orientations have been demonstrated [8]. A major missing piece is the substrate. GaN substrates are premium and not readily available commercially (rare and expensive) as of today. Several heteroepitaxial substrates have been proposed, yet growth techniques are still too immature to compete against the c-plane growth. The spectral shape of light emission from an LED typically appears as a smooth curve with a single peak. Occasionally an emission spectrum exhibits a “shoulder,” which is a little bump in a smooth spectral curve on its high-energy tail. In a confinement structure like QWs, energy levels are quantized (a set of single values rather than a continuous energy band) in the direction of confinement.13 Under normal operation of a QW LED, the first quantized level contributes the light emission almost exclusively. When current is increased the second quantized level is populated with carriers and participates in the recombination, creating a secondary emission peak in the spectrum (which appears as a shoulder). It is not uncommon to find a spectrum decorated with Fabry-Pérot modes. This wavy spectrum is caused by interference of emitted light within the epi layer. InGaN with high In compositions tend to exhibit broader spectral widths due to In segregation. Narrower bandgaps of In segregated regions stretch the low-energy tail of the spectrum,14 which would rather exhibit an abrupt cutoff in InGaN with low In compositions. This is called inhomogeneity broadening. Spectral shifts of AlInGaP LEDs are predominantly caused by temperature. Both ambient temperature and self-heating by drive current cause the emission to red-shift significantly due to bandgap shrinkage. InGaN LEDs exhibit slight red-shift with temperature as the bandgap shrinks. Increased current (apart from heat generation) causes a major blue-shift due to band filling 13 Refer to Appendix G. 14 Refer to Fig. G.1d.

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and In-segregation localized-state filling and due to the QCSE in InGaN LEDs. White-LED characteristics are affected by spectral shifts of the blue pump not only because the blue is part of the white spectrum but also because phosphor absorption changes when a blue spectrum shifts. For example, absorption of YAG:Ce phosphor is very low around 400 nm and peaks at 450–460 nm. Hence, white hue can change noticeably when the pump blue wavelength is varied.

4.2.3

Crystal Defects in GaN

The periodic arrays of atoms constituting a crystal are never perfect and defects are those imperfections in the periodic arrays. It has been emphasized that it is essential to reduce defects in a device crystal to achieve high luminescence efficiency. That is why the homoepitaxy and lattice-matching (or at least pseudomorphic) heteroepitaxy are desired. GaN epitaxy, as we have seen so far, is a lattice-mismatched technique to produce commercial products; therefore understanding and controlling defects in heteroepitaxial GaN are of a great interest to materials scientists. Point defects include vacancies (missing atoms), substitutes (substituted atomic sites with foreign atoms), and interstitials (excessive atoms). Point defects are difficult to find experimentally. A major point defect known in GaN is the N vacancy, which causes naturally n-type GaN crystals. The extended defects are dislocations (1D extension) and grain boundaries (2D extension). A commonly-seen example in GaN of the former is the threading dislocation (TD) along the c-axis. An example of the latter is the mosaicity in the c-plane (Fig. 4.7). These two are related. Extended defects are relatively easy to locate experimentally via diffraction techniques e.g., XRD and TEM. A surface (termination of a periodic array) of a crystal is also considered to be an extended defect. All defects can be NRR centers through various mechanisms. Extended defects may cause electrical leakiness of a pn-junction device as electrons may travel along them with ease. Also, a unique role of TDs in InGaN MQW devices has been reported of assisting carrier injection into MQWs (Fig. 4.8). A proposed model states that when a TD meets an InGaN layer growth, a hexagonal pit (a small hole in InGaN) originates from the TD. Consequently the grown MQW will have pits opening up on its surface, onto which a Mg-doped p-type layer will be grown and the pits will be filled. As a result, all QW layers come into contact with the p-type layer at every pit, where a pn junction is formed. In this way, holes are injected directly into all QWs, rather than by overcoming barrier layers. The island growth discussed in Sect. 3.3 is largely responsible for generating TDs and twisting mosaicity in heteroepitaxial GaN, and is the reason why a GaN buffer layer needs to be grown for several µm for TD density (TDD) to be reduced down to 108 cm−2 for forthcoming active-layer growth. In a lattice-matched system like traditional III-V systems, TDD is around 104 cm−2 and it is known that luminescence efficiency is sensitive to TDD of that range. Thus the extremely high TDD (by four orders of magnitude) in GaN initially

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Fig. 4.7 GaN twisting mosaicity is explained via a top-down view using hexagons as crystal grains. Grains are slightly misaligned rotationally causing the mosaicity. Asymmetric XRD (the beam incident angle and detector angle are set unequal with respect to the sample surface because the target ¯ is used to evaluated the mosaicity. In crystallographic plane is inclined from the surface) on (1012) addition, grains are slightly tilted with each other, which is readily characterized via symmetric XRD on (0002). Grain boundaries are the TDs extending vertically (perpendicular to the page)

Fig. 4.8 Mechanism of carrier injection through pits. Hexagonal pits are spontaneously formed in an InGaN active layer at TDs, and are filled with forthcoming p-type AlGaN/GaN. All InGaN QWs directly meet the p-type material at pits and form pn junctions locally. Holes are injected into QWs via the local pn junctions rather than via overcoming all barrier layers

puzzled scientists from AlInGaP backgrounds, but a conclusion was made that In segregation screened the high-TDD for luminescence, as discussed earlier in the present chapter. For LD devices TDD still needs to be in the 104 cm−2 range. In 1997 an early work on lateral epitaxial overgrowth (LEO) was reported [2, 19]. This was an epitaxial technique to reduce TDD by growing crystals sideways on a substrate with an assist of photolithographic dielectric masks, and soon after the world’s first GaN-based LD was realized. The mosaicity in common Ga-face c-plane GaN is unobvious in optical inspections. It is known that N-face c-plane GaN growth significantly reduces FWHM of (0002) XRD (reduced grain tilts), but increases mosaicity (grain twists). Increased mosaicity causes visible topographical hexagonal features on its surface and growth of QWs on the rough surface is infeasible.

4.3

Phosphor Materials

4.3

Phosphor Materials

4.3.1

Material Types for LED Application

101

Phosphor materials for visible wavelengths experienced extensive industrial research in the previous century for fluorescent lamp (UV excitation) and television (electron excitation) applications. With solid-state technology taking over from vacuum technology, new requirements for phosphors include blue-light excitation by the blue LED pump and broad-band luminescence for high color rendering. The majority (almost 100% of commercial use) of phosphor materials are electrical insulators, often referred to as “ceramics” due to their material synthesis. Similar to semiconductors, phosphors have bandgaps, but, very large compared to the visible spectral range. As a result, they do not have mobile carriers (thus insulating, and the notion of holes is not used in discussing electronic transitions) and do not absorb visible light. To make them function in the visible spectral range, they are intentionally doped to create spatially-localized energy states within their large bandgaps that enable luminescence of visible light. The luminescence-center dopant is called the activator. Because of the strong (deep) electron localization, powder phosphors can luminesce at high efficiency regardless of their surface areas. If one made a crushed semiconductor powder, it would not luminesce because of high surface-state densities that promote NRR. No electrical conduction is required in phosphor materials, hence material selection is solely based on optical properties. For dopants, the lanthanide elements are extensively utilized. While most lanthanide ions in a crystal exhibit 4 f to 4 f electronic transitions that are well-shielded from surroundings by outmost electrons and typically give luminescence in sharp spectral lines, Ce3+ and Eu2+ exhibit unique transitions and this is the reason why they are of special interest for broad spectra and color tunability. Ce3+ has a characteristic electronic transition 4 f 1 5d 0 → 4 f 0 5d 1 . Eu2+ has a parity-allowed transition 4 f 7 5d 0 → 4 f 6 5d 1 . As their 6s electrons are already stripped in these ions and the 5d is thus the outmost shell, an electronic transition disturbs the host crystal, resulting in energetically-spread (i.e., broad-band) emission. For the same reason the 5d can be manipulated by the crystal field15 of the host crystal, which offers absorption and emission band tunability. Therefore Ce3+ and Eu2+ can also function as absorption centers (called the sensitizer). Ce3+ replaces Y3+ in YAG (Y3 Al5 O12 :Ce) that has a luminescence peak at ∼555 nm. The host crystal may be altered by substituting Gd3+ for Y3+ . Larger Gd3+ ions strengthen the crystal field around Ce3+ and the luminescence red-shifts. Smaller Lu3+ can replace Y3+ and the luminescence blue-shifts, all the way to ∼520 nm for 100% replacement (referred to as “LuAG”). A slight amount of Ga can reside in Al sites: Y3 (Al,Ga)5 O12 :Ce3+ (referred to as “GYAG”) shifts its emission peak down to ∼530 nm. The red nitride phosphor CaAlSiN3 :Eu2+ has deep red emission at 650–660 nm, and replacing some Ca with Sr, as in Ca (Sr,Ca)AlSiN3 :Eu2+ , emits shorter high-efficacy 15 The crystal field is the electrostatic field created by atoms in a crystal, and is a strong function of

the position.

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red of 610–640 nm. Chapter 5 of [5] provides an extensive summary of LED phosphors in a chemistry point of view. Phosphor powders are typically in a form of 5–50 µm non-spherical particles. Large particles provide higher QEs because of better crystallinity. In application, however, their granularity may become an issue for spatial color mixing. Refractive indices of YAG and SCASN are nominally 1.84 and 2.2, respectively, and scattering power should be considered in a lower-index binder for sufficient conversion within given light path lengths. An extreme case as an example: a thin slice of a YAG:Ce single crystal has a high QE but may not convert blue light sufficiently within a short path because the blue photons have only a onepath chance to be absorbed without being scattered around. Sintered phosphor plates have heat-sinking benefits, but may require additional scattering mechanisms to gain sufficient path lengths for conversion. Well-known downsides of sintered plates include their manufacturing cost and blending difficulties. It has been a common practice that every phosphor material is subjected to an LED manufacturer’s in-house characterization to evaluate across various phosphor manufacturers, since not all of them use one defined method and condition of characterization. Traditionally, fluorescence spectroscopy (equivalently spectrofluorometry, e.g., Horiba PTI QuantaMaster series) was a versatile technique where excitation and emission spectra were readily acquired along with QE. These spectra help to understand self-absorption and cascade-conversion probabilities when light propagates in a phosphor layer. Phosphor characteristics are a function of temperature and of excitation, referred to as thermal quench and excitation quench, respectively. As LED applications sought high-power operations, high-excitation (∼1 W/mm2 or even higher) and high-temperature characteristics (up to ∼200°C) became more important than ever for phosphors [14]. Accordingly, phosphor characterization methods evolved to suit LED requirements. While spectrofluorometry commonly employed a powder bed (packed powder sample) as its sample format, validity of spatially-uniform excitation was questioned. Characterization engineers invented various dilute methods, e.g., monolayer particle bed, powders dispersed in clear binder or fluid, etc. The concepts of IQE and extraction efficiency were introduced; however, they have not acquired universal usage. To add a few notes for experimentalists, in measuring phosphor luminescence, oil and grease contaminants (e.g., from a finger) must be eliminated, as they can luminesce. Using metal tweezers on phosphor materials can often dismay phosphor chemists due to potential introduction of contaminants. For the last several years one of research trends has been the narrow-spectrum red, e.g., Sr[LiAl3 N4 ]:Eu2+ [11] (SLA, introduced by Lumileds in 2015 and LED products in following years), K2 SiF6 :Mn4+ (patented by General Electric; LED products released by a licensed LED manufacturer Bridgelux in 2021) and quantum dots (QDs) [16]. This is because the broad-band reds extend into spectral deep red where efficacy becomes low. However, it is controversial whether increasing efficacy and R9 values for the sake of numbers improves actual overall color-rendering performances of a white light source. QDs have a different mechanism of luminescence, which is somewhat similar to semiconductor’s QW structure, but applied three-dimensionally to give the core-shell structure. The most-researched mate-

4.3

Phosphor Materials

103

rial is CdSe-ZnS, where larger bandgap ZnS confines carriers in smaller bandgap CdSe. Because of quantum confinement effects, emission color changes as the size of the “dots” is changed. Therefore one material system can realize various colors of luminescence. Other materials e.g., InP-ZnS are researched as Cd has environmental concerns. Rapid degradation under blue irradiation is their weakness, especially at high excitation intensities. QDs are handled as suspensions rather than dry powders, hence they fundamentally need to be chemically compatible with other materials around, e.g., silicone, upon integration. Not only do few QD manufacturers produce large quantities but they also establish strategic partnerships with LED manufacturers. Therefore, QDs do not seem to be over-the-counter ingredients. To date, illumination products using QD converters have relatively low penetration into the market. QD technology is shifting towards remote-phosphor and micro-LED display applications, by taking its advantage of QD’s narrow spectra.

4.3.2

Luminescence Characteristics of Phosphors

Two fundamental characteristics of phosphor luminescence are the emission spectrum and the excitation spectrum. The former is the luminescence that we perceive, while the latter is the indication of the strength of phosphor luminescence produced by various excitation wavelengths. The traditional and widely-used instrument to characterize phosphor luminescence is the spectrofluorometer (Fig. 4.9). A spectrofluorometer consists of a broad-band light source (e.g., Xe lamp) combined with a monochromator, a sample compartment, and a high-sensitivity detector (e.g., PMT) combined with another monochromator. In this way one can vary and choose excitation and detection wavelengths independently. Fig. 4.9 Configuration of a modular spectrofluorometer. The excitation monochromator selects a monochromatic light from the light source and the emission monochromator selects a wavelength introduced to the detector. Two monochromators are independent from each other

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The emission spectrum is the luminescence spectrum of a sample at a fixed excitation wavelength. The excitation spectrum is the inverse: The excitation wavelength is swept while the detection wavelength is fixed. It is common to measure these two spectra in three steps: 1. Emission spectrum at an arbitrary excitation wavelength to find the luminescence peak wavelength, 2. Excitation spectrum using the above found luminescence wavelength, 3. Emission spectrum using the most efficient (i.e., the peak in the excitation spectrum) excitation wavelength. It is a common practice not to sweep across the fixed wavelength in order to avoid a strong reflected light going into the sensitive detector. Another spectral measurement often done is the reflectivity, where the two monochromators are set at similar wavelengths (e.g., off by a few nm. See also the slit width discussion below) and swept at an equal rate. Using the same wavelength on both monochromators is avoided so as not to damage the sensitive detector by over-exposing. The range of wavelength sweep is determined by the sample material. In our case, the visible wavelength range suffices. Integration time (detector exposure time) can be short as far as a reasonable S/N ratio is maintained. One parameter that is not very intuitive is the slit width. There are two slits on a monochromator: Entrance and exit (Fig. 4.10). The exit slit is located on the rainbow plane where grating-dispersed light is focused on. Hence the exit slit is to select a width in the wavelength. A monochromator optics is associated with a characteristic property called the reciprocal linear dispersion, measured in units of nm/mm. nm is for the spectral width and mm is for the slit width. It indicates how wide the rainbow is spread on the exit slit plane (= the rainbow plane). If an exit slit is 2 mm wide and the grating has a 4 nm/mm dispersion, the spectral width called the band pass is 8 nm. The entrance slit is typically set to the same width as the exit slit. The reason is that the two slits are mutually images of each other through the monochromator optics. If the entrance slit is set narrower, the monochromator loses light intensity unnecessarily. If the entrance is set wider, the monochromator blurs its wavelength resolution because the entrance slit is an angle selector of the incoming source light. The source light is focused onto the entrance slit plane, yet the filament or arc of the source lamp has a finite extent. By widening the entrance slit it increases the amount of light by accepting light coming from a slightly broader range of angles. The band pass of excitation and of emission can be chosen based on samples under evaluation. If a sample is anticipated to have sharp excitation spectral lines the excitation band pass should be chosen accordingly in order to resolve the sharp lines. If the sample is anticipated to show sharp emission lines the emission band pass should be chosen accordingly so that the sharp lines are resolved. One thing to remember is that the band pass does not represent a sharp spectral cutoff: Spectral tails typically extend twice as wide as the band pass. Otherwise, slits may be set reasonably wide to obtain less noisy spectral data.

4.4

Silicone Encapsulant

105

Fig. 4.10 Configuration of a common monochromator, the Czerny-Turner type. Focused light from the light source passes the entrance slit and projected onto the first mirror that shines collimated light onto the grating. Dispersed light by the grating is focused by the second mirror onto the exit slit plane where a rainbow is formed. Only the wavelength selected by the exit slit can escape from the monochromator and any other wavelengths (one shorter wavelength is represented by broken lines) are blocked. The two mirrors typically have an equal focal length so that the two slits are equal mutual images. When the focal lengths are different, the slit images are magnified accordingly

Accessible optics of a spectrofluorometer (typically only in the sample compartment) are not telecentric (see Sect. 5.4) and adding an optic element (e.g., attenuation filter) may distort its optical paths. Because the wavelength must be calibrated mutually on the two monochromators, attention should be executed to repetitive mechanical movements e.g., minimizing the backlash by consistent operation. The water Raman peak is conveniently used: Emission is observed around 398 nm when excited by a 350-nm monochromatic light.

4.4

Silicone Encapsulant

Silicone is also called polysiloxane, or more explicitly polymerized siloxane (mostly by chemists and chemical engineers). It possesses suitable properties for an LED encapsulant: Optical clarity (also in near-UV and near-IR), electrical insulation, temperature resistance, mechanical and chemical stability, nontoxicity, handling convenience, material design flexibility, and so forth. Shown in Fig. 4.11 is the most basic chemical structure of silicone. Silicone has an inorganic chemical backbone of Si-O. The Si-O bond has a higher bond energy, a longer bond distance, and a wider bond angle than the common organic C-C bond. This fact raises the above useful properties. Attached to the backbone are organic

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4 Semiconductor Crystals and Device Physics

Fig. 4.11 Chemical formula of a basic silicone. Parentheses indicate the repeating unit for n times where n is the degree of polymerization. The backbone is Si-O and two organic groups are attached a Si (except the end where an extra organic group is terminating the chain). In the simplest case silicone purely contains methyl groups (CH3 ); that is PDMS. The phenyl group (C6 H5 ) is another common organic group used in silicone. Note a phenyl is larger than a methyl

groups that can be varied. The simplest (purest) is polydimethylsiloxane (PDMS) which is widely used in the LED industry. PDMS has two methyl (CH3 ) groups attached to each Si of the backbone. This chemical structure gives low refractive index (1.41) and relatively high gas permeability. Higher refractive index (up to ∼1.56) can be obtained by replacing the methyl groups with phenyl groups and at the same time gas permeability is reduced due to denser structure. However, phenyl groups are susceptive to environmental stress of heat and light; thus photothermal degradation characteristics need to be studied thoroughly. Silicones have relatively low thermal conductivity, and therefore high-loading phosphor integration methods were developed for high-power applications. For silicone itself, silica particles are sometimes added to improve thermal conductivity of silicone encapsulants. Because of incomplete refractive index matching, a silica-loaded silicone tends to appear translucent. Strong desire for even higher refractive index leads to the approach of adding high-index nanoparticles e.g., ZrO2 . Mechanical hardness is another important property that can be tuned by the degree of polymerization. Silicones typically used in LEDs include gels, elastomers (rubber), and resins, in order of low to high hardness. Silicone gels are soft and tacky, and can absorb mechanical stress, e.g., around a wire bond, that occurs in a package due to various degrees of thermal expansion of LED package materials. Silicones typically have 200–300 ppm/K of coefficient of thermal expansion (CTE), which is an order of magnitude greater than inorganic constituents in LED devices. Therefore temperature cycling can cause mechanical stress and silicone delamination. Products may collect dust or stick to each other or to packing containers when a gel is used outside of a product package. Silicone elastomers are a common encapsulant for potting of low- and mid-power color-LED packages and goop-in-cup phosphor integration. Silicone resins can resist external mechanical stress and can improve dicing properties for example, though may be prone to cracking and delamination, combined with volume shrinkage effects upon curing. Cured silicone in general increases hardness with aging.

4.4

Silicone Encapsulant

107

For polymerization, two chemical reaction paths are common for LED applications. The condensation type generates byproducts (H2 O) that need to be expelled. Because of this polymerization mechanism, it is only used in thin and small shapes, yet curing is still slow and volume shrinkage can be pronounced because of byproducts. The addition type uses metal (Pt) catalysts producing no byproducts, thus is more suitable for volumetric potting and dome overmolding. Catalytic reaction is promoted by temperature and can be completed in a relatively short duration at an elevated temperature. Thus working pot-life is sufficiently long at room temperature and curing can be completed in a few hours at ∼150°C. On the flip side, catalysts are left in. Catalytic reaction is sensitive to environmental contamination leading to deactivation of catalysts. P, S, and amines (e.g., ammonia) are known to be contaminants. In the past when epoxy resins were also used in the labs, ovens got contaminated by epoxy materials (which often contain amines), and addition-type silicones failed to cure in those ovens. For advanced phosphor integration methods (e.g., film lamination), viscoelastic properties of silicone are finely tuned to control integration processes precisely. Dynamic mechanical analysis (DMA) is required, where mechanical properties of uncured silicone are studied at various temperatures (this field of study is referred to as the rheology). For example, least-viscous temperature of a silicone may be utilized to achieve the best wetting. Thixotropy is another unique property critical for dispensed dam formation in COBs. It is a fluid property, like that of whipped cream, that allows silicone to maintain a shape while still flowable. Discoloration or loss of transparency over time, often referred to as “yellowing” or “browning,” is a very active subject of investigation. As a major organic constituent in an LED device, silicone encapsulant tends to degrade sooner than other constituents. Yet, browning is not only caused by the organic groups in silicone chemistry decomposing but also by volatile organic compounds (VOCs) trapped in/around the LED device diffusing in. The C-H bond in organic substances is generally considered to be a stable atomic covalent bond with a bond dissociation energy of approximately 400 kJ/mol, which is 4 eV per bond. Consequently the C-H bond is prone to dissociation upon being illuminated. A blue photon raises a certain probability of bond dissociation, i.e., a consecutive event where a photon hits a bond, causing it to vibrate violently, followed by another photon which hits the bond before vibrational relaxation, leading the bond to break. Violet and UV photons steeply increase the probability and cause faster generation of graphite-like carbon. Carbon in its graphite phase exhibits a unique absorption characteristic—graphite absorbs the entire visible range, yet more strongly at red wavelengths than blue wavelengths. Participation of environmental gasses (i.e., O2 and N2 ) in browning processes has also been suggested [12]. LED manufactures have published on chemical aspects of environmental degradation of encapsulants [1, 3].

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4.5

LED as a Diode: Electrical Aspects

4.5.1

Diode Equation

The LED is, as its name implies, a type of diode, and consists of a pn junction across which electrical current is carried by both electrons and holes. When a pn junction is formed by placing these two types of semiconductors in contact, there appears an electrostatic potential difference (the built-in potential) between the two at equilibrium (Fig. 4.12). The diode equation was derived to describe diode’s I -V behavior [13, 17]:     q Vapp I = I0 exp −1 (4.1) nkT where I is the current, I0 is the saturation current (device-specific constant), q is the unit charge, Vapp is the applied voltage, k is Boltzmann’s constant, T is the absolute temperature, and n is the ideality factor, which is typically an experimentally-determined constant and strongly tied to the Shockley-Read-Hall (SRH) statistics [18]. The equation shows that current increases exponentially as a function of applied voltage. Hence the diode is a nonlinear device. The exponential increase is a consequence of the thermal energy distribution of carriers.16 A forward bias (a positive bias to the p-type) reduces the potential barrier so that some high-energy carriers can now overcome it and are injected to the opposite sides of the junction where they become the minority carriers (Fig. 4.12). They recombine with the majority carriers readily and disappear. Because carrier distribution is exponential as a function of thermal energy (Boltzmann distribution), a change in applied voltage contributes exponentially to current (mathematical integration of an exponential function is another exponential function). On the reverse side of the I -V curve, there appears a small constant current, called the saturation current. Saturation current is caused by minority carriers at equilibrium: Very small amounts of electrons in the p-type and holes in the n-type are existent as a result of the mass action law at thermal equilibrium. They create only a small current flow under reverse bias and deplete so that no further increase in the reverse current occurs. LEDs are not intentionally used in this reverse regime.17 The greatest shock in the diode equation is that there is no bandgap dependence, opposed to what we see in experiments where a turn-on voltage is found on an I -V curve. The turn-on voltage in units of V is numerically approximately equal to the photon energy 16 At small forward bias, only highest thermal-energy carriers flow across. Simultaneously the system

tries to recover the Boltzmann distribution of carriers. During this action thermal energy is consumed and the device cools down. This refrigeration can be observed experimentally by monitoring Vf increase using a commercial digital voltometer or sourcemeter. Also on such a regime the emitted photon energy in units of eV is greater than V f in units of V, and equivalently, WPE becomes greater than EQE [10]. 17 One can increase the minority carrier density by either raising temperature, illuminating, or injecting carriers electrically. Then the reverse saturation current can be devised as a thermometer, photodiode, and transistor, respectively.

4.5

LED as a Diode: Electrical Aspects

109

Fig. 4.12 Band diagrams of a homo pn junction, accompanied by carrier distribution profiles of electrons on the right and holes on the left. a At thermal equilibrium, a very small amount of carriers (the minority carrier) can distribute on the opposite side of the junction because of the potential barrier q Vbi . b When a positive bias is applied, which reduces the height of the potential barrier by q Vapp , high thermal-energy carriers (hatched areas) overcome the potential barrier and start distributing on the opposite side of the junction (carrier injection, indicated by gray arrows) due to concentration gradient (diffusion current)

in units of eV. The lack of bandgap dependence in the diode equation has rarely been explained explicitly in textbooks. Consider a GaN pn junction with majority carrier density in the n-type and p-type neutral regions being n n = 4 × 1018 and p p = 1 × 1018 cm−3 , respectively. With the intrinsic carrier density n i = 2 × 10−10 cm−3 , the law of mass action n i 2 = n n pn = n p p p predicts the free-electron density in the p-type neutral region (thus minority carrier density), n p = 1 × 10−38 cm−3 . As far as physical dimensions of a diode chip are reasonable (typically ∼1 mm3 or less), practically no free electrons exist in the p-type neutral region.18 An electron can be injected from (that is, can statistically reside in) the n-type side when the potential barrier has been reduced to approximately 0.5–0.8 eV (at RT, depending on materials and doping levels) by forwardly biasing. This is the starting point of forward current flow and the origin of the turn-on voltage. In a GaN pn junction the turn-on voltage appears around 3.4 − 0.8 = 2.6 [V]. For the same statistical reason (i.e., no minority carriers exist), reverse saturation current is practically zero on LEDs. Appendix C provides a further discussion. 18 It may be a fun exercise to look for a minority carrier in an n-type GaN crystal. For p = 1 × 10−38 n cm−3 , how large would an n-type GaN crystal need to be to have a hole? The volume of the earth is 1 × 1027 cm3 . Or, how long one would have to wait to find a hole at a probability? Use an arbitrary time constant e.g., 1 × 109 [1/s] of recombination speed. The human lifespan is approximately 3 × 109

seconds.

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Caution should also be exercised towards the ideality factor. The ideality factor was inserted to account for the effects of mid-gap (within the bandgap) recombination centers (e.g., unintentional impurities, crystal defects, etc.) in conventional diodes. Reference [17] explains that recombination within the depletion region must be assisted by mid-gap states and would give n = 2 in a symmetrical junction, whereas recombination of injected carriers (recombination in neutral regions) would give n = 1 regardless of band-to-band or via-mid-gap recombination. In later years, the physical significance of the ideality factor was explicitly interpreted as a voltage-partitioning factor Vapp /n [9]: The potential at a location where recombination occurs (thus current is generated) changes as Vapp /n. Note that Vapp is externally measured, and hence includes electrical behaviors of metal-semiconductor interfaces and not solely the pn junction. The fundamental difference of the LED from the conventional diode is the fact that carriers are intended to recombine within the depletion region. Thus, highly-efficient sound LEDs should not give the ideality factor at unity. In InGaN LEDs especially, research efforts for the last 20 years or so have revealed the mechanisms for large n values (n > 2) observed in measurements [7]. As for the terminology, the Shockley-Sah-Noyce (SNS) original work (during the preLED era) called current due to recombination in neutral regions “injection current” and “diffusion current,” and fully articulated it as “diffusion-recombination current.” Current due to recombination in the space-charge layer was termed “recombination current,” “recombination-generation current,” and “space-charge layer current.” In the modern LED realm the term “injection” implies carrier injection into an active region (e.g., QW) and carrier injection into a neutral region is referred to as “carrier overflow.”

4.5.2

Real LED Devices

Experimental I -V curves of LEDs are barely fitted with or interpreted using the diode equation, not only for the reasons above, but also for more pronounced effects of metal contacts on large bandgap materials. Consequently, for phenomenological understanding it is more practical to read those experimentally-obtained I -V characteristics. The simplest model is that current begins to rise linearly from the turn-on voltage (Fig. 4.13). This model is characterized with two numbers: Turn-on voltage and dynamic resistance. The turn-on voltage, on the abscissa at which the tangential line of the I -V slope intersects, is determined by interfacial properties of the device, such as the pn junction (built-in potential), metalsemiconductor contacts (Schottky or Ohmic), metal interfaces of wire bond and solder attach, etc. Bulk properties of ingredient materials determine the dynamic resistance, e.g., conductivity of metals and semiconductors, etc. Each of these has its own temperature response. Within the normal operational temperature range, with temperature rising, the

4.5

LED as a Diode: Electrical Aspects

111

Fig. 4.13 A simplified I -V characteristic defined only by two quantities: Turn-on voltage and dynamic resistance. This simplified model is often used in designing of elemental external circuits around LEDs, as the LED can be treated as a linear device above the turn-on, making circuit designing easier

bandgap shrinks and semiconductor conductivity becomes greater,19 while metal resistance increases. Altogether the forward voltage is typically reduced with a temperature rise. A defective pn junction often exhibits a leaky I -V curve where a small but appreciable amount of current flows below the turn-on and/or on a reverse bias. It is useful to plot the I -V curve with the current axis in a logarithmic scale to identify leaky current, as illustrated in Fig. 4.14. Good pn junctions show the noise floor of the instrument (lower than 1 nA on a decent instrument) below the turn-on and on reverse bias. Beyond the turn-on the curve rises exponentially (a straight line graphically) where any resistive components of the device are negligible. At higher currents the curve rolls off due to nonnegligible series resistances at increased currents. Leaky current is caused by either crystallographic defects in the pn junction or device processing imperfections, e.g., defective passivation layers, or sometimes defective packaging. An often-seen attempt is to extract ideality-factor values by fitting an I -V curve (n as a fitting parameter) using the diode equation Eq. (4.1) in order to assess SHR-type recombination and/or leaky current occurring in an LED device. This attempt is inadequate for these reasons below. • An LED typically has a nonnegligible series resistance from the bulk materials, especially in typical current ranges of LED operation. The diode equation does not account for series resistance and no longer holds in those current ranges. Only in very low current ranges the series resistance may be ignored. • According to the SNS analysis, n = 2 is caused by recombination at the middle of a symmetric pn junction (metallurgical junction), and the SRH statistics rationalize a recombination mechanism within a depletion region where recombination is typically omitted 19 With temperature, carrier mobility drops due to increased lattice vibration while carrier density

increases due to increased thermal ionization.

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Fig. 4.14 Schematic illustration of an I -V characteristic graphed in a semi-log plot. Below turn-on the noise floor of the instrument is exhibited. Above turn-on an exponential rise in current (straight line in the plot) appears first, followed by a rolloff due to resistance in the device. A defective device may show leaky current below turn-on. An example is indicated by broken lines. The negative value of reverse current is plotted as the absolute value because of logarithmic plotting

due to the built-in field. When there is another mechanism to promote recombination in the depletion layer, such as a QW, n = 2 can result. The SNS analysis only implied that asymmetric junctions would result in n < 2 regardless of SHR-type or band-to-band recombination. • SRH-type recombination in the SNS analysis requires some forward bias to populate both types of carriers at a common location. It must be above the turn-on for the SHRtype recombination to occur in the neutral regions, and it may be slightly lower to occur around the middle of the pn junction. Premature current flow at very small bias is not generated by any type of recombination but must be caused by unipolar leaky paths. I -V curve fitting is hence only used in special occasions in R&D. The LED is a photon-generating device; at the same time, it can absorb photons and generate photocurrent just like photodiode does. Hence LED’s I -V characteristics vary depending on how the LED is illuminated. It is well known that the reverse saturation current increases with illumination due to the fact that photo-generated carriers are swept in the reverse direction by the built-in field (Fig. 4.15, left). Near the flat band condition under forward biasing, photocarriers are pushed in the forward direction by the concentration gradient (i.e., diffusion current, Fig. 4.15, right). As a consequence, an I -V curve under illumination intersects with the dark I -V curve in the first quadrant. It then follows that, when two LEDs are placed in proximity, mutual absorption can occur causing changes in the dark I -V curves. Photons emitted by an LED and absorbed by a neighboring LED turn into

4.5

LED as a Diode: Electrical Aspects

113

Fig. 4.15 Movement of photo-generated carriers depending on external biasing (electrons and holes are indicated by closed and open circles, respectively). Left: Generated photocarriers cause a drift current in the reverse direction. Right: Part of photocarriers contribute to the forward current due to the strong concentration gradient, while the majority may recombine radiatively (photon recycling) Fig. 4.16 A simple circuit of a step-up optical transformer. When the four diode are the same, Vout ∼ 2Vin

photocarriers, and a forward bias sweeps the generated photocarriers out of the neighboring LED. This “carrier sweep-out” mechanism can be observed in the neighboring LED as a reduction in Vf (when the neighboring LED is operated at constant current) or an increase in current (when the neighboring LED is operated at constant voltage). From a different point of view, this carrier sweep-out may be seen as deterioration of carrier injection efficiency into the active region. This is a “silent efficiency loss” (efficiency loss not generating extra heat) and may become explicitly noticeable in applications where LEDs are used as densified arrays including COBs and pixelated LEDs. Photon absorption by pn junctions can be utilized: A photodiode is a common photon detector. Another example is an optical transformer. As illustrated in Fig. 4.16 a step-up transformer can be built by stacking up multiple pn junctions. This type of construction is possible because electrostatic energy of electrons in a circuit is measured from a common ground potential, whereas photon energy does not require a common ground or a reference energy level. LEDs are somewhat current-modulated at high frequencies, where capacitance associated with their pn junction (the space-charge layer) starts playing a role. Approximately speaking,

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a cutoff frequency typically occurs around 1 MHz (thus ∼1 µs of response time) despite the fact that carrier recombination takes place within much shorter time, on the order of 1 ns.20 Care should be exercised when designing a pulsed measurement or operating in a pulsed mode, to allow a DUT to have sufficient time to respond to the input electrical pulses. A Fourier transform reveals that a square wave consists of high-frequency components, up to 100–1000 times higher frequencies21 than the fundamental frequency.

4.6

Further Reading

• Blasse G, Grabmaier BC (1994) Luminescent materials. Springer Berlin, Heidelberg • Coldren LA, Corzine SW, Mašanovi´c ML (2012) Diode lasers and photonic integrated circuits, 2nd edn. Wiley, New York • Davies JH (1998) The physics of low-dimensional semiconductors: An introduction. Cambridge University Press, Cambridge • Freund LB and Suresh S (2010) Thin film materials: Stress, defect formation and surface evolution. Cambridge University Press, Cambridge • Huang JJ, Kuo H-C, Shen S-C (eds) (2018) Nitride semiconductor light-emitting diodes: Materials, technologies, and applications, 2nd edn. Elsevier-Woodhead, Cambeidge • Mishra UK, Singh J (2008) Semiconductor device physics and design. Springer, Dordrecht • Nakamura S, Chichibu SF (eds) (2000) Introduction to nitride semiconductor blue lasers and light emitting diodes. Taylor&Francis, London • Nakamura S, Pearton S, Fasol G (2000) The blue laser diode: The complete story. Springer Berlin, Heidelberg • Pankove JI (1971) Optical processes in semiconductors. Dover, New York • Rosencher E, Vinter B (2002) Optoelectronics. Cambridge University Press, Cambridge • Schubert EF (2006) Light-emitting diodes, 2nd edn. Cambridge University Press, Cambridge • Shchekin O, Craford MG (2017) History of solid-state light sources. In: Karlicek R, Sun CC, Zissis G, Ma R (eds) Handbook of advanced lighting technology. Springer, Switzerland, p 41–70 • Stringfellow G (1999) Organometallic vapor-phase epitaxy: Theory and practice, 2nd edn. Academic Press, Cambridge, Massachusetts 20 To achieve fast modulation, the super luminescent diode (SLD) is used. SLD’s emission mechanism

is the same as LD’s, but the SLD lacks a resonant cavity. In SLDs stimulated emission prompts faster recombination, while the junction capacitance is suppressed by their small junction areas. 21 It is fascinating to realize that 1 GHz of a sinusoidal signal has 33 cm of wavelength. That is, electrical polarity alternating every 17 cm at any time, and every 1 ns at any location on an electrical cable. EM waves are generated when charges are shaken fast; thus to prevent electrical cables from radiating power out into air like antennas, electrical shield becomes absolutely necessary in highfrequency experiments.

References

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References 1. Cree LED (2022) Cree XLamp LEDs chemical compatibility. Support Document CLD-AP63 REV 8. https://assets.cree-led.com/a/da/x/XLamp-Chemical-Compatibility.pdf Accessed 4 Dec 2022 2. Fini PT (2000) Threading dislocation reduction in gallium nitride thin films on sapphire via lateral epitaxial overgrowth. Dissertation, University of California, Santa Barbara 3. Hanna B, Lin I-H (2018) Chemical compatibility of LEDs. OSRAM Opto Semiconductors GmbH Application Note No. AN122. https://dammedia.osram.info/media/resource/hires/osram-dam3813126/Chemical%20compatibility%20of%20LEDs.pdf. Accessed 4 Dec 2022 4. Hayashi H (2011) Development of compound semiconductor devices: In search of immense possibilities. SEI Technical Review 72:4 5. Huang JJ, Kuo H-C, Shen S-C (eds) (2018) Nitride semiconductor light-emitting diodes: Materials, technologies, and applications, 2nd edn. Elsevier-Woodhead 6. Krames MR Christenson G, Collins D et al (2000) High-brightness AlGaInN light-emitting diodes. In: Yao HW, Ferguson IT, Schubert EF (eds) Proc SPIE Light-Emitting Diodes: Research, Manufacturing, and Applications IV. 3938:2 7. Masui H (2011) Diode ideality factor in modern light-emitting diodes. Semicond Sci Technol 26:075011 8. Masui H, Nakamura S, DenBaars SP et al (2010) Nonpolar and semipolar III-nitride lightemitting diodes: Achievements and challenges. IEEE Trans Electron Devices 57:88–100 9. Mishra UK, Singh J (2008) Semiconductor device physics and design. Springer, Dordrecht 10. Narukawa Y, Sano M, Ichikawa M et al (2007) Improvement of luminous efficiency in white light emitting diodes by reducing a forward-bias voltage. Japan J Appl Phys 46:L963 11. Pust P, Weiler V, Hecht C et al (2014) Narrow-band red-emitting Sr[LiAl3 N4 ]:Eu2+ as a nextgeneration LED-phosphor material. Nat Mater 13:891–896 12. Roitman DB, Wadud S-E, Laughner M et al (2020) Precise bondline control between LED components. US 2020/0091377 A1, 19 Mar 2020 13. Sah CT, Noyce RN, Shockley W (1957) Carrier generation and recombination in p-n junctions and p-n junction characteristics. Proc IRE 45:1228–1243 14. Shchekin OB, Schmidt PJ, Jin F et al (2016) Excitation dependent quenching of luminescence in LED phosphors. Phys Status Solidi RRL 10:310 15. Shen YC, Mueller GO, Watanabe S et al (2007) Auger recombination in InGaN measured by photoluminescence. Appl Phys Lett 91:141101 16. Shimizu KT, Böhmer M, Estrada D et al. (2017) Toward commercial realization of quantum dot based white light-emitting diodes for general illumination. Photonic Research 5:A1–A6 17. Shockley W (1949) The theory of p-n junctions in semiconductors and p-n junction transistors. Bell Sys Tech J 28:435 18. Shockley W, Read WT Jr (1952) Statistics of the recombinations of holes and electrons. Phys Rev 87:835; Hall RN (1952) Electron-hole recombination in germanium. Phys Rev 87:387 19. Zheleva TS, Nam OH, Bremser MD et al (1997) Dislocation density reduction via lateral epitaxy in selectively grown GaN structures. Appl Phys Lett 71:2472

5

Optics

5.1

Light as EM Wave

Light generated in an LED’s active layer will experience refraction and reflection in the chip and package until it exits into free space. Light is an electromagnetic (EM) wave and refraction and reflection of EM waves have been studied thoroughly. Therefore, it is a good idea to fully utilize the EM wave knowledge to understand the behavior of light in LED devices. Total internal reflection (TIR) and the Fresnel equation are important consequences of EM wave physics in the optical wavelengths, deduced from theory of refraction and reflection of light, respectively. The idea of optical polarization is strongly related and therefore introduced during the following discussion. When light arrives at an interface formed by two dissimilar materials (for example air and sapphire), a fraction of its energy is reflected and the rest is refracted (transmitted with a change in its direction of propagation). This behavior is understood by applying a set of laws of physics as boundary conditions: Poisson’s law for the electric field E and Ampere’s law for the magnetic field M. Consequently, Snell’s law is a compact way of describing what happens to the EM wave at the interface: n2 sin θ1 = sin θ2 n1

(5.1)

where n is the refractive index (RI)1 and θ is the angle of light propagation as indicated in Fig. 5.1. Suffixes indicate either of the two materials forming the interface. Equation (5.1) 1 RI of a material is a weak function of wavelength; this is referred to as the dispersion. Dispersion

is often omitted in introductory discussions for simplicity. Common optical materials exhibit higher RI values at shorter wavelengths, typically with a rapid increase nearing their own absorption edges e.g., bandgaps. It used to be typical that RI of a material was reported by its value at 633 nm, which was the wavelength of the readily accessible HeNe laser. Today RI can be measured easily at various wavelengths. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4_5

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Fig. 5.1 Illustration showing Snell’s law at an interface. When light is incident at an angle θ1 in Medium 1 (refractive index n 1 ), a fraction of light energy is reflected to the direction of the angle θr where θr = θ1 . The rest is refracted (transmitted) into Medium 2 (refractive index n 2 ) at an angle of θ2 , where sin θ2 = (n 1 /n 2 ) sin θ1 . When n 1 < n 2 (e.g., air to water), θ2 > θ1 , thus refraction always occurs. When n 1 > n 2 (e.g., sapphire to air), no refraction occurs beyond θ2 = 90◦ . This angle of θ1 is called the critical angle θc . The result is TIR. It is called “internal” because interior of a material is typically higher index than surroundings and TIR occurs inside the material. An interesting question may be, what if one photon is incident at an interface. A photon must not split, rather it will either be reflected or transmitted with a certain probability. After so many photons have been incident, Snell’s law is observed

predicts the existence of a critical angle θc for the incident light when light is going from a dense (higher RI) material to a light (lower RI) one. Beyond the critical angle (more glancing angles), refracted light would not be allowed (prevented by laws of physics) to propagate into the lower RI material and incoming light is fully reflected back into the higher RI material. TIR occurs only when light goes from a denser material to a less dense material; for example, from sapphire to air. In three dimensional space, the critical angle makes an imaginary cone within which incident light can pass the interface. This imaginary cone is called the light escape cone, or simply the escape cone. Despite this simple notion of the escape cone, one should keep it in mind that light transmission at a flat interface is not an on/off phenomenon at θc . Light transmissivity within the escape cone changes with the angle of incidence (see Fig. 5.4), thus it is not constant within an escape cone. Even under a TIR condition E and M penetrate slightly beyond the interface before fully getting reflected. This type of penetrating field is called the evanescent field. The depth of penetration is, approximately speaking, a micron or less. When another interface is right behind the first interface within the range of evanescent fields (e.g., a low-RI thin film sandwiched by high-RI materials), light can pass the second interface even beyond the critical angle because evanescent fields reach the second interface. This phenomenon is used in multilayer optical structures, e.g., anti-reflective (AR) coatings. From the discussions above, light seemingly likes to stay in denser materials. This is because E strength (thus the energy, which is proportional to E2 ) is lower in denser materials. This fact is utilized in semiconductor laser (also called diode laser and laser diode, LD) designs, but in LEDs confined light is not preferred as we want to extract light into

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Fig. 5.2 Optical microscope image of a Soraa’s triangular vertical InGaN chip “Tri-LED” [2] accomplished by its GaN-on-GaN technology. Approximately 400 µm long triangle, which nests well in c-plane GaN’s 6-fold symmetry. It can be surmised that triangular chips would confront singulation and die-handling challenges to overcome in using conventional die fab machines. Reprinted from [2], with the permission of AIP Publishing

free space, the very lowest index material. Surface roughening is a method to avoid TIR. Chip shaping interrupts repetitive TIR occurring within a chip by making chips geometrically less symmetrical [4]. There were also publications in 2012 reporting triangular chips (Fig. 5.2) were introduced to commercial lighting products by Soraa. These approaches are expressed as “reducing the number of bounces,” referring to the repetitive reflection of a light ray as a photon repetitively bounced back and forth by interfaces.2 In L1 and L2, a typical hemispherical dome lens changes the geometry to arrange the incident angle closer to surface-normal at the package-air interface so that TIR is unlikely. The same applies for the encap gain experiment discussed in Chap. 2. Inserting an intermediate material of parallel interfaces does not alter the TIR angle, but only helps to reduce Fresnel reflection, as will be seen below. Reflection at an interface, sometimes referred to as Fresnel reflection, is caused by a RI step, regardless of whether going from dense to light or light to dense. One can see his face faintly reflected on a transparent glass window because of Fresnel reflection. Reflectance (reflectivity) is angle-dependent as described in the comprehensive Fresnel equation, which simplifies at normal incidence where reflectivity maximizes: RF =

(n 1 − n 2 )2 . (n 1 + n 2 )2

(5.2)

Because of the square terms in the equation, index stepping and index grading (graded index, GRIN) are effective to reduce Fresnel reflection.

2 The wave nature of light allows us to formulate all these interfacial characteristics and polarization

characteristics. The particle nature of light describes all these characteristics in terms of probability. When an interface has 50% of reflectivity, an impinging photon has a 50% probability of being bounced back. When a number of photons are impinging, half of them will be bounced back.

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Fig. 5.3 A 3D view of Fig. 5.1 is provided to define the plane of incidence. The plane of incidence in Fig. 5.1 is the plane of the page. On each light ray (thick black arrows), two thin arrows indicate directions of electric and magnetic fields. Light with its E lying in the plane of incidence is TM polarized ( p-polarized). M lying in the plane of incidence is TE polarized (s-polarized)

Within an unbounded medium light propagates in the TEM mode3 and common light is unpolarized, meaning that E’s point equally in all directions perpendicular to the propagating direction. When an unpolarized EM wave encounters an interface at an angle, analysis is performed by defining the plane of incidence: A plane that includes the direction of incoming light propagation (Fig. 5.3). The component of an EM wave with M parallel to the interface is called the TM polarization, and that with E being parallel to the interface is the TE polarization.4 Both components must satisfy the boundary conditions independently, and resulting are different transmission and reflection characteristics between the two polarization components. Figure 5.4 is an example of reflectance of a sapphire/air interface. Once light leaves the interface after reflection or refraction, the EM wave propagates in the TEM mode as partially polarized light. When light is traveling into a higher RI material (e.g., air to sapphire), reflected light at the interface has experienced a 180◦ phase change in its E. Chapter 4 discussed how light emission in InGaN is polarized because of its hexagonal crystal structure. Light polarization is of strong interest in LDs. In a stripe LD geometry, polarization is defined with respect to the stacked layer interfaces: E parallel to the layers is 3 Transverse electromagnetic mode. That is E and M are both perpendicular to the direction of propa-

gation. Transverse electric (TE) and transverse magnetic (TM) modes occur in bounded propagation in metal waveguides, which are not covered in this book, and in dielectric waveguides like optical fibers and LD stripes. TE and TM modes have a non-transverse component to the direction of propagation in M and E, respectively. The mode is a form of propagation. The polarization is a characteristic of a propagating EM wave. 4 Polarization of an EM wave is defined by the direction of E. The TM polarization is also called the p (parallel) polarization, because E is parallel to the plane of incidence. The TE polarization is called the s (senkrecht) or perpendicular polarization as E is perpendicular to the plane of incidence. The p and s polarizations were named after German words, however, may be memorized as “primary” and “secondary”.

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Fig. 5.4 Reflectance of TE and TM polarizations at a sapphire/air interface as a function of angle of incidence: a from air to sapphire and b from sapphire to air. TE polarization shows a monotonic change over angle while TM polarization has a characteristic angle called the Brewster angle at which light is fully transmitted. There is no distinction between TE and TM polarizations at normal incidence. For LED calculations the average reflectance between TE and TM polarizations is used for a first-order approximation. Transmittance is one minus reflectance when an interface has no absorbance

TE and nonparallel to the layers is TM polarization. Definition of polarization described in Chap. 4 is consistent with this LD definition. TE-polarized light propagates in a LD cavity (= waveguide) in a TE mode, TM-polarized light propagates in a TM mode (because they are bounded propagation), and stimulated emission into air propagates in a polarized TEM mode. Polarization is not of a major interest or concern in LEDs; nevertheless, TM polarization is undesirable for LEDs, as they are surface-emitting (not edge-emitting) devices. An example of enhanced TM polarization is Al(Ga)N-based deep-UV LEDs [5].

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TIR Devices

As shown with TIR, light likes to stay in higher RI materials. We can utilize TIR to guide light and bring it to where light is required using a rod of a high-RI and low absorption material (e.g., quartz glass). This is the idea of lightguides (waveguides) and the optical fiber. An optical fiber consists of a core (high RI) and a surrounding cladding (low RI) that are typically sheathed in a protective jacket. Light propagates in the core based on the TIR mechanism against the cladding. Optical absorption (loss) in the core and cladding materials is made very low. Because of TIR mechanism, extreme bending of a fiber induces loss due to locally lost TIR. Coupling with other optical elements e.g., light sources and lenses, and between two fiber ends is accomplished by minimizing reflection or misalignment. Singlemode and multi-mode fibers differ in their core diameters. Single-mode fibers are designed thinner to carry only a single propagation mode. A projected light profile from a fiber end has a single hotspot. Multi-mode fibers are thicker and can carry multiple modes, and thus more power. A projected profile exhibits multiple hotspots. A lightguide relies on the same principle and is typically a more exposed structure made of clear plastic (or even clear fluid like water) with air as its low RI cladding. Coupled light can escape from an end of the structure or from surface imperfections (e.g., scratches) to be seen by a spectator. It is in many cases used for decorative purposes. TIR is also utilized in external optics of LED lighting systems. A common TIR lens is a clear plastic lens molded in a truncated conical shape. Shown in Fig. 5.5 is a TIR lens used in a commercial MR16 lamp.5 Because of TIR its conical surface does not have to be coated with a foreign reflector yet provides 100% reflectance.

5.3

Reflectance and Transmittance Spectra

An LED device consists of many interfaces and at each interface the above reflection and refraction (transmission) occur. Therefore it is of general interest to study reflection and transmission characteristics of relevant materials individually. Reflectance is a numerical expression of reflection characteristics. It is also called reflectivity. These two terms are used similarly; nevertheless, the former receives more generic usage while the latter tends to be used for specular reflection cases. Transmittance and transmissivity receive similar distinction (though still somewhat ambiguous) for transmission characteristics.

5 The MR lamp is a type of directional lamps using a multifaceted reflector (MR). Various sizes

were standardized; 16 indicates a diameter in units of 1/8 in., thus two inches (∼50 mm). Today, regardless of the use of a multifaceted reflector, the lamp is called MR16. The MR lamp series covers a smaller diameter range (MR8–MR20) than the PAR (parabolic aluminized reflector) lamp series (PAR16–PAR64). The MR lamp is typically more challenging in terms of thermal design.

5.3

Reflectance and Transmittance Spectra

123

Fig. 5.5 TIR lens used in an MR16 lamp. An LED light source is placed at a truncated apex and the base plane is to emit light. Base surface is often corrugated to manage the light projection pattern. The cross sectional illustration shows how light rays are reflected at conical surface, called the compound parabolic collector (CPC). Light rays without TIR are redirected by the convex lens formed in the middle of either the base or top plane

Spectral response of interface characteristics is always of primarily interest, while angular response is secondary and often compromised in experimental characterization due to resource constraints of tool expenses, labor for measurements, and data analysis capability. In addition, angular information is less critical as light propagates in all directions in an LED device and diffusive interfaces are often used, e.g., a mixture of TiO2 powder and silicone. In this type of volumetric diffusive reflectors, a light ray experiences a number of refraction within the reflector volume and eventually turns its direction backward to exit at a random angle [1], raising Lambertian angular characteristics collectively. And because of RI dispersion blue light is reflected sooner than red light, which goes deeper in the volume and causes noticeable transmission when the volume is smaller than penetration depth. These facts lead the experimental methods to employ an integrating sphere connected to a spectrometer, while some commercial instruments are dedicated only to specular reflection and transmission at fixed angles of light incidence. A few common arrangements of integrating spheres are shown in Fig. 5.6 [3]. Figure 5.6a indicates a reflectance characterization setup where the sample is exposed at an interior wall. The source light beam (collimated or focused) of broadband white is directed to the sample from an opposite open port through the sphere interior. Figure 5.6b is the same sphere arrangement used for transmittance characterization where the sample is placed at the source light entrance. When a Lambertian (= non-directional) incident light is of interest, an integrating sphere with an interior lamp may be used to replace a directional light source. (Fig. 5.6c). On the opposite side of the sphere is a telescopic detector focusing onto the sample for surface-normal reflectance. The choice of source light depends on the spectral range of interest. The white LED is a stable light source and may be sufficient for the visible range. The incandescent lamp has a broad spectrum covering a wide spectral range, but it requires thermal stabilization and bulb lifetime is limited compared to a white LED. When a wide spectral range is required it is also common to employ a Xe lamp, which emits high-quality white light but may be costly due

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Fig. 5.6 A few basic arrangements of an integrating sphere for reflectance and transmittance measurements. a Reflectance measurement with a collimated or focused light source. It is a common practice to tilt the beam slightly (several degrees) to avoid direct reflection back into the light source or into a sphere opening. Baffle plates are equipped to avoid any line-of-sight light interaction. b Transmittance measurement with a collimated or focused light source. Fresnel reflection may need to be accounted for, depending on sample’s nature. c Integrating sphere used as a light source to generate a Lambertian light source. A detector (spectrometer) with focusing optics is placed outside the sphere normal to the sample. When configuring an integrating sphere it is generally a good exercise to image oneself at the sample location and envision what the light leaving a sample would see. Ideally one wants to see only white reflective interior walls, not optical fiber end, open port, and other irregular surfaces

to need of a dedicated power supply and limited bulb lifetime. When measuring a luminescent material (e.g., phosphor), photoluminescence may occur and distort the reflection and transmission spectra. To suppress sample’s luminescence, a long-pass filter may be applied at the light source to cut off short wavelengths that would excite the luminescing sample. Measured reflectance spectra are compared to a known reflectance spectrum (“reference”) to deduce samples’ absolute reflectance. The reference may be a known metallic film of Au or Al. In transmittance the reference may be air. The same idea of self-absorption correction discussed in Chap. 2 is applied as necessary. Angular characterization may be performed by a rotational method on specular-reflection samples, which may not require an employment of an integrating sphere. Transmittance is more difficult because of existence of TIR, where a cylindrical lens can be used to man-

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125

age the angle of source light incidence into the sample. Nevertheless, because of all these complications, other techniques have been developed and commercialized, especially for diffusive surfaces and materials, using imaging techniques. Bidirectional reflection distribution function (BRDF), BTDF (transmission), and BSDF (scattering) are obtained on a sample using an imaging sphere that generates high-resolution digital images of reflection, transmission, and scattering (commercial instruments were developed by Radiant Vision Systems).

5.4

Geometrical Optics

Geometrical optics is an analytically simpler way to treat light and very useful in optical systems consisting of lenses. Beyond packaged LEDs, many applications employ secondary optics placed in the vicinity of LEDs. In addition, microscope observation is an everyday operation in R&D. In this section we discuss some basic ideas in geometrical optics and apply them to optical system examples. Within geometrical optics, light is treated as a set of rays and the wave nature of light is omitted. Even by this great simplification, full and rigorous mathematical formulation of light behavior is still extremely complex, thus geometrical optics has accepted many practical assumptions and approximations. Consequently certain deviations from rigorous formulation will result. These deviations are treated as aberrations and corrected later in a comprehensive analysis via geometrical optics. For example, one of the major aberrations (known as the five Seidel aberrations) is the spherical aberration. The spherical aberration is caused because the ideal surface curvature of a lens for focusing light cannot be expressed with a simple mathematical equation and is approximated by a spherical surface for ease of formulation. The resulted aberration will be patched up appropriately when it causes nonnegligible consequences. Given this spirit of assuming and approximating, geometrical optics starts with Gaussian optics where 1. spherical surfaces are considered, 2. optical systems to be analyzed are symmetric around their optical axes, and 3. light rays are contained near the optical axis. The thin-lens approximation (∼ one principal plane in an optic element or system) is then added to Gaussian optics. The resulting formulation is still comprehensive for most interests even with these approximations. A lens placed in front of an LED can capture a fraction of light emitted from the LED. One can draw a cone around the optical axis connecting the LED at the apex to the perimeter of the circular lens (Fig. 5.7). When the lens forms a parallel (collimated) beam on the other side, the point light source on the axis is said to be at the focal point of the lens. Under this configuration a few quantities are defined. The focal length f is the distance from the

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Fig. 5.7 a Light-ray tracing around a thin lens. Light leaving a point (very small) light source on the optical axis and propagating towards the lens is captured by the lens and change its direction of propagation by refraction. When the passed light beam has become collimated (parallel beam), the light source is at the focal point of the lens. Note that a collimated beam maintains its luminous flux and illuminance of a projected surface is constant regardless of the distance (refer to the discussion at the end of Sect. 2.6). The distance between the focal point and the principal plane (the middle of a symmetric lens) is called the focal length. The same applies when the optic is a group of lenses, although the principal plane of such an optic is no longer obvious. This becomes often problematic, when one tries to place a light source at a focal point of a given optic with a value of focal length. That is why the back focal length is defined. The back focal length is a geometric distance between the focal point and the end of a lens group. In a lens setup if one actually tries to look at the lens from the image space (the righthand side of the lens in the figure) where the light is collimated (thus the lens is not forming an image), it appears that the whole lens area is glowing since the point light source is expanded across the entire lens area. b When a light source or an object is placed farther than the focal point, light past the lens converges and forms an image where the distance of an object and that of its image obey the lens equation Eq.(5.3). To draw a sketch, light rays going through the principal point (intersection of the principal plane and the optical axis) are approximated not to bend and drawn as straight lines. One will then find that the farther the object is from a lens, the smaller the image becomes, and the longer the focal length of a lens is, the larger the image becomes

principal plane (the middle plane of a symmetric lens) to the focal point. The back focal length is the distance from the end of the lens to the focal point. The f -number N is defined as the focal length divided by the lens diameter D, N = f /D (also refer to the discussion of the aperture stop later in the present section). The numerical aperture (NA) is a quantity to indicate the collection (acceptance) angle of light as N A = sin θ where θ is the half apex angle. However, it important to note that NA is determined by an object-lens distance in

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this single lens configuration, regardless of a focal length6 . In practice, an optic system is in many cases a collection of lenses. Nevertheless, a lens system can be treated as a single lens to define the above quantities. In doing so, the principal plane becomes nonobvious among multiple lenses. The back focal length instead becomes a convenient quantity to find the focal point in designing mechanicals around a lens system. The focal length is nevertheless still helpful to inform the magnification provided by a lens system. For example, photographers know the image magnification (or a viewing angle) that a camera lens of 200-mm focal length would provide in their viewfinders of a given film format. Figure 5.7b is a case where an object is placed farther than the focal length of a lens. Light rays past the lens converge and form an image of the object. If the object is moved farther from the lens, the image moves closer to the lens and becomes smaller, and vice versa. The lens equation describes that the distance of an object, f obj , and that of its image, f ima , change as 1 1 1 + = . f obj f ima f

(5.3)

Because of various aberrations of optics, an image is never perfect, and equally a light beam cannot be focused to an infinitesimal point. Making a beam spot size less than 1 mm may be straightforward using rudimentary optics. A 100-µm beam spot will require some elaborate optics. Great efforts have been put into suppression of aberrations in commercial products, e.g., microscope objective lenses. Microscope objectives are traditionally categorized in three grades in terms of aberration correction. The achromat is the least expensive option due to minimal aberration correction. Chromatic aberration is corrected for two colors: blue and red. Spherical aberration is corrected for monochromatic green. The apochromat is the bestquality option where chromatic aberration is corrected for RGB (or sometime more colors) and spherical aberration is corrected at two monochromatic colors (or sometimes more). The semi-apochromat (for a historical reason it is also called the fluorite) is somewhere in-between the quality of the achromat and apochromat. Apart from these three grades, an add-on correction is the plan. A plan achromatic objective, for example, is corrected for field curvature. Chromatic aberration is fundamentally due to RI dispersion of lens materials and does not directly originate from geometrical optics. For this reason many optical glasses have been developed to reduce RI dispersion, and at the same time to increase RI. Crown glass is a low dispersion optical glass. A well-known commercial product is Schott BK7. Flint glass is a Pb-containing high-RI glass, e.g., Schott SF11. Optical microscopes in a laboratory belong to a group called the compound microscope, in contrast to simpler magnifying glasses and loupes, due to their mechanism that the eyepiece magnifies the real image cast by the objective lens. Metallurgical microscopes are those that observe opaque samples (e.g., grains of minerals) via reflected light. Stereo microscopes 6 The notion of NA is not related to focusing: An optical fiber has a NA but no focal length. When a

single lens is followed by another optical element e.g., a lens or a stop, this pair of optical elements establishes its own NA as an optical system apart from object placement.

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are of this type, with low magnifications. Biological microscopes are to observe transparent samples (e.g., biological cells between a glass slide and a cover glass) via transmitted light. A set of glass slide and cover glass has been included in microscope’s optical design. In an extreme case, the immersion technique is used to enlarge the NA by filling the space between the sample and the objective with liquid. In both types, an image cast via direct light is called the bright field (BF) image and via scattered light (hence illumination is oblique) is the dark field (DF) image. Modern high-performance microscopes are, however, more of a multi-functional cross-over type and differentiation between metallurgical and biological has become imprecise with added features. Fluorescence was originally done on the biological (the transmission type) but today epifluorescence (top illumination) is more common. It is frequently used for photoluminescence of LED active regions. Differential interference contrast (DIC, a.k.a. Nomarski) and phase contrast techniques are used to resolve subtle height and refractive-index differences. They are useful for studying epilayer surface morphologies. Polarization of luminescence can be analyzed by adding a set of polarizers (called a polarizer on the illumination side and an analyzer on the observation side). Confocal microscopy is a technique to eliminate undesired light from off-focal planes reaching the detector (Fig. 5.8b) by making the detector area smaller (e.g., placing a pinhole, using an optical fiber, etc.). In microscope observation, because of large NAs of objective lenses, a microscope may show top-down images that are not strictly surface-normal observation. This fact is highlighted in following examples. When a point light source has a nonuniform COA characteristic (Fig. 5.8a), the image formed by a microscope would not show the nonuniformity but appears as a mixed color. This is because the objective lens collects light from a wide range of angles that its NA permits and focuses the whole collected light into one point on the image plane (CCD plane or observer’s eye). When a volumetric luminescence is being imaged by a microscope (Fig. 5.8b), a glare appears in the image where expected to be dark otherwise. This is because light from off-focus planes can lie within the light collection angle of an objective lens and is projected on the image plane unfocused. Microscopes are equipped with an aperture stop (AS) which is a mechanism of an adjustable pinhole placed in a collimated (“telecentric”) part of an optic system and used to constrain light rays nearer to the optical axis (Fig. 5.9). By adequately utilizing the AS, image quality improves (because outer areas of a lens cause more severe aberrations) at the price of a dimmed image, and observation becomes closer to true surface-normal observation. Most biological microscopes use highNA objectives in order to collect weak luminescence efficiently from biological specimens. LEDs are far brighter, lifting the light-collecting constraints, and small AS can be used effectively. Another accessory found on a microscope is the field stop (FS). This is to limit the area of illumination on the objective plane (sample surface) to suppress unnecessary damage from a microscope illumination light source on sensitive specimens. The FS becomes useful in some fluorescence characterization of semiconductors. Another convenient, though not always recommended use of a microscope is that an eyepiece can be used as a magnifier when a conventional magnifier is not handy. This is because a microscope functions in a

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Fig. 5.8 Two examples examining the fact that microscope observation is not truly surface normal. a When imaging a light source, angular characteristics are converged at a 2D detector. This representation demonstrates when a white LED has a COA issue (bluish light going upward and yellowish light going downward) the two tinted light rays fall on the same pixel of the detector in addition to the surface-normal light ray and the resulting image appears as somewhat averaged white. For the same reason, light polarization characteristics of a light source are not well reproduced at the image plane. b When a volumetric emitter is inspected, light from out-of-focus planes can create a glare in the image. This is simply because nothing limits light collection only to the focused plane. The confocal method is a conventional technique to limit light collection in the optical axis direction to only the vicinity of the focused plane by introducing a small aperture in front of a large-area detector or using a thin optical fiber at the imaging plane. The aperture stop (Fig. 5.9) is another convenient feature built in a microscope to suppress these issues

way that an eyepiece magnifies an image created by an objective lens, and an eyepiece can magnify not only an image but also an object by itself. Take an eyepiece off a microscope, flip it, and bring it close to an object. A photographic camera lens is convenient to obtain surface-normal imaging, as it has a stop built in. A telephoto lens may be chosen to gain a large working distance. The f -stop ( f for the focal length, equivalent to the aperture stop) provides various f -numbers; that is, various effective lens diameters. For example f /8 corresponds to 7° of the apex angle (NA ∼ 0.06). Optical fibers are also subjected to limited collection angles due to their TIR

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Fig. 5.9 Schematic representation of the principle of the aperture stop (AS) in a telecentric system. An aperture stop is a mechanically-variable (bladed diaphragm) aperture around the optical axis to constrain the light beam nearer to the optical axis, thus without restricting the field of view (FOV). The element that restricts the FOV is the field stop (not shown here). By utilizing the AS, aberrations are improved because the periphery of a lens contributes more to image distortion than the central portion of a lens. Stray light is also suppressed and image contrast improves. The cost paid is that the image becomes dimmer as collection/illumination angle (i.e., NA) narrows. Since the light beam is contained closer to the optical axis, it approaches to true surface-normal observation/illumination. The AS should be well aligned to the optical axis or the image gets distorted. The AS is typically built into the illumination side of commercial epi-illumination-type microscopes, not in the collection side

nature of wave-guiding. Their NAs are commonly in the 0.2–0.3 range, determined by core and cladding materials. On a separate note, a circular polarizer is sometimes used in measurements and imaging. This is to depolarize incoming light to a detector which may be polarization-sensitive. Another note—digital color imaging relies on built-in RGB color filters. Therefore the image color depends on the filter characteristics and on dynamic-range characteristics of the camera sensor unit used.

5.5

Fourier Optics

The theory of Fourier optics makes a nice contrast with geometrical optics: Fourier optics heavily considers the wave nature of light, i.e., diffraction and interference. As a consequence, the theory arrives at a different destination from that of geometrical optics (which included optical elements like lenses and apertures, and optical instruments like microscopes). A statement of Fourier optics is that the Fourier transform (FT) of an object is obtained as a far-field image as a result of diffraction and interference. We would like to see what is inside of this statement: How a physical phenomenon generates an optical image of a mathematical formulation.

5.5

Fourier Optics

5.5.1

131

Fourier Transform by Wave Diffraction and Interference

To commence the discussion, let us review the Fourier transform. Fourier series/expansion is a mathematical technique where any function can be constructed by a sum of multiple harmonic functions, i.e., the sine and cosine. For example, a square wave can be expressed as a sum of sine waves of various wavelengths with appropriate amplitudes. The fundamental harmonic defines the period of the square wave, and high harmonic components contribute to compose sharp edges. Fourier-transform (∼ ultimate Fourier expansion) of a single squarepulse wave is a sinc function, which describes the amplitude distribution over the wavelengths of constituting harmonics. Given Euler’s formula eiθ = cos θ + i sin θ , the comprehensive formulation of Fourier transform is written as  f(κ) =

+∞

−∞

f (x)e−iκ x d x,

(5.4)

f ( r )e−i κ ·r d r.

(5.5)

or in 3D,  f( κ) =

+∞ −∞

f is the Fourier transform of the original function f and x and r are space coordinates. We use the symbol κ (kappa) for the Fourier variable and reserve k for the source light as it soon follows. What is κ really? It is a coefficient to the original variable, and has a dimension of inverse length in the present case. It is a place holder until we find it explicitly. Some textbooks attach a constant like √1 in defining the Fourier transform Eq. (5.4) or (5.5), 2π which is just to balance the constants between Fourier transform and inverse transform. In the Fourier optics discussion, those constants are grouped together, so they are not of primary importance. Now, a plane wave is expressed as U = Ae−ikx where U is the field of the EM wave (either electric or magnetic)7 of amplitude A. The exponent is negative because the farther from the source, the older the phase is at a given moment (we will see it explicitly in Fig. 5.12). Then a spherical wave is U (r ) = A

e−ikr r

(5.6)

where r > 0, and r −1 indicates the radial decay. We can already see a similarity between Fourier transform and light propagation. We are ready to set up a virtual experiment where monochromatic light (a plane wave) passes a 2D object (e.g., a slit) perpendicularly, and propagating light is projected onto a screen. This experimental setup is sketched in Fig. 5.10. The incoming plane wave is merely 7 In Fourier optics imaging, what is experimentally observed is light intensity (of an interference

pattern) which is proportional to the square of the EM field. Therefore, the choice of the field is unimportant. For the same reason, constants and constant phase terms are not of major importance. Nevertheless, we will keep them in forthcoming equations for clear illustration of formulation.

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Fig. 5.10 A conceptual setup of a diffraction experiment. Source light propagates in the +z direction. g(x0 , y0 ) is an object, e.g., a slit, an array of apertures, or a monochromatic photograph. The distance between the object and the screen is R. Note that the lateral coordinates (x0 , y0 ) and (x2 , y2 ) are used as the space coordinates and also as the variables

to actuate the setup by defining a single wavelength. A spherical wavelet starting at (x0 , y0 ) is e−ikr . (5.7) r It is Kirchhoff’s diffraction formula which states the field amplitude U2 at (x2 , y2 ) on the screen is a sum of spherical wavelets starting at every point of the object plane: U0 (r ) = g(x0 , y0 )A

i U2 (x0 , y0 ) = λ

 g(x0 , y0 )A

e−ikr d x0 dy0 , r

(5.8)

 where r = R 2 + (x2 − x0 )2 + (y2 − y0 )2 . λ is the wavelength of the EM wave. If the object is a slit, g(x0 ) = 1 between x0 = −x0 and x0 (so that 2x0 is the slit width), otherwise g(x0 ) = 0. Thus a slit has the same mathematical form as a single square pulse. In Eq. (5.8) we do not have to pay particular attention to the constant i/λ, which has been generated by the wave equation and Green’s theorem. We then apply an approximation to decouple x and y from z. First, 1/r ∼ 1/R so that 1/R goes outside the integral. This is a coarse approximation but it is acceptable (within the paraxial approximation, i.e., small-angle approximation). The phasor part (the exponent) requires a little more attention because that determines the interference. Using a binomial expansion, (x2 − x0 )2 + (y2 − y0 )2 , 2R which we call the Fresnel approximation. By inserting it into Eq. (5.8), r ∼ R+

(5.9)

5.5

Fourier Optics

133

U2 (x2 , y2 ) = =

i A −ik R e λR

i A −ik R − ik x2 2 +y2 e e 2R λR



  2





ik 2 2 g(x0 , y0 )e− 2R (x2 −x0 ) +(y2 −y0 ) d x0 dy0



(5.10)



ik ik 2 2 g(x0 , y0 )e− 2R x0 +y0 e R (x2 x0 +y2 y0 ) d x0 dy0 . (5.11)

This is the Fresnel diffraction regime and we will use Eq. (5.11) when introducing a lens in a later discussion. For a much farther distance, the quadratic term in the integral may be omitted, leading to what we call the Fraunhofer diffraction regime:

U2 (x2 , y2 ) =

i A −ik R − ik x2 2 +y2 2  e 2R e λR



ik

g(x0 , y0 )e R (x2 x0 +y2 y0 ) d x0 dy0 ,

(5.12)

where r has been approximated as x2 x0 + y2 y0 x2 2 + y2 2 − , (5.13) 2R R which we call the Fraunhofer approximation, applicable for a large distance. We realize that Eq. (5.12) resembles Eq. (5.4). Let us inspect Eq. (5.12) in detail. Viewing it as a Fourier transform, Fourier variables are − kxR2 and − kyR2 , and thus it is a 2D FT (we are glad to find the Fourier variables explicitly!). It is apparent that they are the space coordinates on the screen and mutually orthogonal. What does it mean? It means that the 2D FT of the object appears in the x2 –y2 plane. These Fourier variables are lateral components of the wavenumber k (which is still constant) and have been generated by diffraction. Therefore, the magnitudes of the lateral components have a direct correlation with the angle of diffraction as kxR2 = k sin θx ∼ kθx and kyR2 = k sin θ y ∼ kθ y . Then it must follow θx = xR2 and θ y = yR2 which are correct within the small angle approximation. These Fourier variables are sometimes called the spatial frequency. It can be said that Fourier optics convert the angle of diffraction to the displacement on the screen, so that phase shifts (a function of the diffraction angles) are mapped on the screen as a consequence of interference. Equation (5.12) can be concisely written as  i A −ik R − ik x2 2 +y2 2  kx2 ky2 2R , (5.14) e g − U2 (x2 , y2 ) = e ,− λR R R r ∼ R+

where g is the Fourier transform of g(x0 , y0 ). g(x0 , y0 ) has been drawn in Fig. 5.10 as a simple aperture-like function for the sake of illustration, but it can be as complicated as a monochromatic photograph with g(x, y) being its transmittance function. 2D FT certainly constructs such a photograph by a sum of an infinite number of harmonics. Why on earth does natural light propagation attain Fourier transform? The trick is, that we have chosen the Fourier transform. Fourier series/expansion is only one of many options to construct an arbitrary function. The same can be achieved using an infinite series of step functions, for example, but it would not be an appropriate choice, as a monochromatic EM

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wave is a harmonic function. Therefore, it should be stated that Fourier transform was chosen to represent the far-field diffraction patten, not the other way around. In the Fourier transform formulation, it is common that the symbol k is used as the Fourier variable, while we are using k as a constant wavenumber of the monochromatic light source. It is very helpful to be conscious that k in e−ikr is constant and this is not the wave expanding the function g(x, y). We have chosen the symbol κ for the Fourier variable to make this point clear, while some textbooks replace k with λ via λ = 2π/k. To rephrase, the plane 2π wave e−ikr = e−i λ r is only fuel for the experiment. It is the diffraction that expands the object g(x, y) via the lateral components (caused by the diffraction angle) of the constant k. Interference creates the intensity distribution on the screen. Another insufficiently-articulated condition is the monochromaticity: The 2D object g(x, y) must be described by the wavelength of interest. Imagine, if g(x, y) = 0 for blue light but g(x, y) = 1 for red light (e.g., a slit made of a pair of dichroic layers rather than metal blades), experiments using blue light and red light would lead to completely different results. Thus, g(x, y) appearing to the human eye is not necessarily the same as appearing to the experimental setup, which may use IR or microwave, or even X ray or electron beam. For this reason, Fourier optics become extremely powerful in microscopic scales we cannot readily observe via visible light. Crystals possess atomic periodicity which suits X-ray and electron diffraction techniques as seen in the study field of crystallography. The Fourier image (i.e., the diffraction pattern) is studied to understand the nature of 2D objects in various ways. Changing gears, we introduce the convolution for later purposes. Rewriting Eq. (5.10),    ik i A −ik R 2 2 g(x0 , y0 )e− 2R (x2 −x0 ) +(y2 −y0 ) d x0 dy0 e U2 (x2 , y2 ) = λR  ≡A g(x0 , y0 )h(x2 − x0 , y2 − y0 )d x0 dy0 (5.15) with ie−ik R − ik (x2 −x0 )2 +(y2 −y0 )2  . (5.16) e 2R λR Thus, the field (i.e., the image on the screen) is a 2D convolution between g(x0 , y0 ) and h(x2 − x0 , y2 − y0 ) =

h(x2 , y2 ) =

ie−ik R − ik x2 2 +y2 2  . e 2R λR

(5.17)

We can simply write U2 (x2 , y2 ) = g0 (x0 , y0 ) ∗ h(x2 , y2 )

U2 (κx2 , κ y2 ) = g0 (κx0 , κ y0 ) · h(κx2 , κ y2 ),

(5.18) (5.19)

5.5

Fourier Optics

135

where script letters indicate the Fourier transform of the original functions. The relation between Eqs. (5.18) and (5.19) is referred to as the convolution theorem. We call h the transfer function. h can actually be calculated from Eq. (5.17):

ik 2  ik 2  ie−ik R FT e− 2R x2 FT e− 2R y2 λR  

2Rπ − 2R κx2 2 2Rπ − 2R κ y2 2 ie−ik R = e 4ik e 4ik λR ik ik

h(κx2 , κ y2 ) =

=

(5.20)

ieik R 2Rπ i R κx2 2 +κ y2 2  e 2k λR ik iR

= e−ik R e 2k



κx2 2 +κ y2 2



.

(5.21)

In this way it becomes a simple multiplication. Note that the Fourier transform of Eq. (5.20) is that of the Gaussian function and again, κ’s are place holders. We use this transfer function later in the following lens discussion.

5.5.2

The Use of a Lens

The Fraunhofer approximation works well only for a large distance (for instance, several meters for a 1-µm aperture in the visible wavelength). At a far distance under this regime, neighboring spherical waves are propagating almost parallel towards a point (x2 , y2 ) with different phases caused by the path length difference. It is, nevertheless, quite a counterintuitive situation because a FT image is a result of interference of parallel beams converging at (x2 , y2 ), though parallel beams do not converge by definition. Yet, we know how from geometrical optics—use a focusing lens (NB for the wavelength of interest. In visible wavelengths it may be a convex glass lens but in TEM it is an electromagnetic lens). The use of a collimating lens makes the Fourier transform image “easier” to observe, within a shorter distance and with more controllability. From our knowledge of geometrical optics, collimated beams incident on a lens at various angles focus at different positions on the focal plane (refer to Fig. 5.7). First, let us find out what a lens does in Fourier optics. The lens medium with refractive index n retards light propagation and causes a phase delay, which is a function of lens thickness. A circular biconvex lens with spherical surfaces (radii of curvature are R1 and R2 for the two surfaces) has a lens thickness distribution t(x, y) described as t(x, y) ∼ t0 −

x 2 + y2 2



1 1 − R1 R2

,

(5.22)

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5 Optics

where t0 is the thickness at the lens center. With lens maker’s formula 1f = (n − 1)   1 1 − R1 R2 , the phase change caused by the lens (“the lens factor”) for a propagating wave is calculated (assuming that light rays propagate perfectly parallel to the axis for the sake of calculation) to be e−iknt0 e

ik x

2 +y 2 2f

.

(5.23)

Now let us place this lens immediately behind g(x0 , y0 ) in Fig. 5.10. We should use the Fresnel diffraction regime, Eq. (5.11), as the distance we will be looking at is not too far (it will be the focal length): i A −ik R − ik x2 2 +y2 2  e 2R · e λR     2  x 2 +y 2 ik ik 2 ik 0 2 f 0 g(x0 , y0 )e−iknt0 e e− 2R x0 +y0 e R (x2 x0 +y2 y0 ) d x0 dy0 , U2 (x2 , y2 ) =

(5.24)

and for R = f , i A −ik f − 2ikf x2 2 +y2 2  −iknt0 e e · e λ f  ik (x x +y y ) g(x0 , y0 )e f 2 0 2 0 d x0 dy0  kx2 i A −ik f − 2ikf x2 2 +y2 2  −iknt0 ky2 e e g − = e ,− . λ f f f

U2 (x2 , y2 ) =

(5.25) (5.26)

A part of the lens factor has wonderfully been cancelled (Eq. (5.25)). Thus, the lens has treated the setup the same as the Fraunhofer diffraction regime. A light ray passing the periphery of the lens has to travel longer in air than one passing the center of the lens, to arrive at the focal point. The phase change due to this air path length difference is cancelled wonderfully by the path difference in the lens medium. How amazing it is! This phenomenon can fundamentally be derived from Huygens-Fresnel principle or equivalently from Fermat’s principle. Note that the integral in Eq. (5.25) is the FT of g(x0 , y0 ), where the Fourier variables are − kxf 2 and − kyf 2 , as shown in Eq. (5.26). The real challenge is the next one, whose experimental setup is shown in Fig. 5.11. The object has been detached from the lens. By sending a monochromatic plane wave U (r ) = Ae−ikr from the left, the field is Ag(x0 , y0 ) at (x0 , y0 , 0) from which a spherical wavelet starts to propagate. The field in front of the lens, U1− (x1 , y1 ), is a sum of all these spherical wavelets starting at z = 0: U1− (x1 , y1 ) =

i λ

 g(x0 , y0 )A

e−ikr1 d x0 dy0 r1

(5.27)

5.5

Fourier Optics

137

Fig. 5.11 A lens arrangement for Fourier optics. Although the calculation is begun with an arbitrary distance d between the object and the lens, as conventionally done in most textbooks, d will be set the focal length of the lens, f . The focal length is used because of beam collimation. This optic is telecentric and another lens can cast a real image farther down in z

with r1 =



d 2 + (x1 − x0 )2 + (y1 − y0 )2 . Past the lens, the field U1+ (x1 , y1 ) becomes U1+ (x1 , y1 ) = U1− (x1 , y1 ) e−iknt0 e

ik

x1 2 +y1 2 2f

,

(5.28)

where the exponential terms are the lens factor, Eq. (5.23). U1+ (x1 , y1 ) of every point in the x1 –y1 plane contributes to the field at the x2 –y2 plane: i U2 (x2 , y2 ) = λ

 U1+ (x1 , y1 )

e−ikr2 d x1 dy1 r2

(5.29)

 with r2 = f 2 + (x2 − x1 )2 + (y2 − y1 )2 . We again disentangle x–y and z using the Fresnel approximation and r11 ∼ 1f and r12 ∼ 1f . Rewriting Eq. (5.29),

i λ i = λ i = λ =

  (x −x )2 +(y −y )2 −ik f + 2 1 2 f 2 1

e U1+ (x1 , y1 ) d x1 dy1 f   x x +y y x 2 +y 2 1 −ikd −ik x2 22+yf 2 2 ik 2 1 f 2 1 −ik 1 2 f 1 U1+ (x1 , y1 )e e e d x1 dy1 e f   x x +y y 1 −ik f −ik x2 22+yf 2 2 −iknt0 ik 2 1 f 2 1 U1− (x1 , y1 )e e e d x1 dy1 e f  kx2 1 −ik f −ik x2 22+yf 2 2 −iknt0 ky2 , e e U1− − e ,− f f f

U2 (x2 , y2 ) =

i λ



(5.30) (5.31) (5.32) (5.33)

which is the same as Eq. (5.26) but FT{g(x0 , y0 )} replaced with FT{U1− (x1 , y1 )}. A part of the lens factor has again been beautifully cancelled. However, further substitution for the

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5 Optics

object g(x0 , y0 ) (Eq. (5.27) into Eq. (5.32)) would become a little cumbersome. Instead, the convolution theorem is commonly used to circumvent such direct substitution.

U1− (κx1 , κ y1 ) = U0 (κx0 , κ y0 ) · h(κx1 , κ y1 ) 

U1− −

kx2 ky2 ,− d d



= Ag(κx0 , κ y0 ) e−ikd e = Ag(κx0 , κ y0 )e−ikd e

id 2k

id 2k



κx1



2 +κ

y1

2

(5.34)



2    kx ky 2 − d2 + − d2

(5.35) .

(5.36)

d is the distance between the object g(x0 , y0 ) and the lens, which we set as f by the requirement of arguments in Eq. (5.33). Continuing on U2 (x2 , y2 ), 

i U2 (x2 , y2 ) = λ i = λ i = λ

kx

2 

id 2 + 1 −ik f − 2ikf (x2 2 +y2 2 ) −iknt0 2k f e e Ag(κx0 , κ y0 )e−ikd e e f  2  ikd A −ik f − 2ikf (x2 2 +y2 2 ) −iknt0 x2 +y2 2 e e g(κx0 , κ y0 )e−ikd e 2 f 2 e f    A −ik f −iknt0 − ik x 2 +y2 2 1− df e g(κx0 , κ y0 )e−ikd e 2 f 2 . e f

 ky2 2 f



(5.37) (5.38) (5.39)

And again for d = f (which has actually happened in Eq. (5.37)), i λ i = λ

U2 (x2 , y2 ) =

A −ik f −iknt0 e g(κx0 , κ y0 )e−ik f e f  kx2 A −i2k f −iknt0 ky2 . e g − e ,− f f f

(5.40) (5.41)

Thus, it has been shown that U2 is a 2D FT of g. There is a slightly more intuitive formulation. Let us consider only the x lateral displacement, as sketched in Fig. 5.12. The field U2 (x2 ) created by the radiation from a single point x0 is U2 (x2 ) = Ag(x0 )eikx2 sin θx .

(5.42)

The exponential term indicates the phase difference (a leading phase when the exponent is positive) with respect to the point x2 = 0 as indicated from Fig. 5.12. sin θx ∼ x0 / f can be understood in Fig. 5.12. Similarly for the perpendicular orientation y, which is orthogonal to x, the path difference is −y2 sin θ y . Collecting all point sources on the x0 -y0 plane,

5.6

Electron Optics

139

Fig. 5.12 A more intuitive way of understanding Fourier optics. The path difference with respect to x2 = 0 is −x2 sin θx . Accordingly, the phase difference is eikx2 sin θx , which is a leading phase. The same discussion applies to the y orientation. On the right of the figure is an enlarged sketch near the screen

 U2 (x2 , y2 ) =

i k (x x +y2 y0 )

Ag(x0 .y0 )e f 2 0  kx2 ky2 . = Ag − ,− f f

d x0 dy0

(5.43) (5.44)

To summarize, we have shown that light with phase information arriving at a lens is focused onto a focal plane with the phase information intact, from which a diffraction pattern is constructed by interference.

5.6

Electron Optics

At the university, I remember when the solid-state physics class taught students the reciprocal lattice, which to me seemed somewhat disconnected from other study topics and never showed up anywhere in my study area again. The reciprocal lattice finally reappeared in an advanced diffraction physics class in graduate school. In fact, the reciprocal lattice plays a central role in diffraction physics. As already seen in the TD discussion in Sect. 4.2, diffraction techniques are useful analytical methods in crystallography. In the present section we make a few remarks on the diffraction techniques in the context of optics. Transmission electron microscopy (TEM) and scanning electron microscopy (SEM) utilize electron beams steered by electromagnetic lenses (beam bending, collimating, focusing, etc.). These lens systems are called electron optics, despite not handling light or EM waves. An electron is a small particle (the classical electron radius is 2.8×10−6 nm), though it behaves as a wave (the duality), and thus is not able to resolve figures as small as itself in electron microscopy. Electrons are ejected from a gun made of LaB6 (low work function material = ease of electron ejection) via field emission and consequently accelerated by electric fields to acquire short wavelengths. A 10-keV SEM reaches 1.2×10−2 nm of electron

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5 Optics

wavelength. A 100-keV TEM accelerates electrons to 3.9×10−3 nm of wavelength, which is not yet quite as small as an atom. Even in an advanced 300-keV TEM, electrons acquire 2.0×10−3 nm of wavelength at 78% of the speed of light. Because of relativistic effects, their mass becomes 60% greater than the rest mass, hence it becomes harder and harder to accelerate them further. These high-speed electrons run through a sample crystal that has been prepared very thin, and get diffracted just slightly by atomic potentials which may be only several eV deep. Their finite wavelengths exert diffraction limits in TEM imaging. Electron optics suffer from aberrations as well. These facts determine magnification and resolution limits of an electron microscope in a similar way as in an optical microscope. When wavelengths become close to the scale of crystal lattices, both electron waves and EM waves interact intimately with crystal’s electric fields around atoms. By analyzing those waves after passing a semiconductor crystal, one can “see” the interior of the crystal. TEM uses electron waves (SEM is not a diffraction technique and only observes the object’s surface, not its interior), while an equivalent technique using EM waves is X-ray diffraction (XRD). The most common wavelength used in XRD is 1.54×10−1 nm from a copper target. When an EM wave is incident on a crystal lattice, atoms are shaken by the incoming electric field and reradiate EM waves causing interference (as a lattice is a periodic array of atoms), known as the Laue diffraction. Constructive interference (as described by Bragg’s law) creates high-intensity lines (called “streaks”) from a planar crystal. An experimental example is the reflection high-energy electron diffraction (RHEED) often equipped on a molecular-beam epitaxy (MBE) tool. From a 3D crystal, diffraction constructs a pattern of high-intensity dots arranged in a reciprocal lattice geometry. TEM and XRD charts typically presented as characterization results are slices of a 3D reciprocal lattice, where Fourier transform exhibits its great power to back-construct a real-space lattice of the sample crystal. Diffraction physics is a vast field of study in itself and we will have to let dedicated books e.g., by Fewster8 and Humphreys discuss this topic further.

5.7

Further Reading

• Balanis CA (2012) Advanced engineering electromagnetics, 2nd edn. Wiley, New York • Born M, Wolf E (1999) Principles of optics, 7th edn. Cambridge University Press, Cambridge • Fewster PF (2003) X-ray scattering from semiconductors, 2nd edn. Imperial College Press, London

8 In 1999 Philips Analytical (later became PANalytical) introduced a versatile XRD instrument called

the X’Pert MRD (standing for Materials Research Diffractometer) that made all asymmetric and skewed geometries readily accessible and thus became very popular in the III-nitride research community.

References

141

• Hummel RE (2011) Electronic properties of materials, 4th edn. Springer, Dordrecht • Humphreys CJ (1979) The scattering of fast electrons by crystals. Rep. Prog. Phys. 42:1825

References 1. Chemours (2019) Ti-Pure titanium dioxide for coatings. C-10416-2. https://www.tipure.com/fr/-/ media/files/tipure/legacy/titanium-dioxide-for-coatings.pdf Accessed 4 Dec 2022 2. Cich MJ, Aldaz RI, Chakraborty A et al (2012) Bulk GaN based violet light-emitting diodes with high efficiency at very high current density. Appl Phys Lett 101:223509 3. Labsphere (2017) Technical guide integrating sphere theory and applications. PB-16011-000 Rev.00. https://www.labsphere.com/wp-content/uploads/2021/09/Integrating-Sphere-Theoryand-Applications.pdf Accessed 4 Dec 2022 4. Masui H, Nakamura S, DenBaars SP (2007) Analytical light-ray tracing in two-dimensional objects for light-extraction problems in light-emitting diodes. Appl Optics 47:88 5. Taniyasu Y, Kasu M, Makimoto T (2007) Radiation and polarization properties of free-exciton emission from AlN (0001) surface. Appl Phys Lett 90:261911

Eight-Page Introduction to Semiconductor Basics

This appendix introduces elementary science of semiconductors to those who have not been exposed much to semiconductor basics. Following discussions are what semiconductor engineers may assume people already know, regardless of what one’s technical background may be.

A.1 Formation of Semiconductor Crystals When we say a “crystal,” that is a solid having periodic atomic structure. In other words, atoms are positioned in a crystal in a very well ordered manner. Sapphire is an electricallyinsulating crystal. A metal is a crystal with high electrical conductivity. A semiconductor crystal is somewhat in between: A crystal where we can change electrical conductivity artificially. The opposite of a crystal is an amorphous material, e.g., glass, where atoms are randomly positioned with respect to each other. Therefore, there is no such a thing as “crystal glass,” in material science. We are mostly interested in crystals, and only occasionally in amorphous materials. A solid composed of micro-sized crystals of the same kind is called polycrystalline, which is barely encountered in our discussions. There are hundreds of crystal structures identified; among those there is a special geometry that we are particularly interested in. That is the close-packed structure. There are two types of close-packed structure: One is cubic, called the diamond or zincblende structure, and the other is hexagonal, called the wurtzite structure. The Si crystal belongs to the diamond structure, while the zincblende structure is a two-constituent cubic, e.g., GaAs. GaN has a wurtzite structure. In either case, each atom constructing a semiconductor crystal is surrounded by eight outer-shell electrons (valence electrons). Atoms are always happy being surround by eight electrons due to their nature of closing the outmost shell. A set of two valence electrons are shared with a neighboring atom, and an atom has four neighbor atoms. 2D analogy of this atomic construction is illustrated in Fig. A.1. Shared electrons © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

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Fig. A.1 2D schematic illustration of close-packed structure: Si on the left and GaAs on the right. Two valence electrons (black circles) between two atoms form a covalent bond. In a compound semiconductor like GaAs, atomic bonds include some character of ionic binding due to charged nuclei, in addition to covalent binding. In 3D, each atom has a tetrahedral coordination with four pairs of valence electrons and the tetrahedral coordination leads to close-packed structure

provide atomic bonding (covalent bond) between two atoms, because both atoms want to keep the shared two electrons with them for, again, their nature of filling the outermost shell. A Si atom has four valence electrons; thus, Si atoms can form a nicely close-packed crystal by sharing their valence electrons. There would be no excess electrons nor lack of electrons. Since all electrons are rigidly held in covalent bonds, there is nothing that can carry current through a pure Si crystal. Thus a pure semiconductor is an insulator. The distance between atoms determines the lattice constant, which is defined as a unit length of a cubic or hexagonal unit cell of a crystal. A broader type of semiconductor is the compound semiconductor. A compound semiconductor consists of two or more atomic elements while fulfilling the above condition about valence electrons. A pair of Group-III and Group-V elements have eight valence electrons in total, thus are able to share two valence electrons with each neighbor atom, just like a Group-IV semiconductor. A compound semiconductor consisting of two elements is called a binary semiconductor or alloy. A ternary alloy can be made by replacing some of Ga atoms with another Group-III element, e.g., In, while fulfilling the condition about valence electrons. Although, because Ga and In are different in atomic size, a larger In atom pushes (applies a stress/force to) surrounding atoms. Surrounding atoms try to stay where they are, but are forced to displace themselves (displacement is the strain), resulting in local crystal lattice deformation, which appears as a change in lattice constant at the macroscopic scale. Displaced atoms are not very comfortable, but not uncomfortable enough to destroy their atomic bonds (= to create defects). An analogy for large-atom substitution: a sumo champion sits next to you in a standard cabin of a fully-seated aircraft. Although you try to stay

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in the middle of your seat, you may feel a force (i.e., stress) one way and end up shifting sideways (i.e., strain) a little bit so as to make yourself as much as comfortable. With several sumo wrestlers in an aircraft cabin, they may want to cluster together to establish their own comfort zone. This is the In segregation that we saw in Chap. 4. A characteristic property of semiconductors is the bandgap, which is a consequence of periodic atomic structure interacting with electrons. When a number of atoms are brought together, their atomic orbitals (electrons of an atom sit in atomic orbitals) become energy bands. An energy band consists of multiple orbitals spreading in an energy width. Two energy bands may or may not have an energy overlap. When there is no overlap, there is a finite energy gap where there are no states or no “chairs” for electrons to stay. This energy gap is called the bandgap. In semiconductors, below the bandgap is the valence band, which is filled with valence electrons. Above is the conduction band where no electrons exist, though electronic states (i.e., empty orbitals) are there.

A.2 Controlling Electrical Conductivity in a Semiconductor How can we change electrical conductivity of a semiconductor material? When an appropriate impurity atom is inserted in a Si crystal network by substituting a Si atom, we can change the number of electrons in a crystal, as schematically shown in Fig. A.2. A Group-V atom (e.g., P) has five valence electrons so that there will be an excess electron in a crystal, loosely bound to its native impurity atom which has only weak electrical attraction coming from its positively-charged nucleus. A small amount of energy is sufficient to liberate the excess electron from its nucleus into the conduction band to be physically mobile in the crystal (Fig. A.2). Thermal energy of room temperature (∼26 meV) is typically sufficient: A dopant (intentionally-inserted impurity atom) is in fact chosen to be ionized (to release an excess electron) at room temperature. Otherwise, an impurity atom not releasing a mobile charge is a deep-level impurity, which is generally unfavored. A mobile charge (called a carrier) can carry a current, thus an insulator has become a conductor, an n-type semiconductor (n for negative) in this case, and the impurity is called a donor (donating an electron). A typical range of carrier concentration (or density) is 1 × 1017 –1 × 1019 cm−3 . The number of atoms in a crystal is on the order of 1022 cm−3 , thus doping is typically much less than 1%. A pure (or rather “ideal”) undoped semiconductor (called an intrinsic semiconductor) has neglegibly low carrier concentration (1 × 1010 cm−3 in Si) insufficient to flow a useful amount of current. In a real undoped semiconductor ∼ 1 × 1016 cm−3 of carrier concentration may exist due to unintended impurities and/or spontaneously (thermodynamically) occurring crystal defects. Thus an undoped semiconductor is sometimes referred to as an unintentionally doped semiconductor. We can do opposite, creating a lack of a valence electron (called a hole) in a crystal. A p-type (p for positive) semiconductor is obtained by doping a Group-III atom in a Si crystal. The impurity is called an acceptor. A hole possesses a positive charge and can accept

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Fig. A.2 Concept of doping. A Group-V impurity atom (a donor, e.g., P) provides an excess electron (left). A Group-III impurity atom (an acceptor, e.g., Al) causes a lack of valence electron (right). The former is an n-type and the latter is a p-type Si. Thermal energy from room temperature is sufficient to liberate the excess electron and the lack of electron getting filled by one of surrounding valence electrons, so that they become mobile, as a free electron and a hole, respectively. In corresponding energy diagrams (bottom), a donor level E D is close to the conduction band edge E C , and an acceptor level E A is close to the valence band edge E V . Note each E D and E A are spatially localized to their native atoms. Hence a charge (an electron or a lack of electron) energetically locating within a bandgap is not mobile, and thus not contribute a current flow. An open circle indicates a lack of valence electron or a hole

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an electron from surrounding valence electrons by thermal energy. Consecutive action of receiving electrons one after another makes a hole wander, thus a hole also carries a current. In the case of a III-V compound semiconductor, dopant selection requires a little more attention. A Group-II element sitting in a Group-III site makes the crystal p-type. A GroupVI element substituting a Group-V atom makes the crystal n-type. Group-IV elements are not obvious which of the two constituents they would substitute, therefore experimental confirmation is required. Si is known to be a donor in GaAs.

A.3 The pn Junction and Built-In Potential A single semiconductor would not do much as an electronic device, but a pn junction, or n-type and p-type semiconductors in contact with each other, can generate useful functions. A single-junction device is called a diode, while a transistor consists of two pn junctions. A junction between a single type of crystal is called a homo junction, and that with two dissimilar crystals is called a hetero junction. A pn junction is formed in LEDs by layering, or by depositing a p-layer on an n-layer, or vice versa. Historically, pn junctions were made by impurity diffusion or implanting methods which did not achieve abrupt junction profiles compared to modern layering methods based on epitaxy. When a pn junction is formed, majority carriers (electrons in an n-type and holes in a p-type) move towards the opposite sides of the junction due to concentration gradient. This is because an n-type semiconductor has excess electrons and a p-type is lacking electrons (in excess of holes). Electrons move from the n side to the p side when the two semiconductors come in contact, such that electrons’ energy is constant everywhere in a pn junction system. This situation may be envisioned as a leveled water surface of two connected lakes of different depths. Electrons’ energy “surface” is leveled everywhere across the junction at thermal equilibrium. This electrostatic energy of electrons is drawn as an energy diagram (band diagram) shown in Fig. A.3. At thermal equilibrium (i.e., no external disturbance other than constant and stable thermal energy) the energy “surface” is called the chemical potential in general, and in semiconductor science it is called the Fermi level, always denoted with a symbol E F . The Fermi level is rigorously defined as an energy level of half probability of statistical electron existence. Because of this statistical definition, a Fermi level can be within a bandgap. Because of this carrier relocation, a potential step is created between the two sides, called the built-in potential or potential barrier, as shown in Fig. A.3. The height of the built-in potential depends on doping levels. Along with the potential barrier, there is created a region where an electric field exists. This region is called the space-charge layer or depletion region because carriers are depleted by the electric field created by ionized dopants (immobile “space” charges). We can vary the height of the built-in potential by applying electrical bias externally. Accordingly, the width of the depletion region changes. When the potential barrier is lowered, carriers start flowing towards the opposite side of the junction, creating

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Fig. A.3 Formation of a pn junction. The vertical axis is electron’s electrostatic energy (against positively-charged nuclei) and the horizontal axis is the position. When an n-type and a p-type semiconductors are brought in contact, free electrons flow spontaneously from an n-type to a p-type to be the same energy level. The energy level is expressed by the Fermi level E F , thus E F must agree between the two types after contacting. Far from the junction both types are unaffected and stay neutral. As a result, the conduction-band edge E C and the valence-band edge E V change around the junction forming a potential step called a built-in potential or potential barrier. The region where the built-in potential spans is called the depletion region or space-charge layer, since carriers are depleted due to the built-in electric field (a tilted band) created by the spatially-fixed charges of ionized dopants. It can be calculated that the built-in field changes quadratically (for constant doping profiles) as a function of the spatial coordinate. Note E F is different from either E D or E A , although they may coincide accidentally

various useful effects. When the barrier is made higher by externally biasing, not too much happens for LED’s interest because only insignificant current can flow due to the increased barrier height. A space-charge layer is a confrontation of opposite charges and acts as a capacitance, slowing high frequency response of a pn junction.

A.4 Current Flow: Carrier Transport and Recombination A moving carrier is a current. By reducing the potential barrier by an external positive bias (the n-side to a negative voltage; equivalently the p-side to a positive voltage), carriers start moving (electrons from n to p; holes from p to n) by their concentration gradient. An analogy is that water is pushed around from an end of a garden hose lying flat on the ground. The current caused by this mechanism is called the diffusion current. Diffusion current is dominant in a positively-biased pn junction (Fig. A.4) and the phenomenon of majority carriers going into the opposite side is called carrier injection or current injection. Another way to move carriers is by creating an electric field. An analogy is water on a slope. The current flow by this mechanism is the drift current, although it is only a conceptual difference from the diffusion current. In either case, moving carriers feel some resistance in a crystal, thus their mobility (defined as a carrier velocity per unit electric field) is finite. The amount of current is proportional to both the number of carriers and the average velocity of carriers. In a pn junction of conventional diodes, injected carriers become minority carriers (electrons in a p-type and holes in an n-type) in the opposite side of the junction. They find so many opposite carriers (i.e., majority carriers) and thus are given plenty of chances of recombination, as implied in Fig. A.5. This is pair annihilation: A free electron readily finds a lacking covalent bond and settles there. An injected hole is immediately filled by one of

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Fig. A.4 By applying positive bias (in a band diagram, lowering the p-type side and raising the n-type side) electrons and holes are provided from the external circuit through metal contacts into the n- and p-type neutral regions, respectively, causing carrier diffusion by concentration gradient thus a diffusion current. Quasi-Fermi levels (“quasi” since nonequilibium) are typically drawn in the neutral regions (regions without electric fields). E F = E Fn − E F p corresponds to the applied voltage. Further biasing may generate electric fields in the neutral regions due to limited conductivity of semiconductors, as drawn on the right, and carriers gain a drift component. Quasi-Fermi levels in this case may not be trivial

Fig. A.5 Carrier injection in a conventional diodes and an LED. Conventional diodes do not assume recombination within the depletion region; all recombination occurs in neutral regions. LEDs are designed for recombine to occur in/near the depletion region where an active layer is placed. Carriers that pass the active layer and reach the opposite side are undesired, referred to as current overflow

majority-carrier electrons. Farther from the junction, there are no injected minority carriers left. In the case of LEDs, carrier injection into opposite sides is suppressed by design; rather both carriers are injected into a common active region prepared within the depletion region where recombination is designed to take place. To enable efficient electron exchange between a semiconductor device and an external electrical circuit, metal is deposited on a semiconductor as a contact. Choice of a metal is important as explained in Figs. A.6 and A.7: An ohmic contact is a good metal/semiconductor interface where current flows without being obstructed, while a Schottky contact creates a potential barrier at the interface. These contact properties are commonly described using the work function and Fermi level. A metal of larger work function is required for a p-type semiconductor so that electrons can more easily fall into the metal. We always express that holes are injected from a p-contact; in reality, the p-contact sucks out valence electrons from a p-type semiconductor. A metal of a small work function is appropriate for an n-type because electrons fall from the metal into an n-type. Sometimes metal-semiconductor interfaces are annealed for alloying to achieve better interfacial electrical properties.

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Fig. A.6 Energy diagrams of metal-semiconductor junctions. A shaded area indicates metal’s energy levels filled with electrons. In ohmic contacts electrons can easily move into (p-type) or out of (n-type) a metal. In Schottky contacts electrons need extra energy (typically obtained from external bias) to move into (p-type) or out of (n-type) a metal. Work functions of metals are tabulated in handbooks. The work function is the energy required to extract an electron from a metal to free space (vacuum level). These energy diagrams have ignored the band bending around the interface for the sake of simplicity: A band bending is caused by electron relocation across an interface to establish a system Fermi level as explained in Fig. A.7

Fig. A.7 Formation of a Schottky barrier in an n-type in contact with a metal. To inject electrons into an n-type semiconductor, electrons have to overcome a Schottky barrier in the case of Schottky contact (under a positive bias; when raising the metal side and lowering the n-type side in the band diagram, the Schottky barrier stays tall). Band bending near the interface is caused by electrons relocating from the n-type to the metal upon contact until the Fermi level is established. Metal has much more mobile electrons than a semiconductor, and is barely affected by contacting a semiconductor

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A.5 Further Reading • Streetman BG, Banerjee SK (2014) Solid state electronic devices, 7th edn. Pearson, London

Hole Generation and Transport in Mg-Doped GaN

Current is carried by the two types of carriers: Free electron and hole. They are generated by ambient thermal energy in doped semiconductors. Magnesium in GaN is a unique dopant in this respect, as it resides deep in the bandgap compared to other common dopants of semiconductors and its ionization energy is much greater than the thermal energy of room temperature. As a consequence, p-type GaN suffers from thermal ionization. It is a good exercise to evaluate this dopant as an acceptor.

B.1 Thermal Ionization of Mg in GaN With an assist from Fig. B.1 we can write out ionized acceptor concentration N A− and hole concentration p as  EF − EA and = N A exp kT   EV − E F p = N V exp , kT

N A−



(B.1) (B.2)

respectively. The Boltzmann distribution function has replaced the Fermi-Dirac function in the above equations for the reason that E A − E F and E F − E V will be found sufficiently greater than kT . Let the doping level be N A = 1 × 1020 cm−3 . Mg is 200-meV deep: E A − E V = 200 meV. Effective DOS at the valence band edge, N V , of GaN is 4.1 × 1019 cm−3 . We can readily understand N A− = p as charge neutrality. Solving these equations for RT (kT = 26 meV) gives us p = 1.4 × 1018 cm−3 . The Fermi level E F is calculated to be at 88 meV above the valence band edge E V . E F is farther from the acceptor

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

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Appendix B: Hole Generation and Transport in Mg-Doped GaN

Fig. B.1 Four energy levels in p-type GaN. The difference between the valence band edge E V and the acceptor level E A is 200 meV for Mg. The conduction band edge E C is far in term of energy, and participation in carrier concentration is negligible under thermal equilibrium. As a result, E F resides between E A and E V . Drawn on the right is the Fermi-Dirac probability function associated with the −1   F . When the exponent is a few times greater band diagram on the left, F(E) = 1 + exp E−E kT than unity, the Fermi-Dirac function becomes almost the same as the Boltzmann function

level E A because N V < N A . This computation exhibits the mechanism of holes generated at such a low ratio. N A is approximately 100 times greater than p at RT. 1 × 1020 cm−3 is a very high impurity concentration that potentially disturbs fluent carrier movement in a crystal. If an InGaN LED is cooled in a laboratory to the liquid-nitrogen temperature 77K, p = 1.7 × 1013 cm−3 : Here would practically be no holes. This is carrier (hole) freezeout, where we cannot thermally generate sufficient carriers for our needs at extremely low temperature. The coldest temperature on earth is approximately 190K. This temperature gives p = 1.2 × 1017 cm−3 , which is a reasonable carrier concentration, therefore an InGaN LED would work.

B.2 Current Carried by Holes Even if we secure sufficient concentration of holes, flowing a current is a different issue. We need to move carriers to generate a current. A current flow in a material is a sum of electron contribution and hole contribution. In terms of current density J , J = q(nve + pvh )

(B.3)

where q is the unit charge and n and p are the free-electron and hole concentrations, respectively. Their velocities ve for electrons and vh for holes are average velocities parallel to the current flow (carrier collisions cause random motions of carriers. Perpendicular components

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Fig. B.2 Current continuity in a pn device, Je = Jh . Free electrons carry current in the n-type region and holes carry an equal amount of current in the p-type region, thus nve = pvh . Near the metallurgical junction recombination occurs as a change of the majority carrier. The rate of recombination must be equivalent to the current

Fig. B.3 Two regimes of carrier velocity are shown. In the linear regime the carrier velocity changes linearly as a function of the electric field. The slope is the carrier mobility. This is ohmic because current increases as external voltage increases. In the saturation regime carrier velocity becomes constant. Any additional electric field cannot accelerate carriers further because carriers already feel strong resistance in a crystal

to the current flow have no contribution). Typically one of the two terms of the righthand side in Eq. (B.3) overwhelms (i.e., majority carrier, Fig. B.2) the other. In a pn device, freeelectron current is predominant in the n-type region and hole current is in the p-type region, and recombination occurs in the middle. Current continuity must be maintained across the device. At 77K, current would have to be carried by free electrons in the GaN:Mg layer as well, likely injected from the n-side, i.e., via carrier overflow, rather than recombination. The magnitude of current flow can be increased by moving carriers (under the same carrier concentration) faster. There are two regimes in carrier velocity as indicated in Fig. B.3. One is linear with the electric field. Carriers are accelerated by the electric field E: v = μE where μ is called the mobility. This is an ohmic regime because current increases linearly as applied voltage (i.e., electric field) is increased. The other regime is saturation at a constant maximum carrier velocity regardless of stronger E. Carriers cannot be accelerated indefinitely because

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they feel resistance in a crystal. For a p-GaN, for 1 A per 1-mm2 chip (100 A/cm2 ), vh ∼ 450 cm/s. It is believed that this is within the linear regime. Hole mobility reported is in the range of 10–20 cm2 V−1 s−1 , hence the field is calculated to be approximately 45 V/cm, which is 1 mV over a 200-nm thick p-GaN layer. This is a rather weak field strength not graphically recognizable on a band diagram.

C

Origin of the Turn-On Voltage

The turn-on voltage is understood as the voltage at which forward current starts flowing through a pn junction. It is typically depicted visually on a linear I –V chart like Fig. 2.18. Yet this can be subjective to observer’s perception as well as scales of chart axes. The turn-on is more explicitly when carrier injection begins across the pn junction, and a larger-bandgap material naturally requires a greater voltage in consideration of the band diagram. We discuss how this fact can be incorporated in the diode equation.

C.1 Voltage Aspect: Quantization of Injected Minority-Carrier Concentration To rationalize the turn-on voltage in the diode equation, the key idea is quantization of minority-carrier concentration. The law of mass action n p p p = n i 2 requires very low minority carrier concentrations as already seen in Sect. 4.5. This is equivalent to saying that the built-in voltage in a pn junction is established such that the law of mass action is satisfied in the two neutral regions. Before beginning our discussion, the reader is informed that all symbols have been tabulated at the end of this chapter (Tables C.1 and C.2). For current to flow, minority carrier (e.g., free electron) injection from one side into the other can be found by using the Boltzmann distribution. The Boltzmann function is mathematically a smooth continuous function but appears to be a collection of step functions when probability is very low far at its tail, corresponding to carrier granularity. This situation is illustrated in Fig. C.1. Taking a GaAs homojunction here as a computation example, assume p p = 1 × 1018 cm−3 so that n p = 4 × 10−6 cm−3 at thermal equilibrium in a dark environment. That is, there are practically no free electrons in the p-type neutral region of the junction, provided the physical dimensions are sane, approximately speaking less than 1 mm. To inject one free electron into © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

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Fig. C.1 Quantization of the Boltzmann tail. E 1 is the energy at which one minority carrier is statistically generated in a pn junction. n ∗p is the unit of minority carrier quantization. NEDOS is the effective density of states of the relevant band

the p-type side, the potential barrier needs to be reduced to E 1 in Fig. C.1. Using a relation n p = Nc exp[−(E cp − E F )/(kT )] this potential barrier reduction is formulated as below, E 1 being E cp in this case (Fig. C.2), by introducing a quantization unit n p ≡ n ∗p which may be one free electron in a p-type region: E cp − E Fn = kT · ln

Nc . n ∗p

(C.1)

To envision generation of a minority carrier, we take a concentration of one in a 100 µm cube (or a slab of 1 mm2 × 1 μm). That is 1 × 10−6 cm3 . Consequently Eq. (C.1) is computed to be 26.7kT = 0.69 eV at 300K. E cp − E cn = 0.65 eV is the remaining potential barrier at the beginning of carrier injection: Injection potential Vinj . Vinj is the potential barrier to allow one free electron to be generated in the p-type. Similarly for pn , Vinj is computed slightly larger 29.7kT due to a dissimilar effective density of states and majority carrier concentration. We can summarize that Vapp = (E Fn − E F p )/q = Vbi − Vinj = 0.68 eV is the turn-on voltage. Rewrite Eq. (C.1) to generalize Vinj : q Vinj = kT · ln

NEDOS . pn∗

(C.2)

It typically happens around 0.5–0.8 eV (depending on the material and doping levels) at room temperature. The turn-on voltage may be approximately generalized to be E g /q − Vinj when quasi-Fermi levels are close to the associated band edges or equivalently majority carrier concentration is similar to the associated NEDOS . In the Ge diode that the original diode equation was derived on, no clear turn-on existed as the bandgap was 0.7 eV. Room-temperature thermal energy is therefore sufficient to overcome the built-in voltage, in addition to the diode equation being irrespective of physical dimensions by itself.

Appendix C: Origin of the Turn-On Voltage

159

Fig. C.2 Band diagram of GaAs homojunction a at equilibrium and b under positive bias. Carrier concentration is in units of cm−3 . The law of mass action leads to the minority carrier concentration being a very small number analytically, and zero practically. In both parts the quantized function from Fig. C.1 is superimposed to assist the idea of quantization

C.2 Current Aspect: Experimental Observation of the Turn-On Experimental instruments have own lower detection limits. Therefore, very small currents cannot be measured, and a measurable current appears on an instrument when the amount of current has reached the level of its lower detection limit. Let us estimate the smallest current using a Si junction. In general, the saturation current is given as [3]

 Is = q

pn

Dp + np τp

Dn τn

.

(C.3)

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Appendix C: Origin of the Turn-On Voltage

Using this equation for our estimation of one minority carrier in each neutral region (say, 1 mm3 ) at a positive bias, which is n ∗p = pn∗ = 1 × 106 [cm−3 ],

 ∗

I =q

pn∗

Dp + n ∗p τp

Dn τn



= 5.3 × 10−12 [A/cm2 ]

(C.4)

= 0.053 [pA/mm2 ]. This is an extremely small current. Let us assume our experimental instrument can reliably measure down to 0.5 nA, and then it would require 10 000 times higher injected carrier concentration to detect a current flow. Hence we take n ∗p = pn∗ = 1 × 1010 [cm−3 ], leading to Vinj ≈ 0.56 [V]. Vbi = 0.84 [V] can be calculated for n n = p p = 1 × 1017 [cm−3 ]. Conse-

Table C.1 Symbols p p , nn

Majority carrier concentration

n p , pn

Minority carrier concentration

n ∗p , pn∗

np and pn at quantization

Nc , Nv

Effective DOS of the band

NEDOS

Effective DOS of the relevant band

E cp , E cn , E vp , E vn

Band-edge energy levels

E F , E F p , E Fn

Fermi level and quasi-Fermi levels

E1

Quantization energy level

Eg

Bandgap energy

Vinj

Injection potential [V]

Vbi

Built-in potential [V]

Vapp

Applied voltage [V]

Vturnon

Turn-on voltage [V]

k

Boltzmann’s constant

q

Unit charge

T

Absolute temperature

I

Current

Is

Saturation current

I∗

Current at turn-on

D p , Dn

Diffusivity of carriers

μ p , μn

Carrier mobility

τ p , τn

Carrier lifetime

Appendix C: Origin of the Turn-On Voltage

161

Table C.2 Material parameters. kT (300K) = 26 meV Parameter

Ge [1]

Si [1, 2]

GaAs [1]

E g [eV]

0.74

1.11

1.42

n i [cm−3 ] Nc [cm−3 ] Nv [cm−3 ]

1 × 1013

2 × 1010

2 × 106

1 × 1019

3 × 1019

4 × 1017

6 × 1018

1 × 1019

8 × 1018

Diffusivity [cm2 /s]

− −

D p = 11.1 Dn = 2.77D p

− −

Lifetime [μ s]

− −

τ p = 0.012 τn = 4.3

− −

quently, the turn-on (as in Fig. 4.14) of a Si diode may be observed around 0.84 − 0.56 ≈ 0.3 V in the laboratory. All above are about the injection current (caused by recombination in neutral regions). For the recombination current (current caused by recombination within the depletion region), slight corrections in computation are necessary.

References 1. Mishra UK, Singh J (2008) Semiconductor device physics and design. Springer, Dordrecht 2. Sah CT, Noyce RN, Shockley W (1957) Carrier generation and recombination in p-n junctions and p-n junction characteristics. Proc IRE 45:1228–1243 3. Shockley W (1949) The theory of p-n Junctions in semiconductors and p-n junction transistors. Bell Sys Tech J 28:435, Eq. (4.13) therein

D

Wave-Particle Duality and the Wavefunction

The energy of a photon is given as hc/λ (Planck-Einstein relation) where h is the Planck constant, 6.63 × 10−34 [J·s], and c is the speed of light, 3.00 × 108 [m/s]. By converting the unit of energy from joule [J] to electronvolt [eV] by dividing by the unit charge q = 1.60 × 10−19 [C] and taking the unit of wavelength λ as nanometer [nm], our memorized number 1240 appears. In general, matter has wave character, called the de Broglie wave. The de Broglie wavelength is given as h (D.1) mv where m and v are the mass and velocity of a matter, respectively, and the product mv is the momentum. Momentum of a wave is equal to hk/(2π ), with k being the wave number. For electrons, their wave nature is described by the wavefunction. The wavefunction  is a mathematical operation and not physically tangible. Yet  2 is the probability of finding an electron (thus nonnegative values) and experimentally observable. Note where  = 0, probability is also zero. To describe an electron’s wave nature in a crystal rather than a vacuum box, the Bloch wave comes in as discussed in Sect. 4.2 and in Appendix E. The significance of  changing its phase may be understood in Fig. D.1. When a wavefunction maintains a phase over two neighboring atoms, it is smoothly continuous and so is the probability  2 . In contrast when a wavefunction changes its phase between two neighboring atoms, there must be a point of  = 0 where the probability is also zero (an electron will never be found there) and not smoothly continuous. λ=

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

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Fig. D.1 Schematic of s-electron wavefunctions  over two neighboring atoms: a in the same phase and b in different phases. Small circles indicate nucleus positions. When  maintains the same phase as in a it is smoothly continuous, whereas b is opposite, generating a  = 0 point in between (pointed by an arrow). The same analysis applies to transverse p-orbitals. Longitudinal p-orbitals have the opposite characteristic as seen in Appendix E

E

Crystal Momentum and the E–k Diagram

The E–k diagram is regarded by some as a difficult chart to read, simply because k is not readily intuitive. k indicates the wave number, the inverse of wavelength of the electron wave in a crystal. In most cases in optoelectronics, we treat the electron as an elementary particle, but here the electron is treated as a wave (the duality). Via a quantum mechanical relationship p = k, p (thus k, since  is a universal quantum constant) is what is called the crystal momentum.

E.1 Electron Wave in a Crystal An electron behaves like a wave due to the duality and the wave nature is called the wavefunction. The electron wave is confined in a piece of crystal: Electrons do not escape from a crystal spontaneously. The Bloch theorem describes an electron in a crystal as a product of a local wavefunction around an atom, u, (that is approximately an atomic orbital of an electron e.g., an s- or a p-orbital) and an envelope wavefunction:  = u · sin kx.

(E.1)

 is the wavefunction of an electron. The envelope function is sin kx indicating a wave belonging to an entire crystal with x being a spatial coordinate. The wavenumber k comes from the envelope function and thus k implies how an electron belongs to a crystal. A simple example of a 1D crystal is shown in Fig. E.1. Electrons do not spill out of a crystal; there is zero probability of an electron at edges of a crystal, leading to the possible longest wavelength λ = 2L, where L is the length of a crystal (Fig. E.1a). A comprehensive discussion should be 3D where k simply becomes a 3D vector. k = 2π/λ and L is typically very large (almost infinite) compared to atomic © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

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Appendix E: Crystal Momentum and the E–k Diagram

distances, therefore k ∼ 0. On the opposite side, the shortest meaningful wavelength is 2a where a is the lattice constant (a repetitive unit of a crystal). This is depicted in Fig. E.1b.

Fig. E.1 Electron waves in a crystal as a result of the Bloch theorem. a The envelope function of the wavefunction  has λ = 2L (k ∼ 0). L is the length of a crystal. Small white circles indicate atoms in a crystal which is drawn as a gray block. The lattice constant a is insignificant under a condition L  a. b  has λ = 2a (k = π/a). c Neighboring s- and p-orbitals when k ∼ 0. White and gray coloring of the drawing indicates differences in the wavefunction phase. d Neighboring sand p-orbitals when k = π/a

When k ∼ 0, all local functions around all atoms are in the same phase each other, as schematically shown in Fig. E.1c. The s-orbitals of all neighboring atoms are intimate (the wavefunction is nicely continuous), and so are the transverse p-orbitals. Note a p-orbital has a phase difference within, hence the longitudinal p-orbitals are different from transverse ones. Between two atoms, there is a phase change causing a position where the wavefunction becomes zero. This fact is an impactful difference from the above intimate binding. With k being nonzero, a part of a crystal becomes opposite in phase. For example when λ = L, half of a crystal is in the same phase and the other half is in the opposite phase with a point of zero wavefunction in between. When k = π/a the phase of the envelope function changes at every atom, as schematically drawn in Fig. E.1d: This situation is inverse of when k = 0. For the s- and transverse p-orbitals  becomes zero between two atoms (no probability of electron existence) which is not energetically favored by an electron. Instead, the longitudinal p-orbital is now forming intimate bonding between atoms.

Appendix E: Crystal Momentum and the E–k Diagram

167

E.2 E–k Diagram In E–k diagrams k = 0 is named the  point. At the  point the whole crystal is in the same phase, which the reader can envision like a calm waveless ocean. Moving away from the  point, the ocean becomes agitated and wavy. The largest k plotted in an E–k diagram is π/a. Atomic arrangement of a crystal is direction-dependent; this is expressed in an E–k diagram using multiple panes. Low-index directions are named: X for [100] and L for [111] at π/a  where a  is a relevant repetitive distance. This is how the E–k diagram expresses the k vector. Electrons are subjected to the exclusion principle as an elemental particle called a Fermion. When two or more atoms of the same type are brought close, any two electrons cannot have an identical state (one energy state can hold up to two electrons with spin-up and spin-down). As a consequence, electron orbitals shift sightly in energy from each other and start piling up in the energy scale, and with many atoms they form an energy band. Thus a band is in a sense a collection of electron orbitals. As electrons climb up in an energy band, they must gain finite k (momentum). This energy-momentum relationship is described in the E–k diagram. The crystal momentum (i.e., the wavelength belonging to a crystal) is what puts electrons in higher energy states. If an electron was in a vacuum box, E = p 2 /(2m) so that the E–k diagram would only show a simple parabola. In a crystal an electron is not as free as in vacuum because of the periodic potential wells created by positively charged nuclei (See Appendix G.3). That is the reason why E–k diagrams exhibit unique features, e.g., a bandgap. Approximately speaking, in direct-bandgap materials at the  point, s-orbitals become the lowest energy (the conduction band edge, all s-orbitals in the same phase) and p-orbitals become the highest energy (the valence band edge). An indirect-bandgap material has the lowest conduction band energy off the  point. That implies that an electron wave nests better in an indirect-gap crystal when k > 0. For example, Si has the conduction band edge along slightly before the X point. The reader should try looking at the atomic arrangement of Si (100), and imagine whether conduction-band electrons like to be near the X point.

F

Entropy and Thermal Carrier Distribution

Entropy appeared as a very abstract notion in thermodynamics. Modern science often interprets it as a measure of randomness, which may be an even more confusing interpretation to those who try to understand entropy in thermodynamics and solid-state physics, where thermal carrier distribution is intimately tied to entropy. Many (including the author) seem to have confronted similar confusions about entropy and the confusion or ambiguity may last for many years, while various types of introductory articles have been written on entropy since everyone has a slightly different difficulty from others in grasping the concept of the entropy. Below is the author’s attempt to approach the notion of entropy in terms of the solid-state physics that we are interested in. Thermal carrier distribution in energy, e.g., Boltzmann distribution, is a form of entropy. Thermal physics analyzes how thermal carrier distribution arises, and reveals what the entropy means in solid-state physics.

F.1 Classical View Qualitatively speaking, the entropy is a mechanism for a system to store thermal energy. For example, a piece of metal stores given thermal energy as electron distribution (i.e., electrostatic potential energy). Gas in a cylinder with a piston stores a given thermal energy as velocity of gas molecules (i.e., kinetic energy). This fact was implied in classical thermodynamics as the thermodynamic identity: dU = T d S − pd V .

(F.1)

Equation (F.1) expresses the idea of thermodynamics: a combined field of thermal and mechanical work. U is the internal energy stored in the system. T is the temperature, S is the entropy, p is the pressure, and V is the volume. Equation (F.1) explains that a change © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

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in internal energy consists of thermal energy (the first term) and mechanical energy (the second term). The second term is negative because internal energy increases when volume decreases (e.g., a piston is pushed into a cylinder to compress a cylinderful of gas). Let us consider the mechanical term first, and then interpret the thermal term by analogy. When one squeezes a block of metal using a vise, applied work is stored in the metal block as a part of its internal energy via volume shrinkage (or equally, displacement) under a certain pressure. Force (pressure times area) times distance (displacement) is work, which is energy, as we know. The stored energy can be released to push back the vise by the same displacement. Thus, energy was stored in the system as the displacement (the metal block was shrunk when storing the energy) at a pressure. The same principle applies to gas in a cylinder. Now consider the thermal work. When thermal energy is put in a metal block by heating it up, the metal block needs to store the given energy somewhere but not by changing its volume (no mechanical activity must be involved. Ignore thermal expansion for this thought experiment). Thermodynamics physicists back then believed a system had something that could store thermal energy based on their experiments and mathematical efforts, and that “something” was named the entropy. The physicists worked to reveal the tangible significance of the entropy, but were unable to provide an explicit answer what the entropy physically was. Today we know thermal energy is stored in a piece of metal by excited electrons and in gas in a container by velocity of gas molecules. One might say “pressure of gas increases in that case” but no one would be able to tell the increase of internal energy from system appearance until d V has become nonzero (i.e., a mechanical work has participated). In mechanical displacement, the pressure is a proportionality constant. When pressure is high the system is less disturbed (smaller displacement) by mechanical addition of energy. The temperature is another proportionality constant. When temperature is high the system is less disturbed (smaller entropy change) by thermal addition of energy.

F.2 Quantum Mechanical View Modern understanding of entropy is a measure of quantum states accessible to a system. Combined with the qualitative description above, entropy measures the number of quantum states accessible to a system when internal energy (here considering thermal energy only) is specified. In the Boltzmann distribution, when internal energy is increased, carriers are redistributed in such a way as to store the added thermal energy. We take a look at a simple example of a 10-electron system (Fig. F.1). When internal energy is the lowest (the lowest temperature), all ten electrons have zero energy. When temperature is raised and the system gains one unit of energy (U = 1), this energy is stored in the 10-electron system by one of electrons escalating to an ε = 1 state (ε is the number of energy units that an electron has). These ten electrons are different electrons, but we cannot distinguish the difference. Any of ten electrons is eligible, so that there are ten combinations of achieving a U = 1

Appendix F: Entropy and Thermal Carrier Distribution

171

Fig. F.1 A table showing ways of energy split and the number of combinations of a 10-electron system. Ten electrons are labeled A through J (for the example purpose, electrons are fundamentally indistinguishable to us!) between which the externally-provided thermal energy U is split. When temperature (i.e., thermal energy) is zero, U = 0; hence all electrons are at the ε = 0 state (ε is the energy of the electron). When U = 1 at a raised temperature, one of ten electrons can (must) have the energy, and there are ten combinations of assigning the one energy unit over ten electrons. When U = 2 there are two ways to assign the energy: Two units to one electron and one unit to two electrons. The numbers of combinations are 10 and 45, respectively. System behavior becomes more continuous when a system is larger (many electrons) and the granularity seen in this 10-electron example weakens

system. When the system has acquired three units of energy by increased temperature, there are three ways of achieving a U = 3 system. One electron can take all three units and there are ten combinations of achieving this. Two electrons can split the three energy units, and there are 90 combinations of achieving this. Three electrons can share the three energy units evenly, and there are 120 combinations to achieve this. The system must be at one of these 10 + 90 + 120 states, and the third way (the 1-1-1 split) is the most likely that one would find when observing a U = 3 system. The observer may encounter the second way (the 2-1 split) once in a while due to statistical energy exchange between the ten electrons. But it is unlikely to find an ε = 3 electron. When the system gains four energy units in a hotter environment, the most likely is the 2-1-1 energy split. Here we find a primitive Boltzmannlike distribution: more lower-energy electrons and less higher-energy electrons, although it is still granular because of the small number of electrons in this example. When the number of electrons is very large like 1017 to 1023 per cm3 and U  ε, the granularity disappears and a distribution function appears smooth like the Boltzmann function. In such a large system, the most likely state of the system (that is the thermal equilibrium state) is far more probable than the next likely state of the system, leading to a consequence that one can only observe the most likely state of a system however long he waits. The above discussion finds that the entropy, or measure of the number of accessible states by electrons in a system, is related to the probability of energy split between available electrons, and to the most likely state of the system. Phonons (thermal lattice vibration) stores

172

Appendix F: Entropy and Thermal Carrier Distribution

energy as well, and their contribution may be discussed separately. The above discussion applies to thermal equilibrium, and systems in transition are excluded.

E.3 Logarithmic Definition In the above 10-electron system at U = 1, the number of combinations, g, is 10. Entropy σ is defined as σ = loge g.

(F.2)

Therefore σ (U = 1) = 2.30. At U = 0 (zero temperature), g = 1 and thus entropy is zero. The logarithm is a monotonic function and convenient for treating large values. If we bring a clone of the 10-electron system at U = 3 and consider it with the original system at U = 1, the total accessible states of the combined system (the number of combination) is 10 × 120 = 1200. In terms of entropy, log 10 + log 120 = 2.30 + 4.79 = 7.09. Addition is more natural than multiplication when combining multiple systems. If one considers two identical blocks of metal, entropy doubles. And if it is three, entropy triples. If one uses g instead, g needs to be squared and cubed, respectively. What may be more annoying is when one cuts a block into three equal pieces. Entropy becomes one third per piece but g would need to be a cube root. No one prefers a cube root to a division by three, unless he has an electronic calculator. Electronic calculators were not available to physicists two hundred years ago. Thus, the logarithm definition is convenient. Next we put the two systems in contact so that thermal energy flows between the two. Each system comes to U = 2 after establishing thermal equilibrium, and as a whole system U = 4 over 20 electrons. g (of the most probable energy split) becomes 4845, hence σ = log 4845 = 8.49. It is apparent that entropy has increased by the thermal energy flow. Modern physics has shown experimentally and theoretically that the entropy as defined above agrees with the classical definition. In statistics and information theory, the concept of entropy is commonly explained using black and white balls or cards printed 0 or 1 on. There each “particle” has only two possible states (and the base of Eq. (F.2) is taken to be 2 instead of e, but this only changes the scale of the logarithm), whereas a thermally excitable electron has an unlimited number of possible states. Such a two-state particle system is unintuitive for our purposes. Nevertheless, a twostate particle system becomes relevant when electrons are in a magnetic field. An electron will be in one of two states: spin parallel and antiparallel to the field.

F.4 Further Reading • Kittel C, Kroemer H (1980) Thermal physics, 2nd edn. W. H. Freeman and Company, New York

G

Density of States and Quantum Effect

Because two electrons cannot be in an identical state (Pauli’s exclusion principle), there can only be up to two electrons (spin-up and spin-down) occupying a k state, and the next electrons have to take the next available (greater) k states of slightly higher energy. Band diagrams are drawn in terms of energy, so that there is an interest in knowing how many electrons can reside at an energy level, or more accurately, within a small energy range. This notion is called the density of states (DOS), a function of electron energy in a crystal. In low-dimensional structures like QWs, quantum effects are predicted by electron’s wave nature. This is the common “potential well” problem encountered so frequently in quantum mechanics and solid-state physics.

G.1 Computing DOS It is not so difficult to calculate DOS as a function of k. One considers an electron in a box and finds using its wave nature, that allowed k values are equally spaced in the k space (that is, k = ik0 where k0 is a unit of k and i is an integer in a 1D k space. It is readily generalized to a 3D k space). After some careful math operations, DOS per unit volume, n(k), can be written as n(k) =

2 (2π )3

(3D)

(G.1)

which is constant in terms of k, as a natural consequence of the equally spaced k. To convert to a function of energy E, again after some careful math operations, n(E) for a 3D crystal per unit volume is obtained as

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

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m √ 2m E (3D) (G.2) π 2 3 where m is the mass of the particle and √  is equal to h/(2π ): h is the Planck constant. Here the important consequence is the E dependence. Crystals are large (k can be ∼ 0 and is practically continuous), therefore n(E) is a smooth function as shown in Fig. G.1a. When one wishes to know the existence of electrons (or holes) at an energy level, it is calculated as a product of DOS (the number of available states, i.e., the number of “chairs” available for electrons) and probability given by an appropriate statistical function (e.g., a Boltzmann function, how likely an electron sits in a “chair”). The total number of carriers is then obtained by integration over energy in the band. There is a convenient notion of “effective DOS” defined at band edges, whose values are tabulated in literature. Carrier concentration is simply calculated as NC · exp[(E C − E F )/kT ] (NC is the effective DOS for a conduction band edge) involving no integration. The theoretical background of the effective DOS, as a partition function, comes from a thermal physics discussion. The interested reader should consult the reference introduced in Appendix F for further information. n(E) =

G.2 In Low-Dimensional Structures In a QW, one of three dimensions (i.e., thickness) is not so large compared to lattice constants. It is said that an electron is “confined in one dimension.” In such a case k ∼ 0 does not apply. k starts from a state depicted in Fig. G.1b and takes explicitly discrete values. This confined k creates quantum effects. One of these is that the lowest energy becomes slightly higher than E C and so does in the valence band (for holes). The lowest electronic transition energy is then greater than E C − E V . DOS changes as well. The other two dimensions are still large (unconfined), therefore a QW can be considered as a 2D structure. For a 2D crystal n(E) is calculated to be m (2D) (G.3) π 2 and it is constant in terms of E. Because of discrete states of confined k, the DOS becomes a sum of step functions as drawn in Fig. G.1c, and its effect can appear in a luminescence spectrum as discussed in Sect. 4.2.2. The confined k can increase only up to 3 or 4 in a real QW since potential wells are finite (barrier layers are not infinitely high). Higher-energy electrons than the barrier will not be confined. Although the lowest quantized level is denoted symbolically as k = 1, it is actually k = π/a where a is the width of the potential well (i.e., QW thickness). In our earlier discussion on the E–k diagram we saw k = π/a also, where a was the atomic periodicity. The reader is advised not to be confused. This square potential well problem is referred to as a “particle in a box” problem. Note that the spacing of quantized energy levels is not n(E) =

Appendix G: Density of States and Quantum Effect

175

√ Fig. G.1 a DOS changing as E representing a 3D crystal. E = 0 is typically taken at a band edge. Because a square root is a slowly varying function compared to a statistical function in solid-state physics, it is often treated as nearly constant. b A schematic cross section of a thin crystal (e.g., QW) with k (envelope function) sketched in. Here “thin” means that L  a does not hold (see Appendix E). c DOS of a thin crystal. At E(k = 1) DOS step-increases (the first confined k is allowed; the in-plane k component ∼ 0), then maintains a constant value towards higher energy as the in-plane k component increases. When k = 2 becomes allowed at a higher energy, additional DOS is available and maintains constant again due to increase of the in-plane k component with k = 2. The graphical √ envelope function is proportional to E as shown by a broken curve. This fact confirms it is 1D quantization of a 3D crystal. d A model of DOS of InGaN. Near the band edge (E = 0) DOS deviates from Eq. (G.2) representing localized states of In segregation

equal. This is a consequence of the potential well profile, which is “square” in this case. A parabolic potential well leads to equally-spaced energy levels as we see in Appendix H below. Indium segregation (Sect. 4.1) can be considered as higher-dimension carrier confinement. DOS of these localized state ensembles is modeled qualitatively as sketched in Fig. G.1d rather than quantitatively computed. This is because spontaneously-formed

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Appendix G: Density of States and Quantum Effect

confinement has distributed energy depths and physical dimensions, rather than tightlycontrolled as in intentionally-created QDs.

G.3 Use of the Particle-in-a-Box Problem When a QW is repeated in an active layer we call it a MQW. From another aspect of interest, it is also called a superlattice, because it consists of a periodic array of identical (i.e., depth and thickness) unit structures superimposed on an atomic lattice. Behavior of a particle in a superlattice may be analyzed as a connected particle-in-a-box problem. The Kronig-Penney model is based on the same notion of connected potential wells applied to an atomic lattice. The atomic potential is a Coulomb potential (proportional to the inverse of distance), rather than a square well, but it was found to be adequate to derive fundamental properties like generation of a bandgap in a crystal. A set of two square potential wells illustrates energy splitting of two electrons. When an electron is in a two-well system with different phases between the two wells,  tends to be pushed out towards higher potential energy for  to avoid the area of  = 0, compared to the case where two wells have the same phase. As a result, the former has to have slightly higher energy than the latter. This two-square-well model resembles a diatomic molecule, e.g., H2 . Computation of an E–k diagram is an extended problem of the same type.

G.4 Further Reading • Davies JH (1998) The physics of low-dimensional semiconductors, Cambridge University Press, Cambridge

H

Phonons and Their Role in Electronic Transitions

The phonon is a quantization of lattice vibration; however, this may not be a readily intuitive concept. Lattice vibration only takes discrete frequencies that are separated by an equal step; hence, each step can be considered as a particle. It is a “quasi” particle, because this particle cannot be taken out into free space by itself. The phonon is not a major player in modern LED devices, yet it does have a role to play in solid-state luminescence in general.

H.1 Notion of the Phonon Lattice vibration (primarily caused by thermal energy) can be modeled as mechanical vibration of mutually connected masses and springs. This is another potential well problem repeatedly encountered in solid-state physics, where the potential profile is a parabola, as in Hooke’s law in mechanics. The striking finding from this model is that frequency of lattice vibration (thus energy as exhibited in Eq. (H.1)) can only take discrete values and the values are equally spaced. Hence, it can be expressed as 1 E = (n + )ω (H.1) 2 where n is an integer (the number of phonons) and ω is the base angular frequency. This vibration model is called the harmonic oscillator and one-half represents the so-called zeropoint energy. Since vibration energy has an equal step (ω), each step can be considered as a particle (quantization). This particle (quasiparticle) is the phonon. When a crystal lattice is thermally excited, phonons are born. In thermal equilibrium at zero temperature, no phonons exist. Because masses can vibrate in 3D, there are transverse (T) and longitudinal (L) modes in relation to the propagating direction of a vibrational wave. When a crystal is ionic, a © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

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Appendix H: Phonons and Their Role in Electronic Transitions

Fig. H.1 Electronic transition in an indirect-bandgap material explained in an E–k diagram. When an electron at the conduction band edge of k = 0 makes a transition, it exchanges momentum with phonons and releases its energy by arriving at the valence band edge at k = 0. The released energy is approximately that of the bandgap because phonons have only small energy but large k

neighboring pair of positively-charged and negatively-charged atoms can vibrate in phase or out of phase. The former are called acoustical (A) and the latter are optical (O) modes. In LT PL, LO phonon replicas (spectral lines) are commonly observed.

H.2 In Electronic Transitions In an indirect-bandgap material, phonons assist electron-hole recombination by compensating their momentum difference (Fig. H.1). In a wave picture, when an electron makes a transition from k > 0 of the conduction band to k = 0 of the valence band, it momentarily shakes the lattice, and then the lattice goes back to equilibrium vibration after a short while. Phonons play a great role in phosphor luminescence to generate spectrally broad emission as implicitly discussed in Sect. 4.3. Each electronic transition has a different degree of phonon interaction depending on its local crystallographic/chemical environment, causing a spread in photon energy collectively.

H.3 Further Reading • Kittel C (1996) Introduction to solid state physics, 7th edn. Wiley, New York

Spontaneous and Piezoelectric Polarization Fields in III-Nitrides

As discussed in Chap. 4, the wurtzite structure causes electrical polarization in a crystal. Spontaneous polarization originates from a geometrical deviation of a wurtzite crystal from ideal geometry. Ideal hexagonal close-packed (hcp) structures possess the ratio of lattice constants c/a = 1.633. Relaxed III-nitride binary crystals are naturally squashed along the c-axis, hence c/a < 1.633. Positive changes (Ga ions) are shifted towards the −c direction (N-face) and negative charges (N ions) towards the Ga-face. This is the origin of spontaneous polarization. Piezoelectric polarization is added on top of spontaneous polarization when external stress causes internal strain (i.e., further deformation of crystal lattice). A GaN/InGaN QW is a direct example where InGaN is compressed in plane and elongated in the polar c direction as a result. Instructive examples of polarization field calculation are given below.

I.1 Spontaneous Polarization Field in GaN A thought experiment involves a film of a c-plane GaN crystal. It exhibits spontaneous polarization that creates an electric field within the film. Using Poisson’s equation, the internal electric field E is expressed with spontaneous polarization Psp and permittivity ε (= ε0 · εr ) and calculated from the numbers given in Table I.1 as E=

−Psp = 3.9 × 108 [V/m]. ε

(I.1)

This is an enormous electric field. For example, air breaks down at 3.0 × 106 V/m. With this strong of a field one may wonder—when a GaN film becomes thick, how large of a potential difference can it withstand? An explanation is that when the potential difference has reached the bandgap, electrons start moving and screen the polarization field (Fig. I.1). © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

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I

180

Appendix I: Spontaneous and Piezoelectric Polarization Fields in III-Nitrides

Table I.1 Polarization related values. For an alloy, Vegard’s law may be applied GaN

InN

AlN

a [Å]

3.189

3.533

3.112

c [Å]

5.185

5.760

4.982

εr

8.9

15.3

8.5

E g [eV]

3.4

0.7

6.2

Psp [C/m2 ]

−0.029

−0.032

−0.081

2 31 e31 – C C e33 [C/m ]

−0.68

−0.90

−0.86

C31 , C33 e31 , e33

See the Morkoç book p. 39 (C13 = C31 ∵ symmetry) See the Morkoç book p. 82 ( is used as a symbol for e)

33

Fig. I.1 GaN has strong spontaneous polarization along its c-axis causing an internal field. Because of the field, E C at one end and E V at the other end reach the same energy level (E F ) in a crystal thicker than 9.2 nm. This means electrons in the valence band move from one end to the other end to screen the polarization field. For a thick layer the internal field becomes practically zero

A theoretical calculation gives the thickness for this to happen as 9.2 nm. Therefore, there is practically zero field within a thick GaN layer.

I.2 Polarization Fields in a Strain InGaN QW We follow here a calculation given by Morkoç.1 Let us imagine a QW: c-plane InGaN sandwiched by thick pseudomorphic GaN layers. That is, relaxed GaN layers stressing an

1 Morkoç H (1999) Nitride Semiconductors and Devices, p 70–73. Springer Berlin, Heidelberg.

Appendix I: Spontaneous and Piezoelectric Polarization Fields in III-Nitrides

181

InGaN layer to cause strain in it. The internal electric field can be calculated by taking following steps. 1. Find in-plan strain according to In composition, then out-of-plane strain via Poisson’s ratio (or via stiffness coefficients). 2. Find piezoelectric polarization of InGaN from the strain using piezoelectric constants. 3. Add spontaneous polarization of InGaN and calculate the internal electric field as a sum.

In-plane strain (⊥ ) is calculated from lattice mismatch (x x =  yy ) between GaN and InN as forced lattice constant – relaxed lattice constant 3.189 − 3.533 = . (I.2) relaxed lattice constant 3.533 Because of biaxial stress, ⊥ = x x +  yy resulting in −0.195, which is multiplied by the In composition x. Or, a lattice mismatch value of an Inx Ga(1−x) N alloy may be obtained directly by using Vegard’s law2 on the lattice constant instead. Piezoelectric polarization is given as Ppe = {e31 −

C31 e33 }⊥ . C33

(I.3)

It is computed as a function of in-plane strain where the proportionality constant is e31 − (C31 /C33 )e33 . e31 and e33 represent piezoelectric polarization induced by in-plane and out-of-plane strains, respectively, in units of C/m2 (charge per unit area). A set of stiffness coefficients C31 /C33 (unitless) converts the in-plane strain to the out-of-plane strain. These four numbers are material specific and mutually tied (in the study field of continuum mechanics), hence they are put in one term in the equation. The Morkoç computation uses −0.90 C/m2 for InN, and (−0.195x) × (−0.90) = +0.176x. It is not stated explicitly in the reference whether –0.90 can be used for an InGaN alloy. It may be more reasonable to apply Vegard’s law to the proportionality constant (equivalently to all C coefficients and e constants).3 The reference finally computes that piezoelectric polarization for x = 0.15 (∼414 nm) is 0.176 × 0.15 = 0.0264 [C/m2 ] = 1.65 × 1013 [unit charges per cm2 ]. Before we take the computation further to the final field strength, we revise this number to 0.0208 C/m2 by the use of Vegard’s law to the piezoelectric proportionality constant –0.713 C/m2 to reflect the Ga/In ratio. Spontaneous polarization of In0.15 GaN is –0.0295 C/m2 via Vegard’s law. The total polarization charge comes to –0.0086 C C/m2 . Using Poisson’s equation (Eq. (I.1)) with Vegard’s law on the dielectric constant, the internal field is obtained to be 990 kV/cm. 2 See Glossary. 3 Romanov AE, Baker TJ, Nakaura S et al. (2006) Strain-induced polarization in wurtzite III-nitride

semipolar layers. J Appl Phys 100:023522.

182

Appendix I: Spontaneous and Piezoelectric Polarization Fields in III-Nitrides

Fig. I.2 Schematic drawing showing polarization components in a QW structure for a case of x = 0.25. Values have been computed using Vegard’s law. Spontaneous polarization (indicated in the top half of the drawing) is negative with respect to +c, so that the electric field (defined to be from a positive charge to a negative charge as indicated by a thick arrow) due to spontaneous polarization points +c. Piezoelectric polarization (indicated in the bottom half of the drawing) changes the polarity when strain becomes large reflecting elongation in c. Resulting polarization is the sum of the two. Note that the middle QW experiences extra polarization from surrounding GaN barriers

This is still significantly strong, but the direction of the field is the same, towards the Gaface. This direction is the same as the built-in field, so the internal field is weakened when positive bias is applied on a pn junction. For x = 0.25 (∼455 nm emission), the internal field becomes –650 kV/cm; the field direction has turned over. This internal field of the opposite direction to the built-in field causes devastating QCSE in a positively-biased pn junction. For example, this field strength creates 0.16-eV band edge shift over a 2.5 nm thick QW. The above computation did not count charges outside the QW; it may apply to a SQW given that spontaneous polarization of surrounding GaN layers has been screened (Sect. I.1). For a MQW however, GaN barrier layers may maintain unscreened spontaneous polarization. By adding Psp of GaN at a well-barrier interface (Fig. I.2) the internal field becomes –2340 kV/cm for x = 0.15, pointing to the N-face. Despite the apparent complexity of the calculation above, all these computations appear streamlined once put in a computer spreadsheet.

J

The ABC Model for Recombination Dynamics

The so-called ABC model is widely used in analyzing carrier recombination dynamics. Its name reflects the model equation for the recombination rate R, R = An + Bn 2 + Cn 3

(J.1)

with n being the carrier (free-electron) density in a recombination volume. A, B, and C are coefficients to the linear, square, and cube terms, respectively, and are also experimental fitting parameters. This analysis method has recently been gaining popularity to elucidate droop phenomena in InGaN materials. The ABC formulation had been used in evaluation of LD loss mechanisms and the equation was explicitly written out for InGaN LEDs in 2007.4 Various modifications of the model have been proposed since. The present appendix provides a compact description of the basic idea of the ABC model.

J.1 Formulation Under High-Injection Approximation If all possible carrier interactions in carrier relaxation across a bandgap are considered, a rate equation −dn(t)/dt = R may be written fully as R = An n + A p p + Bnp + Cn n 2 p + C p p 2 n (+ possible higher polynomial terms) (J.2) (where A’s, B, and C’s are coefficients) by placing every possible permutations between n and hole density p at every polynomial order. The linear terms may be single-carrier relaxation, the square term implies pair annihilation, the cube terms are three-particle processes, 4 Shen YC, Mueller GO, Watanabe S et al. (2007) Auger recombination in InGaN measured by

photoluminescence. Appl Phys Lett 91:141101. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

183

184

Appendix J: The ABC Model for Recombination Dynamics

and so forth. Higher-order terms are generally omitted because of the comparably lower probability of those multi-particle processes. The benefit of the ABC model comes from introducing appropriate approximations to establish a coarse picture of carrier recombination dynamics. The most popular (and almost universal) is the high carrier-injection (EL) or excitation-intensity (PL) approximation. It is considered “high” compared to carrier density at thermal equilibrium. If we write the carrier density under excitation, n = n 0 + n 1 (n 0 is the thermal free-electron density and n 1 is the excess electron density generated by excitation), n ≈ n 1 under high excitation. Similarly p ≈ p1 regardless of any intentional doping. Therefore Eq. (J.2) becomes R ≈ An n 1 + A p p1 + Bn 1 p1 + Cn n 12 p1 + C p p12 n 1 ≈ An 1 +

Bn 12

+ Cn 13

(J.3) (J.4)

with a fact n 1 = p1 by definition of electron-hole pair generation (either EL or PL). In experiments, what we may be able to observe is the net recombination rate rather than the total recombination rate. That is, the thermal generation rate G 0 , which is equal to the recombination rate at thermal equilibrium, R0 , by definition, is subtracted from the total recombination rate. Thus we can state the following using the intrinsic carrier density √ n i = n 0 p0 G 0 = R0 = An 0 + Bn i2 + Cn i2 n 0

(n-type)

(J.5)

(for the p-type, replace n 0 with p0 ). Hence the net recombination rate Rnet is Rnet = R − G 0

(J.6)

Rnet ≈ R

(J.7)

(∵ R  G 0 ).

This is good because n ≈ n 1 , which is proportional to excitation intensity. Therefore, an experimentally-measured recombination rate (typically a radiative recombination rate via measuring luminescence intensity) can directly be plotted by varying excitation intensity without worrying about thermal equilibrium values. By assigning NRR processes to the linear and cube terms of Eq. (J.4), this 3-term formulation readily describes experimental observations phenomenologically.

J.2 Curve Fitting of Steady-State Experiments A common way of plotting an experimental data set is to show EQE as a function of excitation intensity (under n 1 ≈ n),

Appendix J: The ABC Model for Recombination Dynamics

185

Bn 2 (J.8) G where G is the carrier generation rata under excitation, e.g., current divided by the unit charge in an EL experiment. Although it is experimentally difficult to quantify IQE, the ABC model Eq. (J.1) expresses IQE as ηEQE ∝

Bn 2 Bn 2 . (J.9) = G An + Bn 2 + Cn 3 The ABC model is therefore known as an intuitive and powerful tool to probe recombination efficiency, potentially including IQE. Various theoretical and experimental efforts have been made around the concept of the ABC model. Equation (J.9) may be differentiated to find a carrier density n max for the maximum IQE ηIQE,max . By calculating dηIQE /dn = 0 for the maximum (empirically known that it would not be a minimum) of the IQE curve, ηIQE =

 Bn 2 (J.10) An + Bn 2 + Cn 3  Bn 2 1 2Bn − = (An + Bn 2 + Cn 3 ) (J.11) An + Bn 2 + Cn 3 An + Bn 2 + Cn 3 ≡0 (J.12)

dηIQE = dn



and discarding a solution n → ∞ as not physical,

Bn 2 2Bn

= 2 3 An + Bn + Cn n=n max (An + Bn 2 + Cn 3 ) ηIQE,max



n=n max

(Bn 2 )

= (An + Bn 2 + Cn 3 ) n=n max

(J.13) (J.14)

where  (prime) indicates differentiating by n. It is interesting to find ηIQE to reappear after differentiation. Another manipulation that has been done is that Bn 2 is proportional √ to detected luminescence intensity Idet . Consequently n ∝ Idet . The fact (or a feasible assumption) that G is proportional to excitation intensity Iexc allows us to rewrite Eq. (J.1) using experimental parameters and plot a set of experimental data as   3 Iexc = A1 Idet + B1 Idet + C1 Idet

(steady state)

(J.15)

where A1 , B1 , and C1 are another set of fitting parameters. By applying polynomial fitting this may be an experimental chance to determine IQE.

186

Appendix J: The ABC Model for Recombination Dynamics

Fig. J.1 Electroluminescence characteristics reported in a publication by A. David et al. The present plots (circle markers) have been produced by reading the data points graphically off from Fig. 12a of the original publication (the red markers indicate 130°C therein). J stands for the current density and ηEQE for the external quantum efficiency. A constant luminescence wavelength was reasonably assumed upon the present graphic production. a Proposed plot using Eq. (J.15) where the polynomial fitting has been applied (the solid line and the displayed equation). A good-quality fitting is confirmed in the entire excitation range. b Another presentation of the same data set that the power-law fitting has been applied (the solid line and the displayed equation). Systematic deviation is graphically visible at both ends of the fitting line due to the monotonic curvature of the data set

A fitting attempt using Eq. (J.15) is exhibited in Fig. J.1 using a data set reported by David et al.5 The attempt is compared to another common model of power-law fitting. Although the ABC model may be considered as a relatively coarse model with preceding approximations, better data fitting can be obtained than with other proposed recombination-dynamics models. Analytically, Iexc can be converted to n. Yet a fundamental difficulty is that n is likely a function of position, n(r). The above argument is valid when n(r) is nearly constant within a recombination volume (e.g., a QW without QCSE). Another aspect is that the ABC model does not account for carrier transport. Unless electrically injected carriers (i.e., current) are fully captured by and confined within a recombination volume in an EL experiment, analytical conversion from Iexc to n may introduce significant errors.

J.3 Time-Decay Analysis Since the ABC model is formulated as a rate equation, time-varying experiments can be analyzed using the model; for example, a PL decay experiment where pulsed excitation 5 David A, Young NG, Lund C,et al. (2020) Review—The physics of recombinations in III-nitride

emitters. ECS J Solid State Sci Technol 9:016021.

Appendix J: The ABC Model for Recombination Dynamics

187

is applied and time-resolved luminescence is recorded after an excitation pulse turns off. Under a nonsteady condition, dn 1 (J.16) = An 1 + Bn 12 + Cn 13 . dt Time-varying carrier density may be found in the following way. When excitation is low enough that the cube term has little contribution, −

dn 1 = An 1 + Bn 12 dt   dn 1 = −dt n(A + Bn 1 )   1 n1 = −t + k0 ln A A + Bn 1

(J.18)

 n 1 (t = 0) . A + Bn 1 (t = 0)

(J.20)

−

(J.17)

(J.19)

where k0 is k0 =

1 ln A



Equation (J.19) can be plotted on a spreadsheet as is to evaluate the dependence of the carrier density transient on the two coefficients. Or it can be analytically solved for n 1 (t) as n1 =

A k1

e At

(J.21)

−B

where k1 is k1 =

A +B n 1 (t = 0)

(J.22)

and n 1 → 0 as t → ∞. Next, when excitation is so high where the linear term has little contribution, dn 1 = Bn 12 + Cn 13 dt   dn 1 = −dt n 12 (B + Cn 1 )   C B + Cn 1 1 = −t + k2 + 2 ln − Bn 1 B n1 −

(J.23) (J.24) (J.25)

where k2 is k2 = −

1 C + 2 ln Bn 1 (t = 0) B



B + Cn 1 (t = 0) n 1 (t = 0)

 (J.26)

188

Appendix J: The ABC Model for Recombination Dynamics

and n 1 → 0 as t → ∞. Equation (J.25) is difficult to solve for n 1 analytically, but it can be plotted on a spreadsheet as is to evaluate the dependence of the carrier density transient on the two coefficients. Finally, as Idet ∝ n 12 , the above carrier density transient can be fitted to experimental time-decay data.

J.4 Mechanism Assignment and Low Injection Approximation Physical mechanisms of carrier relaxation have been assigned to the three terms. Recent research efforts into the assigned mechanisms aim to refine the relaxation mechanisms by introducing modifications regarding the InGaN efficiency droop phenomena and the surface recombination dynamics of micro LEDs. Square term. The square term is the normal pair-annihilation (a two-particle process, np ≈ n 2 ) where a photon is expected to be generated in the LED case, thus a radiative process. Near-band-edge emission (Fig. 4.2) is typically included regardless of assisted carrier relaxation (refer to the linear-term paragraph below). It is worthwhile to evaluate here the conventional approximation of low injection. It is a very common approximation in a doped semiconductor; discussions are seen in elementary electronic-device textbooks. Injected carriers to the opposite side of a pn junction experience a net recombination rate (only considering pair annihilation): R − G 0 = B( pn − p0 n 0 ) =

(J.27)

B[( p0 + n 0 )n 1 + n 12 ]

≈ B( p0 n 1 )

(in a p-type material).

(J.28) (J.29)

This is to say, the minority carrier density determines the net recombination rate rather than the product np or n 1 p1 . In this case, the rate equation leads excess carrier density to an exponential time decay as

−

dn = R − G 0 = Bp0 n 1 (t) dt 1 dn = −Bp0 dt n 1 (t) n 1 (t) = n 1 (t = 0) · e−Bp0 t

(J.30) (J.31) (J.32)

Low excitation is defined relatively against thermal carrier density, and pn junctions are almost universally doped in electronic devices (unipolar devices like field-effect transistors may not always be doped as they function based on a different mechanism). The net recom-

Appendix J: The ABC Model for Recombination Dynamics

189

bination rate is linear with the excess carrier density, not the total carrier density in those doped materials. Cube term. The cube term is generally assigned to the Auger process which is nonradiative involving three particles. As we already saw, this term becomes dominant when n has increased under high excitation. The Auger process is also anticipated to increase at high carrier densities. As an exercise, we may evaluate the low-injection approximation on the cube term. The Auger recombination rate in this case is deduced proportional to the excess minority carrier density R − G 0 ∝ p02 n 1

(p-type)

(J.33)

by starting from Eq. (J.2). Yet the cube term really gains its power when carrier density becomes large via carrier injection/excitation, and the low-injection approximation is not seriously concerned for cubed terms. Linear term. A single-particle process implies a nonradiative process. In many cases (common in low-excitation PL experiments) the linear term is attributed to the SRH recombination. Sze6 writes the SRH recombination rate as R=

σ p σn vth ( pn − p0 n 0 )Nt −Ei −Ei σn [n + n i exp( E tkT )] + σ p [ p + n i exp(− E tkT )]

(J.34)

where σ ’s are capture cross sections [cm2 ], vth is the thermal carrier velocity [cm/s], Nt is the trap density [cm−3 ], E t is the trap energy level in a bandgap, and E i is the intrinsic energy level. k is Boltzmann’s constant and T is the absolute temperature. In Sze’s discussion E t ≈ E i , which may not apply to our trap/impurity levels, making the denominator of Eq. (J.34) greater. Using the same low-injection approximation above in Eq. (J.29) to the numerator of Eq. (J.34), R is found to be linearly proportional to the excess minority-carrier density. Thus under low injection, Eq. (J.34) reduces to R ∝ p1

(n-type)

(J.35)

as shown in Sze’s book (Eq. (60) in p. 37 therein). On the high injection side Eq. (J.34) becomes

6 Sze SM (1981) Physics of semiconductor devices, 2nd edn., p 35–37. John Wiley and Sons, New

York.

190

Appendix J: The ABC Model for Recombination Dynamics

R=

σ p σn vth pn Nt σn n + σ p p

σ p σn vth n 2 Nt n(σn + σ p ) ∝ n.

=

(J.36) (J.37) (J.38)

Thus the SRH process contributes linearly to the recombination rate. Deep-level emission (e.g., broad-spectrum yellow luminescence from a large bandgap semiconductor) can be controversial in the ABC model as it is a trap-level-assisted luminescence. In a pn junction the linear term may be a complex of multiple mechanisms, both PL and EL, including leaky current, relaxation via surface states, and hot-carrier overflow (not recombining in a semiconductor but reaching a contact metal of the opposite side). Leaky current may be distinguished from SRH recombination which requires both types of carriers to be populated under excitation. It is implied from the above that, if writing out the ABC model in low excitation n 1 (possible in a heavily doped material), R = An 1 + Bp0 n 1 , coefficients A and B may not be resolved only by varying excitation intensity in a low-excitation regime.

J.5 Approximation Validity Let us inspect the validity of the approximation to see what the high injection really is. If we inject 1 A of current into a 1-mm2 active area of an LED (thus current density is 100 A/cm2 ) and accept an assumption that recombination speed is one per ns, the active layer receives 1010 electrons (equally holes) per recombination cycle. Let us say that the active layer is 10-nm thick, meaning 1010 electrons on average stagnate in a 1-mm × 1-mm × 10-nm box, and then injected electron density becomes 1 × 1018 cm−3 . Intrinsic carrier density of optoelectronic semiconductors is much smaller than 1 × 1018 cm−3 ; in reality, carrier density of an undoped semiconductor may be on the order of 1 × 1016 cm−3 . Thus, in an undoped QW, the high injection approximation likely holds in a normal LED operational range. If not, corrections may be needed to Eq. (J.4) to account for not having n 1  n 0 . On the low injection side, if a 10-nm-thick layer were doped, low current density of 1 A/cm2 would result in 1 × 1016 cm−3 of excess carrier density, which is probably an order or two lower than the doping concentration. This comparison between thermal carrier density from impurity doping and injected excess carrier density is graphically presented in Fig. J.2. When the two densities differ by an order of magnitude, the approximation is mostly valid. When they differ by two orders, the approximation is sufficiently valid. Figure J.3 provides visual understanding of recombination rates under low and high injections. Under low injection, the total recombination rate (the entire rectangle area) is dominated by the shaded rectangle area p0 n 1 . Under high injection, the total recombination rate is dominated by the shaded area n 12 .

Appendix J: The ABC Model for Recombination Dynamics

191

Fig. J.2 Sum of thermal and excess carrier densities is plotted as a function of the latter for various values of the former. Low and high excitation approximations are valid where the graphical slope of the log-log plot is close to zero and unity, respectively

Comprehensively, it is true that deviations in data fitting are always observed in practice and corrections are proposed on a case-by-case basis. Yet the main framework of the ABC model is maintained, because of its power and simplicity. Approximations first, corrections later—similar to what we saw in geometrical optics.

192

Appendix J: The ABC Model for Recombination Dynamics

Fig. J.3 Visualization of recombination rates for a low and b high injections. By laying p and n on a 2D graph of a relative linear scale as shown, rectangle areas indicate corresponding recombination rates. It is recognized that the shaded area takes up the most of the entire rectangular area as claimed in the approximations. Note that p0 , n 0 , and n 1 differ by orders of magnitude in reality, making the shaded area completely dominate the total recombination rate

K

The Exciton

In elucidating recombination mechanisms, excitons occasionally become a focus of discussion. The exciton is a particle of a mutually-attracted (bound) electron-hole pair in a semiconductor material. It is a quantum mechanical conclusion via Schrödinger’s equation (involving the wave nature) that a set of an electron and a hole can be treated as a single particle (moving around together) using their center of mass with the reduced mass.7 This exciton model is similar to a hydrogen atomic model where the positively-charged particle is a proton. Hence an exciton can be analyzed in a similar way as the hydrogen atom to define a Bohr-radius equivalence and discrete energy levels. The attractive Coulomb force is readily calculated via two elementary charges in a dielectric material with discrete possible distances (the particle nature) determined by atomic periodicity. The binding energy is typically smaller than RT energy (thus they are only loosely bound) so that an exciton dissociates into two independent particles (i.e., particles independently move around without feeling Coulombic attraction to each other). The exciton is of particular interest in GaN because excitons are believed to be bound in GaN even at RT. Hence, RT experiments may reveal excitonic luminescence to study exciton’s characteristics, otherwise requiring cryogenic apparatus. Yet it is controversial in the research community whether the exciton should be treated as a single particle or two attracted particles in the ABC model introduced earlier in this book. In LED devices, however, the role of excitons is not so pronounced and it is mostly sufficient to treat them as electrons and holes.

7 The effective inertial mass when two particles move together as a single body. The reduced mass of Particle A (mass m A ) and Particle B (mass m B ), m R , is m R = (1/m A + 1/m B )−1 .

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

193

L

Organic LEDs

This book declared at the beginning that topics of organic LEDs would be excluded. Nevertheless, it is briefly touched upon as a competing technology against our LEDs. Electroluminescence of an organic material was reported in 1987.8 Its principle was based on carrier transport, which was similar to the conventional inorganic LEDs, accompanying low operation voltage. In organic-LED’s luminescence theory, the terminology of lowest unoccupied molecular orbital (LUMO, the excited state) and highest occupied molecular orbital (HOMO, the ground state) is used in the place of the conduction band edge and the valence band edge of the semiconductor, because organic molecules do not construct a conventional band structure. Carrier transport is explained via the hopping conduction mechanism as molecules may be contiguous but not continuous. Carrier transporting layers are called the electron transport layer (ETL) and the hole transport layer (HTL). Because of molecular structure, excitons (or excited states) are localized and an excitonic state is described as either a singlet or triplet due to electron-hole spin states. Singlet-state excitons contribute to fast luminescence (fluorescence, ∼1 ns) while slow luminescence (phosphorescence, ∼100 ms) occurs from triplet-state excitons due to the need for spin compensation. Device structures are made by layering functional thin films, including transparent electrodes, via common thin-film techniques, e.g. vacuum evaporation, solution printing, etc. Materials are molecule based, so that there is no notion of lattice matching nor impact from surface states or dangling bonds. Since organic LEDs are based on organic molecules, a fundamental advantage is that material choice is limitless. Engineering advantages include large-area luminescence and pixelated displays, owing to non-epitaxy processes. Bendable display devices are feasible when films are formed on flexible substrates.

8 Tang CW, VanSlyke SA (1987) Organic electroluminescent diodes. Appl Phys Lett 51:913.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

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196

Appendix L: Organic LEDs

Organic-LED’s weakness is robustness. Organic substances are more sensitive to environment, e.g., moisture and oxygen, therefore device encapsulation is critical for reliable operation. Organic substances suffer from extremely accelerated degradation under harsh operational conditions (high drive current, high temperature, high humidity, etc.). Overall, device lifetime is a major concern especially in outdoor applications. Many organic substances can function as phosphors (called organic converters or dyes) but reliability is a serious concern under harsh conditions. Hence they are not popular in our LED applications.

Glossary

Bandgap An energy band of a semiconductor where no electronic states exist. It occurs between conduction and valance band edges in the electrostatic energy scale. As the former, it is also called a forbidden band, and the latter also called an energy gap. Binning (sorting) For a type of product, completed units and/or units in fabrication are grouped by performance (LOP, Vf, dominant wavelength, etc.) via pre-determined specs. This grouping is beneficial for controlling production, reducing out-of-spec units, and strategic applications and sales. See Sects. 2.1 and 3.4. Carrier injection efficiency The ratio of carriers captured in the active region to those supplied from the external circuit. It is thus a measure of carrier overflow. It is believed in modern LED structures that carrier injection efficiency is very high (∼ 100% in many cases). Because of that the notion of carrier injection efficiency has been incorporated in IQE, yet elaborate efficiency analysis separates the carrier injection efficiency from the IQE. The term “carrier injection” refers to the active region in optoelectronics discussions, whereas carrier injection may refer to the other side of a pn junction (electronic-device discussions) or that into a semiconductor device. It should be apparent from the context. Carrier overflow A phenomenon where injected carriers into an LED structure miss the active region (or are once captured in the active region but escape interruptedly) and reach the other side of the pn junction. Overflowed carriers will not contribute intended light emission and may or may not cause parasitic luminescence corresponding to the bandgap of the neutral regions. Cascade down-conversion It is a probable path of down conversion in a phosphor blend where a photon from a phosphor excited by a pump LED is absorbed by another phosphor to generate another photon. Thus down conversion occurs on a photon consecutively twice or more in a system. For example, in a green + red phosphor blend applied onto a pump blue LED, a cascade down conversion can be blue → green → red whereas a direct down © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 H. Masui, Introduction to the Light-Emitting Diode, Synthesis Lectures on Materials and Optics, https://doi.org/10.1007/978-3-031-30716-4

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198

Glossary

conversion is blue → red. A resulting photon may be the same, but because of multiple conversion cascade conversion leads to increased QE loss. CIE illuminant CIE has defined standard illuminants (theoretical light sources) of various CCTs as spectra that are used as references in industrial applications. Illuminant D65 is a common one representing daytime sunlight. Competitive analysis Investigational work on competitors’ products. The technical aspect includes datasheet analysis, performance evaluation, and reverse engineering (although in many cases product procurement is not straightforward). It also includes marketing and sales aspects e.g., market price and share analysis. Also called benchmarking. Droop An experimentally observed phenomenon that EQE of InGaN LEDs drops at high current density. It is also called “current droop” or “efficiency droop.” It is believed that Auger recombination causes the droop. An EQE drop caused by raised temperature is sometimes referred to as “thermal droop.” See Sect. 4.2. Edge exclusion Epi wafers experience irregular gas flow around their peripheries during growths resulting in deteriorated crystal qualities and layer structures. This is called the edge effect. These peripheral areas are excluded from chip fabrication, typically in a few mm width along the wafer circumference. Electron volt A unit of energy that a unit charge (e.g., an electron) at an electrostatic potential of 1 V has. 1 eV is equal to q [J] where q is the value of the unit charge 1.6 × 10−19 . Encapsulation Within the LED work area, encapsulation implies encasing LED chips using clear materials, e.g., silicone. Such an encapsulant can contain a phosphor material; in that case it tends to be called phosphor integration. Fermi level Equivalent to the chemical potential. An energy level of a system below which states are occupied by particles (electrons in our case) at zero-temperature equilibrium. At finite temperature particles are statistically spread around the Fermi level, so that particle distribution deviates from a step function. When a Fermi level occurs in an energy gap it is defined to be an energy level of one-half occupancy probability. Particles move (diffuse) in real space to maintain a flat Fermi level to establish thermal equilibrium. Gage R&R Experiment to evaluate repeatability and reproducibility of a measurement, e.g., a luminous flux measurement via an integrating sphere using a prescribed set of samples. Repeatability (via single operator) is indicative of tool consistency, and reproducibility (via multiple operators) is an evaluation of measurement operation consistency. It may be controversial that a supervised gage-R&R experiment may not represent quality of daily measurements adequately due possibly to operators’ task loads, mind states, etc. The notion of gage R&R can be extended to a measurement service where a requestor hires a service (which is a black box “tool” to some extent) repeatedly; similarly whether multiple requestors receive the same result from a service reproducibly. SEM imaging is an example—Results of SEM imaging can vary by the tool or the operator (that the requestor may or may not have a control over) as well as how well a requestor is familiar with SEM imaging techniques to prescribe imaging conditions and parameters.

Glossary

199

Kitting A manufacturing technique to improve usage of binned components by combining various bins to achieve a final product specification. See Sect. 3.4. Lambertian Radiation or illumination pattern where radiant or luminous intensity changes as cosine of the polar angle from surface normal. Equivalently, radiance or luminance is constant over the polar angle. Perfectly randomized luminescence from a diffusive surface is considered to be Lambertian. Because of its mathematical simplicity, the Lambertian pattern is widely used as first-order approximation. Leaky current Premature current flow below turn-on or noticeable reverse current at low reverse bias. A device that exhibits leaky current is called a leaky device or leaky junction. See Sect. 4.5 Localized states Energy and/or quantum states of spatially localized carriers. In III-nitride discussions it often implies In segregated regions of InGaN alloys. See Sect. 4.1. Lumen per dollar A measure of cost effectiveness of LED products. It indicates how much light (lumens) is generated per unit product cost. It is used as a figure of merit predominantly in general illumination applications. Neutral density (ND) filter Optical filters of gray appearance due to their flat attenuation spectra. They are used to reduce light intensity evenly not to saturate a detector and to vary illumination intensity. Optical density (OD) filters are the same in most context. Laser safety goggles are rated via optical density for their attenuation power but attenuation spectra are not flat. Attenuation power is expressed either in dB or in log10 : For example ND20 and OD2 are both 1/100 attenuation. Number of bounces A photon exits a system (e.g., an LED chip or package) with a certain probability when it impinges on an interface to free space. A photon may experience multiples impinges (the number of bounces) before making a successful exit. This notion is applied as an average number over many photons, not individual photons. The number of bounces is large in an LED chip with a large refractive index or a cube shape, and decreases in a shaped chip. Packaging In most cases it means to complete a discrete device (L0 or L1) by protecting semiconductor chips with encapsulant and making electrically accessible. Preparing a shipping container (e.g., pocket tape and reel) is also called packaging. Photocurrent Current flow caused by photo-excited carriers (photocarriers). A photodiode utilizes photocurrent to measure light intensity. Photocurrent also occurs within an LED via photon recycling. Photon recycling A process in an LED that photons generated via carrier recombination get absorbed by the active layer and turn back into carriers. Pick-and-place (p&p) An automated machine process in device fab and packaging where discrete chips are individually transferred from one carrier to another, e.g., from a bin tape (tape-laminated ring frame) to another bin tape like in binning and from a bin tape to a lead frame like in DA. Pick-and-place can flip chips and change distances between chips on carrier. It is considered to be a time consuming and thus costly process.

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Punch through Establishment of a pn junction requires spatial extension (called a depletion layer or space-charge layer) into both sides from a metallurgical junction. Width of spatial extension depends on doping levels. When a doping level is low and/or a doped layer is thin, there is a chance that a depletion layer is not fully established (punches through the physical doped layer), leading to an incomplete junction. Reflow In contrast to a soldering iron process, this indicates a reflow soldering process: A method to attach electronic components onto a board using solder. Solid solder applied between a component and board “reflows” when heated above its melting temperature in a reflow oven and solidifies again when cooled. For this notion, reflow also applies precasted silicone films. A half-cured silicone film reflows on a tile with chips to make a conformally coated phosphor layer. Reverse engineering Tear-down of a device or product to study its construction and ingredients. When reverse engineering is done on a failed unit, it is called failure analysis (FA). Sah-Noyce-Shockley (SNS) analysis Analytical work to derive diode’s electrical characteristics incorporating SRH statistics. An important conclusion was the diode equation. The analysis distinguished two regions of recombination: Neutral regions and the depletion layer. Resulting current was called injection current and recombination current, respectively. By introducing a notion of the ideality factor n, the former raised a unity ideality factor while the latter raised n = 2. The original work was performed on a symmetrically doped Si junction reasoning that wide bandgap Si (compared to Ge) would be more likely to have midgap states at a metallurgical interface (the middle of the pn junction) where the potential would change as V f /2. Shockley-Reed-Hall (SRH) statistics Carrier recombination statistics when an energy state (e.g., created by an impurity) in a bandgap exists and participates. An important finding of the original work was that a midgap energy state participated more efficiently than any other state closer to a band edge whose contribution was determined significantly less. SRH-type recombination implies nonradiative recombination in LED discussions. Singulation A manufacturing process of cutting up a device-processed wafer or chippopulated tile into individual chips or devices. Common methods include scribe-andbreak, saw-blade dicing, and laser dicing. Starboard A type of PCBs in a hexagonal shape. Commonly used in LED industry. Not related to the starboard of ships. See Sect. 2.2. Super luminescence diode (SLD) A special type of LEDs that utilizes stimulated emission as its luminescence mechanism as in LDs. SLDs do not have a cavity, thus laser emission (coherent light and line spectrum) is not established. It is used in high-speed modulation applications. Tape transfer A process to transfer a wafer or chips from one carrier tape to another in order to flip the wafer/chips. It typically needs to be from a low-tackiness tape to a high-tackiness tape.

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Telecentric Nonfocusing (collimated) optical components and systems that have a section of a collimated beam path. Because insertion of an optical element (e.g., ND filter, polarizer, etc.) does not alter the path of light rays, it provides design flexibility in optical equipment and systems. It is a very common optic system used today in microscopes, for example. See Sect. 5.4. Test vehicle A testing platform for chip/device handling, e.g., starboard. A common test vehicle is not only convenient in a R&D facility but needed also for data consistency. See Sect. 2.2. Traceability More explicitly the measurement traceability, is the ability of tracing the calibration history and/or inheritance path of an instrument to a known calibration standard. Optical instruments (e.g., an integrating-sphere measurement tool) are of major interest to the entire LED industry. A standard lamp may be a NIST-calibrated/certified LED lamp (often nicknamed a “golden” lamp), from which secondary (and even tertiary) standard lamps (similar LED lamps calibrated regularly to the standard lamp, but they are private-institute local) may be prepared for instrument calibration use in order to avoid excessive usage of the primary certified lamp. In such a case, traceability is still known and maintained. Vegard’s law An empirical rule of alloy properties that properties change approximately linearly between two (or more) constituents. For example, lattice constants of In x Ga(1−x) N change approximately linearly with x between GaN and InN. The linearity is seldom guaranteed, yet the law is sufficient in many cases for first order approximation. When a property noticeably deviates from linearity, a bowing parameter is inserted in the linear equation. We did not use a bowing parameter in the calculation given in this book. Via Small hole made in a chip or submount to achieve electrical connection by metallization from surface to a buried layer or backside. The latter case is called a through-via. Voltage partitioning factor Another name for the ideality factor (See Sah-Noyce-Shockley analysis) indicating its physical significance. Volumetric reflector A type of light reflector using a refraction mechanism in a mixture of two or more transparent materials that have different refractive indices. Because of its repetitive refraction mechanism it requires a certain volume compared to a thin specular reflector, and reflected light becomes diffusive. Walk-off In chip singulation process, when a sapphire wafer is subjected to breaking after scribing, break lines in sapphire wiggle around the scribe line. This wiggling is called the walk-off. See Sect. 3.4. Yield off In manufacturing, defective devices found during a fabrication process are eliminated from further process steps to avoid spending unnecessary production efforts. See Sect. 3.4.