Organic Semiconductor Devices for Light Detection (Springer Theses) 3030944638, 9783030944636

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Springer Theses Recognizing Outstanding Ph.D. Research

Jonas Kublitski

Organic Semiconductor Devices for Light Detection

Springer Theses Recognizing Outstanding Ph.D. Research

Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists.

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More information about this series at https://link.springer.com/bookseries/8790

Jonas Kublitski

Organic Semiconductor Devices for Light Detection Doctoral Thesis accepted by Technische Universität Dresden, Dresden, Germany

Author Dr. Jonas Kublitski IAPP-Dresden Integrated Center for Applied Physics and Photonic Materials TU Dresden Dresden, Germany

Supervisor Prof. Karl Leo IAPP-Dresden Integrated Center for Applied Physics and Photonic Materials TU Dresden Dresden, Germany Center for Advancing Electronics Dresden (cfaed) TU Dresden Dresden, Germany

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-3-030-94463-6 ISBN 978-3-030-94464-3 (eBook) https://doi.org/10.1007/978-3-030-94464-3 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 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

Supervisor’s Foreword

For humans, the eyes are the most important channel to obtain information about what surrounds us. In our modern world, where electronic devices assist us in many ways, optical sensors play the role of the eyes. This applies not only to the visible range of wavelengths, but even more to infrared wavelengths: Here, materials have “fingerprints” which can be used to identify substances. Thus, sensitive and versatile infrared sensors find many applications in areas such as healthcare, food monitoring, manufacturing and more. Current photodetector technologies are mostly based on inorganic crystalline semiconductors which have limitations in size, flexibility, cost, etc. Recently, sensors based on organic semiconductors have been intensively researched. These carbon-based devices can be deposited on practically any surface, enabling flexible components that could be integrated, for example, on plastic films, but also in clothing, packaging and even in the human body. The main challenge is to raise the detectivity of these organic photodetectors: Key factors are here to improve responsivity related to the external quantum efficiency and reduce noise. The thesis of Dr. Kublitski presents major advances in both parameters: First, he realizes a new type of photomultiplication gain detector which reaches EQEs of almost 2000%, combined with narrowband spectral response obtained by a microcavity design. Thus, these devices allow to obtain the “fingerprints”, i.e., spectroscopic information in the infrared range with very high sensitivity. A second major innovation presented in this thesis was a much-improved understanding of the sources of noise in organic detectors. Dr. Kublitski proved that the main contribution to the spectral noise density results from the high dark current commonly observed in these devices. So far, it has been assumed that this was mainly due to non-optimized structures. However, Mr. Kublitski’s results show that the dark current results from the thermal generation of charge carriers. In particular, mid-gap trap states contribute to this, increasing the intrinsic current very significantly. Using a number of techniques, Dr. Kublitski examines the trap states and determines their energy and energetic distribution. He observes a direct correlation between the trap properties and the magnitude as well as the field dependence of the dark current and thus confirms the defect as origin. A theoretical model is able to reproduce the v

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Supervisor’s Foreword

experimental results excellently, further supporting the findings. In particular, the model demonstrates that the high electric fields contribute to detrapping of charge carriers. The results of the thesis of Dr. Kublitski are important steps on the way to improved devices and will definitely have strong impacts on future applications. August 2021

Prof. Karl Leo Director IAPP-Dresden Integrated Center for Applied Physics and Photonic Materials Chair of Optoelectronics, Technische Universität Dresden Dresden, Germany

Abstract

In the last decades, the way human beings interact with technology has been significantly transformed. Already in 2011, a video viralized showing a 1-year girl trying to zoom in a photo in a printed magazine. In our daily life, ever less manually controlled devices are used, giving way to automatized houses, cars and devices. A significant part of this technological revolution relies on signal detection and evaluation, placing detectors as core devices for further technological developments. One of the most explored detector types is based on the photovoltaic effect. Absorbed photons generate charge carriers, which are extracted, thereby, creating an electric output. So far, the inorganic semiconductor industry has been able to provide efficient devices to supply most of costumer’s needs. However, the intrinsic limitations of this technology enlarge the integration gap between the user and the final product. These constraints include brittle and inflexible devices as well as high processability costs and toxic materials for near- and infrared detectors. Besides that, applications such as health- and healing-monitoring require biocompatible and even biodegradable devices. While these applications are nearly inconceivable with inorganic semiconductors, they can certainly be foreseen with organic semiconductor materials. The focus of this thesis is organic photodetectors (OPDs), where the elucidation of important parameters necessary to improve device performance are targeted. In general, detectors are characterized in terms of their specific detectivity. For light detecting devices, the specific detectivity depends on the External Quantum Efficiency (E Q E), i.e., the amount of extracted electrons per incoming photons, and on the output generated by the device in the absence of signal, i.e., the device’s noise. For OPDs, the latter is the main responsible for the rather low performance as compared to inorganic PDs. Therefore, substantial emphasis is given in understanding the sources of noise in OPDs. We demonstrate that the major contribution to the noise spectral density arises from the shot noise component, which is a result of the high dark current in these devices. Moreover, we show that unoptimized device structures, which had been thought to be the reason for the high dark current of OPDs, are less important. Instead, our results indicate that the dark current results from thermal generation of charge carriers via mid-gap trap states, in addition to vii

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the intrinsic component generated via charge-transfer (CT) states. By quantifying and characterizing the trap states in different material systems, we draw a direct correlation between the trap properties and the magnitude as well as the field dependence of the dark current. Our theoretical model is capable of reproducing the dark current by taking into account the generation via trap states and the lowered energy for detrapping, which is a consequence of the omnipresent high electric field in thin-film devices operated in the extraction mode. Understanding the interplay between traps, CT states and dark current helps to refocus the research in the OPD field to material properties rather than device optimization to achieve higher device performance in the future. In addition to the dark current, the E Q E of OPDs is also examined. While in photovoltaic-type OPDs, the E Q E is intrinsically limited to 100%, in devices attaining photogain, this constrain is not present, opening a large room for improvement. With that in mind, we designed organic devices with photomultiplicative gain, in which E Q Es of almost 2000% in broadband OPDs are demonstrated. By carefully controlling the donor-acceptor ratio of bulk heterojunctions and the appropriated choice of interfacial layers, we intentionally cause an accumulation of photogenerated electrons close to the cathode. Under reverse bias, this accumulation leads to an increased electric field and a decreased energetic tunneling barrier for holes, which are thereby injected into the donor phase. Due to the efficient hole transport, the transit time for injected holes is shorter than the lifetime of photogenerated electrons, leading to a photogain. Such an amplification is also realized in the CT absorption band, showing that direct excitation of CT states also triggers photomultiplication. Furthermore, by embedding these devices into optical microcavities, narrowband photomultiplication-type OPDs (PM-OPDs) are fabricated. The PM-OPDs performance is superior to other strategies for achieving narrowband detection combined with photomultiplication. Moreover, this approach has a great potential to overcome the performance of state-of-the-art narrowband OPDs based on the CT absorption band, where one of main limitations is the low EQE in the CT state absorption region.

Acknowledgments

Adapting to a different life is always a struggle and it hasn’t been different when starting my Ph.D. in a different country, in a different culture. But when you leave your comfort zone it’s when you learn the most. Some people, however, make this journey more pleasant, and I would like to take this opportunity to thank them. Thank you, Vasilis, Johannes and Donato for being always available to teach how to operate UFO, among many other techniques, as well as for sharing nice moments. Thanks also to my former lunch mates, Yoonseok, Jaebok, Martin, Koen, Vasilis and Johannes for sharing a good time at Mensa, besides forcing me to have lunch in the Sun. I still hate it, though. I’m also very much grateful for the scientific supervision during these years. Therefore, I would like to thank Prof. Dr. Karl Leo for supervising me and not only for always providing me scientific and bureaucratic support but also for guaranteeing a very nice working environment at IAPP. Moreover, thanks to Prof. Dr. Koen Vandewal for co-supervising most of the work shown in this thesis and for teaching me so much about science and scientific practice. An especial thanks to my coauthors Dr. Andreas Hofacker for putting so much effort in the simulations shown in this thesis, Dr. Bahman Kheradmand for building and measuring the noise of my OPDs, Łukasz Baisinger for performing the transient current measurements, and Dr. Axel Fischer for the fruitful discussions. Besides that, I would like to thank: Dr. Johannes Benduhn for reading and correcting this thesis multiple times. Thank you for putting so much effort and time in polishing not only this thesis but also all the work shared along these years. Dr. Donato Spoltore for the fruitful discussions on experimental and theoretical aspects which are reflected in this thesis. My former colleagues, as well as my dear Lehrerin Frau Grad, from the Deutschkurs in Berlin for sharing those beautiful six months of intensive Deutsch learning. Ich bedanke mich! Shen, Xiangkun, Natalia, Sascha, Jinhan, Katrin and Yazhong from IAPP for helping me with so many measurement techniques.

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Acknowledgments

The OSOL/OSens group for sharing so much knowledge, good moments and experiences. The organizational and technical staff at IAPP for ensuring that scientific work runs smoothly. The Deutscher Akademischer Austauschdienst (DAAD) for the funding provided during the four years of my Ph.D, as well as the Graduate Academy of the TU Dresden, for the three months wrap up scholarship granted. To my parents! Thank you for teaching me the most valuable lesson, that knowledge is the only thing that emancipates us. In every small achievement of mine there is a little bit of you, because in each one there is a little piece of this understanding. To the rest of my family, who have supported me unconditionally since my early years. Thank you for always being there! To all my dear friends, in Germany and in Brazil, for all the encouragement. To Raiza, Nara and Marco, this group of almost all doctors. Thanks for listening to all my complaints, scientific or personal (more personal lol), for giving me strength and for sharing moments that I will never forget.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Detection of Electromagnetic Radiation: A Growing Demand . . . . . 1.2 Challenges of the Current Technology . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Organic Electronics and Organic Photodetectors . . . . . . . . . . . . . . . . 1.4 Challenges for OPDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Outline of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 3 5 7 7

2 Fundamentals of Light Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Radiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Radiometric Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Black-Body Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Inorganic Light Detecting Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Fundamentals of Inorganic Semiconductor Physics . . . . . . 2.2.2 From Radiation to Chemical Energy . . . . . . . . . . . . . . . . . . . 2.2.3 From Chemical Energy to Electrical Energy . . . . . . . . . . . . 2.2.4 Interfaces Metal/Semiconductor . . . . . . . . . . . . . . . . . . . . . . . 2.2.5 pn-Junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.6 Photoconductors for Light Detection . . . . . . . . . . . . . . . . . . . 2.3 Figures of Merit of Photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Power Spectral Density Sx ( f ) . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Noise Current i n  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Responsivity R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Noise Equivalent Power N E P . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5 Specific Detectivity D ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.6 BLIP Limit for D ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.7 Dynamic Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.8 Response Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11 12 12 14 14 15 23 26 28 29 38 39 39 41 43 43 44 44 45 47 47

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3 Organic Semiconductors for Light Detection . . . . . . . . . . . . . . . . . . . . . . 3.1 Organic Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Molecular Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Solid State Physics of Organic Semiconductors . . . . . . . . . . 3.1.3 Traps in Organic Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Working Principle of Optoelectronic Devices . . . . . . . . . . . . . . . . . . . 3.2.1 Donor-Acceptor Systems and Charge-Transfer States . . . . 3.2.2 Impact of Charge-Transfer States on Optoelectronic Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 From Light Absorption to Electric Output . . . . . . . . . . . . . . 3.2.4 Organic Photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Photomultiplication-Type OPDs . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49 50 50 58 67 69 69

4 Materials and Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Donors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Acceptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Hole Transporting Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Electron Transporting Layers . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Dopants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Characterization Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Temperature-Dependent Electric Measurements . . . . . . . . . 4.3.2 Current-Voltage Measurements . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Temperature-Dependent Current-Voltage Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Suns-VOC Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.5 External Quantum Efficiency Measurements . . . . . . . . . . . . 4.3.6 Sensitive External Quantum Efficiency Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.7 Noise Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.8 Impedance Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.9 Transient Photocurrent Measurements . . . . . . . . . . . . . . . . . 4.3.10 Spectroscopic Ellipsometry Measurements . . . . . . . . . . . . . 4.4 Drift-Diffusion J V -Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91 92 94 94 94 94 96 96 97 97 98

101 102 103 111 111 112 113

5 Reverse Dark Current in Organic Photodetectors: Generation Paths in Fullerene Based Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The Role of Dark Current on the Specific Detectivity . . . . . . . . . . . . 5.3 Device Optimization for Dark Current Studies . . . . . . . . . . . . . . . . . . 5.3.1 Contact Selectivity and Blocking Layers . . . . . . . . . . . . . . . 5.3.2 Shunt Paths in OPDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Device Structuring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117 118 118 120 120 122 123

74 76 77 79 81

100 101 101

Contents

5.4 Diode Saturation Current Generated via Charge-Transfer States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Traps as the Main Source of Reverse Dark Current in OPDs . . . . . . 5.6 Generation-Recombination Statistics Due to a Distribution of Traps and Drift-Diffusion Modeling . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Trap-Assisted JD Generation Model . . . . . . . . . . . . . . . . . . . 5.6.2 Modeling Trap-Assisted JD Generation in OPDs . . . . . . . . 5.6.3 Ideality Factor in Trap-Assisted JD . . . . . . . . . . . . . . . . . . . . 5.6.4 Arrhenius Activation Energy of Trap States . . . . . . . . . . . . . 5.6.5 The Impact of the Trap Distribution Characteristics on JD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.6 The Interplay Between CT States and Trap States . . . . . . . . 5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Enhancing Sub-Bandgap External Quantum Efficiency by Photomultiplication in Narrowband Organic Near-Infrared Photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Photomultiplication in ZnPc:C60 Devices . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Enhancing the External Quantum Efficiency . . . . . . . . . . . . 6.2.2 Effect of Acceptor Concentration on Photomultiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 The Role of Dark Current in PM-OPDs . . . . . . . . . . . . . . . . 6.2.4 Enhancement of Charge-Transfer State Response in PM-OPDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.5 Transient Photocurrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Dynamic Range of PM-OPDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 On the Origin of the Dark Current of Organic Photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 Enhancing EQE via Photomultiplication in Organic Photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.3 Related Topics Investigated Alongside with this Thesis (Not Shown) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Open Research Topics for Photovoltaic-Type OPDs . . . . . . 7.2.2 Open Research Topics for Photomultiplication-Type OPDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Open Research Topics for OPDs in General . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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124 127 133 133 135 138 139 140 141 144 144

151 152 154 154 156 158 160 164 165 165 166 171 172 172 174 175 176 177 177 178 178

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Appendix: Impedance Spectroscopy in Organic Blends . . . . . . . . . . . . . . . . 181 Curriculum Vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Symbols, Physical Constants and Acronyms

Symbols Symbol

Description

Unit

α(E)

Absorption coefficient

cm−1

T

Absolute temperature

K

A(E)

Absorption

a. u.

Y (ω)

Admittance

S

ω

Angular frequency

rad s−1

θ

Angle

◦

ν0

Attempt-to-scape frequency

s−1

Cn , Cp

Auger recombination constants for electrons and holes

cm6 s−1

Eg

Band gap

eV

E eq

Bindinding energy

eV

+ , −

Bonding and antibonding wave functions

−

σ

Broadness of a Gaussian density of state

eV

φbi

Built in potential

eV

C(ω)

Capacitance

F

σn , σp

Capture cross-section

m2

ξn , ξp

Chemical potential for electrons and holes

eV

τc,n , τc,p

Collision time for electrons and holes

s

n, p

Concentration of electrons and holes

cm−3

G(ω)

Conductance

S

EC , EV

Conduction and valence band

eV

E CT

Charge-Transfer (CT) state energy

eV

Ibias

Current driven through the device by an applied bias

A

xv

xvi

Symbols, Physical Constants and Acronyms

Symbol

Description

Unit

J

Current density

A m−2

JD

Dark current density

A m−2

Nt

Density of traps

m−3

Ad

Device area

cm2

d

Device thickness

nm

ε(ω)

Dielectric function

–

Dn , Dp

Diffusion coefficient for electrons and holes

m2 s−1

Ln, Lp

Diffusion length for electrons and holes

m

R0

Distance between two atoms

Å

ND , NA

Donor and acceptor concentration

cm−3

DOS(E)

Density of states

cm−3 eV−1

DR

Dynamic range

dB

NC , NV

Effective density of states in the conduction and valence band cm−3

m ∗n , m ∗p

Effective mass for electrons and holes

1

ηchemical

Efficiency

1

Q

Electric charge

C

σn , σp

Electric conductivity for electrons and holes

S cm−1

F

Electric field

V m−1

P

Electric power

W

ηn , ηp

Electrochemical potential for electrons and holes

eV

μn , μp

Electron and hole mobility

cm2 V−1 s−1

Pn , Pp

Electron and hole polarization

eV

N(E)

Emission

a. u.

en , ep

Emission coefficients for electrons and holes in the SRH theory

–

E

Energy

J or eV

E0...n

Energy eigenvalues

–

EQE

External quantum efficiency

1

E Q E el , E Q E EL

Electroluminescence external quantum efficiency integrated over all energies (scalar) and energy dependent (spectrum)

1

c1 , c2

Expansion coefficient of 1 and 2

–

f (E, T )

Fermi-Dirac distribution

1

EF

Fermi level

eV

FF

Fill factor

a. u

Symbols, Physical Constants and Acronyms Symbol

xvii

Description

Unit

VF , VR

Forward and reverse bias

V

f, ν

Frequency

Hz

G

Gain

1

i G−R

Generation-recombination noise current

A

E+ , E− Hˆ e

Ground and first excited energy state

–

Hamiltonian

–

Hi, j

Hamiltonian integral between atom i and j

–

n id

Ideality factor

1

j

Imaginary part of a complex number

–

Z (ω)

Impedance

ni

Intrinsic carrier concentration

cm−3

Ei

Intrinsic level

eV

IQE

Internal quantum efficiency

1

I

Irradiance

W m−2

a

Lattice constant

m

LDR

Linear dynamic range

dB

req

Lennard-Jones equilibrium distance

m

vn , vp 

Mean velocity of electrons and holes

m s−1

μm , μsc

Electrochemical potential of the metal and of the semiconductor

eV

n p , pn

Minority charge carrier concentration

cm−3

NEP

Noise equivalent power

W Hz−1/2

Sn

Noise spectral density

A Hz−1/2 or V Hz−1/2

i 1/ f

1/f noise current

A

VOC

Open-circuit voltage

V

E opt

Optical gap

eV

f CT

Oscillator strength

eV2

Si, j

Overlap integral between atom i and j

–

ΦBB ri , R

Photon flux density

#photons m−2 s−1 m−1

Positional vectors

m

xviii

Symbols, Physical Constants and Acronyms

Symbol

Description

Unit

Sin

Power spectral density

A2 Hz−1 or V2 Hz−1

E F,C , E F,V

Quasi-Fermi levels

eV

L

Radiance

W sr−1 m−2

M

Radiant exitance

W−2



Radiant flux

W

ΔVrad , ΔVnonrad

Radiative and non-radiative voltage losses

V

Vrad

Radiative limit of VOC

V

J0,rad

Radiative saturation current

A m−2

r1 , r2 , r3 , r4

Rates of emission and capture in the SRH theory

s−1

X (ω)

Reactance

βbimolecular,SRH

Recombination constant

m3 s−1

vR,n , vR,p

Recombination velocities

cm−1 s−1

n, k

Refractive and extinction coefficients

–

ε

Relative permittivity

1

λCT

Reorganization energy

eV

Ri

Resistance of element i

R

Responsivity

A W−1 or V W−1

ton , toff

Rise and fall time

s

T0

Room temperature

K

J0

Saturation current

A m−2

i shot

Shot noise current

A

S0...n

Singlet states

–

Ω

Solid angle

sr

W

Space charge width

m

D∗

Specific detectivity

cm Hz1/2 W−1

B(ω)

Susceptance

S

i thermal

Thermal noise current

A

t

Time

s

τt

Time constant

s

in

Total noise current

A

ΦBB,total

Total photon flux

#photons s−1 m−2

total , el , spin , vib

Total, electronic, spin and vibrational wavefunction

–

W

Transport bandwidth

eV

Symbols, Physical Constants and Acronyms Symbol

Description

xix Unit

Et

Trap energy

eV

T0...n

Triplet states

–

vn , vp

Thermal velocity

m s−1

E vac

Vacuum level

eV

σLJ

Van der Waals radius

–

ωi

Vibrational frequency

Hz

V

Voltage

V



Wave function

–

1 , 2

Wave function of atom 1 and 2

–

λ

Wavelength

m or nm

φm , φsc

Work function of the metal and of the semiconductor

eV

Physical Constants

Quantity

Symbol

Value

Unit

Elementary charge

q

1.60×10−19

C

Electron mass

me

9.11×10−31

Kg

c

2.99×108

m s−1

Speed of light Pi

π

≈ 3.14

–

Planck constant

h

4.13×10−15

eV s

Reduced Planck constant



h 2π

eV s

Boltzmann constant

kB

8.62×10−5

eV K−1

ε0

8.85×10−12

F m−1

Vacuum permittivity

xx

Symbols, Physical Constants and Acronyms

Acronyms α-6T MoO3 A A* AC Ag AMOLED Au BHJ BLIP BTJ C CCN CIN CMOS CN-PPV CT CT-OPD CuPc D D* D-A DAAD DFT DOOS DTFT EA EBL EMA EMA ES ETL FC FOV FT FWHM GaAs GDM Ge GS H HBL

Subnaphthalocyanine Molybdenum trioxide Acceptor Excited acceptor Alternated current Silver Active matrix organic light emitting diode (OLED) Gold Bulk heterojunction Background limited infrared photodetection Bipolar-junction-transistor Carbon Charge collection narrowing Charge injection narrowing Complementary metal oxide semiconductor Dialkoxy derivative of poly(p-phenylene vinylene) with cyano groups Charge-transfer Microcavity narrowband OPD based on the absorption of the CT band Copper phthalocyanine Donor Excited donor Donor-acceptor Deutscher Akademischer Austauschdienst Density functional theory Density of occupied states Discrete time Fourier transform Electron affinity Electron blocking layer Effective medium approximation Effective medium approach Excited state Electron transporting layer Free carrier Field of view Fourier transform Full width at half maximum Gallium arsenide Gaussian disorder model Germanium Ground state Hydrogen Hole blocking layer

Symbols, Physical Constants and Acronyms

HgCdTe HOD HOMO HPF HTL HVAC IAPP IC InGaAs InP IP IR IS ISC ITO LCAO LED LPF LUMO Me-PTC MEH-PPV NFA NIR NMP OFET OLED OPD OPM OPV OSC P3HT PbS PCBM PCE PD PHJ PM PM-OPD PV PVK PVS QCM RMS SCLC Si

xxi

Mercury cadmium telluride Hole-only device Highest occupied molecular orbital High-pass filter Hole transporting layer Heating, ventilation and air conditioning Dresden Integrated Center for Applied Physics and Photonic materials Internal conversion Indium gallium arsenide Indium phosphide Ionization potential Infrared Impedance spectroscopy Inter system crossing Indium tin oxide Linear combination of atomic orbitals Light emitting diode Low-pass filter Lowest unoccupied molecular orbital Me-PTC(3,4.9,10-perylenetetracarboxylic 3,4:9,10-bistmethylimide) Poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene] Non-fullerene acceptor Near infrared N-methyl-2-pyrrolidone Organic field effect transistor Organic light emitting diode Organic photodetector Organic photomultiplicator Organic photovoltaic Organic solar cell Poly(3-hexylthiophen-2,5-diyl) Lead sulfide [6,6]-phenyl-C61 -butyric acid methyl ester Power conversion efficiency Photodetector Planar heterojunction Photomultiplication Photomultiplication-type OPD Perylene tetracarboxylic Poly(9-vinylcarbazole) Personal vision systems Quartz crystal microbalance Root mean squared Space charge limited current Silicon

xxii

SMU SNR SOMO SRH SubNc TMM TSC UV VR ZnO

Symbols, Physical Constants and Acronyms

Source meter unit Signal-to-noise ratio Singly occupied molecular orbital Shockley-Read-Hall Subnaphthalocyanine Transfer matrix method Thermally stimulated current Ultraviolet Vibrational relaxation Zinc oxide

Chapter 1

Introduction

1.1 Detection of Electromagnetic Radiation: A Growing Demand As humankind discovers new physical phenomena, new applications are developed as well as new challenges arise. In the case of electromagnetic radiation, this was not unlike. The observation that light could be decomposed into different colors, later elucidated by Sir Isaac Newton, was followed by the question whether such colors would generate different temperatures. In 1798, Sir William Herschel observed that a thermometer placed away from the last seen reddish light measured a higher temperature than when placing it under any color. The near infrared (NIR), a type of radiation undetectable by the human eye, had just been discovered. Later, with the knowledge of the entire spectrum, also its manipulation became possible, i.e, we use radiation to measure distances, to cure diseases, to drive our cars. We could cite countless examples, however, all of them rely on a basic principle: we should be able to quantify where, of which kind and how strong the radiation is, i.e., we should be able to detect electromagnetic radiation. Unfortunately, in many periods of history, science was pushed further, financed by and used for non idyllic means. In case of detection, military needs were the driving force of study during a long period. The “Infrared Eye”, a device developed during the 1st World War and capable of detecting steamships and icebergs [1], was the first advanced application of infrared (IR) technology for security. Even nowadays, military applications still take up 32% of the market of imagers, amount which is expected to grow until 2024, see Fig. 1.1. Apart from that, however, other applications are of interest, such that our daily life is surrounded by devices which use different portions of the electromagnetic spectrum to facilitate our tasks. In fact, in 2017 the consumer electronics segment, which entails smartphones, optical disk drives, tablets, digital televisions, digital cameras, webcams, and compact disk players, held 42% of the total photodetector (PD) market [2]. Beyond automatically adjusting the brightness of our smartphone screen or simply lighting up the halls as we walk in, photodetectors are also used in telecommunica© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Kublitski, Organic Semiconductor Devices for Light Detection, Springer Theses, https://doi.org/10.1007/978-3-030-94464-3_1

1

2

1 Introduction

Fig. 1.1 Infrared imagers and detectors market status and forecasts for 2019 | HVAC stands for heating, ventilation and air conditioning. PSV are systems such as thermal cameras and binoculars. Reproduced from Ref. [3]

tions, medical diagnostics, control systems, scientific applications, quality control, surveillance, automobile industry and many others. Most of these applications rely on the NIR detection technology, as summarized in Fig. 1.1, which shows the usage of IR PDs and imagers in 2018 compared to the expected evolution until 2024. Interestingly, while the usage of imagers is expected to experience smaller changes in these years, PDs will be applied in larger scale in smart buildings and retail marketing, where a growth of 32% is expected [3]. While these applications are already in use, innumerable others will appear/be needed, not all of which can be provided by the current inorganic semiconductor industry. With a market development of USD 1.73 billion expected from 2018 to 2022 [2], it is clear that detection is an alive developing field. Below, we discuss what are the main limitation of current technology, which emphasizes the urge for further research towards new detecting concepts.

1.2 Challenges of the Current Technology Inorganic materials dominate the market of PDs, which is a result of decades of research leading to high performance devices. However, as the demand for highspeed data transmission increases, the current technology will face more challenges

1.2 Challenges of the Current Technology

3

in providing suitable devices. Silicon (Si) is the most used semiconductor, remaining attractive due to its low processability costs and very well-established technology, which grounds most of integrated circuits based on complementary metal oxide semiconductors (CMOSs). However, because Si is an indirect bandgap material, its absorption coefficient is low, requiring bulky devices to absorb radiation, which ultimately limits the device speed. Even though the low absorption of Si can be addressed by photon trapping [4], which allows for much thinner (faster) devices, the integrability with the CMOS technology is still not compelling. In fact, the integrability with the COMS technology is also a problem when using direct bandgap semiconductors, such as gallium arsenide (GaAs) and indium phosphide (InP) [5]. Another point refers to the detection range. Figure 1.1 shows that numerous applications are based in IR detecting devices, for which both low processability costs and high performance becomes more challenging. Beyond the Si gap, rare materials such as III–V indium gallium arsenide (InGaAs) or mercury cadmium telluride (HgCdTe) are mostly employed. While the former also suffers from low integrability with CMOS technology [6], the latter still faces many issues, in spite of being the most used technology in the range from 3 to 5 µm and 8 to 12 µm. The main limitations of HgCdTe PDs are the low operating temperatures (77 K), high production costs, unreliable p-doping, large pixel sizes and difficulties in achieving multi-band detection [7, 8]. As discussed, despite the reasonable performance of IR PDs, this field still lacks of cheaper, better processable and non exotic/toxic materials. Extensive research has been performed in that direction including two-dimensional materials [9], perovskites [10] and organic materials [11–13]. The latter is the subject of the next section.

1.3 Organic Electronics and Organic Photodetectors Nearly four decades have passed since the high electrical conductivity of polymers has been demonstrated [14], which boosted a new research and technological field, the so called Organic Electronics. Since then, many research groups have investigated the semiconducting properties of organic compounds and their application in devices, whose first goal was to reproduce the performance of the so far unique and successful inorganic semiconductor industry. The mechanical properties of organic compounds, however, allow for a new way of thinking electronics, which was not possible with the inorganic materials. Organic chemistry is very powerful and versatile, which enables designing new compounds with desired properties, leading to flexible, lightweight, transparent, and even biocompatible devices. These properties reshape the way human beings interact with technology, which can now be integrated to human body proving early diagnosis, health/healing monitoring and artificial replacements such as electronic eyes and electronic skin. Biodegradable devices could also avoid surgical intervention and improve patient recovery. In addition, organic electronics can be fabricated in customized formless fashion to integrate clothes, objects, cars and facades. While

4

1 Introduction

Fig. 1.2 Commercial application of organic electronic devices | a Smartphone Samsung Galaxy Z Fold 2. b Flexible organic solar cells (OSCs) applied in semitransparent windows and c under fabrication in a vacuum-processing production line. d NIR Organic photodetector used to fabricate the Portable NIR organic spectrometer by Senorics GmbH shown in (e). The copyrights of the pictures are a © Samsung Group, b © Sunew LIGHTTM , d and e © Senorics GmbH, c © Heliatek GmbH

research is still ongoing and these applications seem to be far from being ready, organic electronics is already available at the market in different products. The most successful representatives are OLEDs. These devices, integrated with an active matrix, form the so-called AMOLED technology and are now found in the most advanced smartphones and TVs. In Fig. 1.2a, an example of a flexible screen developed by Samsung is shown. In this case, vacuum-processed OLEDs are employed in a foldable device, paving the way for this sort of application. Although OLEDs were the first branch of organic electronics to take off, also other applications are now reaching the costumers. In Fig. 1.2, organic solar cells (OSCs) under operation (b) and fabrication (c) are shown. Both flexibility and semitransparency can be achieved, enabling energy harvesting in conditions which opaque materials do not render. Even though the lower performance of OSCs will likely place these devices in alternative usages [15–17], such as smart windows, formless surface coverage and energy harvesting in idle places, a broad market is expected for the OSC technology.

1.3 Organic Electronics and Organic Photodetectors

5

Apart from OLEDs and OSCs, several electronic components based on organic materials have already been demonstrated. With the aid of such devices, entire wearable, stretchable and even soluble circuits can be fabricated [18–24]. Such modules are expected to transform the way human beings interact with electronics. Areas as medical diagnosis and monitoring will certainly benefit from this technology, where degradable devices can, for example, decrease the number of surgical interventions and improve monitoring. A vast range of applications relies on signal detection, as already presented at the beginning of this chapter. Also in this branch, organic devices are available in the ultraviolet (UV) [25, 26], visible [27–29] and NIR range [30–32]. Broadband as well as narrowband OPDs with specific detectivities comparable to those of inorganic devices were demonstrated. These devices combine the advantages of the plastic electronics with high performance, suggesting that new applications can be achieved as compared to those provided by the current semiconductor technology. Similarly, to OLEDs and OSCs, the current scientific development of OPDs has already enabled the emergence of companies such as Senorics GmbH, whose focus is providing spectroscopic detection for different applications. Figure 1.2d shows the OPD used to build the portable spectrometer depicted in Fig. 1.2e. By using the weak absorption band of CT states and the optical properties of a Fabry–Pérot microcavity, narrowband OPDs are achieved [33–35]. The miniaturized spectrometer with 16 active channels shown in Fig. 1.2e comprises varying cavity lengths, which triggers different enhanced resonant wavelengths and enables the identification of chemicals, such as medicines and others. From what was presented so far, it is clear that new technologies such as organic electronics can address a wide range of applications, including signal detection, which is the subject of this thesis. Besides the several assets discussed here, OPDs still suffer from many weaknesses, motivating this research. Since the focus in this thesis is on improving and understanding different aspects of OPDs, in the following section their main limitations are presented, aiming to guide the reader through the reason why such aspects have been investigated.

1.4 Challenges for OPDs The performance of a photodetector is evaluated in terms of its specific detectivity (D ∗ ), which depends on two parameters, namely, the device external quantum efficiency (EQE) and the device noise spectral density (Sn ). Therefore, in order to improve D ∗ of OPDs, both parameters need to be optimized. Apart from that, also the device speed and linearity are generally required. Below, the main challenges for realizing commercializable OPD-based applications are summarized: • Low-noise devices: Detecting faint light is essential for most applications. Therefore, the PD must be able to distinguish the input signal from its off state. In fact, this defines the so called signal-to-noise ratio (SNR) of detectors, which must

6

•

•

•

•

•

1 Introduction

be as high as possible. In organic OPDs, the high dark current usually observed in these devices increases the shot noise contribution, reducing D ∗ by orders of magnitude as compared to the background limited infrared photodetection (BLIP) limit [36]. Although this is a well-known limitation, a comprehensive understating of the problem was still missing. In Chap. 5, research insights to explain this phenomenon are presented. High EQE: In photovoltaic-type OPDs, the EQE is intrinsically limited to 100%. At maximum, every photon can generate only one electron in the final current. For this type of devices, several examples exist for which EQE is sufficiently high, with internal quantum efficiency (IQE) approaching unity. However, another class of device has been demonstrated, where EQE can be higher than unity. Based on photogain, these devices are an alternative to detect low signals. Small light inputs can generate higher currents, and therefore are easier to detect. Nonetheless, amplifying EQE while keeping reasonable noise current is challenging. In Chap. 6, this aspect is addressed, where vacuum-processed small molecule photomultiplication (PM)-type OPDs are realized. Narrowband response: Many materials show characteristic absorption features, allowing the quantification of their properties. For material sensing, e.g. identification of substances, contamination of products and food quality, small changes in the spectra must be detected. This requires narrowband devices, for which different strategies have been proposed. However, achieving tunability over a wide spectral range, avoiding parasitic absorption and achieving high IQE in the NIR is still desired. In Chap. 6, this issue is addressed by embedding photomultiplication-type OPDs (PM-OPDs) in Fabry–Pérot microcavities. High speed: As argued in at the beginning of this chapter, high speed is required when detectors are aimed for communication, for example. In this aspect, OPDs are limited by the character of organic materials, whose mobilities are generally orders of magnitude lower than in Si. Traps, a common feature in organic materials, are also believed to influence the response speed. While OPDs comprise much thinner active layers in comparison to Si, which enhances speed, the capacitance of thin-OPDs is increased, thereby increasing the RC time. Wide linear dynamic range (LDR): A linear response to an input signal is important for the interpretation of detected signals, as it facilitates the device calibration. Although linear dynamic ranges as high as 120 dB were already reported for OPDs [37], most devices show non-linear behavior at high light intensities, due to an increased bimolecular recombination. On the other hand, at low light intensities, detrimental traps diminish the lower limit for detection, when the device can no longer discriminate signal from noise. Integration with circuit read out: For the development of imagers, for example, arrays of OPDs integrated with read out circuits are necessary. This can be done either by integrating OPDs with state-of-art CMOS or building completely organic based imagers, which is more challenging, as also organic transistors are required. Although some examples are found in the literature in that direction [23, 32, 38– 40], further research is needed.

1.4 Challenges for OPDs

7

• High performance in the IR spectral range: As shown in Fig. 3.1, the demand for photodetectors extends further into the IR region. Beyond 2500 nm, in the region currently covered by HgCdTe PDs, no OPDs have been demonstrated [41]. In fact, it has been suggested that intrinsic limitations of organic materials will preclude the operation of OPDs in the spectral region above 2000 nm [42]. Despite the huge potential for application of OPDs, many questions are still to be answered. This thesis is focused on three of them: sources of noise, enhancement of EQE and narrowband response. The complete outline of this thesis is given below.

1.5 Outline of This Thesis The goal of this thesis was developing novel OPDs as well as understanding fundamental properties of these devices, aiming to improve their performance. For that, the fundamentals of light detection are revised in Chap. 2, where also classic semiconductors are discussed. This helps us to understand the main properties of charge carrier generation/recombination in semiconductors and to derive fundamental limits for device performance. In Chap. 3, organic materials are introduced, where the emergence of semiconducting properties are considered. This is followed by a brief discussion of solid-state physics in organic thin films, charge transport and light matter interaction. In this chapter, the most update knowledge of physical phenomena in organic materials is presented with regard to charge generation/recombination processes and their effect on the open-circuit voltage (VOC ) of OSCs, which is connected to the OPD performance. In Chap. 4, the experimental methods for device preparation and characterization are presented. Chapter 5 is dedicated to experimental findings on the origin of the high dark current of OPDs. Here, with the aid of drift-diffusion simulations, the interplay of CT states, trap states and device engineering is revealed. In Chap. 6, another type of device is introduced, which is used to demonstrate the possibility of achieving EQE > 100% via photomultiplication. These results are used to develop a new device concept, which unifies the photomultiplication effect and optical microcavity OPDs, enabling amplified EQE in the sub-bandgap region. In Chap. 7, the findings of this work are summarized and the future prospects in the field of OPDs are presented.

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1 Introduction

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18. Crone B, Dodabalapur A, Lin Y-Y, Filas R, Bao Z, LaDuca A, Sarpeshkar R, Katz H, Li W (2000) Large-scale complementary integrated circuits based on organic transistors. Nature 403(6769):521–523. https://doi.org/10.1038/35000530 19. Hammock ML, Chortos A, Tee BC-K, Tok JB-H, Bao Z (2013) 25th anniversary article: the evolution of electronic skin (e-skin): a brief history, design considerations, and recent progress. Adv Mater 25(42):5997–6038. https://doi.org/10.1002/adma.201302240 20. Mannsfeld SC, Tee BC, Stoltenberg RM, Chen CVH, Barman S, Muir BV, Sokolov AN, Reese C, Bao Z (2010) Highly sensitive flexible pressure sensors with microstructured rubber dielectric layers. Nat Mater 9(10):859–864. https://doi.org/10.1038/nmat2834 21. Takei K, Takahashi T, Ho JC, Ko H, Gillies AG, Leu PW, Fearing RS, Javey A (2010) Nanowire active-matrix circuitry for low-voltage macroscale artificial skin. Nat Mater 9(10):821–826. https://doi.org/10.1038/nmat2835 22. Park S, Fukuda K, Wang M, Lee C, Yokota T, Jin H, Jinno H, Kimura H, Zalar P, Matsuhisa N et al (2018) Ultraflexible near-infrared organic photodetectors for conformal photoplethysmogram sensors. Adv Mater 30(34):1802359. https://doi.org/10.1002/adma.201802359 23. Wu Y-L, Fukuda K, Yokota T, Someya T (2019) A highly responsive organic image sensor based on a two-terminal organic photodetector with photomultiplication. Adv Mater 31(43):1903687. https://doi.org/10.1002/adma.201903687 24. Kublitski J, Tavares AC, Serbena JP, Liu Y, Hu B, Hümmelgen IA (2016) Electrode material dependent p-or n-like thermoelectric behavior of single electrochemically synthesized poly (2, 2’-bithiophene) layer-application to thin film thermoelectric generator. J Solid State Electrochem 20(8):2191–2196. https://doi.org/10.1007/s10008-016-3223-6 25. Guo F, Yang B, Yuan Y, Xiao Z, Dong Q, Bi Y, Huang J (2012) A nanocomposite ultraviolet photodetector based on interfacial trap-controlled charge injection. Nat Nanotechnol 7(12):798–802. https://doi.org/10.1038/nnano.2012.187 26. Büchele P, Richter M, Tedde SF, Matt GJ, Ankah GN, Fischer R, Biele M, Metzger W, Lilliu S, Bikondoa O et al (2015) X-ray imaging with scintillator-sensitized hybrid organic photodetectors. Nat Photon 9(12):843–848. https://doi.org/10.1038/nphoton.2015.216 27. Pierre A, Gaikwad A, Arias AC (2017) Charge-integrating organic heterojunction phototransistors for wide-dynamic-range image sensors. Nat Photon 11(3):193–199. https://doi.org/10. 1038/nphoton.2017.15 28. Lochner CM, Khan Y, Pierre A, Arias AC (2014) All-organic optoelectronic sensor for pulse oximetry. Nat Commun 5(1):5745. https://doi.org/10.1038/ncomms6745 29. Gasparini N, Gregori A, Salvador M, Biele M, Wadsworth A, Tedde S, Baran D, McCulloch I, Brabec CJ (2018) Visible and near-infrared imaging with nonfullerene-based photodetectors. Adv Mater Technol 3(7):1800104. https://doi.org/10.1002/admt.201800104 30. Xie B, Xie R, Zhang K, Yin Q, Hu Z, Yu G, Huang F, Cao Y (2020) Self-filtering narrowband high performance organic photodetectors enabled by manipulating localized frenkel exciton dissociation. Nat Commun 11(1):2871. https://doi.org/10.1038/s41467-020-16675-x 31. Armin A, Jansen van Vuuren RD, Kopidakis N, Burn PL, Meredith P (2015) Narrowband light detection via internal quantum efficiency manipulation of organic photodiodes. Nat Commun 6(1):6343. https://doi.org/10.1038/ncomms7343 32. Rauch T, Böberl M, Tedde SF, Fürst J, Kovalenko MV, Hesser G, Lemmer U, Heiss W, Hayden O (2009) Near-infrared imaging with quantum-dot-sensitized organic photodiodes. Nat Photon 3(6):332–336. https://doi.org/10.1038/nphoton.2009.72 33. Siegmund B, Mischok A, Benduhn J, Zeika O, Ullbrich S, Nehm F, Böhm M, Spoltore D, Fröb H, Körner C, Leo K, Vandewal K (2017) Organic narrowband near-infrared photodetectors pased on intermolecular charge-transfer absorption. Nat Commun 8:15421. https://doi.org/10. 1038/ncomms15421 34. Tang Z, Ma Z, Sánchez-Díaz A, Ullbrich S, Liu Y, Siegmund B, Mischok A, Leo K, Campoy-Quiles M, Li W, Vandewal K (2017) Polymer: fullerene bimolecular crystals for nearinfrared spectroscopic photodetectors. Adv Mater 29(33):1702184. https://doi.org/10.1002/ adma.201702184

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1 Introduction

35. Kaiser C, Schellhammer KS, Benduhn J, Siegmund B, Tropiano M, Kublitski J, Spoltore D, Panhans M, Zeika O, Ortmann F et al (2019) Manipulating the charge transfer absorption for narrowband light detection in the near-infrared. Chem Mater 31(22):9325–9330. https://doi. org/10.1021/acs.chemmater.9b02700 36. Kublitski J, Hofacker A, Boroujeni BK, Benduhn J, Nikolis VC, Kaiser C, Spoltore D, Kleemann H, Fischer A, Ellinger F, Vandewal K, Leo K (2021) Reverse dark current in organic photodetectors and the major role of traps as source of noise. Nat Commun 12(1):551. https:// doi.org/10.1038/s41467-020-20856-z 37. Fang Y, Guo F, Xiao Z, Huang J (2014) Large gain, low noise nanocomposite ultraviolet photodetectors with a linear dynamic range of 120 dB. Adv Opt Mater 2(4):348–353. https:// doi.org/10.1002/adom.20130053 38. Ng TN, Wong WS, Chabinyc ML, Sambandan S, Street RA (2008) Flexible image sensor array with bulk heterojunction organic photodiode. Appl Phys Lett 92(21):213303. https://doi.org/ 10.1063/1.2937018 39. Baierl D, Pancheri L, Schmidt M, Stoppa D, Dalla Betta G-F, Scarpa G, Lugli P (2012) A hybrid CMOS-imager with a solution-processable polymer as photoactive layer. Nat Commun 3(1):1175. https://doi.org/10.1038/ncomms2180 40. Shekhar H, Fenigstein A, Leitner T, Lavi B, Veinger D, Tessler N (2020) Hybrid image sensor of small molecule organic photodiode on cMoS-integration and characterization. Sci Rep 10(1):7594. https://doi.org/10.1038/s41598-020-64565-5 41. Zheng L, Zhu T, Xu W, Liu L, Zheng J, Gong X, Wudl F (2018) Solution-processed broadband polymer photodetectors with a spectral response of up to 2.5 µm by a low bandgap donoracceptor conjugated copolymer. J Mater Chem C 6(14):3634–3641. https://doi.org/10.1039/ C8TC00437D 42. Gielen S, Kaiser C, Verstraeten F, Kublitski J, Benduhn J, Spoltore D, Verstappen P, Maes W, Meredith P, Armin A, Vandewal K (2020) Intrinsic detectivity limits of organic near-infrared photodetectors. Adv Mater 32:2003818. https://doi.org/10.1002/adma.202003818

Chapter 2

Fundamentals of Light Detection

In this chapter, the main aspects of light detection are discussed. A brief introduction to radiometry, the field of physics dedicated to detection of electromagnetic radiation, is given in Sect. 2.1, in addition to important quantities used to characterize light sources and detectors. Classic detecting devices based on traditional semiconductors technologies are considered in Sect. 2.2, where basic concepts of semiconductors physics are introduced. Additionally, two of the most used approaches for classical detecting devices, pn-junctions and photoconductors, are presented within this section (Sects. 2.2.5, 2.2.6). Finally, general characterization parameters for photodetectors are introduced in Sect. 2.3.

Major references for this chapter are: Radiometry A. Rogalski [1] E. F. Zalenwski [2] Classical Light detecting devices and device characterization: C. Kittel [3] S. M. Sze and K. K. Ng [4] P. Würfel [5] S. H. Simon [6] D. A. Johns and K. Martin [7] G. Rieke and R. George [8] S. L. Chuang [9]

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Kublitski, Organic Semiconductor Devices for Light Detection, Springer Theses, https://doi.org/10.1007/978-3-030-94464-3_2

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2 Fundamentals of Light Detection

2.1 Radiometry Radiometry is a field of physics which deals with detection of electromagnetic radiation, including ultraviolet (UV), human eye visible and infrared. Different, but equivalent, physical quantities are used to express the radiometric properties of the electromagnetic radiation, namely frequency (v), energy (E) and wavelength (λ), which are connected by the Planck–Einstein relation, cf. Eq. (2.1). We can therefore define radiometry as branch of physics which discuss electromagnetic detection from 1013 Hz (10 nm, 120 eV) to 1016 Hz (10 µm, 0.12 eV). However, along this chapter we will mostly use E and λ. E=

hc = hν. λ

(2.1)

Our body is maybe the first electromagnetic detector that we can think of. We are able to see and feel specific ranges of electromagnetic field, with different accuracy: our eyes are more sensitive to yellowish-green color, for example, which makes them a bad detector for blue. In fact, every detector is designed to operate in a specific range. In order to define this range, we first need to know what the characteristics of the source we want to detect are and the characteristics of our detector. Considering the light detected by the human eye, a branch called photometry deals with the measurement of light in the visible range, and the quantities are then weighted by the spectral response of the eye. More generally, we want to express radiometric quantities in terms of E, λ or ν weighted by area and/or time.

2.1.1 Radiometric Quantities Below, we define quantities which are useful to understand the concept of specific detectivity, black-body radiation in its different representations and BLIP limit. A comprehensive discussion of these parameters can be found in Ref. [1]. Radiant flux (Θ) or radiant power is the energy, E, radiated by a source per unit of time, t, defined as: Θ=

  dE , with unit W = J s−1 . dt

(2.2)

Irradiance (I ), sketched in Fig. 2.1a, is the density of incident radiant flux at a surface point, A, defined as: I =

  ∂2 E ∂Θ = , with unit W m−2 . ∂A ∂t∂ A

(2.3)

Radiant exitance (M), represented in Fig. 2.1b, is the density radiant flux sent out from a surface (not to confuse with irradiance (I )), defined as:

2.1 Radiometry

13

Fig. 2.1 Geometric representation of Radiometric quantities | a Irradiance, b radiation exitance, and c radiance of an extended source. Adapted from Ref. [1]

M=

  ∂2 E ∂Θ = , with unit W m−2 . ∂A ∂t∂ A

(2.4)

Radiance (L) is defined as the radiant flux per unit solid angle (Ω) emitted in a direction, per unit of projected area of the surface element perpendicular to that direction. L is used to characterize an extended source, as shown in Fig. 2.1c, and can be expressed as: L=

  ∂2Θ , with unit W sr−1 m−2 . ∂Ω∂ A cos θ

(2.5)

Using Eq. (2.5), we can calculate what is the radiant exitance (M) emitted by the source. Therefore, we rewrite Eq. (2.5) for the detector, with index “d”, and for the source, with index “s”, as: ∂ 2 Θ = L∂ As cos θs ∂Ωd .

(2.6)

Assuming a Lambertian radiator, for which the light intensity in independent of the direction and integrating with respect to the detector gives radiant exitance from the source: ∂Θ = ∂ As







2π

π 2

1 = πL . 2 0 Ωd 0 (2.7) The relation M = πL is important because, for a Lambertian source which we will discuss in the next section, we can calculate radiant exitance at the background “source” from the radiance, described at any point and direction. M =

L cos θs dΩd =

dφ

L cos θs sin θdθ = 2πL

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2 Fundamentals of Light Detection

2.1.2 Black-Body Radiation The concept of black-body source/radiator is used to derive many properties in physics. According to Zalewski, “an ideal black-body is a completely enclosed blackbody containing a radiation field which is in thermal equilibrium with the isothermal walls of the enclosure that is at a known absolute temperature. The radiation in equilibrium with the walls does not depend upon the shape or constitution of the walls provided that the cavity dimensions are much larger than the wavelengths involved in the spectrum of the radiation” [2]. Planck’s law of radiation describes the relationship between the absolute temperature (T ) and radiance (L). Using Eq. (2.7), we can write the radiant exitance (M) for a black-body as:    −1   hc 2πhc2 exp − 1 , with unit W m−2 m−1 5 λ λkB T = πL BB .

MBB (λ, T ) = MBB

(2.8)

Equation (2.8) represents the rate of emission of energy per unit area per unit time per unit wavelength interval. Since the energy carried per photon is defined by Eq. (2.1), we can calculate the number of photons emitted per unit area per unit time per unit wavelength interval, which equals the photon flux density: ΦBB (λ, T ) =

   −1   hc 2πc −2 −1 −1 exp − 1 , with unit #photons m s m λ4 λkB T (2.9)

ΦBB = πL BB,γ .

(2.10)

L BB,γ is the number of photons per unit solid angle emitted in a direction, per unit of projected area of the surface element perpendicular to that direction. Note that, in expressing the relations above in terms of E, d E = − λhc2 dλ. In Fig. 2.2, Eqs. (2.9) and (2.8) are plotted for different temperatures, including T = 5778 K, the surface temperature of the Sun. The maximum intensity is emitted in the yellow and green, when plotted over wavelength.

2.2 Inorganic Light Detecting Devices Light detection is manly carried by devices based on inorganic semiconductors such as Si, GaAs and germanium (Ge). Therefore, in order to understand the working mechanism of these devices, an introduction to semiconductor physics is needed. Below, fundamental concepts such as band structure and electronic properties are discussed.

2.2 Inorganic Light Detecting Devices

15

Fig. 2.2 Radiant exitance (dashed blue lines) and photon flux density (solid black lines) of an ideal black-body according to Planck’s law of radiation for different temperatures. The human visible range of the electromagnetic radiation is highlighted by colors

2.2.1 Fundamentals of Inorganic Semiconductor Physics 2.2.1.1

Semiconductors and Band Structure

A rigorous treatment of a semiconductor requires a 3D analysis of its properties. However, many of these properties can be equivalently derived in one dimension, simplifying the derivation. Below, this approach is used, keeping in mind that we are dealing with tridimensional phenomena. When an electric field (F) is applied to a material sandwiched between two terminals, a current density (J ) flows proportionally to its electric conductivity (σ). For electrons, it reads: J = σn F.

(2.11)

σn or p on its turn depends on the charge carrier concentration (n, p) and on the mobility of the material (μn , μp ). For electrons, we can write: σn = qnμn .

(2.12)

The first criteria to define a semiconductor stands on its conductivity, whose values range from 10−8 to 103 S cm−1 . More precisely, a semiconductor is defined by the electronic character of the electric conductivity for electrons and holes (σn , σp ), which can be modified by temperature, light absorption and doping.

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2 Fundamentals of Light Detection

Most used semiconductors and the theory discussed within this section lies on the formation of crystalline solids, where atoms are covalently bonded to each other. In these materials, the length of the electron wave function is on the order of the lattice constant, which means that interference takes place. Therefore, to understand the electronic properties of semiconductors, we have to describe them based on the concepts of quantum mechanics, as an electron in the periodic lattice behaves as a wave. The solution of the Schrödinger equation for the large amount of electrons, in the order of 1023 , is impossible, requiring several approximations. On the basis of Bloch’s theorem, which states that the wave function of an electron in a periodic potential may be written as a plane wave modified by a periodic function of the potential, the Kronig–Penney model was the first one-dimensional solution to deal with the problem of an electron in a crystal. In spite of several assumptions, already from the solution of this model, the concepts of a bandgap, different effective masses and negatively charged particles (holes) emerge [10]. Treating crystalline solids from a 3D perspective, however, requires us to describe how waves behave in a crystal. In view of the periodicity of their structure, the optoelectronic properties of crystalline solids can be derived using the concept of the “unit-cell”, which in the reciprocal space becomes the “Brillouin zone”. More accurately, for a perfect crystal, we derive the optoelectronic properties on the bases of the first Brillouin zone, which in real space is called Wigner–Seitz unit cell. Ultimately, the strength of the periodic potential determines the energetic separation between the highest occupied valence band and lowest occupied conduction band, which is defined as the semiconductor bandgap. For this class of materials, a moderate interaction is observed, avoiding the overlap of bands, but keeping the energetic separation (E g = E C − E V ) at around 1 eV [4, 6]. The energetic dispersion the kspace leads to the formation of many energetic gaps, which cannot be occupied by charge carriers. However, for the operation of semiconductor devices, the first bandgap is the most relevant, as it defines the main properties of the semiconductor. At 0 K, the valance band is completely filled and the conduction band completely empty. However, at room temperature (T0 ), the thermal energy is sufficiently large to excite electrons over E g . The vacancies left in the valance band are called holes. Holes in the valence band can be treated equivalently to electrons in the conduction band, participating on the charge transport, i.e., on the electric conductivity.

2.2.1.2

Semiconductors Statistics

To further understand the properties of semiconductors, it is important to characterize the charge carrier concentration, that is, the amount of electron (holes) in the conduction (valence) band at a given temperature. As these particles are fermions, we describe the occupation of states by the Fermi–Dirac statistics ( f (E, T )), see Eq. (2.13). The product of f (E, T ) by the density of states (D O S(E)) integrated over the entire conduction band gives concentration of electron, cf. Eq. (2.14). An analogous treatment can be done for holes, accounting for the empty states in the valence band 1 − f (E), see Eq. (2.15). Both approaches are shown below:

2.2 Inorganic Light Detecting Devices

17

Fig. √2.3 Intrinsic semiconductor | a Band diagram. b In 3D, the density of states is proportional to E. c Fermi–Dirac distribution for T > T0 . d Carrier concentration. Adapted from Ref. [4]

 −1   E − EF +1 f (E, T ) = exp kB T  ∞ n= f (E)D O S(E)d E p=

EC  EV −∞

[1 − f (E)] D O S(E)d E,

(2.13) (2.14) (2.15)

where kB is the Boltzmann constant, T the absolute temperature and E F the Fermi level. In Fig. 2.3, a schematic representation of these quantities is shown. Using the Boltzmann approximation to solve the above equations, the charge carrier density for electrons and holes can be derived:     (E C − E F ) (E C − E F ) = NC exp − (2.16) exp − kB T kB T       2πm ∗p kB T 3/2 (E F − E V ) (E F − E V ) = NV exp − . (2.17) p=2 exp − h2 kB T kB T 

n=2

2πm ∗n kB T h2

3/2

NC and NV are the effective density of states in the conduction and valence band, respectively. The effective mass for electrons and holes (m ∗n , m ∗p ) in Eqs. (2.16) and (2.17), respectively, refers to the reciprocal curvature at the extreme of the respective band. For an anisotropic medium, the effective mass is a tensor and can be calculated for Cartesian coordinates, i, j, as follows:

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2 Fundamentals of Light Detection

(m ∗n or p )i, j

 =

1 ∂E 2 ∂ki ∂k j

−1

.

(2.18)

The concept of effective mass has no relation with the physical meaning of real mass, but rather with how they behave in a periodic potential: if an electric field is applied to the crystal, an electron (hole) is accelerated with respect to its effective mass. For an intrinsic semiconductor, the Fermi level (E F ) is also named intrinsic level (E i ), which is obtained from Eqs. (2.16) and (2.17):   kB T NV EC − EV . (2.19) + ln EF = Ei = 2 2 NC Using Eqs. (2.19), (2.17) and (2.16), the intrinsic carrier concentration (n i ) can be determined:   Eg . (2.20) np = n 2i = NC NV exp − kB T n i depends mainly on the absolute temperature and on the band gap, therefore, high gap materials show lower intrinsic concentration. For example, at room temperature, n i of Si (E g = 1.11 eV) is 9.65 × 109 cm−3 , while for GaAs (E g = 1.43 eV) n i is 2.25 × 106 cm−3 [4].

2.2.1.3

Doping of Semiconductors

An important aspect in the field of semiconductors is the possibility of changing their electronic properties by doping. In fact, the doping has enabled the applicability of inorganic semiconductors. When donating (D) or accepting (A) atoms are inserted into the intrinsic semiconductor matrix (Si, GaAs, …), these semiconductors become the so-called extrinsic semiconductors. As shown in Fig. 2.4, E F shifts towards the conduction (valence) band upon introduction of donor (acceptor) atoms, with the concentration NA (ND ). Under the condition of total ionization, where the thermal energy at room temperature is enough to ionize every dopant and the dopant concentration is much higher than n i , n = ND or p = NA . It is also useful to express these quantities in therms of n i :     (E F − E i ) (E i − E F ) and p = n i exp . (2.21) n = n i exp kB T kB T When both types of impurities are present, the one in greater amount will determine the electronic properties of the semiconductor. The extrinsic character of the semiconductor depends on the temperature; if the temperature is too low, dopants are not ionized. The semiconductor is then in the “freeze-out region”. If the temperature

2.2 Inorganic Light Detecting Devices

19

Fig. 2.4 n-Doped√semiconductor | a Schematic band diagram. b In 3D, the density of states is proportional to E. The donor level, ND , is also shown. c Fermi–Dirac distribution, which is shifted to E C due to the doping. d Carrier concentration. Note that the mass action law is still valid for extrinsic semiconductors and ND : np = n 2i . Adapted from Ref. [4]

is too high, n i becomes comparable to NA or ND , and the semiconductor gets into the intrinsic regime. In Si, doping concentrations typically range from 1013 to 1018 cm−3 .

2.2.1.4

Generation and Recombination

Any process capable of providing an energy E ≥ E g can lead to the generation of charges, i.e., an electron is promoted from the valence band to the conduction band, leaving a hole in the former. The most common process of generation is the absorption of light, which grounds the operation of photodetectors and solar cells. Competing with generation, recombination is the inverse process, where an excited electron looses energy and returns to the valence band, filling a hole in the latter. Similarly to generation, which can occur from different processes, also recombination takes place via several mechanisms. While some of these processes are used in devices, e.g. light emission used in light emitting diodes (LEDs), most of them are detrimental for photodetectors and solar cells, especially if energy is lost without emitting a photon. Absorption of photons occurs when a photon with E ≥ E g causes a generation process, as described above. The probability of this event to happen depends on absorption coefficient (α(E)), which is proportional to the density of states. Additionally, when the transition does not require a change in photon momentum, it is called a direct transition; while when a change in the momentum is required, the transition is called indirect. The change in momentum is provided by phonons which can be absorbed or emitted by the lattice, making the process less probable than that for a direct transition. Because these are material properties dictated by its band structure, GaAs is known as a direct semiconductor, while Si and Ge are known as indirect semiconductors. A consequence of an indirect transition is the low absorp-

20

2 Fundamentals of Light Detection

tion coefficient. Crystalline Si, for examples, requires at least 100 µm thick wafers to absorb all photons from the solar spectrum. In thermal equilibrium, the generation of charges must equal the recombination of emitted photons (γ). For a source whose spectral shape can be described by the black-body radiation, the generation and recombination rates are G p = G n = Rγ = αΦBB (E),

(2.22)

where the photon flux density (ΦBB ) is expressed in the form of Eq. (2.9), but integrated over a solid angle of 4π, instead of π. By setting the solid angle to π, we would be considering the generation caused by incident photons. However, as a consequence of the law of refraction, photons remitted by the medium undergo internal reflection at the interface medium/vacuum and are reabsorbed by the medium. The isotropic character of the remission contributes to generation and, therefore, must be taken into account, which is done by setting the solid angle to 4π, a sphere. Finally, we can calculate the generation rate caused by the background radiation at room temperature (T0 ), using the energy-dependent version of Eq. (2.9):  ∞ α(E)E 2 8π

d E. (2.23) G0 = 3 2 h c 0 exp E − 1 kB T0 The index 0 in the generation term refers to the dark condition at T0 . If the solar spectrum is considered, for example, T = T0 . Radiative recombination of photons is the inverse process of generation, therefore, electrons loose an energy E = hv by emitting a photon, as shown in Fig. 2.5a. The radiative recombination is proportional to the amount of charges, as the probability of electron and holes to meet increases with the concentration. In dark, the equilibrium is achieved when generation equals recombination, therefore, the radiative recombination can be expressed as: R0 = βn 0 p0 = G 0 .

(2.24)

The recombination constant (β) can be expressed from Eq. (2.24) as β = G 0 (n 0 p0 )−1 . Out of equilibrium, e.g., under light absorption, injection or extraction, where np = n 2i , the distribution of electrons and holes are still determined by Fermi–Dirac distributions (Eq. (2.13)) at the lattice temperature. Therefore, out of equilibrium conditions, charges recombine with the same energy distribution, but with a modified rate:

G n,p = Rn,p

np G0 = βnp = np = G 0 2 = G 0 exp n 0 p0 ni



E F,C − E F,V kB T

 .

(2.25)

2.2 Inorganic Light Detecting Devices

21

Fig. 2.5 Recombination processes | a Radiative recombination, b Shockley–Read–Hall (SRH) recombination, c Auger recombination, and d Surface recombination

Where we also expressed the generation rate in terms of the quasi-Fermi levels (E F,C , E F,V ) which are energy levels used to describe separately the Fermi–Dirac distribution of holes and electron out of equilibrium. This will be further discussed later on. Since Eq. (2.25) depends on n and p, it is often refereed to as “bimolecular” recombination. Equation (2.25) is an approximated version of the generalized Planck law [11], which is able to describe the emission of any kind of radiation and reads: M(E) =

  E − (E F,C − E F,V ) −1 2π E 2 A(E) exp . h 3 c2 kB T

(2.26)

Note that Eq. (2.26) is integrated over a solid angle of π, which accounts for photons leaving the surface. Therefore, it assumes the form of Eq. (2.9), modified by the so-called chemical potential, ξ, of emitted photons. In equilibrium, ξ = (E F,C − E F,V ) = 0, Eq. (2.26) represents thermal radiation. Non-radiative recombination of photons. Besides radiative recombination, another processes can take place in semiconductors, leading to recombination. The energy of charges involved is not transformed by emitting a photon, but by thermalization to the lattice. Every non-radiative recombination finds a reverse process, whose excitation arises from the absorption of energy from the lattice, guaranteeing the equilibrium. Below, we describe each of these processes, which are also represented in Fig. 2.5b–d. Shockley–Read–Hall (SRH) recombination: this is one of the most important recombination processes in solar cells and photodetectors. The presence of states within the gap facilitates recombination and generation with a non-radiative character, i.e., not requiring photons to be absorbed or emitted, but rather acquiring energy from or losing energy to phonons in the lattice. This process was described theoretically by Shockley and Read [12], concomitantly with Hall [13], who observed the same effect experimentally. An impurity level, herein named trap level, with energy E t located within the gap of the semiconductor, participates on the generation and recombination. The rates at which this process happens depend on the density of traps (Nt ), their energetic

22

2 Fundamentals of Light Detection

position, E t , the capture cross-section for electrons (σn ) and holes (σp ), the thermal velocity for electrons (vn ) and holes (vp ), and the concentration of carriers n, p and n i . Finally, the recombination rate for a single trap level can be described as follows:

RSRH =

σp vp



 vn vp σn σp Nt np − n 2i 

 ·

E t −E i t p + n i exp Eki B−E + σ n + n v exp n n i T kB T

(2.27)

The recombination described by Eq. (2.27) finds its maximum when E t = E i , which means that traps close to the mid-gap are the most relevant for generation and recombination. The reason for that lies on the statistical distribution of charges. We can think of an electron in the conduction band losing half of its energy and being captured by a trap at E i (step i in Fig. 2.5b), followed by second loss which fills a hole in the valence band (step ii in Fig. 2.5b). Each process is determined by the energy difference from E c − E t and E t − E v , respectively. As E t approaches the conduction band, the first process becomes more efficient. However, concomitantly, the second process becomes less efficient, since the energy increases. The same happens when E t approaches the valence band. Although electrons sitting at E t fall very easily to the valence band, there will be too less occupied trap states. The same happens for generation. Another way to understand this relation is by assuming that holes, as electrons, are captured to the trap state and need to meet there. The maximum amount of electron and holes at E t together will be when E t = E i . More details about SRH recombination and its implication on photodetectors will be given in Sect. 2.2.5 and Chap. 5. Auger recombination is the inverse process of impact ionization, where the kinetic energy of an incoming electron is transferred to another electron in the valence band of a semiconductor exciting it to the conduction band. In Auger recombination, the energy transferred by an electron which recombines from the conduction band to the valence band excites another electron from the conduction band to higher energetic level. The excited electron thermalizes non-radiatively to the bottom of the conduction band, thereby releasing energy. This process is represented in Fig. 2.5c and described by Eq. (2.28): RAug,n = Cn n 2 p

and

RAug,p = Cp np 2 ,

(2.28)

where Cn and C p are constants. This type of recombination is very important in pnjunctions operating at high charge carrier concentrations, e.g, for emission in LED, limiting the efficiency in these devices. Surface recombination happens via states created by atoms at the surface of the crystal which did not complete the available bonds, the so-called, dangling bonds. These atoms form a quasi continuous distribution of states, as shown in Fig. 2.5d, through which charges can recombine. Analogous to SRH recombination, surface recombination is also more effective for states close to the mid-gap. The surface recombination rates for electrons and holes are:

2.2 Inorganic Light Detecting Devices

RS,n = vR,n n

23

and

RS,p = vR,p p,

(2.29)

where vRn and vRp are the recombination velocities. This type of recombination is especially problematic at the metal/semiconductor interfaces, where the recombination velocities of metals can be considered infinite.

2.2.2 From Radiation to Chemical Energy Light detecting devices must convert any received radiation into an electrical output. In between this step, after absorption of light, charges build up a chemical potential, which means that the optical input has been converted into a chemical energy. Ultimately, we want to know how efficiently the optical input can, in fact, be converted. To better understand that, let us consider a three steps process when a semiconductor is exposed to a light source. In dark and in thermal equilibrium, the occupation of states is described by the Fermi–Dirac distribution at T0 , see Fig. 2.6a. Upon illuminating the semiconductor, charges are photogenerated via absorption and the occupation changes. As charges are in thermal and chemical equilibrium with the temperature of the light source, we represent that also by a Fermi–Dirac distribution, but now using the temperature of the thermal radiator, Tsource , as shown in Fig. 2.6b. Thus, the electron concentration are: 

(E C − E F ) n = NC exp − kB Tsource

 and

  (E F − E V ) p = NV exp − . kB Tsource

(2.30)

Subsequently, charge carriers interact to each other and with the lattice to achieve thermal and chemical equilibrium, thereby, thermalizing to the edge of the band,

Fig. 2.6 Conversion of radiation to chemical energy | a In dark the semiconductor is in thermal equilibrium with the background radiation. b Light absorption excites electrons to higher energetic levels in the conduction band. c About 1 ps later, all charges thermalize, occupying the bottom of the conduction band

24

2 Fundamentals of Light Detection

Fig. 2.6c, where they reside until they recombine. During that period, a minimum of free energy is established in both conduction and valence band. However, as the amount of charge carriers is higher in both bands than the concentration in dark conditions, each band requires its own Fermi–Dirac distribution to describe the occupation. This is solved by defining the quasi-Fermi levels, E F,C and E F,V , as shown Fig. 2.6c, representing the distribution of thermalized electron and holes.   (E C − E F, C ) n = NC exp − kB T0

  (E F − E F, V ) and p = NV exp − . kB T0 (2.31) With the aid of Eqs. (2.16) and (2.17), we can determine the quasi-Fermi level splitting, known as the chemical potential (ξn,p ), which is sum of chemical potential for electrons (ξn ) and holes (ξp ):  np = n 2i exp

(E F, C − E F, V ) kB T0

ξn,p = ξn + ξp = E F, C − E F, V = kB T0 ln

 (2.32) 

 np . n 2i

(2.33)

Once the illumination is ceased, charges will recombine, following the recombination processes discussed before, and the semiconductor returns to its initial state, where the occupation is described by a single Fermi level. In order to find out the maximum conversion efficiency, the following assumptions are made. Firstly, from the thermalization process shown in Fig. 2.6b, it is clear that the energy of photons with hv > E g is lost to the lattice and does not contribute to the chemical energy. To estimate the upper conversion limit, we therefore assume hv = E g . Secondly, we assume that only radiative recombination takes place, which means that every electron excited by absorbing a photon recombines by emitting a photon of the same energy. Additionally, there is no charge extraction. If only radiative recombination takes place, emission and absorption rates are the same. Using this condition, the semiconductor would reach the light source temperature, unless the semiconductor is kept in thermal equilibrium with a heat sink, such as the environment at T0 and the light source is far away. By doing so and using Eq. (2.26), we find:     E − (E F,C − E F,V ) −1 E − (E F,C − E F,V ) −1 2π E 2 2π E 2 A(E) exp = 3 2 A(E) exp 3 2 kB T0 kB Tsource h c h c   T0 ξn,p = ξn + ξp = E g 1 − Tsource ξn + ξp T0 ηchemical = =1− . Eg Tsource

(2.34) (2.35) (2.36)

2.2 Inorganic Light Detecting Devices

25

ηchemical represents the upper limit for converting heat into chemical energy. Note that Eq. (2.36) is, in fact, equivalent to the Carnot efficiency, which express the assumption of having only radiative recombination, i.e., a completely reversible thermodynamic process. Now, we focus on the electrical current generated by light absorption. As discussed so far, under open-circuit condition, no charges are extracted, resulting in zero current. Therefore, we need to find the relation between extractable current and chemical energy. Solving the continuity equation in steady-state conditions leads to:   ξn + ξp , (2.37) Jn,p = Jγ,abs − Jγ,emit = Jγ,abs − Jγ,0 exp kB T where Jγ,0 is the photon flux absorbed and emitted at T0 . In order to result in a current density, the amount of emitted photons has to be lower than the amount of absorbed photons, as described by Eq. (2.37). In Fig. 2.7 a representation of Eq. (2.37) is shown. At low chemical energies, where a small amount of photons is emitted, almost the whole absorbed current can be extracted, while for high chemical energies, no current can be extracted. The maximum extractable power is represented by the gray area as the product of the current the and chemical energy. The efficiency can be calculated by taking the ratio of the gray rectangle by the dashed rectangle (absorbed power). From a light source at 5800 K, e.g., the Sun, the maximum reachable efficiency is 86% [5]. This representation is important for solar cells, where the power is the main figure of merit. For photodetection, however, we are only interested in obtaining an electrical output, by giving up of or even providing with extra energy to extract current.

Fig. 2.7 Chemical energy versus extractable current density | Redrawn from Ref. [5]

26

2 Fundamentals of Light Detection

2.2.3 From Chemical Energy to Electrical Energy So far, the discussion of conversion of radiation has been treated in terms of chemical energy. In a device, however, charge carrier also needs to be extracted. While different forces act on electrons and holes directly, we focus here separately on the two major components, namely, the gradient of electrical potential and the gradient of chemical potential. This implies that components such as the gravitational force and temperature gradients are ignored.

2.2.3.1

Drift Current

Drift current is the current driven by an electric field (F), represented in Fig. 2.8a. Under spatially uniform concentration, the chemical potential for electron and holes varies equally along the position, which results in ∇ξn = ∇ξp = 0. Therefore, the only contribution for transport arises from F. Electrons with concentration n, travel a mean free path within the time interval τc,n at the mean velocity vn , carrying along the charge −qn. Therefore, the drift current for electron can be expressed as: qτc,n F m ∗n

Jdrift,n = −qn vn ,

where vn = −

Jdrift,n = qnμn F,

where μn =

Jdrift,n = σn F,

where σn = qnμn .

qτc,n m ∗n

(2.38) (2.39) (2.40)

Fig. 2.8 Kinetic energy of charge carriers | a Potential gradient for uniformly distributed charge carriers in presence of an electric field. b Potential gradient in the absence of an electric field in gradient of charges carriers

2.2 Inorganic Light Detecting Devices

27

As an equivalent expression can be written for holes, the total drift current is described by: Jdrift = (−qn vn + qp vp ) = q(nμn F + pμp F) = (σn + σp )F Jdrift = −(σn + σp )∇φ.

(2.41) (2.42)

σn and σp are the proportionality constants between drift current and applied electric field, as already expressed by Eq. (2.11). In absence of electric field, vn = vp = 0, and, therefore, no net current flows. Importantly, the drift current is limited by the scattering of charge carriers. In a perfect crystal, charges are rapidly accelerated away from the conduction band minimum, but are likewise decelerated, leading to Bloch oscillations [14], instead of a resultant mean velocity different of zero [15], phenomena already observed experimentally in superlattices [16].

2.2.3.2

Diffusion Current

Another component of the current arises when the charge carrier concentration is not uniform within the device. In the absence of an electric field, ξn,p changes along the sample, as depicted in Fig. 2.8b. For electrons, the usual representation by Fick’s law reads:

Jdiff,n = q Dn ∇n n ,

∇n = n∇(ln n − ln NC ) = n∇ ln using n n



n NC

 =

n ∇ξn kB T (2.43)

Jdiff,n =

with

Dn kB T . = μn q

(2.44)

Jdiff,n

where σn = qnμn .

(2.45)

qn Dn ∇ξn , kB T σn = ∇ξn , q

Dn is the diffusion coefficient for electron, which is related to μn by the Einstein relation. Deriving an equivalent expression for holes allows us to write the total diffusion current: Jdiff =

2.2.3.3

σp σn ∇ξn − ∇ξp . q q

(2.46)

Total Current

The total electrical current is the sum of its drift (Eq. (2.42)) and diffusion (Eq. (2.46)) component, resulting in:

28

2 Fundamentals of Light Detection

σn σn (q∇φ − ∇ξn ) = ∇ηn , q q σp σp = − (q∇φ + ∇ξp ) = − ∇ηp . q q

Jn = Jdrift,n + Jdiff,n = −

(2.47)

Jp = Jdrift,p + Jdiff,p

(2.48)

Where we defined the electrochemical potential for electrons, ηn = ξn − qφ, and for holes, ηp = ξp + qφ. The gradient of electrochemical potential describes the combination of forces acting on the charge carriers and, thereby, driving the electric current. Using this relation, it is also possible to write the final current in terms of the quasi-Fermi levels, since ηn = E F,C and ηp = −E F,V : J = Jn + Jp σp σn J = ∇ E F,C + ∇ E F,V . q q

(2.49) (2.50)

2.2.4 Interfaces Metal/Semiconductor To achieve real devices, semiconductors are connected to external circuits via metallic or metal-like contacts. The interface between both material classes shows specific characteristics that affect the performance of devices. Below, we address the main properties of metal/semiconductor interfaces. Due to the difference in electrochemical potential of metals (ηm ) and semiconductors (ηsc ), charge carriers migrate through the interface to achieve thermal equilibrium, when these materials are brought together. In this condition, the electrochemical potential becomes equal (ηeq = ηm = ηsc ). Electrons (holes) are driven to the lower (higher) electrochemical potential, forming a region in the material called depletion region or space charge region. In metals, the amount of free charge carriers is high, therefore, this region is very small. In intrinsic semiconductors, however, the concentration of free charge carriers is small, extending this region to a few nanometers. The difference in electrochemical potential gives rise to two cases: ohmic contact and Schottky barrier. The relation between the work function of semiconductor and metal defines the type of contact formed. Schottky barrier occurs when the work function of the metal (φm ) is higher than that of the semiconductor (φsc ), that is φm > φsc . Ohmic contact, on the other hand, occurs when the work function of the metal is lower than that of the semiconductor, i.e. φm < φsc . Figure 2.9 represents the energy diagram before (a) and after (b) the contact between a metal and a p-type semiconductor. The accumulation of charges happens in both semiconductor and metal, but, as mentioned before, extends for longer distances in the case of the semiconductor. In addition, Schottky barriers are characterized by their rectifying property. This means that in the so-called forward bias direction, i.e., when a positive potential is applied to the p-type semiconductor, an energy barrier φBp has to be overcome in order to achieve injection of holes into the valence

2.2 Inorganic Light Detecting Devices

29

Fig. 2.9 Formation of a Schottky barrier | When the eletrochemical potential of the metal is higher than that of the p-doped semiconductor (φm > φsc ) a Schottky barrier is formed. Junction a before and b after the contact of both materials. The space charge width (W ) is also represented

band of the semiconductor. As the positive potential applied to the semiconductor increases, the energy barrier decreases, allowing injection. At reverse bias, however, the energy barrier increases and only the saturation current flows through the device; an aspect which will be discussed in the context of photodetectors. From the working mechanism of a Schottky junction, a diode-like curve results, with an exponential increase of the current after the barrier is overcome and a very small current in reverse bias. Likewise, Fig. 2.10 shows the formation of an ohmic contact. Characterized by its non-rectifying property, ohmic contacts have negligible energy barriers, allowing for injection and extraction in both direction. To achieve more efficient ohmic contacts, doped layers are commonly used. The excess of free charges in highly doped semiconductors reduces the extension of the depletion width to very narrow regions close to the interface, reaching less than 1 nm depending on the doping ratio [17]. Therefore, tunneling through the barrier becomes possible and dominates the injection, leading to high injection currents. The desired contact depends on the application. While Schottky barriers are targeted only for some devices, as discussed in Chap. 6, most optoelectronic devices such OLEDs, organic photovoltaics (OPVs), and OPDs rely on ohmic contacts for electrons and holes at the cathode and anode, respectively.

2.2.5

pn-Junction

One of the most well-known realization in the field of semiconductors, which is used also for photodetection, is the pn-junction. A device formed by p-doped semicon-

30

2 Fundamentals of Light Detection

Fig. 2.10 Formation of an Ohmic contact | When the eletrochemical potential of the metal is lower than that of the p-doped semiconductor (φm < φsc ), an Ohmic contact is formed. Junction a before and b after the contact of both materials. The space charge width (W ) is also represented

ductor in contact with an n-doped semiconductor, whose rectifying behavior of its J V characteristics allows for an enormous applicability in electronics. Because a large part of the physics used to understand pn-junctions can, to some extent, also be used to discuss OPDs, here, the main features of pn-junctions are introduced.

2.2.5.1

Ideal J V Characteristics

Before contact of both materials, p and n semiconductors have their specific Fermi level determined by the doping concentration, as shown in Fig. 2.11a. When these materials are brought together, the difference in charge concentration gives rise to a diffusion current. Electron and holes diffuse into the opposite region. While electrons and holes are mobile in the lattice, ionized donating and accepting atoms are bonded to it and, therefore, cannot migrate, resulting in a space charge region, positively (negatively) charged in the n( p) side. From the space charge region, an electric field results, inducing a drift current in the opposite direction to that of the diffusion current, therefore, compensating each other. The total potential created across the junction is called built-in potential (φbi ) and can be calculated from the difference in Fermi levels in the doped neutral regions, E Fn and E Fp , see Fig. 2.11a.

2.2 Inorganic Light Detecting Devices

31

Fig. 2.11 pn-junction operated at different conditions | a Before contact, p- and n-type semiconductor show a specific Fermi level, according to Eq. (2.21). c After contact, equilibrium is achieved and a single Fermi level is established. b In forward regime, after overcoming the built-in potential, charges are injected and the Fermi level split of q(Vbi − VF ) is observed. d In reverse bias, the injection barrier is increased by the applied bias and an inverse Fermi level splitting is observed

    NC NV − kB T ln φbi = q Vbi = E Fn − E Fp = E g − kB T ln n p     NC NV NC NV − kB T ln = kB T ln np n 2i   NA ND .  kB T ln n 2i

(2.51)

The width of the space charge region is obtained by solving the Poisson equation, considering abrupt boundaries of depletion region, restricted between xn and xp : ⎧ 0, for x > xn ⎪ ⎪ ⎪ ⎨ 2 d φ q −ND , for 0 < x ≤ xn = (2.52) dx2 εε0 ⎪ NA , for − xp ≤ x < 0 ⎪ ⎪ ⎩ 0, for x < xp .

32

2 Fundamentals of Light Detection

Integrating Eq. (2.52) once gives the electric field (F), which is linear in x. The second integration results in Vbi :  Vbi = − =

xn −xp

q NA xp2 2εε0

 F(x)d x = − +

q ND xn2 2εε0

0 −xp

   F(x)d x  



xn

− p-side

0

  F(x)d x 

n-side

(2.53)

1 = Fmax W, 2

where Fmax is the maximum field that exists at x = 0 and W = (xn + xp ) is the space charge width. According to the charge neutrality in the semiconductor, the total number of charges per unit area in the p-side has to equal the total number of charges per unit area in the n-side, therefore: NA x p = ND x n . Using Eqs. (2.54) and (2.53), W can be written as:    2εε0 NA + ND Vbi , W = q NA ND

(2.54)

(2.55)

which can also be rewritten in terms of material parameters by using Eq. (2.51). W is, therefore, proportional T . Such a dependence can also be understood as follows: the diffusion current (Eq. (2.44)) is temperature dependent. Therefore, if the diffusion current increases as a result of an increased temperature, an increase in the drift current must occur to maintain equilibrium. This is only possible by an increased electric field, which translates into a thicker W [15]. The most interesting features of a pn-junction arise when a voltage is applied across the junction. We distinguish the J V in two regions, forward and reverse. In the forward region, the applied bias injects electron into the n-side and holes into the p-side, while in reverse, the opposite occurs. In forward bias, as electrons coming from the n-side compensate positive ions in space charge region and move into p-side, recombination takes place, due to the large amount of holes in p-side. The same process happens for holes. Forward bias reduces the width of the space charge region because the applied bias reduces the electrostatic potential, as shown in Fig. 2.8b. Since every minority charge carrier recombines, the current is carried only by majority carriers. The balance in drift and diffusion current is disturbed, as the drift current increases in relation to the diffusion component. This is the operation regime of LEDs. In reverse bias, electrons are pulled away from the n-side of the junction, thereby, increasing the depletion region. The electrostatic potential increases, as shown in Fig. 2.8d, reducing the diffusion current. Charges thermally generated in the depletion region are driven by reverse bias, but represent a very small amount at T0 . Thus, the

2.2 Inorganic Light Detecting Devices

33

Fig. 2.12 J V characteristics of a pn-junction operated at different conditions | a J V curves of a pn-junction according to Eq. (2.56) (black lines). Red curve represents J V for a real device, indicating the regions where the J V deviates from Eq. (2.56). b J V curves in linear scale showing the fill factor (F F), used to characterize solar cells, as well as short-circuit current (JSC ) and open-circuit voltage (VOC )

current in reverse bias is a sum of small diffusion component and the thermally generated drift component. J V characteristics for pn-junctions can be easily derived under the assumptions of abrupt boundaries of the depletion region, treating the low injection regime and constant electron and hole current in the space charge region. Following that, the Shockley equation reads: 



  qV −1 J (V, T ) = J0 exp kB T q D p pn q Dn n p where J0 = + . Lp Ln

(2.56) (2.57)

J0 is the saturation current, proportional to the diffusion coefficients, Dn and Dp , and corresponding diffusion lengths, L n and L p , for electrons and holes, respectively. pn and n p are the monority charge carrier concentration, i.e., the concentration of holes and electrons in the n- and p-region, respectively. Under illumination, charges are generated and driven by the built-in potential towards the contacts, the additional concentration of charge carriers forces the Fermi level to split, defining the extractable electrochemical potential for electrons and holes (ηn , ηp ). If the generation of charges is independent of the applied field, Eq. (2.56) can be modified to account for the illumination [18]:     qV − 1 − JSC . (2.58) J (V, T ) = J0 exp kB T By setting extracted current to zero, VOC can be calculated:

34

2 Fundamentals of Light Detection

    qV − 1 − JSC 0 = J0 exp kB T     JSC JSC kB T kB T . ln ln +1  VOC = q J0 q J0

(2.59) (2.60)

In Fig. 2.12a, Eqs. (2.56) and (2.58) are plotted together with a schematic representation of a real dark current (JD ). Given the assumptions taken to derive Eq. (2.56), many features of the real J V curve cannot be described by the Shockley theory. In reverse bias, (i), and at low forward biases, region (ii), the current strongly deviates from the theoretical J0 , due extrinsic features, such as pin-holes in the semiconductor or bad selectivity of the contacts, as well as intrinsic properties, such as SRH generation (reverse) and recombination (forward). Region (iii) of the real curve, corresponding to exponential part of Eq. (2.56), is well described because at moderate injection conditions, other effects are irrelevant. Nevertheless, this condition breaks down as the injection becomes higher, shown in region (iv). Here, the assumption of no charges in the space layer is no longer valid. When flat band is achieved, region (v), voltage does not drop across the depletion region and the current is limited by the mobility of the semiconductor.

2.2.5.2

Generation-Recombination Effects

The region (i) in Fig. 2.12a strongly differs from the curve predicted by Eq. (2.56). In large gap semiconductors, where the intrinsic charge carrier concentration is low, region (i) is dominated by the generation via intra-gap states, discussed before in the context of SRH recombination. However, when the device is negatively biased, the SRH recombination is no longer important, because the capture of charge carriers depends on the charge carrier concentration, which is very low in this regime. Instead, the inverse process takes place, i.e, SRH generation. Therefore, assuming that n < n i , p < n i and that σn = σp = σ0 , we can re-write Eq. (2.27) for generation:

G SRH = ≡

σ0 vth Nt  ni

i 2 cosh Ekt B−E T ni τG, SRH

.

(2.61) (2.62)

Similarly to the recombination, the hyperbolic cosine in the denominator of Eq. (2.62) finds its minimum around E t = E i , such that the generation is more efficient in this region, falling exponentially as the trap energy approaches conduction or valence bands (E C , E V ). As this effect takes place within space charge width, the current can be calculated by integrating Eq. (2.62) over W . The total reverse current for p n results to:

2.2 Inorganic Light Detecting Devices

35

 JD = q 

Dp n 2i ni W +q . τp N D τSRH     

Diffusion

(2.63)

G, SRH

When n i is large, e.g., in Ge, the diffusion term dominates and Eq. (2.56) is able to describe the experimental curve. However, for materials such as Si and GaAs, the SRH term dominates and Eq. (2.56) has to be modified. The effect of traps can also be observed in region (ii) in Fig. 2.12a. For pn  n p and V > 3kB T q −1 , another correction can be derived for the forward region, originating from the maximum recombination rate,

RSRH

  1 qV  σ0 vth Nt n i exp 2 2kB T ni ≡ , 2τR, SRH

(2.64) (2.65)

integrated over W : 

    Dp n 2i ni W qV qV JF = q +q exp exp τp N D kB T τR, SRH 2kB T   qV . JF  exp n id kB T

(2.66)

n id is the ideality factor, which varies from 1, when the diffusion current dominates, to 2, when the SRH recombination current dominates. In experimental curves of Si and GaAs pn-junctions, for example, it is common to observe two regions where the effect of impurities and diffusion can be identified separately. In Fig. 2.12a, where n id is the slope of the curve in log-scale, this corresponds to region (ii) and region (iii), respectively. In the former, n id approaches 2, as the SRH recombination dominates, while in the latter n id approaches 1. Although the empirical form of Eq. (2.66) is largely used to explain experimental curves, care must be taken when dealing with devices for which the assumptions of the derivation are no longer valid. In many devices, the concept of n id > 1 as an indication of trap states and/or trap properties is misleading. This will be addressed in more detail for OPDs in Chap. 5.

2.2.5.3

Detailed Balance Theory and Dark Current

Perhaps the most frequent application of pn-junctions are solar cells. In fact, except for Sect. 2.2.1, where we discussed classic semiconductors, the entire discussion of Sect. 2.2 is originally done for this class of devices. As photodetectors and solar

36

2 Fundamentals of Light Detection

cells are the same devices, only operated in different conditions, for the former, we only need to exchange the light source, i.e, the Sun by any other optical input. In this direction, although the power conversion efficiency (PC E) is not relevant for photodetectors, from the derivation of its thermodynamic limit, useful information can be obtained. Shockley and Queisser showed that the maximum PC E of a pnjunction solar cell is about 33.9% [19]. Following their derivation, when each surface element d A of a pn-junction receives an amount of photons L γ from a radiance (L) per solid angle dΩ in the form of Eq. (2.5), the current generated can be written as:    JSC = q L γ (θ, φ, E)E Q E( r , θ, φ, E)dΩd Ed A, (2.67) Ω

E

A

where E Q E is the external quantum efficiency of the device. Under dark condition, the photodetector is in thermal equilibrium with the surrounding, therefore,L can be obtained from the black-body radiance, see Eq. (2.10), and the current generated by the thermal excitation, JSC,0 , can be calculated [20]. To guarantee thermal equilibrium, JSC,0 = Jem,0 , i.e., the device must emit as much as it absorbs. For an infinitesimal interval: r , θ, φ, E). δ JSC,0 = δ Jem,0 = q L BB,γ (θ, E)E Q E(

(2.68)

Injected electrons that recombine radiatively cause an excess of emission current, following an exponential law and can be added up to the current in the form of Shockley’s diode equation [20],     qV − δ JSC,0 = δ Jem,0 exp −1 kB T        qV Jem = q L BB,γ (θ, φ, E)E Q E( r , θ, φ, E)dΩd Ed A × exp −1 . kB T Ω E A 

δ Jem = δ Jem,0 exp

qV kB T



(2.69) (2.70)

Using Eq. (2.9) and assuming that E Q E( r , θ, φ, E) is measured at normal angle and averaged over the device area, the excess of emission current is:      qV −1 . (2.71) Jem = q ΦBB (E)E Q E(E)d E × exp kB T   E J0,rad

Equation (2.71) corresponds to the emission current of a perfect photodetector in which every charge recombines radiatively. In reverse bias, in addition to a small diffusion current, a contribution to the current arises from charges thermally excited with a given E Q E, which are extracted leading to a value of J0,rad . For photodetector, J0,rad can be used to estimate the radiative limit of the specific detectivity. As already discussed in previous sections, non-radiative processes can play a major role in recombination and generation (see Fig. 2.12a). To describe that, we need to define a quantity that accounts for how many of the extracted charges are

2.2 Inorganic Light Detecting Devices

37

product of a non-radiative generation. This is equivalent to knowing how many charges recombine radiatively when a current is injected to the device, being the definition of electroluminescence external quantum efficiency (E Q E el ): E Q E el =

Jem Jinj

(2.72)

The radiative saturation current, J0,rad in Eq. (2.71) needs to be corrected to account for charges which are generated non-radiatively and increase the total dark current. If we know the fraction of charges which recombine radiatively, namely E Q E el , the total saturation current (J0 ) is:  q J0 = ΦBB (E)E Q E(E)d E. (2.73) E Q E el E Equation (2.73) represents the lower limit for dark current in photodetectors, in which also non-radiative generation is present. For solar cells, Eq. (2.73) can be used to derive the radiative limit for VOC and to estimate voltage losses corresponding to non-radiative recombination processes.

2.2.5.4

Capacitive Character of a pn-Junction

In addition to the rectifying character of the pn-junctions, this device can also be thought as a plate capacitor. In fact, important properties can be derived from the capacitive character of a pn-junctions; an approach which can also be used to certain extent in organic photodetectors. Depletion Capacitance: The first capacitive effect arises in the depletion region, where charges are stored at the edges of the region xp < x < xn , see Fig. 2.11. The depletion capacitance, Cdepl , is voltage dependent, as variations in voltage change W , cf. Eq. (2.55). An increment of electric charge d Q causes an increment on the electric field d F = d Q/(εε0 ), therefore: dQ dQ = dV W dεεQ0 εε0 , = W

Cdepl = Cdepl

(2.74)

which describes the capacitance per unit area as a function of the applied reverse bias [4]. In the forward regime, another type of capacitance arises, as discussed below. Diffusion Capacitance: When the pn-junction is in its forward regime, electrons and holes are injected from the n and p side, respectively. As these charges enter the opposite region, they become minority charges and recombine with the majority charges. In the process of entering the opposite region, a large amount of

38

2 Fundamentals of Light Detection

electron (holes) accumulate at the p (n) interface, separated by a very thin depletion region. The accumulation at both sides act as if the plates were separated by a dielectric (the depletion region), forming therefore a capacitor. Its capacitance increases exponentially with increasing voltage. For minority holes, pn , it reads:   Aq 2 L p pn qV exp , (2.75) Cdiff = kB T kB T where A is the device cross-section area, and L p the hole diffusion length. Because Cdiff becomes much higher than Cdepl , this term dominates the overall capacitance in forward bias. Freeze-out of charge carriers: This is an effect related to the mobility of charge carriers, which happens at a certain frequency, when charge carriers can no longer follow the AC modulation of a signal, i.e., their transit time from electrode to electrode is longer than the modulation period. The capacitance, which so far was dominated by charges accumulated at the depletion region, gets dominated by charges accumulated at the electrodes. This contribution is usually lower than Cdepl , as the thickness of device is larger than W . From this effect, it is possible to estimate the geometrical capacitance, Cgeom .

2.2.6 Photoconductors for Light Detection Another important realization for light detection is based on the change of electric conductivity for electrons and holes (σn , σp ) showed by a semiconductor when light with photon energy E ≥ E g impinges on the material. In most photoconductors, the conductivity is determined by electrons. When a photon flux Φflux reaches a device of area Ad , an excess of electrons n is created with a certain E Q E. If a voltage (V ) is applied to the device, the photocurrent can be written as: z Iph = q E Q E(E)Ad Φflux G = qwnμn , l

(2.76)

where w is the device width, z the device thickness and l the device length. The right side of Eq. (2.76) is the Ohm’s law for the device. It follows from Eq. (2.76) that the gain (G), whose physical meaning will be discussed later, can be calculated as: G=

z nμn V . l 2 Φflux E Q E

(2.77)

The excess of electron concentration can be determined from the following rate equation [1]:

2.2 Inorganic Light Detecting Devices

39

Φflux E Q E n dn = − dz z τ τ E Q EΦflux n = . z

(2.78) (2.79)

Therefore, using Eqs. (2.77) and (2.79), G reads: τ μn V nμn V l 2 Φflux E Q E τ = . ttransit

G=

(2.80) (2.81)

ttransit is the transit time of electrons between both ohmic contacts. Thus, G is the ratio of the free carrier lifetime, τ , by the transit time. When an electron is able to cross the device faster than its lifetime, G is higher than one and the electron is immediately replaced by an injected electron in the opposite electrode. Before recombination, electrons are continually extracted and injected, which is equivalent to say that for each absorbed photon, n > 1 electrons are extracted, leading also to the interpretation of an E Q E higher than 100%. The dependence of G on V is limited by the transit time of the minority charges. If V is too high, also minority charges cross the device with shorter time than τ , reducing G. Called Sweep-Out, this effect becomes important in the infrared, where devices are usually cooled to reduce thermal generation, leading to long life times of 10 µs in small devices in the order of 250 µm2 .

2.3 Figures of Merit of Photodetectors 2.3.1 Power Spectral Density Sx ( f ) The figures of merit of a detector are strongly dependent on its noise. A good tool to analyze the noise of a detector is through its power spectral density, Sx ( f ) [7]. This quantity is a measure of the amount of power carried by a signal within a frequency band  f . Sx ( f ) can be calculated for any signal x(t). Here, we deal with a noise signal x(t) which can be a time-dependent voltage or current signal. Ideally,  f should be as narrow as possible such that the spectral shape of the power density can be resolved. However, the power within  f decreases proportionally to its magnitude. Therefore, we have to normalize the measured power per  f . We define Sx ( f ) as: Sx ( f ) = lim

 f →0

Px, f . f

(2.82)

40

2 Fundamentals of Light Detection

Fig. 2.13 Power of signal | a A time-dependent signal is recorded and b filtered in a bandwidth of 1 Hz. c The average power is estimated, leading to the power density at a given frequency, f 1 . d By scanning different frequencies, the power spectral density is recorded. The amount of power in the frequency interval  f is represented in orange

Let us assume that we are dealing with a noise current signal, i n . Firstly, i n (t) is recorded, see Fig. 2.13a and filtered with a chosen  f (Fig. 2.13b). The power is recorded and normalized to the chosen bandwidth. As we are analyzing a current signal, Sin has the unity of A2 Hz−1 . Note that the quantity Px, f in Eq. (2.82) not necessarily means the physical power in Watts. The physical power could be calculated by multiplying by the resistance. As we go from Fig. 2.13a–d, we pass from the time domain to the frequency domain. This can also be done mathematically via the discrete time Fourier transform (DTFT). In fact, it can be shown that Sin is the Fourier transform of the correlation function of i n . One important feature of the Fourier transform is that the total energy is conserved. Therefore, we can estimate the root mean squared (RMS) value of i n within a certain range from Sin as shown in the region colored in orange in Fig. 2.13d. This is given in a general expression by the Parseval’s theorem. In our case:  i n2

∞

=

Sin ( f )d f

0

or simply i n2 = Sin ( f ) f ·

(2.83)

2.3 Figures of Merit of Photodetectors

41

From Eq. (2.83), the RMS value of i n can be calculated, i n , whose unit is A. Moreover, using the properties of Sin ( f ) with respect to DTFT and Eq. (2.83), the expected Sin ( f ) and i n from different sources of noise can be derived, as it is discussed in the next section. Here, we define the noise spectral density, Sn [A Hz−1/2 or V Hz−1/2 ], which is the linearized version of Eq. (2.83). This quantity is commonly used in the literature and is also used to calculate the specific detectivity. Sn reads: Sn := Sn =

 

Sin

i n2

. f

(2.84)

2.3.2 Noise Current i n  Perhaps the best way of starting this section is by referring to a statement that dates back to the 1980s: “While we can describe the physical consequences of order parameter fluctuations in intricate detail, we have comparatively little knowledge about the microscopic origins of voltage fluctuations in a simple resistor”. Unfortunately, this statement by Dutta and Horn [21], reproduced in a recent review [22], still holds true. In literature, it is common sense to analyze the noise of photodetectors by means of its shot and thermal noise. The reason for that lies, on the one hand, in the facility of characterizing these two components and, on the other hand, in the difficulty of measuring the real noise of the device via its Sn , as described in the previous section. While this might be reasonable for some devices, it is certainly not a completely reliable approach, leading to an overestimation of D ∗ , as it is discussed below. Besides being an ongoing research topic, noise is ultimately described by three major components, namely the shot noise, the thermal noise, and the 1/ f noise. These noise sources are considered to act independently, where the total magnitude is calculated as a quadratic sum. A more realistic analyzes of the noise must take into account the frequency-dependent component, namely the 1/ f noise, which belongs to one of the less understood sources of noise. Below, these main three components are described in detail [8]. A derivation of each contribution in terms of Sin can be found in Ref. [7, 9]. Shot noise (i shot ): Due to the discrete character of charge carriers, when these particles cross an energy barrier, a fluctuation in the signal is observed. In heterojunctions, such as pn-diodes, for example, the current experiences time-dependent variations as a result of single charge carriers crossing the depletion region. i shot is therefore proportional to the average dark current, which can be calculated from the photon count [s−1 ] and the E Q E [8]:

42

2 Fundamentals of Light Detection 2 i shot

= 2q 2 ϕ × E Q E ×  f,

(2.85)

where  f is the measured bandwidth [Hz]. G-R noise (i G-R ): In dark, any detector is subjected to the background radiation. The amount of photon reaching the detector entails temporal variations, leading to the so-called generation-recombination (G-R) noise. The fluctuation in charge carrier concentration affects the photoconductivity in photoconductors or the photocurrent in photodiodes. Often, the G-R noise is mistakenly confused with the shot noise, due to the mathematical equivalence of both in specific conditions, being the G-R noise attributed to photoconductors and the shot noise to photodiodes. The reason lies on the approximation made for the G-R noise for photodiodes operated in reverse bias, which leads to the same mathematical expression as that of shot noise. In reverse bias, only generation must be taken into account, as charges are extracted efficiently and do not recombine. In photoconductors, however, both processes are randomized. Yet, the physical nature of these two sources of noise is different [23, 24]. Generally, G-R noise is frequency independent but a pink behavior can be present depending on the dynamics of the system. For band-to-band processes, for example, G-R noise becomes frequency dependent at the frequency corresponding to the reciprocal of the transit time [23]. Finally, G-R noise is expressed as: 2

= 4q 2 ϕG 2 × E Q E ×  f, i G-R

(2.86)

which assumes the mathematical form of (2.85) for photodiodes operated under reverse bias. In this case, the (G) equals one, as every photon can generate only one electron-hole pair. For photoconductors, G can be higher than one if one charge carrier has a drift time shorter than the lifetime of the excited carrier. Thermal noise (i thermal ): Also referred to as Johnson or Nyquist noise, this component is a fundamental thermodynamic noise, which arises from the thermal motion of charges and is independent of any sort of external excitation. 2

= i thermal

4kB T ×  f. Rshunt

(2.87)

1/ f noise (i 1/ f ): While a physical reasoning has been addressed to the aforementioned sources of noise, 1/ f noise remains a huge challenge, being reflected in the lack of a proper name. It is common to observe a frequency dependent increase of the noise at low frequencies, which follows an 1/ f behavior. The most accepted explanation for the origin of this effect is related to surface traps and bulk traps, leading to a fluctuation in the charge carrier density, as charges fall into and are released from these states. However, none of these effects has been completely clarified [8]. A phenomenological expression for the 1/ f noise can be written as follows: 2 i 1/ f = K

ib ×  f, fa

(2.88)

2.3 Figures of Merit of Photodetectors

43

where K , a and b are constants. Total noise current (i n ): The RMS of the total noise current (i n ) [A] can be written as the quadratic sum of Eqs. (2.85), (2.86), (2.87) and (2.88): i n =

 1/2  4kB T ia 6q 2 ϕ × E Q E + + K b f . Rshunt f

(2.89)

2.3.3 Responsivity R Responsivity is the conversion efficiency from photon energy into electric current, therefore, proportional to external quantum efficiency (E Q E), see Eq. (2.90). While the latter takes into account the ratio of number of electrons per number of incident photons, R is the ratio of output electric current or voltage per incident power, having, therefore the unit A W−1 or V W−1 . R = E QE

  qλ , with unit A W−1 . hc

(2.90)

2.3.4 Noise Equivalent Power N E P The noise equivalent power is used to characterize the sensitivity of photodetectors. It is defined as the electric power (P) generated by noise that delivers a signal-to-noise (S N R) ratio of 1, in a 1 Hz output bandwidth, which is equivalent to half second of integration time. RP Sn R.N E P 1= Sn Sn NEP = , R SN R =

(2.91)

where Sn and R are defined by Eqs. (2.84) and (2.90), respectively. N E P is therefore measured in W Hz−1/2 .

44

2 Fundamentals of Light Detection

2.3.5 Specific Detectivity D∗ Photodetectors are analyzed and ranked in terms of their specific detectivity (D ∗ ) [25], which is the inverse of noise equivalent power (N E P), see Eq. (2.91), normalized by the device area ( Ad ). This parameter takes into account the capability of generating an electrical output as current upon light absorption and the noise generated by the device. D ∗ is commonly expressed as: √ R Ad , (2.92) D∗ = Sn where Ad the device area (cm2 ). Measured in cm Hz1/2 W−1 or Jones, D ∗ can be understood as the SNR produced by a detector of 1 cm2 when 1 W of light power impinges, measured with electrical bandwidth of 1 Hz [22].

2.3.6 BLIP Limit for D∗ Assuming an E Q E of 1, we can derive an upper limit for D ∗ which depends only on the background radiation spectrum. Considering that the resistance of a device is zero, in the absence of the 1/ f noise component or any other source of noise, the device would be limited only by the background radiation. In this case, the noise induced in the device is describe by Eq. (2.85). This limit is called background limited infrared ∗ . For photodiodes, using Eqs. (2.90), (2.84) photodetection (BLIP) detectivity, DBLIP and (2.85), we find: √ R Ad D = Sn  λ Ad ∗ . DBLIP = hc 2ϕ ∗

(2.93)

ϕ [s−1 ] represents the total photon flux (ΦBB,total ) emitted by an ideal black-body normalized by the area. It can be obtained from Eq. (2.9) by integrating over all wavelengths. Because Eq. (2.9) is already normalized by the area, we can omit the area normalization in Eq. (2.92), resulting in: ∗ = DBLIP



λ

hc 2ΦBB,total

  , with unit 100 · cm Hz1/2 W−1

(2.94)

Note that ΦBB, total accounts for photons received in a 2π field of view (FOV), which means photons arriving from the entire semi-hemisphere above a planar photodetector, i.e., θ = 180◦ in Fig. 2.14. If the photodetector is shielded by a case which

2.3 Figures of Merit of Photodetectors

45

Detector Fig. 2.14 Angle θ of a Field of view for a detector embedded into a shielding case | The background noise increases with increasing θ. Most commonly, the BLIP limit is represented at 2π FOV, which in this 2D representation means θ = 180◦ . In 3D, 2π FOV is a semi-hemisphere above the detector

limits the FOV, the ΦBB, total arriving to the device from the conic aperture with angle θ can be calculated as [1]:   θ ΦBB (θ) = sin2 . (2.95) ΦBB (2π) 2 ∗ Therefore, when expressing DBLIP , FOV as well as temperature should be specified. ∗ can be derived for photoconductors using Eq. (2.86) A similar expression for DBLIP and assuming G √= 1. As already mentioned, the noise in photoconductors is higher by a factor of 2, which results in a slightly lower detectivity. This difference is plotted in Fig. 2.15 and compared to available detection technologies. A comparison including OPDs is presented in Chap. 5, Fig. 5.1.

2.3.7 Dynamic Range Another important parameter for PDs is the dynamic range. This parameter describes the range within which an input signal induces a predictable and reproducible output. A large dynamic range is desired, as it simplifies the operation and calibration of the device. The dynamic range is quantified as:   Imax , (2.96) DR = 20 log Imin where Imax and Imin are the maximum and minimum irradiance for which a predictable behavior in the PD response is observed. Commonly, the dynamic range is represented in a double-logarithmic scale of the PD photocurrent versus irradiance. The linear dynamic range is obtained by defining the lower and upper limits within which a linear relation in the double-logarithmic plot is observed.

Fig. 2.15 Specific detectivity for different inorganic technologies | Dashed lines represent the BLIP limit at 2π FOV and 300 K. Solid lines show experimental detectivities of different devices. Abbreviations in this figure are: PC—photoconductors, PV—photodiodes or photovoltaic detectors, PEM— photoelectromagnetic detectors, and HEB—hot electron bolometer. Reproduced from Ref. [27]

46 2 Fundamentals of Light Detection

2.3 Figures of Merit of Photodetectors

47

2.3.8 Response Speed The speed of PDs is analyzed with regard to the time that the device takes to turn on and turn off, also known as rise and fall time, respectively. The on state is defined as 90% of the maximum signal, whereas the off states is defined as 10% of the maximum signal. Alternatively, the response speed can be characterized by the −3 dB cut-off frequency ( f −3 dB ), which is the frequency at which the photoresponse decreases to −3 dB of its maximum value. This corresponds to 70.71% of the maximum photoresponse. While both quantities can be measured separately, it is possible to convert rise time into f −3 dB using [26]: −1 f −3 dB  0.35ton

(2.97)

Equation (2.97) is valid if the system’s response resembles that of an RC-circuit.

References 1. Rogalski A (2010) Infrared detectors, 2nd ed. CRC Press, Boca Raton. https://www.routledge. com/Infrared-Detectors/Rogalski/p/book/9780367577094. ISBN: 9780367577094 2. Zalewski EF (1995) Radiometry and photometry (Chap 24). In: Bass M, Stryland EWV, Williams DR, Wolfe WL (eds) Handbook of optics volume II devices, measurements, 2nd edn. McGraw-Hill, New York. http://optics.sgu.ru/~ulianov/Students/Books/Applied_ Optics/Handbook/0070479747. ISBN: 0070479747 3. Kittel C (2004) Introduction to solid state physics, 8th edn. Wiley, New York. https://www.wiley.com/en-us/Introduction+to+Solid+State+Physics/9780471415268. ISBN: 9780471415268 4. Sze SM, Ng KK (2007) Physics of semiconductor devices. Wiley, New Jersey. https://www.wiley.com/en-us/Physics+of+Semiconductor+Devices/9780470068304. ISBN: 9780470068304 5. Würfel P, Ruppel W (2010) Physics of solar cells: from basic principles to advanced concepts, 2nd edn. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. https://www.wiley-vch.de/ de/fachgebiete/naturwissenschaften/physik-11ph/festkoerperphysik-11ph6/physics-of-solarcells-978-3-527-41312-6. ISBN: 9783527408573 6. Simon SH (2013) The Oxford solid state basics. Oxford University Press, Oxford. https:// global.oup.com/academic/product/the-oxford-solid-state-basics-9780199680771?cc=de& lang=en&. ISBN: 9780199680771 7. Johns DA, Martin K (2008) Analog integrated circuit design, 2nd edn. Wiley, New Jersey. https://www.wiley.com/en-us/Analog+Integrated+Circuit+Design/9781118214909. ISBN: 9781118214909 8. Rieke G (2003) Detection of light: from the ultraviolet to the submillimeter, 2nd edn. Cambridge University Press, Cambridge. https://www.cambridge.org/9780521816366. ISBN: 9780521816366 9. Chuang SL (2012) Physics of photonic devices, 2nd edn. Wiley, New York. https://www.wiley. com/en-us/Physics+of+Photonic+Devices/9780470293195. ISBN: 9780470293195 10. Kronig RDL, Penney WG, Fowler RH (1931) Quantum mechanics of electrons in crystal lattices. In: Proceedings of the royal society of London. series A, containing papers of a mathematical and physical character, vol 130, no 814, pp 499–513. https://doi.org/10.1098/rspa. 1931.0019

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11. Würfel P (1982) The chemical potential of radiation. J Phys C: Solid State Phys 15(18):3967. https://doi.org/10.1088/0022-3719/15/18/012 12. Shockley W, Read W Jr (1952) Statistics of the recombinations of holes and electrons. Phys Rev 87(5):835. https://doi.org/10.1103/PhysRev.87.835 13. Hall RN (1952) Electron-hole recombination in germanium. Phys Rev 87(2):387. https://doi. org/10.1103/PhysRev.87.387 14. Bloch F (1929) Über die Quantenmechanik der Elektronen in Kristallgittern. Zeitschrift für Physik 52(7–8):555–600. https://doi.org/10.1007/BF01339455 15. Tress W (2014) Organic solar cells: theory, experiment, and device simulation. Springer, Linköping. https://www.springer.com/gp/book/9783319100968. ISBN: 9783319100968 16. Leo K, Bolivar PH, Brüggemann F, Schwedler R, Köhler K (1992) Observation of bloch oscillations in a semiconductor superlattice. Solid State Commun 84(10):943–946. https://doi. org/10.1016/0038-1098(92)90798-E 17. Lüssem B, Riede M, Leo K (2013) Doping of organic semiconductors. Phys Status Solidi (a) 210(1):9–43. https://doi.org/10.1002/pssa.201228310 18. Shockley W (1949) The theory of p-n junctions in semiconductors and p-n junction transistors. Bell Syst Techn J 28(3):435–489. https://doi.org/10.1002/j.1538-7305.1949.tb03645.x 19. Shockley W, Queisser HJ (1961) Detailed balance limit of efficiency of p-n junction solar cells. J Appl Phys 32(3):510–519. https://doi.org/10.1063/1.1736034 20. Rau U (2007) Reciprocity relation between photovoltaic quantum efficiency and electroluminescent emission of solar cells. Phys Rev B 76(8):085303. https://doi.org/10.1103/PhysRevB. 76.085303 21. Dutta P, Horn P (1981) Low-frequency fluctuations in solids: 1/ f noise. Rev Modern Phys 53(3):497. https://doi.org/10.1103/RevModPhys.53.497 22. Fang Y, Armin A, Meredith P, Huang J (2019) Accurate characterization of next generation thinfilm photodetectors. Nat Photon 13(1):109–114. https://doi.org/10.1038/s41566-018-0288-z 23. Müller R (1978) Generation-recombination noise. In: Wolf D (ed) Noise in physical systems. Springer series in electrophysics, vol 2. Springer, Berlin, Heidelberg, pp 13–25. https://doi. org/10.1007/978-3-642-87640-0_2 24. Cohen J (1983) Three guises of generation-recombination noise. NBS Technical Note 1173, National Bureau of Standards, Washington, D.C. Apr 1983 25. Jones RC (1953) A method of describing the detectivity of photoconductive cells. Rev Sci Instrum 24(11):1035–1040. https://doi.org/10.1063/1.1770585 26. Klompenhouwer MA (2005) 51.1: temporal impulse response and bandwidth of displays in relation to motion blur. SID Symp Digest Techn Papers 36(1):1578–1581. https://doi.org/10. 1889/1.2036313 27. Rogalski A (2012) History of infrared detectors. Opto-Electron Rev 20(3):279–308. https:// doi.org/10.2478/s11772-012-0037-7

Chapter 3

Organic Semiconductors for Light Detection

In this chapter, aspects of organic semiconductor are discussed as well as their applicability in optoelectronic devices with emphasis on light detection. The origin of the semiconducting properties of organic compounds is given in Sect. 3.1, where the molecular and solid-state properties are introduced, including charge transport. In Sect. 3.2, the working principle of organic optoelectronic devices is discussed, where donor-acceptor systems, together with the formation of CT states are explored. In what follows, the impact of such intermolecular states on fundamental limits of OPDs and OPVs are presented. In Sect. 3.2.3, we follow the different processes experienced by a charge carrier, from excitation to extraction, which enables to describe the external quantum efficiency. Finally, an overview of the architecture of OPDs and organic photomultiplicators (OPMs), two organic light detecting devices, is given in Sects. 3.2.4 and 3.2.5. Major references for this chapter are:

A. Köhler and H. Bässler [1, 2] P. W. Atkins and R. S Friedman [3] M. Schwörer and H. C. Wolf [4] W. Tress [5] U. Rau [6]

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Kublitski, Organic Semiconductor Devices for Light Detection, Springer Theses, https://doi.org/10.1007/978-3-030-94464-3_3

49

50

3 Organic Semiconductors for Light Detection

3.1 Organic Semiconductors The name organic matter was introduced by Jon Jacob Berzelius to distinguish chemical compounds derived from living or once-living matter. By itself, this definition already embraces a huge amount of what we use and see on a daily basis. However, the study of these compounds’ properties, as well as the synthesis of new materials, overcame this definition becoming a field in chemistry dedicated to the understanding and synthesis of carbon-based materials. Thus, organic semiconductors are carbon-based molecules with electronic semiconducting properties. These materials can potentially be employed not only to substitute the well-established inorganic technology, but also in new applications, which demand physical properties hardly achieved by inorganic semiconductors, such as flexibility, transparency and low processability costs. The semiconducting properties in organic materials arise from the formation of the so-called delocalized π-systems upon carbon hybridization of the s- and p-orbitals and formation of double carbon-carbon bonds. In what follows, we discuss the formation of such systems and their properties.

3.1.1 Molecular Properties One of the simplest case of a carbon based molecule is ethane (C2 H6 ), a colorless and odorless gas at room temperature. To derive the electronic properties of molecules such as ethane, a many-body problem has to be treated in which the static Schrödinger equation accounting for all the kinetic and potential energies of the interacting atoms must be solved. The solution describes the energy landscape for electrons and their localization probability. Schrödinger Equation and LCAO Model for the H+ 2 Molecule Analytically solving the Schrödinger equation describes the electronic structure of the molecule, but its applicability becomes unpractical for large systems, such as ethane. As a matter of fact, even for the simplest example, a hydrogen molecule (H2 ), no analytical solution can be found, so that the ionized molecule, H+ 2 , has to be used + ˆ to discuss the model. Yet, solving the Schrödinger equation for H2 , He Ψ = EΨ , is only possible by assuming that the nuclei are immobile, owing to their heavier mass as compared to the electron mass [7], which is referred to as Born-Oppenheimer approximation. Thus, the Hamiltonian for H+ 2 can be written as:   1  2 q2 1 1 ˆ · (3.1) ∇ ( r) − + − He = − 2m e 4π0 r1 r2 R The first term on the right hand of Eq. (3.1) represents the kinetic interaction, while the second accounts for the coulombic repulsion between the two nuclei separated by a distance R and the attraction electron-nuclei separated by a distance r1 or r2 .

3.1 Organic Semiconductors

51

q is the elementary charge and  the reduced Planck constant constant in the unit of J s. Eigenenergies {E n } and the Eigenfunction {Ψn } can be found in Eq. (3.1) for H+ 2, but this obviously does not hold true for larger molecules and a more generalized approach has to be used. Therefore, we introduce the so-called linear combination of atomic orbitals (LCAO) theory. In this method, it is assumed that the total wave function is composed by a linear combination of the atomic wave functions, such as: Ψ ( r ) = c1 Ψ1 + c2 Ψ2 ,

(3.2)

where c1 , c2 and Ψ1 , Ψ2 denote the expansion coefficients and the wave functions related to the atoms forming the bond, respectively. We can find c1 and c2 simply by considering that the nuclei are the same, therefore, the probability of finding an electron is the same for both, namely |c1 |2 = |c2 |2 , or c1 = ±c2 . This gives us two possible solutions, here c± , and the wave functions can then be written as: Ψ+ = c+ (Ψ1 + Ψ2 ) Ψ− = c− (Ψ1 − Ψ2 ).

(3.3)

Finally, by normalizing one of Eq. (3.3), we can find c± and write: 1 (Ψ1 ± Ψ2 ), Ψ± = √ 2 ± 2S

(3.4)

where S is the transfer integral. The eigenvalues of Ψ± are: E± =

H1,1 ± H1,2 . 1±S

(3.5)

We can now look in a more general outcome of LCAO where the Hamiltonian integrals Hi, j and the overlap integral Si, j in Eq. (3.5) can be written as   Hi, j = Ψi∗ Hˆ e Ψ j d r and Si, j = Ψi∗ Ψ j d r, (3.6) respectively. Si, j assumes value of 1, in a hypothetical situation when the atoms are at the same position, and 0, when R → ∞. In Fig. 3.1, we represent the formation of bonding and antibonding orbitals. In Fig. 3.1a, the wave functions of Eq. (3.4) are shown, as well as the overlap integral of Eq. (3.6). Note that the probability of finding the electron, shown in Fig. 3.1c, has a minimum exactly in the middle of the two atoms. Oppositely to |Ψ− |2 , the minimum of |Ψ+ |2 is higher than zero, meaning that the electron is shared between both atoms. Alike, in Fig. 3.1b the bonding orbital shows a minimum in energy, on which the molecule stability relies. The exact solution of the Schrödinger equation is sketched, solid lines. Although LCAO cannot exactly describe the system, the

52

(a)

3 Organic Semiconductors for Light Detection

(b) Exact solution LCAO solution

Antibonding Bonding

(c)

(d)

Fig. 3.1 Formation of H2+ | a Representation of 1s orbitals of two Hydrogen atoms (“1” and “2”) and the symmetric (Ψ+ ) and asymmetric (Ψ− ) wave function. b Bonding and antibonding energy landscape solved via LCAO method, compared with the exact solution of the Schrödinger equation. c Probability of finding the electron around atoms 1 and 2. d Energy splinting of E + and E − , where arrows represent the spin direction

proximity of the method to the exact solution is remarkable. Currently, different and more sophisticated methods are used, such as density functional theory (DFT), where also different approximations are implemented, leading to satisfactory results, as compared to experimental findings, when describing the electronic properties of organic compounds. Semiconducting Properties and Formation of Delocalized π-Systems An important outcome of the previous section is that ground state (bonding) and excited state (antibonding) are separated by an energy gap. This holds true, with some especial characteristics due to hybridization, for carbon-based systems. This atom, whose electronic configuration is 12 2s 2 2 p 2 , forms covalent bonds by means of a process called hybridization, allowing carbon to form up to four bonds [8]. As depicted in Fig. 3.2, carbon undergoes three main hybridizations, sp 3 , sp and sp 2 , responsible, respectively, for the existence of ethane, acetylene (C2 H2 ), ethylene (C2 H2 ) and many organic semiconductors.

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Fig. 3.2 Carbon hybridization | Carbon in its ground state, showing s-(violet) and p-orbitals (x, y, z colored in blue, red and green, respectively). The three left panels represent the three main hybridizations in carbon, namely sp, sp 2 and sp 3 , colored in light-blue, yellow and orange, respectively

In its ground state, carbon locates two paired electrons in the 2s orbital and two unpaired ones in the 2 p orbital, leaving only two reactive electrons capable of forming bonds. The hybrid form comes into place when 2 p and 2s orbitals interact with each other, relocating the electrons in new orbitals, leaving four reactive electrons available for bonding. The sp hybridization occurs by the interaction of 2s and 2 px orbitals: two new sp orbitals are formed, while p y and pz remain unchanged. The hybrid form sp 2 relies on the interaction of s, px and p y orbitals, leading to three new sp 2 orbitals plus the remaining pz , while sp 3 is formed when the three components of p orbitals interact with the s orbital and four new sp 3 orbitals arise. As shown in Fig. 3.2, the new configurations assume different angular arrangement, depending on the hybridization type formed. As our focus here is to discuss the formation of delocalized π-systems, we now analyze chemical bonds via sp 2 orbitals, since they are responsible for this property in organic semiconductors. We start by considering two carbon atoms, both in its sp 2 form. By bringing both together, one sp 2 orbital of each atom interact, binding the two carbon atoms. This bond is called σ. As the overlap between these two orbitals is large, the energy difference between bonding (σ) and antibonding (σ ∗ ) is large, leading to localized electron and a strong interaction, i.e., binding energy.

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In the same way, the two remaining sp 2 orbitals form σ bonds to hydrogen atoms. This leads to a planar structure, except for the pz orbitals, which are located out of the plane and still have one electron to share. From the interaction between the pz orbitals of each atom, the most important characteristics of organic semiconductors arises. These two orbitals bind to each other and, as the electron is far from the plane, it becomes delocalized, forming a π-bond. Moreover, because this is a rather weak interaction, the energy difference between bonding and antibonding state becomes small, from 0.8 to 4.0 eV [9], laying energetically in between σ and σ ∗ , as sketched in Fig. 3.3. This difference can be understood as the energy gap E g , governing also the absorption onset observed in these materials. In Fig. 3.3a, we detail this processes and extended it to larger molecules, such as benzene (Fig. 3.3b). Commonly, π and π ∗ are denominated highest ocupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), respectively. Every organic semiconductor is composed of conjugated systems, as presented in Fig. 3.3b. Interestingly, the electronic properties of organic semiconductors can be tuned by different approaches: adding more conjugated rings decreases the energy difference between HOMO and LUMO. For example, E g decreases from around 5.5 eV for naphthalene, with two rings, to around 2.4 eV for pentacene, with five conjugated rings [10]. Excitation Processes Organic molecules interact with the electromagnetic radiation, depending on the energy to which they are exposed. As for many of them the gap (E opt ) is around 2 eV, visible light can be absorbed. From the discussions presented in the previous section, we know that the molecule presents energy eigenvalues that can be probed via excitation. These energy states correspond to electronic, vibrational, rotational and translational motion of the molecule or parts of the molecule [11]. The occupation of energy states follows the Pauli principle, such that electrons should differ in at least one quantum number to occupy the same level. For stable organic molecules, the HOMO is filled with two electrons, i.e., with spin up s = 1/2 and spin s = −1/2, cf. Fig. 3.3, leading to an overall spin of 0 for the electron pair. The multiplicity (2s + 1) then turns to be 1. The singlet energy states, as they are called, assume allowed energy values of S0,1...n . Likewise, states with multiplicity of 3 are named triplet states and assume energy values of T0,1,...n . The energy of triplet states is usually lower than the corresponding singlet states. The Pauli principle allows for electron with antiparallel spins (singlet) to occupy the same eigenstate. Thus, these electrons are found spatially closer to each other, which increases the coulombic repulsion, increasing the overall energy. Given that electrons with parallel spins (triplet) cannot occupy the same eigenstate, their reduced distance decreases the overall energy [5, 11]. Each electronic state is divided in a manifold vibrational sub-levels, whose energetic spacing is around 0.1 eV. The latter are also subdivided in rotational modes, with spacing of  0.01 eV. The possible transitions can be summarized in a Jabło´nski diagram, as shown in Fig. 3.4. In the diagram, absorption happens by light excitation if the energy of the incoming photon is higher or equals the energy difference

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Fig. 3.3 Formation of delocalized π-systems | a Ethene (Ethylene) molecule. The σ bond is formed by the overlap of one hybridized sp 2 orbital in each atom. From the pz orbitals the so-called delocalized π system is formed. b The same process can be observed in the benzene molecule, where the π system is extended over six atoms. The lower panels represent the energetic diagram of the two molecules and their chemical structure

between two states and the transition is not spin forbidden. Oppositely to inorganic semiconductors, where an excitation leads to free charges at room temperature, in organic semiconductors excitons are bonded quasi-particles formed by excited electrons localized on the molecule due to the high binding energy. This aspect will be further discussed in the context of organic solids. Once excited, the molecule relaxes to lower energy states, non- or radiatively, represented in Fig. 3.4 by descending straight and wavy arrows, respectively. From the radiative transitions, fluorescence happens within states with the same spin multiplicity, i.e. Sn → Sm, n>m or Tn → Tm, n>m≥1. , with decay rates of 10−6 to 10−9 s−1 . Phosphorescence is a spin forbidden transition and, therefore, happens with a much smaller rate (10−2 to 102 s−1 ). As the internal conversion (IC) happens much faster than fluorescence, Sn → Sm, n>m≥1. is hardly observed [11]. Non-radiative processes happen via IC when vibrational modes of the electronic levels overlap and have the same spin multiplicity. IC does not change the energy

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Fig. 3.4 Jabło´nski diagram | The solid lines represent radiative transitions, while the wavy lines represent non-radiative transitions. Abbreviations in the sketch are the singlet (S0,1,2 ), triplets (T1,2 ), vibrational relaxation (VR), internal conversion (IC) and inter system crossing (ISC). Rotational modes are not shown. Redrawn from Refs. [5, 11, 12]

of the system by itself, but it is followed by a non-radiative transition. On the other hand, inter system crossing (ISC) refers to a similar process in which a spin change is required. Additionally, vibrational relaxation (VR) is very fast, in the range of 10 ps, implying that the electrons excited with energy higher than the electronic state firstly relax to the vibrationally relaxed electronic state, from where it undergoes one of the processes describe above. Franck-Condon Principle, Born-Oppenheimer Approximation and Stokes Shift The radiative processes indicated in Fig. 3.4 occur with lower energy, as compared to the initial absorption. Such an energy loss cannot be understood in terms of the Jabło´nski diagram, as the latter is drawn for final states and the spatial coordinates are not considered. In fact, the molecule can be solved for different positions of the nuclei and a potential energy curve for each state is generated [1]. The equilibrium position of the molecule (distance between nuclei in a diatomic molecule) on its ground state differs from that of its excited states, as the rearrangement of electrons leads, in most cases, to a larger distance [3]. This happens because the excited state is an antibonding state, whose electron density is not placed in between the nuclei (see Fig. 3.1) and, therefore, the attractive force electron-nuclei decreases, increasing the nuclear separation [1]. To describe the potential energy curve, the total wave function of every state in the molecule, Ψtotal , can be approximated by the product of its (manyelectron) electronic (Ψel ), spin (Ψspin ) and vibrational (Ψvib ) components, Ψtotal = Ψel Ψspin Ψvib .

(3.7)

Such approximation works in many cases, including the processes of light absorption and emission. The Frank-Condon principle [13] relies on the Born-Oppenheimer approximation [14] to state that the nuclei can be considered immobile while these transitions take place. As the nuclear separation of initial and final state are dif-

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Fig. 3.5 Franck-Condon principle | a Diatomic molecule and its ground and excited state, separated by a distance r0 and r1 , respectively. Absorption and emission are represented by straight arrows pointing up and down, respectively. Dashed green arrows represent the most probable absorption from E 2←0 (up) and emission from E 0→2 (down), transitions also represented in b. ωi is the energy difference E n − E n−1 . Thermalization to the ground vibration state of S0 and S1 are represented by wavy arrows. b Absorption and mirrored emission spectra showing the Franck-Condon principle. Redrawn after Refs. [1, 5]

ferent, as explained above, the absorption excites higher vibrational modes of the excited state. The charge relaxes into lower vibrational modes and is emitted to higher vibrational modes of the initial state, relaxing once more to lower vibrational modes non-radiatively. The energy lost in the relaxation processes is translated into the emission spectra, which ideally mirrors the absorption spectra at E 0−0 , transitions involving the relaxed vibration mode of the ground and excited state. These processes are represented in Fig. 3.5, where the potential energy curves for S0 and S1 are sketched. Quantum mechanically, the Franck-Condon principle shows that the most probable excitation is the one from the vibrationally relaxed ground state of S0 [15] to the vibrational state that it most resembles in S1 [3]. In Fig. 3.5a, this wave function is represented right above S0 of the initial electronic state and the transitions are shown by the green arrows. In order to understand the contribution of each component of Eq. (3.7) to the final spectra shown in Fig. 3.5b, we have to account for the interaction of light with the molecule via its Hamiltonian, since the absorption/emission changes its total energy. That can be done by adding the electric dipole operator er as perturbation term in the initial Hamiltonian, and calculating the transition rate by means of the Fermi’s golden rule. The rate of transition from an initial state to a final state caused by the electric dipole operator reads, 2π |Ψel,i Ψspin,i Ψvib,i | er |Ψel,f Ψspin,f Ψvib,f |2 ρ  2π = ρ|Ψel,i | er |Ψel,f |2 × |Ψspin,i |Ψspin,f |2 × |Ψvib,i |Ψvib,f |2 , 

kif =

(3.8)

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where ρ is the density of final states. In Eq. (3.8), the dipole operator acts only in the electronic term, i.e., the electrons move in resonance with the incoming electrical dipole. Because the nuclei is too heavy to respond to the incoming electromagnetic field, whose magnetic component is also too weak to change the spin, the remaining terms are unaffected. er |Ψel,f |, is proportional to the overlap integral The electronic term, |Ψel,i | between final and initial states, describing the strong absorption by states in the same parts of the molecule (e.g. π-π ∗ transitions) and the weak absorption in spatially separated states, such as CT states. Moreover, it scales with the magnitude of the dipole moment, making well-oriented orbitals (with respect to the incident light) to absorb more strongly [1]. Experimentally, this translates into the oscillator strength, f . Being related to the change in the intermolecular distance Δr = r1 − r0 , the vibrational term additionally shapes the intensity of the transition in the spectra by probing er |Ψel, f |2 , depending on the overdifferent vibrational levels with probability |Ψel,i | lap integral of the initial and final vibrational wave functions. In Fig. 3.5 this assumes the strongest value for the E 2←0 and E 0→2 transitions. The spin term in Eq. (3.8) accounts for spin changes and results to values of either 1 or 0 for spin-allowed or spin-forbidden transitions, respectively. Therefore, singletsinglet and triplet-triplet transitions are allowed, while singlet-triplet are not allowed. Nevertheless, phosphorescence can still take place, i.e., emission from T1 → S0 , via spin-orbit coupling, a mechanism which causes a spin flip. All the transitions discussed so far should lead to sharp and well-defined peaks. However, for organics, emission and absorption spectra resemble that of Fig. 3.5b. This is because lower energy modes exist between vibrational modes forming a quasi-continuous of states. At room temperature, electrons in the relaxed ground state populate these modes, such that absorption (emission) of photons with lower (higher) energy than E 0−0 takes place, causing a broadening of the measured absorption (emission) spectra [1]. For rigid molecules, low temperature measurements freeze out these modes, revealing defined peaks, in contrast to less rigid ones, for which very low temperatures would be required [16]. In Fig. 3.6, we use a similar picture to Fig. 3.5 to explain the effect of these states in the spectra. In addition to the broadening of the absorption/emission peaks, the occupation of these states causes the spectra to shift in relation to E 0−0 , which is known as Stokes shift [17]. Note that the Stokes shift is also referred to as the difference between the strongest absorption and emission peak. If defined so, different phenomena cause a Stokes shift [1].

3.1.2 Solid State Physics of Organic Semiconductors In the previous section, we discuss the formation of organic semiconducting molecules. Their applicability in real devices relies on the properties presented by thin films formed by these molecules. Therefore, it is necessary to understand the solid state physics of organic semiconductors. Organic semiconductors can be

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Fig. 3.6 Low-energy modes | a At room temperature, excitons in the relaxed ground state populate low energy modes, such that absorption (emission) of photons with lower (higher) energy than E 0−0 happens, causing a broadening of the measured absorption (emission) spectra. b Absorption and mirrored emission spectra showing the broadening and the Stokes shift caused by the same effect. Redrawn after Refs. [18, 19]

divided in two main categories: polymers and small molecules. The first refers to (macro)molecules of variable length and mass composed of repeated smaller units (mers). Small molecules, on the other hand, do not show such repetition. Being much smaller and lighter makes it possible to be thermally evaporated, in contrast to polymers, usually processed via wet techniques, such as spin-coating and printing. Polymers and small molecules, together with organic crystals (controlled growth), form organic solids with semiconducting properties. Formation of Solids A stable solid-state film, as well as stable molecules, relies on the equilibrium of repulsive and attractive forces. In case of molecules, equilibrium is guaranteed by coulombic forces via covalent bonds. In most polymers and small molecules, however, no electrons are available for covalent bonds and the solid stability takes place via another interaction, the dipole-induced bond. As a consequence of delocalized π-systems, dipoles are easily induced in organic molecules and, by means of the socalled London dispersion, the induced dipoles are stabilized with a resultant attractive force proportional to r−6 . The Pauli exclusion principle provides the repulsive component: if the wave function of the electrons starts to overlap, they have to be promoted to higher energy levels, increasing the energy of the system. This repulsion is proportional to r−12 [20]. The resultant potential curve, called Lennard-Jones potential and represented in Fig. 3.7, can be written as:  σLJ 12  σLJ 6 . (3.9) − V ( r ) = 4E eq r r

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Fig. 3.7 Lennard-Jones potential | Induced dipoles cause an attractive force, whereas the overlap of orbital provides a repulsive component. The red curve represents the resultant potential and the equilibrium position achieved between repulsive and attractive forces at ( req , E eq )

The binding energy E eq , represented in Fig. 3.7, is correlated with the polarizability of the surrounding molecules, which is also correlated with the degree of delocalization of the π-system. Well-delocalized systems tend to polarize more efficiently, increasing E eq . When E eq > kB T0 , where T0 is the room temperature, a solid is formed. E eq is also reflected in the thermal properties of the solid, e.g., the melting point. σLJ is known as the van der Waals radius and represents the distance at which the intermolecular potential between the two particles is zero, giving a measurement of how close two nonbonding particles can get. Because the bonding energy of these interactions is weak, organic solids are named “soft matter” and the spectroscopic properties of organic films resemble the ones of single organic molecules. The majority of them do not present any extended ordering, being therefore either polycrystalline with low order or completely amorphous. Therefore, we focus on the properties of amorphous films. On the other hand, organic crystals, where a band-like structure is formed, will not be discussed in this work. Molecular Versus Thin-Film Properties Experimentally, it has been observed that the fluorescent spectra shifts to lower energies, when going from single molecules to aggregates [21, 22]. The reason for this observation is the molecular polarization. The electric field induced by one molecule propagates to the surroundings, shifting its energy. Even for non-polar molecules, the delocalization of the electronic system, discussed for molecules, also plays a role when they come together in the formation of solids, as it allows for induced dipoles. In a solid, all the adjacent molecules and the orientation of their (induced-) dipoles should be taken into account to describe the final energy levels.

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For molecules, we define the ionization potential (IP) and the electron affinity (EA) as the energy necessary to promote an electron to vacuum level and the change in energy when an electron is added to the molecule, respectively. These quantities, which define many of the semiconducting properties of organic molecules and are therefore important for the device operation, will be affected by the polarization. In general, excited states present stronger polarizability, making them be affected by this effect more strongly [1]. In Fig. 3.8, we demonstrate this effect. Single molecules present lower EA and higher IP. As they aggregate, the polarization forces EA to increase and IP to decrease, narrowing the energy gap. In a complete solid, a number of energy level are randomly found, depending on the polarizability experienced by the molecule and the local effects around. Commonly, these different states are described as Gaussian distribution centered around a mean value E n for electrons:   1 (E − E n )2 . (3.10) exp − gn (E) = √ 2σn2 2πσn σn is the standard deviation of the Gaussian distribution, being referred to as disorder parameter [1], with typical values in the range of 100–150 meV [23, 24]. Similarly to Eq. (3.10), an expression can also be written for holes. In these conditions, absorption and emission of energy happens in the solid similarly to the processes discussed for single molecules, based, however, in the new energy levels. Polarons Charge carriers in organic molecular solids experience electrostatic interactions with the lattice, which affects the charge transport, and the energy levels (IP and EA) of the charged molecule. Furthermore, the presence of additional charge carriers residing temporally in the so far neutral states, LUMO and HOMO, causes a dynamic polarization (phonons). This effect forces the lattice to redistribute its charge density, leading to a geometrical distortion. As charges occupy the so-called singly ocupied molecular orbital (SOMO), they are transferred from molecule to molecule and the distortion of the lattice goes along with it. A charge, together with the static (electron-electron interaction) and dynamic (electron-phonon interaction) polarization is referred to as a quasi-particle called polaron. The formation process of a negative polaron is sketched in Fig. 3.9. In organic molecular solids as those discussed in this thesis, polarons are responsible for transporting electric current, since electrons and holes are not completely free. Nonetheless, hereafter, we use the terms “electrons” and “holes” for negative and positive polarons, respectively. Excitons-Formation and Diffusion The quasi-particle exciton is formed by promoting an electron from the HOMO to the LUMO, leading to a coulombic bond electron-hole pair. Depending on the binding energy and delocalization, excitons can be classified as Wannier-Mott excitons and Frenkel excitons, see Fig. 3.10a. The former are present in inorganic semiconductors and are characterized by binding radius larger than the lattice spacing, being, therefore, very delocalized. Because its

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Fig. 3.8 Energy levels evolving from a single molecule to solids | In the upper panel, the energy levels of the molecule (subscript “M”) change in the solid state (subscript “S”) due to electron and hole polarization Pn and Pp , respectively. As EA becomes lower and IP becomes higher in the solid state, the transport gap bandgap (E g ) decreases. In the amorphous solid state, every molecule is affected differently by the surrounding, leading to a Gaussian distribution of energy levels. The lower panel shows the polarization effects on the excitonic states. The The optical gap is also decreased by the polarization. As it will be discussed below, depending on the degree of ordering, organic solids can also form transport bands, as shown in c. For most organic materials, however, amorphous solids are formed. The energy levels and the excitonic states of the solid are compared by scaling the magenta arrows to the ground state (S0 ) to the respective HOMO energy. Adapted from Ref. [19]

Fig. 3.9 Polaron formation upon excitation | At t = 0 a localized charge is inserted in the neutral lattice causing the neighbor molecules to polarize followed by a reorganization of its charge distribution. Finally, the lattice gets distorted forming a polaron

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Fig. 3.10 Excitons and energy transfers | a Representation of three different excitons. Grey circles represent molecules and atoms in the upper and lower panels, respectively. b Förster and Dexter energy transfer processes

binding energy is lower than kB T0 , it does not exist at room temperature [1]. For amorphous materials, due to the low dielectric constant and the absence of band-like structures the excitation is localized within the molecule, leading to a high electronhole binding energy, in the range of 150–500 meV, much larger than kB T0 . In this systems, the Frenkel exciton is found, a quasi-particle with singlet or triplet nature that can be formed not only via light absorption, but also when free electron and holes get captured by the coulombic interaction between them. In fact, the term Frenkel exciton was firstly used to describe the N -excited states of a chain of N equal molecules strongly coupled. In such a system a coherent motion or energy transfer takes place, similarly to Bloch waves in the context of inorganic semiconductors, being therefore delocalized. However, for most solid films, the coherence is broken because the electronic coupling is lower than the energetic variation from site to site, resulting in the localization of the exciton within the molecule. The term Frenkel exciton is then used, in the context of amorphous organic solids to describe the incoherent energy transfer, which can be of two types: Förster and Dexter energy transfer, see Fig. 3.10b. If the coupling between the excited state of one molecule and ground state of another molecule is described by dipole-dipole interaction, the energy transfer is of Förster type, where the interaction is proportional to the overlap of the absorption and emission spectra, the molecule orientation and the distance between molecules. In this type of transition the spin is preserved, therefore, it is only possible for singlets, since ground states are involved (singlets) and not for triplets [1, 25]. Dexter energy transfer happens when a direct overlap of the molecular wave function occurs and only exchange interactions are taken into account to describe the coupling [1]. This type of energy transfer is not restricted to the spin orientation, and therefore, can also happen for triplets [26]. An electron and a hole are simultaneously exchanged between donor and acceptor molecules, as depicted in Fig. 3.10b. Another excitation type present in organics is the CT exciton. Here, the excitation is followed by an energy transfer to the neighboring molecule. In Addition, the direct excitation of electron residing in the HOMO of one molecule directly to neighboring

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molecule is also possible. CT excitons are very important for OPVs and OPDs, as many of the optoelectronic properties of these devices are implicated by the properties of the CT states. This is discussed in the context of donor-acceptor systems in Sect. 3.2.1 as efficient charge separation takes place via CT between different molecules [27, 28]. Charge Transport—Low Charge Carrier Concentration For most of the situations described within this work, the devices are driven under small charge carrier concentration, since the applied electric field is low. Therefore, charge transport is discussed here with emphasis on this regime. Moreover, as most of the materials used in this thesis are known to form amorphous films, more attention is given to the Gaussian disorder model (GDM), despite a short differentiation made for band and polaronic transport. The main concern of this section is the mobility, as fast charge transport is required for well performing optoelectronic devices. For perfect crystals, the mobility can be derived as a function of the mean relaxation time between collisions of the charge carrier to the lattice ions and an effective mass m ∗ , which accounts for the charge carrier interaction to the lattice, see Sect. 2.2.1. As organic thin-films can be accomplished by a huge variety of materials, charge transport, namely mobility, behaves in different manners, depending not only on the materials properties, but also in the preparation conditions. While most transport features are dictated by the amorphous character of organic molecular solids, exceptions can be pointed out, where, in organic crystals, band-like transport has been achieved [29–31]. To embrace the different materials and transport characteristics, an intuitive approach consists in writing a Hamiltonian to account for each phenomena taking place in organic solids. In spite of its simplicity, this model illustrates the limiting cases in most organic solids. The Hamiltonian is composed of five terms, as follows: Hˆ transport = Hˆ e, vibronic + Hˆ electron transfer + Hˆ on-diagonal dynamic disorder +

(3.11)

Hˆ off-diagonal dynamic disorder + Hˆ static disorder . • Hˆ e, vibronic is the total energy of the system. Lattice and charges can occupy excited states but they do not interact to each other. • Hˆ electron transfer describes the electron transfer from site to site. • Hˆ on-diagonal dynamic disorder and Hˆ off-diagonal dynamic disorder basically accounts for the same effect: polaronic interaction, i.e., interaction between excited charges and the lattice.

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• Hˆ static disorder accounts for variation in rate (off-diagonal) and energy (on-diagonal) unrelated to vibrational modes and which are present because of morphological differences between sites, transition distances, orientation, etc. The off- and on-diagonal separation is usually made based on the matrix notation, where the terms related to energetic changes either static or dynamic appear on the diagonal, while the off-diagonal account for changes in the rate of transitions from site to site. A very comprehensive phenomenological and mathematical description of Eq. (3.11) is given in Ref. [2]. Based on this Hamiltonian, three different limiting cases can be studied, corresponding to different experimental observation: Band transport: when the Hˆ electron transfer dominates the Hamiltonian, the interaction between adjacent sites is the strongest forming wide bands with bandwidth (W ) of around 10kB T . Therefore, charge transport can be described as motion in bands, where the interactions of excited charges with the lattice have a minor effect on the transport, which can be described by Bloch waves. In this limit, the mobility 2 W , where a is the lattice constant, which for organic semiconapproaches μ  qa kB T ductors is around 1 nm. The band transport happens therefore if μ  10 cm2 V−1 s−1 [2]. Polaronic transport: for systems where Hˆ electron transfer is small as compared to polaronic interaction, expressed via the dynamic Hamiltonians, and if Hˆ static disorder can be neglected, the transport can be classified as of the polaronic type. The interaction of excited charges to intra- and inter-molecular vibration is called polaron, as discussed above. Although a discussion about the role of polarons in charge transport is still held in literature [31–33], it is agreed that only polaronic effects cannot explain charge transport. While the quantities related to polaronic effects are not easily accessible, the parameters needed to describe charge transport in terms of polaronic effect are physically unrealistic. On the other hand, it is also accepted that they should, to some extent, affect charge transport. Fishchuk et al. [34] have developed a model called effective medium approach (EMA). The model is a superposition of disorder and polaronic effects, developed on the basis of Marcus rates [35]. The dependence of the mobility on temperature and electric field is expressed by Eq. (3.12).   1.5     σˆ qa E σˆ Ea exp − 2 exp √ , (3.12) μ = μ0 exp − kB T 8ζ 4ζ 2 kB T 2 2ζ 2 where E a is half of the polaron binding energy, σˆ = σ/kB T and ζ =

1 − σ 2 /8qakB T . Disorder-based transport: if the static disorder dominates the Hamiltonian over the already discussed components, charge transport will be characterized by a thermally activated hopping mechanism, from site to site [36]. In such systems, the GDM is commonly used. Proposed by Heinz Bässler (1993), the model considers a Gaussian density of states as defined by Eq. (3.10). Jumps from site to site can be described by the Miller and Abrahams rates [37],

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νi, j

   ε −ε  exp − kj B T i , for ε j > εi , ri, j  × = ν0 exp −2γa a 1, for ε j ≤ εi .

(3.13)

In this framework, jumps from localized site i to site j decrease exponentially with separation distance ri, j and the electronic coupling between adjacent sites, represented by γ, is the inverse of the Bohr radius of a hydrogen-like wave function [4]. For energetically upwards jumps, the rate further decreases exponentially, according to Δε j,i = ε j − εi . As presented, the model accounts for the on-diagonal (energetic) disorder, as discussed above. Applying the GDM under low charge carrier concentration, mobility depends on temperature as it follows:   4 (3.14) μ(T ) = μ0 exp − σˆ 2 . 9 An important outcome of the GDM is the emergence of a common level of thermal equilibrium to which charge carriers relax, namely E ∞ . Moreover, charges

are excited (E tr −E ∞ ) , leading to a to a transport level, E tr , whose activation corresponds to exp − kB T

quadratic temperature term in the exponential, explaining the ln μ ∝ T −2 dependence typically observed. The transport according to the GDM is sketched in Fig. 3.11. In a latter version of the GDM model [38], the positional off-diagonal has been introduced by allowing the electronic overlap parameter 2γa to vary statistically, from where a second disorder parameter, Σ, arises. Σ represents how the strength and distance for electronic overlap is spread in a Gaussian distribution [2]. Using different approaches such as Monte Carlo simulations, analytical effective medium theory, and stochastic hopping theory, the following empirical relation for mobility has been derived, accounting for temperature and electric field dependency [2]:   √ 4σˆ × exp C(σˆ 2 − Σ 2 ) F , for Σ ≥ 1.5, μ(σ, ˆ F) = μ0 exp − 9   √ 4σˆ × exp C(σˆ 2 − 2.25) F , for Σ ≤ 1.5. μ(σ, ˆ F) = μ0 exp − 9

(3.15a) (3.15b)

In Eq. (3.15), the Poole-Frenkel effect is already covered, which, in this formulation, happens due to the interaction of an occupied site with the applied field. Experimentally, however, the distance from site to site (molecule to molecule) is around 0.5–1.0 nm, in contrast, the potential maximum predicted by the GDM is of 6 nm, for F = 105 V cm−1 and  = 3 [4]. The discrepancy arises from the correlation between sites, which, as discussed above, interact to each other via polarization [2]. Another consequence of Eq. (3.15) is that the field dependence can be negative, if σˆ < Σ in Eq. (3.15a) or Σ > 1.5 in Eq. (3.15b). This is a characteristic of positional

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Fig. 3.11 Gaussian disorder model | Electrons move downwards in the energetic scale without requiring any additional activation energy, whereas jumps upwards are field and thermally activated. Hoping from site i to site j separated by a distance, ri, j happens at a rate νi, j , according to Eq. (3.13), decreasing exponentially for upwards jumps. Redrawn after Refs. [4, 39]

disorder. If the next site encountered by a charge carrier migrating in the field direction has an unfavorable electronic coupling, the carrier might circumvent that site. If this involves jumps against the electric field, the jump will be blocked at high fields, leading to decrease in mobility. This effect has been investigated and proven to be a direct consequence of hopping in energetically and positionally disordered systems [38, 40, 41].

3.1.3 Traps in Organic Solids The disordered character of organic semiconductors by itself guarantees a variety of energy states, differently situated in the energy scale. While the Gaussian density of states, depicted in Fig. 3.8, is meant to embrace all those states, energetic sites placed in between the energy gap, hereafter named traps, can also exist. In fact, as it will be discussed below, further distributions of trap states can arise in the gap of these materials, breeding effects in charge transport, recombination, and, more specifically to this work, the dark current of OPDs. Albeit traps are a characteristic of solids and, therefore, commonly discussed in the context of solid-state physics, a new section is dedicated to them, as they turn out to play a major role in describing the behavior of OPDs, see Chap. 5.

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Traps are classified according to their energetic position: if the energy to detrap a charge sitting in a trap level is in the order of kB T0 , these states are named shallow traps. If E t >> kB T0 , the states are then called deep traps. For organic materials, values in the literature point to trap concentrations (Nt ) of around 1016 cm−3 [42], which is rather low compared to the density of states in the conduction and valence band, usually assumed to be of around 1021 cm−3 [43]. Despite their low concentration, traps might play a major role in the mechanism ruling device performance. In amorphous organic semiconductors, the covalent bonds form the molecule by attaching atoms to each other. Electrons in sp 2 orbitals which are not used to form CC bonds, usually are bonded to hydrogen atoms, practically excluding the presence of dangling bonds. Therefore, unlike amorphous silicon, traps in organic semiconductor arise from fundamentally different sources. To form a trap, any process should cause the HOMO of the semiconductor to be larger or the LUMO to be smaller than the average of HOMO and LUMO of the rest of the solid. For small molecules, a solid where sufficient molecular interaction is present, allowing for electron delocalization, removing a molecule leads to an increase in energy. Therefore, vacancies do not lead to traps. As the conjugation length in aromatic compounds increase, the energy gap decreases [44]. This means that lower-than-average conjugation length chain in organic polymers, for example, also should not lead to traps, as HOMO and LUMO becomes lower and higher, respectively [45]. From the same reasoning, if the conjugation length of a chain becomes longer-than-average, the energy gap becomes lower and charges can be trapped either in the HOMO or in the LUMO. The same holds true for regions where the electronic coupling between adjacent molecules becomes stronger, also causing the gap to decrease, where energy levels can serve as traps. In addition to shallow traps, mostly caused by disorder, deep traps are also frequently observed in organic semiconductors, whose origin is often attributed to impurities. On one hand, the amount of traps seems to decrease with purification processes [46]. On the other hand, gap states seem to exist which either do not arise from impurities or are insensitive to the available purification methods. The nature of the impurity also plays a role in defining the final energy position. In the case of water and oxygen, both believed to be omnipresent in organic semiconductors, IP can vary dramatically, from around 12 eV, in the gas phase, to lower than 6 eV, when mixed together in water-oxygen clusters, values that were found to limit hole transport in many materials [47]. Although many effects such as processing conditions, material purity and others can affect the trap distribution leading to different types of distribution along the gap, in general, these states can be described by a Gaussian distribution as follows:  Nt (E) (E − E t )2 . (3.16) exp gt (E) = √ 2σt2 2πσt Measuring and characterizing trap states is not trivial. Many methods have been applied in organic field effect transistors (OFETs) and a interesting comparison of different methods is made by Kalb et al. [48]. In OPVs and OPDs, traps are usually

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studied by means of thermally stimulated current (TSC), impedance spectroscopy (IS) and more recently by sensitive external quantum efficiency (sE Q E) measurements [49]. Using IS to infer trap properties is based on the method proposed by Walter et al. [50] and will be discussed in more detail in Sect. 4.3.8. The effects of traps are generally detrimental to the device performance [45, 51– 53]. In Chap. 5, we will discuss another negative effect in OPDs, in addition to the decreased external quantum efficiency. On the other hand, traps are intentionally used in Chap. 6 to achieve photomultiplication in organic photoconductors.

3.2 Working Principle of Optoelectronic Devices 3.2.1 Donor-Acceptor Systems and Charge-Transfer States Organic semiconductor materials are fundamentally different from inorganic ones. In general, absorption does not lead to a direct formation of free charge carriers. Instead, a bound electron-hole pair called exciton emerges, result of higher dielectric constants in organic molecular solids. While typical dielectric constants of 10 to 13 are found for inorganic semiconductors [54], organic semiconductors show ε  3 [55]. In OPVs, this problem was circumvented by Tang et al. [56], who proposed the use of electron donating and electron accepting materials, donor (D) and acceptor (A), employed together in a bilayer structure forming a planar heterojunction (PHJ). The solar cell comprising copper phthalocyanine (CuPc) and perylene tetracarboxylic (PV) reached 1% efficiency. Years later the concept of bulk heterojunction (BHJ) was developed by Hiramoto et al. [57]. The authors managed to achieve a mixed phase of D-A materials to form the active layer of an OPV in vacuum-processed devices, which reached efficiencies of 0.63% [57]. The same concept was later implemented in solution-processed OPVs, reaching efficiencies of 5.5% [58, 59]. This concept has been largely used for different organic optoelectronic devices and has led power conversion efficiencies of OPVs to rise, remarkably reaching 17.3% efficiency in tandem structures [60] and 18.2% in single cells [61], nowadays. In OPDs, a device whose working principle is very similar to that of OPVs, the concept has likewise been applied, representing the state-of-art in this field. In fact, the success of both approaches lies on the formation of efficient exciton splitting centers, the charge-transfer (CT) states [27, 28]. CT states are related to the ground state by a charge transfer transition [62] and are formed when HOMO and LUMO of the donating material are higher than that of the acceptor, creating a heterojunction of type II. Integer charge transfer can happen in the ground state and release free charge carriers, which is the concept behind doping in organic semiconductors. On the other hand, in the active layer of optoelectronic devices, excited CT states are formed. This means that these intermolecular states exist only on their excited form and, therefore, exhibit a specific absorption and emission features. If their energy

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Fig. 3.12 Donor-acceptor systems | a Planar heterojunction and b bulk heterojunction. The formation of CT states at the interface in both system is also sketched

E CT is considerably lower than the energy of the singlet exited state, the electron is localized on the acceptor molecule/phase and the hole on the molecule/donor phase. As E CT approaches the singlet energy, a hybrid CT state (corresponding to an intensity borrowing effect between singlet and CT state) is formed assuming an excitonic character, which could be observed by a dependence of the polarization of the emission and absorption spectra on the transition dipole moment of the neat materials [63]. BHJ and PHJ are the main path to achieve efficient exciton splitting via CT states, as represented in Fig. 3.12. PHJs (Fig. 3.12a) are accomplished by vertically stacking an A-layer on top of a D-layer in a conventional pin structure or the opposite in an inverted ni p stack. In Fig. 3.12b a BHJ is shown, which is achieved by codepositing both materials D and A in a mixed phase. As a result of a larger amount of interfaces, BHJs are generally more efficient for exciton splitting but also show more nongeminate recombination. However, because BHJs can be made thicker than PHJs, the photon harvesting in BHJs is more efficient, leading to a better performance CT states were firstly observed by photothermal deflection spectroscopy [64] and their ability to generate free charge carrier was later detect by photocurrent spectroscopy [65, 66]. While the first technique proves the capability of exciting blended D-A materials at energies lower than the optical gap of both, the second shows that free charge carriers can, in fact, be generated via CT states and be collected at the electrodes. Likewise, low-energy emission has also been observed via photoluminescence [67, 68] and electroluminescence [69]. From the device’s point of view, characterizing CT states is of relevance, as many of the parameters sought to be improved find their ground on E CT . OPVs [70–72], OLEDs [73] and OPDs [74, 75] depend, to some extent, on the CT state formed at the the donor-acceptor (D-A) interface. In the earlier times of the organic photovoltaic community, the empirical dependence of VOC on the energy difference between the donor HOMO and the acceptor LUMO, HOMOD −LUMOA , and the still unknown characteristics of CT states has led to the current misleading approximation E CT = HOMOD − LUMOA . While this approximation might approach the real relaxed CT energy for some D-A systems, it strongly diverges for others [76, 77]. In addition to HOMOD − LUMOA , E CT is affected by the polarization of the medium and the

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binding energy of the electron-hole pair, which can be observed by a dependence of the emission peak on the D-A mixing ratios [67]. A more robust method to quantify CT states can be done via emisson (N (E)) and/or absorption (A(E)) spectra. When emission arises from electronic states whose sub-levels are populated according to Boltzmann statistics, the emission and absorption are related via [70, 78]:   E 2 . (3.17) N (E) ∝ A(E)E exp − kB T More commonly, the photovoltaic external quantum efficiency spectra are used, based on the assumption that the internal quantum efficiency is independent of the excitation energy, which was proven in the absorption range of CT states [72]. In conformity with the Marcus theory [35, 79], the photovoltaic external quantum efficiency and electroluminescence external quantum efficiency (E Q E EL ) of the CT spectral range can be written as:  (E − E CT − λCT )2 f CT (3.18) exp − E Q E(E) = E √ 4λCT kB T 4πλCT kB T and

 f CT (E − E CT + λCT )2 E Q E EL (E) = E √ exp − , 4λCT kB T 4πλCT kB T 3

(3.19)

respectively. Equations (3.18) and (3.19) can be used to fit the CT spectral range and extract important parameters, such as the relaxed CT state energy the (E CT ), the reorganization energy (λCT ) and the oscillator strengh ( f CT ) [71]. Furthermore, the equations predict a Gaussian-like behavior, peaking at E CT − λCT in the emission spectrum and at E CT + λCT in the absorption spectrum. In Fig. 3.13a, the E Q E spectra of D, A and the blend formed between them, D-A, are shown. Summing the individual component of the D and the A spectra does not reproduce the final spectrum of the blend, whose low energy region shows an additional absorption band, here assigned to the CT state absorption. The CT absorption band can be fitted with Eq. (3.18), from where the characteristic parameters E CT , λCT and f CT can be extracted, as noted in the legend. The optical transitions according to the Marcus theory from the ground state (GS) to the excited state (ES) are represented in Fig. 3.13b, from which also the broadening of the CT band can be understood: vibrational states are spaced with energy lower than that of the thermal energy, kB T0 , enabling higher modes to be excited at room temperature. The spectra as the ones shown in Fig. 3.13 are measured in an OPV device structure and represent, therefore, free charge carriers collected at the electrodes. Within the exciton lifetime of a few nanoseconds, they can follow different paths and the processes responsible for each path compete in a device. In Fig. 3.14, after light absorption and Frenkel exciton formation, they can decay directly to the ground state () 7 or migrate to the interface generating a CT state (), 1 which can dissociate

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Fig. 3.13 CT states in D-A systems | a Schematic external quantum efficiency spectra for a donor, an acceptor and the blend formed by these materials. Upon mixing donor and acceptor a CT absorption band arises. The right axis shows the number of photon emitted by the background at 300 K. b Optical transitions from ground to excited state. Redrawn after Refs. [18, 19]

Fig. 3.14 Processes in donor-acceptor systems | a Schematic representation of the processes in a BHJ system assuming that the excitation occurs in the donor molecule. Adapted from Ref. [80]. b Jabło´nski diagram of the same processes in a. Adapted from [62]

() 2 or decay to the ground state (). 5 Free carriers can fall back to CT states () 3 and recombine () 6 or get free again (). 4 In Fig. 3.14, these processes are represented in the BHJ and in a Jabło´nski diagram. Note that, for simplicity, absorption is considered in the donor phase, while, in fact, absorption takes place also in the acceptor phase and directly by CT states. Electron transfer from the excited donor to acceptor () 1 is known to be very fast, in the order of fs. Hole transfer was also shown to be very fast in D-A systems involving non-fullerene acceptors [81]. Whilst it is well accepted that charge-transfer is fast, an engaging debate has been held on the role played by the commonly named driving

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force, a parameter which describes the energy offset from the LUMO (HOMO) of the D to the LUMO (HOMO) of the A for electron (hole) transfer. Whether such a driving force is needed to complete efficient charge transfer is a compelling challenge for material design, since it also acts as an energy loss for OPVs, which means that a compromise between efficient charge transfer and high open-circuit voltage (VOC ) prevails. Indeed, in the framework of Marcus theory, the electron transfer is more efficient if E CT is lower than E D∗ [35, 82]. Altogether, it is assumed that a driving force of less than 0.1 eV is enough to assist efficient charge transfer when using fullerenes as acceptor, [83–85], albeit newly reported systems show nearly-zero driving force when using non-fullerene acceptors (NFAs) [86, 87]. For NFAs, hole transfer was shown to be extremely efficient in the same conditions [81]. This is an important result, as NFAs generally absorb more light than fullerene acceptors. Yet, as the energy offset E D∗ − E CT gets smaller, repopulation of the singlet states is more likely, whose decay rates are faster than that of the CT state, being identified as a source of losses [88–91]. Moreover, some authors also argue that when the triplet state on the D or A phase lays lower energy than E CT , these states can become an important path for losses [92]. Nonetheless, another study shows that fullerene triplets are the responsible for recombination, whereas the donor triplet states are not an active path, despite their 300 meV lower than E CT energy [93]. Furthermore, it has been demonstrated that triplets are inactive recombination paths for non-geminate recombination [94]. Excitons are strongly bound quasi-particle [95] which, in principle, require energies higher than the thermal energy at room temperature to split. Since efficient charge generation is observed in many systems, the discussion regarding what determines the efficiency of this process arises. The excess of energy necessary to overcome the coulombic capture radius has been suggested to be provided by high-energy CT states, while the yield for charge generation of thermalized CT states would be very low. Instead, internal quantum efficiency measurements with varying energies show that regardless the region of excitation, the yield of charge carrier generation remains constant [72]. The same effect has been observed by different groups under different perspectives, suggesting that the so-called “hot-CTs” are not necessary for efficient charge generation. On the other hand, Bakulin et al. showed that the photocurrent of OPVs increases when infrared pulses impinge on the device, in addition to the steady illumination [96]. Alike, the results of ultra-fast spectroscopy offer a dissenting conclusion than that provided by the measurements of internal quantum efficiency, as hot-CTs were shown to assist charge separation, leading to more efficient charge generation [62]. While experimental and theoretical studies show the potential effect of hot-CTs [97], data found by other groups confront the findings [98]. Finally, the role of the excess of energy on charge carrier generation has been heavily discussed and a final outcome is yet to be found. As discussed above, CT states are indeed efficient exciton splitting centers. On the other hand, these states also act as recombination paths. Before recombining, carriers injected from the electrodes or generated via light absorption form a CT state, which are, by definition, coupled to the ground state, allowing the recombination to take place. This event can happen radiatively by the emission of a photon as explored

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in OLEDs, or non-radiatively, one of the main concerns in current OPVs. Because every photon from the background radiation absorbed by device has to be reemitted to achieve thermal equilibrium, this can be used to determine the unavoidable radiative recombination limit which is the lower limit for recombination (radiative and nonradiative). Non-radiative recombination is still a matter of intense research in the field of OPVs [99], as it limits the VOC of these devices and thereby the maximum reachable power conversion efficiency. A relation between E CT and non-radiative recombination has been observed for a number of devices [100]. Indeed, according to the energy-gap law [101], the non-radiative recombination rate should increase exponentially as the energy difference between the ground- and exited state decreases, which is a result from the increased overlapping between the states manifolds. At VOC , all charges must recombine, which makes it an appropriated point for analyzing recombination. In Sect. 3.2.2, we resume the discussion of recombination, since it also defines the lower limit of the dark current in OPDs and, therefore, the upper limit of the specific detectivity.

3.2.2 Impact of Charge-Transfer States on Optoelectronic Devices In the previous section, we discussed the formation of CT states and described qualitatively how they are related to optoelectronic properties of devices. In this section, the impact of CT states properties are quantified, focusing on two properties, which are, in fact, related: the open-circuit voltage and the saturation current (J0 ). In Sect. 2.2.5, using the Schottky approximation, we showed that VOC is related to J0 via Eq. (2.60). Later, based on thermodynamic assumption, J0 was shown to be generated by absorption of thermal radiation, see Eq. (2.73). In the ideal case, under zero bias, charges are excited by background radiation and decay radiatively according to the generalized Planck law, Eq. (2.26) [6, 102]. In real devices, however, recombination (generation) also takes place non-radiatively, which decreases (increases) VOC (J0 ). To include that, the saturation term in Eq. (2.71) is modified to Eq. (2.73), from which also VOC can be estimated, accounting for the non-radiative losses. Thus, emission, absorption, VOC and J0 are interconnected and determined by thermodynamic processes. For most inorganic devices, where a single material is used, these parameters are linked to the E g of the material. In organic devices, D-A systems guarantee efficient charge separation, and an effective gap is formed with energy E CT . The question then arises, whether and how these states and their energy are related to VOC and J0 . Even before a comprehensive understanding of this relation was given [70, 71], VOC was observed to depend on the HOMO-LUMO difference [103, 104] and CT state formation [66, 105–107]. The main difference when using the detailed balance theory for organics lies on the fact that heterojunctions of type II, E CT is by definition always lower than the optical

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gap of the single materials. Therefore, the equilibrium with free charge carriers is reached via E CT and not via E g . In Fig. 3.13a, we compare a schematic EQE of an OPD, solid green line, with the black-body spectrum at 300 K, blue dashed line. Note that the black-body spectrum coincides with the CT band, causing absorption and emission at T0 more efficiently than the singlet states of the acceptor. Moreover, recalling Eq. (2.73), J0 is determined by integrating the product of these two spectra, which means that, in thermal equilibrium, the remaining part of the EQE spectrum is irrelevant for J0 . Therefore, we can use the description for external quantum efficiency of CT states, Eq. (3.18), together with Eq. (2.9) converted to energy for E >> kB T , into Eq. (2.73) to determine the J0 .

J0 =

2π f CT q E Q E el h 3 c2



J0 

√

   E E (E CT − E + λCT ) exp − dE × exp − 4λCT kB T kB T 4πλCT kB T

(3.20)

  q 2π f CT E CT (E − λ ) exp − . CT CT E Q E el h 3 c2 kB T

(3.21)

For OPDs, Eq. (3.21) represents the lower limit for the dark current (JD ), which, together with E Q E, is one of the most important parameters for specific detectivity (D ∗ ). Importantly, from Eq. (3.21) multiplied by E Q E el the radiative limit of D ∗ for an OPD can be calculated. Note that this calculation differs from the BLIP limit defined by Eq. (2.94), where EQE = 1 is assumed. Now we can use J0 to determine an analytical expression for VOC , inserting Eq. (3.21) into Eq. (2.59), leading to: Vrad

VOC

      E CT kB T 2π(E CT − λCT ) f CT 1 kB T − ln ln = − . q q J h 3 c2 q E Q E el  SC     ΔVrad

(3.22)

ΔVnonrad

Vrad is the radiative limit of VOC , when only radiative recombination, and therefore unavoidable, losses occur. ΔVnonrad represents the non-radiative contribution, which, in principle, can be avoided. In organic solar cells, besides explaining the often observed dependence of VOC on E CT , Eq. (3.22) has already been successfully employed to describe the impact of D-A interfacial area, via f CT [108], and nonradiative losses, which are shown also to be intrinsic for fullerene-based solar cells [100].

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3.2.3 From Light Absorption to Electric Output The final electric current produced by a device depends on the yield of many subprocesses involving the discussion made in the previous sections. From the product of the efficiency of these sub-processes, we can define the final EQE of the device. These sub-processes are [5]: 1. Light absorption with efficiency ηex (λ). It depends mainly on the absorption coefficient of the material used and on the optical field within the absorbing layer. Losses in these process arise from photons reflected by and transmitted through the device. Strategies such as light trapping have been shown to enhance the current generation by increasing the probability of light absorption [109]. In organic photodetectors, the use of Fabry-Pérot microcavities not only enhances the absorption but also allows for wavelength selectivity [74, 75, 110]. 2. Exciton diffusion with efficiency ηdiffus (T ). After photon absorption, excitons have to diffuse to an interface where dissociation is more probable. The efficiency in this process depends on how far an exciton can diffuse before recombining. As in organic systems the diffusion length is expected to be only of a few nanometers [111], the thickness of donor and acceptor layers are limited to this range in PHJ OPVs, to the detriment of photon absorption. In BHJs, the phase separation must be considered, as the diffusion length can be smaller than large domains. 3. Charge-transfer with efficiency ηCT . As discussed in section Sect. 3.2.1, the dependence of the charge transfer efficiency on the driving force ΔCT is still under debate. 4. Exciton dissociation with efficiency ηdiss is also discussed in Sect. 3.2.1. 5. Charge transport with efficiency ηtrans (F, T ). Once excitons are split, carriers are driven to the electrodes by the built-in field and by the external field, when applied. In this process, non-geminate recombination can take place if electron and holes meet. Here, PHJ systems are expected to benefit from the low probability of this event to happen, as charges are located in spatially separated materials. In BHJ, however, the non-geminate recombination represents an important loss, which is believed to be proportional to the probability of charges to meet. This type of recombination can be described by the reduced Langevin recombination, where the reduction factor accounts for the often overestimated recombination rates predicted by the original Langevin description, which has been attributed to the CT kinetics [112]. Improved transport can be achieved either by thinner blends or by larger domains of donor and acceptor, which in turn, compromises the light absorption (1), the exciton diffusion efficiency (2) and the charge-transfer process, as these depend on the amount of interfaces in system [80]. Rare exceptions can be found in literature where thick layers are able to provide good transport [113– 115]. 6. Charge collection with efficiency ηcolect (F, T ). The yield at which charges are collected affects the bimolecular recombination [116, 117], hence, appropriated selective and ohmic contacts are required. This can be achieved with the aid of doped contacts [118], as briefly discussed in Sect. 2.2.4.

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From these sub-processes, one can also define the internal quantum efficiency (I Q E), taking also into account each yield of steps after absorption, and E Q E, which also takes absorption into account. The external quantum efficiency can then be written as: # electrons # photons E Q E(λ, T, F, ...) = ηex (λ) · I Q E(λ, T, F, ...) E QE =

= ηex (λ) · ηdiffus (T ) · ηCT · ηdiss · ηtrans (F, T ) · ηcolect (F, T ) (3.23)

3.2.4 Organic Photodetectors In this section, an overview of the state-of-art of OPDs is given and the main limiting parameters that hinder the usability of these devices are discussed. As clarified in the introduction of this chapter, we use the terminology organic photodetector (OPD) for devices using a diode structure. Indeed, this is the most investigated version of organic detecting devices, which takes advantage of the vast knowledge produced in the field of OPVs. Despite the similar structures, these two devices operate at different condition, which demands their properties to be optimized for distinct operation regimes. The role of an OPV is to convert optical power into electrical power and deliver it to a load with minimal energy losses. OPDs, however, are intended to convert an optical signal into an electrical signal, a process which can or not make use of external energy. In fact, most of OPDs reported in literature operate at zero bias. This is a consequence of the high dark current at reverse bias (JD ) delivered by these devices, a characteristic so far not well addressed which is discussed in Chap. 5. First reports on OPDs date back to the 1990s. In the context of charge transfer interfaces, Heeger et al. published different material system using MEH-PPV as donor and fullerene derivatives as acceptor, realizing OPDs with reasonable performances [58, 59]. These results are contemporary to those by Hall et al., who also studied MEH-PPV as donor blended with CN-PPV [119]. Followed by these reports, years later, an organic imager was achieved [120, 121]. About fifteen years after the first OPDs, the same group reported a broadband OPD, with spectral response extended to the NIR, reaching a specific detectivity of 1012 Jones [122]. Given the intrinsic advantages of organic materials, the applicability of OPDs was rapidly noted. The possibility of realizing flexible and lightweight photodetectors at a low production cost is indeed attractive [123, 124]. However, turning this exciting research topic into commercial applications requires these devices to compete with already available technologies, which relies on the improvement of specific detectivity, response speed, wavelength tunability, and circuit integration. Regarding specific detectivity, we refer to Eq. (2.92) to discuss the current stage of OPDs. Two variables define this quantity, namely, external quantum efficiency

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Fig. 3.15 Commonly used structure of OPDs | a Schematic energy diagram of an OPD based on D-A systems. b Bottom-illuminated OPD in a PHJ and c in BHJ structure

and noise spectral density. Studying optical losses in OPDs, Brabec et al. showed already in 2002 that P3HT:PCBM blends could achieve external quantum efficiency of 90%, if optical losses would be minimized. In the same work, the internal quantum efficiency was shown to approach 100% [125]. Since then, many material systems using polymeric or small molecules were investigated and their properties enhanced to an extent that allow us to state that material combinations exist for which external quantum efficiency is high enough to compete with inorganic technologies. The remaining key limitation is the high Sn of OPDs, in addition to low speed and circuit integration. In Sect. 2.3.2, we discuss the three most studied sources of noise, namely, thermal, shot and 1/ f noise. However, OPDs usually suffer from high dark current (JD ) in reverse bias [126], which promotes the shot contribution as the most important one in these devices [110, 127]. In fact, many reports analyze the device in the so-called self-powered mode, i.e., at 0 V. The reason is that in the self-powered mode the shot noise can be ignored in the noise estimation, given that in most cases noise is not measured but rather calculated from the shunt resistance, Rshunt [74, 75, 122, 128, 129]. The problem of JD was addressed via many optimization paths, which can be summarized by the use of selective/blocking layers [130–132], contact alignment [133, 134], prevention of shunt paths via layer thickness increase [75], and interlayers to smooth the bottom contact [135, 136], as well as charge transport layer structuring [137]. From Sect. 3.2.2, we know that the theoretical limit of JD is J0 , which is a result of thermal generation in the D-A blend via absorbing CT states. This implies that non-idealities in dark current should arise from inefficient device preparation, explaining why the aforementioned authors focused on improving the device physics, aiming to achieve JD → J0 .

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OPDs are usually built following the energy level sketched in Fig. 3.15: a D-A system sandwiched between selective contacts, i.e., ohmic for one charge carrier type and blocking for the opposite one. The most efficient operation regime for high EQE is in reverse bias, where charges are extracted not only by the built-in potential, but also by the applied field. However, D ∗ is directly connected to JD via shot noise, see Eq. (2.85), therefore, the hole blocking layer (HBL), drawn in light blue in Fig. 3.15, has to provide good electron extraction and avoid holes to be injected. Likewise, the electron blocking layer (EBL), drawn in light green in Fig. 3.15, has to provide good hole extraction, while hindering electron injection. Although this seems quite fundamental and besides the dazzling amount of work dedicated to device optimization, which has led to examples in which JD is satisfactory [132, 138], the majority reports are still far from J0 . Given the importance of understating the deviation of JD from J0 in OPDs, in Chap. 5 we discuss this discrepancy in more detail.

3.2.5 Photomultiplication-Type OPDs The photomultiplication phenomena is known in inorganic devices from avalanche photodiodes or impact ionization by hot carriers, leading to effective generation of more than one charge carrier per absorbed photon, resulting in EQE > 100%. The high exciton binding energy in organic materials, as well as their low mobility, hinders these effects to take place in OPDs. New strategies, however, have been proposed to increase the sensibility of OPDs. In this section, we introduce a device class called PM-OPDs. The goal behind every strategy described below is to achieve a two-terminal device which works as a switch: in dark it should show a Schottky barrier rectification, whose energy is decreased upon light absorption by the electric field formed by charge accumulation in the vicinity of the contact. The most used strategy to achieve that is delaying the extraction of one charge carrier type, either by introducing a blocking layer or by charge trapping, thus, inducing accumulation [139]. Photomultiplication was first observed in vacuum-processed organic devices by Hiramoto et al. when working with Me-PTC, an n-type pigment [140]. The authors attributed the photomultiplication effect to trapped holes close to Au/organic interface, which enhanced electron injection. Similar results were later reported by the same group with different materials [141], including enhanced hole injection [142]. Based on influence of metal deposition rate [143], metal electrode and deposition technique [144] as well as morphology studies [145], the authors suggested that charges are trapped in blind alleys formed at the metal/semiconductor interface when field is applied. Corroborating with the hypotheses of trap-assisted injection, oxygen and water were shown to impact charge injection in these devices [146]. In the same direction, Neher et al. detected enhanced hole injection in polymers, depending on the electrode and illumination side [147].

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In 2002, photomultiplication was reported in CuPc:C60 blends, the first D-A system employed in PM-OPD [148]. Together with the interfacial trapping effects described above, the use of D-A system boosted the application of different organic and hybrid systems for achieving enhanced EQEs by photomultiplication. EQEs over 5000% were demonstrated by using P3HT:PCBM forming ternary systems with different nanoparticles [149, 150]. Nanoparticles were also employed with single polymers [151–153], with emphasis on the work by Huang et al., where P3HT: ZnO and PVK:ZnO devices showed EQEs over 105 %, with impressive low dark current at −9 V, leading to D ∗ over 1015 Jones [154]. In the working principle of PM-OPDs mentioned so far, charges are either trapped by states at the interface or by nanoparticles. Another approach was introduced by Zhang et al., who used the different charge transport properties in P3HT:PCBM with low acceptor concentration (100:1 to 100:4) to cause electron accumulation in the vicinity of the cathode [155], achieving an EQE of 16700%. The system was further investigated showing a dependence of transient currents on the illumination wavelength, which can be attributed to the penetration depth of the incoming light. A better performance is achieved when charges are generated near the back/injecting electrode [156]. Besides that, also traps in transporting layers [157–159] and blocking layer [160, 161] were utilized to achieve charge accumulation and, thereby, enhanced charge injection of one carrier type. In Fig. 3.16, the working mechanism of OPMs based on accumulation of electrons is summarized. A low acceptor concentration system is used, which delays electron extraction. Under dark in reverse bias, the energetic barrier blocks the hole injection and a diode-like behavior is observed. When light impinges on the device, charges are generated. Due to the bad transport of electrons by the low-acceptor content phase and/or to the presence of an extraction barrier placed by an additional layer, electrons accumulate close to the contact. The charge build-up causes an electrostatic field, bending the energy levels close to the interface, which allows holes to tunnel into the donor phase, where they are efficiently transported, sketched in Fig. 3.16b. If the transit time of holes is shorter than the life-time of electrons in the donor phase, an EQE > 100% is observed. Limitations of these devices are the slow speed and high dark currents. The former is a result of generally thick active layers formed by low mobility materials and the low modulation frequency of trap states used for enhancing charge injection. Daanoune et al. suggested that both phenomena are intrinsically related to the origin of photomultiplication in OPMs, i.e., trapping of charges [162]. In dark, thermally activated charges would also build up close the contact, thus, facilitating injection and increasing dark current, which is in accordance to SRH generation, discussed in Sect. 2.2.5. Nonetheless, photomultiplication has been extensively exploited in solutionprocessed D-A systems, for which, besides the mentioned references, also narrowband PM-OPDs [163, 164] and PM-OPDs-based imagers [165] were demonstrated. Despite many advantages which could be provided by vacuum-processing, such as

3.2 Working Principle of Optoelectronic Devices

81

Fig. 3.16 Working principle of PM-OPD | a Under reverse bias in dark, no charges are generated. The device shows a blocking character in both contacts. b Under illumination charges are generated. Because electrons are trapped in the acceptor phase or a blocking layer hinders extraction, charges accumulate and create an electrostatic field which bends the energy levels. c Common device stack with low acceptor concentration for electron trapping

highly controlled D-A mixing ratio, device engineering and thickness control, not as many studies were performed using this deposition technique. In Chap. 6, we return to this topic to present PM-OPDs based on vacuum-processed small molecules.

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Chapter 4

Materials and Experimental Methods

In this chapter, the materials and experimental methods are introduced. Firstly, the sample preparation is explained (Sect. 4.1), followed by the materials used in this thesis Sect. 4.2. The materials are grouped according to their function in the device operation. In Sect. 4.3, the characterization methods are presented. Particular emphasis is given to impedance spectroscopy (IS) (Sect. 4.3.8) as this is a complex, yet one of the most important techniques used in this work.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Kublitski, Organic Semiconductor Devices for Light Detection, Springer Theses, https://doi.org/10.1007/978-3-030-94464-3_4

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4.1 Sample Preparation All samples used in this thesis are fabricated via thermal evaporation. Organic and metallic layers are thermally evaporated on glass substrates covered by pre-structured indium tin oxide (ITO)1 at a pressure < 10−7 mbar. Before deposition, substrates are cleaned for 15 min in an ultrasonic bath in NMP, deionized water and ethanol, followed by O2 plasma for 10 min. Materials are sublimed at least twice to ensure purity. Devices are prepared in a customized evaporation tool,2 which allows for a controlled deposition of different materials and stacks, enabling completion of the fabrication process without exposing layers to air. In Fig. 4.1, a simplified sketch of the deposition tool is shown. BHJs are fabricated with the aid of two independent sources heated by a resistive component. The material sublimes and is deposited on the substrate oriented upside down, which rotates to ensure a homogeneous layer. A quartz crystal microbalance (QCM) controls the thickness of each layer separately and shutters as well as shadow masks are employed to structure the samples. At the Dresden Integrated Center for Applied Physics and Photonic materials (IAPP), two different tools are available, Lesker B produces 36 samples as sketched in Fig. 4.2, while Lesker A delivers very similar devices, yielding 16 samples per wafer instead. In Lesker B, it is also possible to set the temperature of the substrate during deposition, an important feature to control crystallization in organic materials [1, 2]. Most commonly, samples are produced as represented on the right side of Fig. 4.2, in a pin structure, or in its inverted version, the so-called ni p architecture. However, as both tools are quite versatile, different structures can be produced, including different contacts, device areas and materials. The structure of the devices used in this thesis are sketched in Fig. 4.3. In Chap. 5, pin and ni p OPDs will be discussed, as shown in Fig. 4.3a, b, while in Chap. 6, Photomultiplication-type OPD (PM-OPD) are fabricated. For each system shown in Fig. 4.3, different combinations of materials can be used, which are selected according to their IP and/or EA, or work function (φ m ), in case of metals. After evaporation, samples are directly transferred to a glovebox with inert atmosphere, where they are encapsulated with a cover glass, fixed by UV hardened epoxy glue. A moisture getter3 is inserted between top contact and the glass to hinder degradation.

1

Corning EagleXG with 90 nm ITO, Thin Film Devices Inc., USA. Kurt J. Lesker Co. Ltd. 3 Dynic (HK) LTD., Hong Kong. 2

4.1 Sample Preparation

93

Fig. 4.1 Schematic representation of an ultra-high vacuum chamber | Multiple independent sources are placed inside the ultra-high vacuum chamber. The organic material in its solid state is placed inside a crucible which is heated by driving an electric current through a resistive component. The material sublimes and is deposited on the substrate, which keeps a constant rotation speed to guarantee homogeneity. The wafer can be structured with the aid of wedges and shadow masks. The thickness of the layers are controlled by quartz crystal microbalances (QCMs)

Fig. 4.2 Standard sample structure | a Lesker wafer containing 36 samples produced in one batch, enabling a very good comparability. (b-d) Basic fabrication processes. b A glass substrate (2.54 cm ×2.54 cm) covered by structured ITO (90 nm, 32 .−1 ) forming four bottom electrodes. c Organic layers are deposited with the aid of shadow masks, usually forming a ni p or pin structure. d A metallic top contact is evaporated and the device area, Ad , is achieved by the cross section of bottom and top electrode, as shown in e

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4 Materials and Experimental Methods

Fig. 4.3 Structure of devices used in this thesis | a pin- and b ni p-OPDs. A BHJ used as the active layer is sandwiched between electron transporting layer (ETL) and hole transporting layer (HTL). n- and p-doped ETL and HTL, respectively, are used to form an ohmic contact with ITO and metallic contacts. c PM-OPD structure. Donor and acceptor are represented by the colors and , respectively

4.2 Materials Below, the materials used to fabricate the devices studied in this thesis are listed according to their role in the device. Note that some materials are used as donors as well as HTLs. Likewise, some acceptors are used as ETLs as well.

4.2.1 Donors See Table 4.1.

4.2.2 Acceptors See Table 4.2.

4.2.3 Hole Transporting Layers See Table 4.3.

4.2 Materials

95

Table 4.1 Donor materials used in this thesis

(continued)

96 Table 4.1 (continued)

4.2.4 Electron Transporting Layers See Table 4.4.

4.2.5 Dopants See Table 4.5.

4 Materials and Experimental Methods

4.3 Characterization Methods

97

Table 4.2 Acceptor materials used in this thesis

4.3 Characterization Methods 4.3.1 Temperature-Dependent Electric Measurements Temperature-dependent electric measurements are performed in a customized cryostat composed by a vacuum chamber (1 mbar air pressure), water cooling, and a Peltier element.4 A temperature controller5 controls the temperature from 200 K to 380 K. Several electrical connection are available, which allow the characteri4 5

PK3 228 A 1614 H200 (81948 TZ051312-01), Peltron GmbH, Germany. HAT Control-K10, BelektroniG GmbH, Germany.

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4 Materials and Experimental Methods

Table 4.3 Hole-transporting materials used in this thesis

zation of the 4 pixels in each sample as well as the usage of extra elements, such as LEDs and photodetectors.

4.3.2 Current-Voltage Measurements Devices are characterized in the dark and under illumination in a customized tool, which automatically measures Lesker wafers. The tool is equipped with a source

4.3 Characterization Methods

99

Table 4.4 Electron-transporting materials used in this thesis

meter unit (SMU),6 a sun simulator7,8 a spectrometer,9 a calibrated Si reference diode,10 and a filter wheel. Under illumination, variable light intensity is provided by a Xenon lamp11 while the SMU applies voltages within a chosen range and measures the current. Under dark, the filter wheel blocks the light and the SMU measures the current-voltage characteristics. Additionally, different gray filters are available, which allows varying the intensity of the incoming light. When the device is measured as OPVs, a spectral mismatch correction is also performed [26], which corrects the light intensity, such that the device J SC illuminated by the Xenon lamp equals that of the device illuminated by the AM1.5g reference spectrum [27].

6

Keithley 2400, Tektronix Inc., USA. 16S-150 V3, Solarlight Company Inc., USA. 8 XPS400 Xenon power supply, Solarlight Company Inc., USA. 9 CAS 140CT, Instrument Systems GmbH, Germany. 10 S1337-33BQ, Hamamatsu Photonics, Japan; calibrated by Fraunhofer ISE, Germany. 11 UXL-300D-O, Ushio Inc., USA. 7

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4 Materials and Experimental Methods

Table 4.5 Dopants used in this thesis

4.3.3 Temperature-Dependent Current-Voltage Measurements Temperature-dependent current-voltage measurements are performed in the setup described in Sect. 4.3.1. A high precision SMU12 is connected to sample. The temperature is varied in the desired range and J V -measurements are performed. SweepMe!13 controls the whole measurement automatically.

12 13

Keithley 2635A, Tektronix Inc., USA. Axel Fischer und Felix Kaschura GbR, Germany.

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101

4.3.4 Suns-VOC Measurements Additionally to the proceeding described in Sect. 4.3.3, different light intensities impinges on the device, while J V -characteristics are recorded12 . A LED14 and a Si photodiode15 are placed inside the vacuum chamber. A dual channel SMU16 controls the light intensity provided by the LED and measures the current generated by the photodiode as reference. The measurement is controlled automatically by SweepMe!13

4.3.5 External Quantum Efficiency Measurements Similarly to the current-voltage measurements, a customized tool allows the automatically characterization of entire Lesker wafers with the aid of mechanical motors, which position the measurement needles at each pixel. The light of a Xenon lamp17 is chopped18 at 160–230 Hz and coupled to a monochromator.19 The monochromatic light shines on the devices covered by a mask with aperture of 2.78 mm2 with the aid of an optical fiber and the current produced by the device is amplified by a low noise current-voltage amplifier.20 The signal is filtered by noise filter and measured at short-circuit condition by a lock-in amplifier21 with frequency coupled to the chopper. The light intensity is measured by a calibrated Si photodiode and the external quantum efficiency calculated by the ratio of extracted electrons and incoming photons. When external bias is used, the device is also connected to an external source,22 which provides the necessary voltage.

4.3.6 Sensitive External Quantum Efficiency Measurements The light of a quartz halogen lamp23 (50 W) is chopped24 at 140 Hz and fed into the monochromator.25 Before impinging the device, the light is further filtered with long14

K2 LXK2-PWC4-0220, Luxeon Ltd., CA S12915-66R, Hamamatsu, Japan 16 Keithley 2602, Tektronix Inc., USA 17 UXL-150D-O, Ushio Inc., USA. 18 300CD, Scitec Instruments Ltd., UK. 19 Cornerstone 260 1/4 m, Newport Oriel, USA. 20 Signal Recovery Preamplifier 5182, Ametek, Inc., USA. 21 7265 Dual Phase DSP Lock-in Amplifier, Ametek, Inc., USA. 22 NEP-6303, Manson Engineering Industrial Ltd., Hong Kong. 23 50 W, TS Electric Inc., USA. 24 SR540 Chopper Controller, Stanford Research Systems, USA. 25 Cornerstone 260 1/4 m, Newport Oriel, USA. 15

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4 Materials and Experimental Methods

pass filters26 at 680 nm, 1030 nm and 1780 nm to avoid higher order overtones from the monochromator, which can be harmful at low intensities. The current generated at short-circuit conditions or at a given bias22 is amplified27 before being measured by a lock-in amplifier.28 The time constant of the lock-in amplifier is chosen to be 500 ms and the amplification of the current-voltage pre-amplifier is increased to resolve low photocurrents. Light intensity is obtained by using calibrated Si29 and InGaAs30 photodiodes. In some cases, the output signal from the device is measured with a Stanford pre-amplifier,31 which also provides a built-in voltage source, used for biasing the devices when necessary.

4.3.7 Noise Measurements The noise measurements are performed by Dr. Bahman Kheradmand Boroujeni32 in the setup schematically represented in Fig. 4.4. The circuit consists of an input stage transimpedance amplifier that converts the current through the OPD into the voltage vo1 , followed by two stages of high-pass filter (HPF) and two stages of signal amplification (gain) plus low-pass filter (LPF). The output signal vout is then sampled at 4–12 million points in real-time using an oscilloscope33 with 16-bit of resolution. The spectrum of vout is calculated using Welch’s method for estimating power spectral density (Sin ) in MATLAB [28]. The LPFs and HPFs significantly attenuate the signal power content outside of the target frequency bandwidth. This prevents any mistranslation of non-target signal power into the target measurement bandwidth. Since the transfer function of each stage and the noise of intermediate components are known, the power spectral density (Sin ) of vo1 can be calculated back from vout . Then the total noise current (i n ) would be vo1 divided by R1 ||C1 impedance. The total noise current has several known sub-components that can be removed by subtracting their power to extract the net OPD noise. The noise voltage and noise current of the amplifiers34 are known from the data-sheet or separate measurements. These subcomponents could dominate the OPD noise at very low or very high frequencies and therefore limit the frequency range that the OPD noise can be accurately extracted.

26

FELH, Thorlabs Inc., USA. DHPCA-100, FEMTO Messtechnik GmbH, Germany. 28 Signal Recovery 7280 DSP, Ametek Inc., USA. 29 FDS100-CAL, Thorlabs Inc., USA. 30 FGA21-CAL, Thorlabs Inc., USA. 31 SR570, Stanford Research Systems, USA. 32 [email protected], Chair for Circuit Design and Network Theory. TU Dresden, BAR 222. Helmholtzstraße 18, Dresden, Germany. 33 RTO 2044, Rohde & Schwarz & Co KG, Germany. 34 AD8656, LT6236, and LTC6240, Analog Devices Inc., USA. 27

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103

Fig. 4.4 Simplified schematic representation of the noise measurement setup | The setup is placed in a shielded box and the devices measured under dark

Very low noise operational amplifiers are used in the circuit; O1 and O2 are CMOS amplifiers with an input bias current of 1 pA and a gain bandwidth product of 28 MHz. O2 and O3 are bipolar-junction-transistor (BTJ) amplifiers with a gain bandwidth product of 200 MHz. On-board batteries are used for biasing the OPD and powering the circuit. Especially, Nickel-Cadmium batteries with < 100 m series resistance are needed for both positive and negative supply rails of the op-amps to eliminate any feedback from outputs of O3 , O4 , and O5 to O1 through supply rails. Therefore, small low-noise resistors are needed in the feedback loops of O3 and O4 that draw high current from the supply rails. For the same reason, the oscilloscope is used in the high impedance input mode.

4.3.8 Impedance Spectroscopy Measuring the response of a system to an applied stimulus can provide information about several physical processes. Impedance Spectroscopy (IS) consists in applying a small electrical stimulus (voltage or current) and measuring the response (current or voltage). IS is widely used to characterize different systems, including organic devices [29–40]. In this thesis, we apply IS to identify trap states in thin-films, with the aid of the method proposed by Walter et al. [41]. Before providing experimental details, an introduction to physics of IS is given.

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4.3.8.1

4 Materials and Experimental Methods

Impedance Spectroscopy

The time-dependent voltage signal V (t) = V0 sin(ωt) applied perturbs the system producing a response I (t) = I0 sin(ωt + θ ), measured in a phase θ . The response signal can be convoluted into real and imaginary part by taking its Fourier transform (FT). In order to derive an Ohm’s law-like form expressions of the response, three assumptions must be fulfilled, namely, linearity, causality, and time-invariance [42]. This can be expressed in terms of the response function, here treated as the impedance of the system, Z (t): ∞ ⇒ linearity I (t) = −∞ Z (t, t  )V (t  )dt  t    I (t) = −∞ Z (t, t )V (t )dt ⇒ causality t (4.1) I (t) = −∞ Z (t − t  )V (t  )dt  ⇒ t  = t − t  ∞ I (t) = 0 Z (t  )V (t − t  )dt  ⇒ time-invariance. In Eq. (4.1), linearity is ensured by employing small amplitude signals, V0  20 mV at room temperature in dark, while time-invariance and causality are properties of any physical system. If these conditions are fulfilled, the DTFT of the signal allows to express the impedance in the frequency domain in terms of its real and imaginary part, corresponding to resistance, R(ω) and reactance, X (ω), respectively. Z (ω) = R(ω) + j X (ω) = |Z (ω)| exp [ jθ (ω)] ,

(4.2)

where |Z (ω)| is the amplitude of the signal and j refers to the imaginary part of X (ω).  |Z (ω)| = R 2 (ω) + X 2 (ω) , (4.3) and θ the phase angle, which can be obtained as:   −1 X (ω) . θ (ω) = tan R(ω)

(4.4)

Given the aforementioned conditions, not only Z (ω) is accessible, but also several other important quantities, such as the admittance (Y (ω)), which is the inverse of Z (ω) and is a measure of how easily a device allows electric current to flow: R(ω) X (ω) −j |Z (ω)|2 |Z (ω)|2 = G(ω) + j B(ω).

Y (ω) = Z −1 (ω) =

(4.5)

4.3 Characterization Methods

105

Y (ω) represents also the sum of the conductance (G(ω)) and the susceptance (B(ω)). Moreover, Y (ω) is connected to the dielectric function, ε(ω), as: ε(ω) =

Y (ω) = ε (ω) + jε (ω), jωC0

(4.6)

which describes the dielectric response to a plane-wave electric field. Equation (4.6) is normalized by the vacuum capacitance. In case of a plate capacitor, C 0 can be written as: C0 =

ε0 Ad , d

(4.7)

where Ad is the device area, d is the device thickness and ε0 the vacuum permittivity.

4.3.8.2

Basic Frequency Response

Very commonly, capacitance spectra are fitted with equivalent circuits to extract physical properties of the device. Given the variety of circuits which are able to fit the same set of experimental data, this can lead to debatable results. Therefore, in this thesis, we do not use this approach. Nonetheless, in order to obtain the Cf spectrum from the IS measurement, a circuit has to be assumed. This however does not mean adjusting circuit components to fit the spectra, but rather deriving an analytical expression for C(ω) from specific circuits through which the C- f spectrum can be calculated. Therefore, it is appropriate to understand the main features and the graphical representation of the quantities of these circuits. • RC-parallel circuit. One of most frequently used circuits to represent real devices is shown in Fig. 4.5a. When multiple units k of such circuit are connected in series, the impedance function can be written as: −1  2  1 jω Rp,k Cp Rp,k + jωCk = − · (4.8) Z (ω) = Rp,k 1 + ω Rp,k Cp,k 1 + ω Rp,k Cp,k k k When the capacitance is calculated from Eq. (4.8), an equivalent constant value of capacitance should be observed independently of the ω. However, an analytic solution is only possible for k = 1, which reads C(ω) = −

X (ω) B(ω) Z  · = = ω|Z (ω)|2 ω|Z (ω)|2 ω

(4.9)

As organic devices are generally much more complex than that of Fig. 4.5a, the capacitance spectra calculated with the aid of Eq. (4.9) never resemble that of Fig. 4.5a(iii). However, this simple approach allows for an empirical identification of features in the shape of the spectra related to physical phenomena, such as trap occupancy. In Ref. [41], Walter et al. use capacitance spectra to study the trap

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4 Materials and Experimental Methods

Fig. 4.5 Graphical representation of RC circuits | a, b and c show the circuits RC-parallel, RC-series and R-RC, respectively. (i), (ii) and (iii) represents the Nyquist, Bode and capacitance plot, respectively. The capacitance spectra is calculated using Eq. (4.9), which explain the frequency independent spectra shown in aiii and the dependence on frequency shown in b–ciii. Circuits are composed by resitors and capacitor connected in series and in parallel, as depicted. The Magnitude of each component is chosen to allow better visualization. Adapted from [43]

density in thin-film devices. As this is also our goal, Eq. (4.9) is of main importance in this thesis and will be used along the analysis to calculate C, keeping in mind that such circuit does not reproduce the real device. Let us now study the graphical representations of the RC-parallel derived from Eq. (4.8) for k = 1. The Nyquist plot, Fig. 4.5a(i), shows a semicircle with diameter R p , whose X → 0 when ω → 0 or to ∞. At low frequencies, the circuit is dominated by the resistor, as the impedance in the capacitor becomes extremely large. When the frequency increases, both components contribute to the response. |Z (ω)| → 0 for high frequencies along with θ → −90◦ , indicating a perfectly capacitive system. The capacitance shown in Fig. 4.5a(iii) is constant at C = C p . • RC-series circuit. This is one of the simplest circuits which can be used to represent a real device. As shown in Fig. 4.5b, it consists of a resistor connected in series with a capacitor. The impedance of such system is described as the sum of the impedances of the resistor (R s ) and the capacitor:

4.3 Characterization Methods

107

Z (ω) = Rs +

1 . jωCs

(4.10)

At high frequencies, the resistor dominates the impedance of the system, as can be seen in the Bode plot, Fig. 4.5b(ii). When the frequency decreases, however, the contribution from the capacitor adds up to the overall impedance and |Z (ω)| increases proportionally to 1/ω, along with a change in the θ . The Nyquist plot, Fig. 4.5b(i), shows a delta-like behavior, which tends to R = R s for ω → ∞. The capacitance spectra is zero at high frequencies, as the capacitor has no time to respond to the applied signal. This changes at low frequencies, when the spectra tends to C = C s . • R-RC parallel circuit. The last circuit to be considered has a second resistor connected in series with the RC-Parallel system, as shown in Fig. 4.5c. Therefore, the impedance of both circuits adds up: Z (ω) = Rs +

Rp . 1 + jω Rp Cp

(4.11)

Similarly to that of the RC-parallel, the Nyquist plot for the R-RC circuit shows a semicircle with diameter R p , but now tending to R s as ω → ∞, cf. Fig. 4.5c(i). At low frequencies, the impedance of the capacitor becomes much higher than the resistance of the resistor. Therefore, |Z (ω)| → (R s + R p ), see Fig. 4.5c(ii). For high frequencies, the capacitor shunts the parallel circuit and |Z (ω)| → R s . The capacitance function can be written as: C(ω) =

Cp Rp2 (Rs + Rp )2 + (ω Rp Cp )2

,

(4.12)

which tends to zero when ω → ∞. This trend can be seen in Fig. 4.5c(iii). In the limit of ω → 0, the capacitance function reads: C(ω → 0) = Cp

Rp2 Rs + Rp

2 .

(4.13)

Therefore, if R p  R s , C → C p , else, C(ω → 0) is determined by the ratio of the resistors.

4.3.8.3

Frequency Response of Dielectric Material Relaxation

Upon an electric stimulus, a material tends to polarize according to the applied field. However, this process happens with a time constant τ D depending on the material properties [44]. In the case of an AC signal, the material is able to follow the modulation for f < τ1D . In this case, the impedance of the device behaves an ideal

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4 Materials and Experimental Methods

Fig. 4.6 Graphical representation of a double R-RC circuit | a Schematic circuit. b Capacitance spectrum according to Eq. (4.9). c Modulus of Z (ω) and phase, calculated according to Eqs. (4.8) and (4.4), respectively. Adapted from [45]

resistor. However, as the frequency increases, the material is no longer able to follow the modulation. In such a scenario, for f > τ1D , the material behaves as a capacitor. In Fig. 4.6, we use an equivalent circuit to represent the frequency response of a device comprising two different layers. Each layer and its relaxation time is represented by one RC-parallel unit with a specific time constant. In |Z (ω)|, shown in Fig. 4.6c, three plateaus are visible, corresponding to the resistors shown in Fig. 4.6a. Along these plateaus, an ohmic behavior is observed, while in between these plateaus, the device switches to the capacitive mode. In the capacitance spectrum, two plateaus are present, also corresponding to the capacitors represented in Fig. 4.6a. If the time constant of two processes are different, these can be identified as frequency independent regions in the C- f spectra, as well as by plateaus in |Z (ω)|. However, because different time dependent processes happen concomitantly in the device, such distinction is not always possible, as will be shown below.

4.3.8.4

Frequency Response of Charge Trapping

As discussed in Sect. 3.1.3, traps states are a common characteristic in organic materials. The process of charge trapping/detrapping is time dependent and can therefore be observed in the C- f spectra. To model this process, also an RC unit can be used [42, 45–47], as shown in Fig. 4.7a, describing a single trap level causing an energy loss (R t ) and a capacitance C t . Since traps in organics usually comprise a distribution of states in the form of Eq. (3.16) in Sect. 3.1.3, also a distribution of RC units should be used for a concrete modeling, which becomes unpractical for the determination of trap characteristics. Here, we assume a single trap level to understand the main characteristics in the frequency response. 35 Because the trap occupancy, and therefore its time constant τt , depend on temperature as well as the trap density, the parameters governing the product Rt Ct are not independent. This makes it impossible to determine the trap density and its energy by a single fit of the C- f spectrum. To unveil the parameters, temperature depen35

Zview®, Scribner Associates Inc., USA.

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109

Fig. 4.7 Graphical representation of single-layer device with a single trap level | a Equivalent circuit. b Capacitance spectrum according to Eq. (4.9). c Modulus of Z (ω) simulated with the commercial software and phase calculated according to Eq. (4.4). Adapted from [45]

dent spectra must be recorded. As can be seen in Fig. 4.7c, the impedance spectrum resembles the one shown in Fig. 4.6c, although the circuits, and therefore the processes involved, are meant to be of different nature. This exemplifies the ambiguity of describing real devices with circuit fitting. Moreover, as shown in Fig. 4.6b, the capacitance no longer represents the real values of the capacitors used in Fig. 4.6a. This is a consequence of the coupling of the time constant of both RC units in Fig. 4.6a, which once more shows that fitting the spectra to representative circuits can be misleading. Instead, Walter et al. [41] proposed a method in which spectra fitting is not required. Both trap density and energy can be revealed by measuring temperature-dependent C- f spectra.

4.3.8.5

Reconstruction of the Trap Density of States via Impedance Spectroscopy

The trap distribution is determined using the method proposed by Walter et al. [41]. In this method, the trap concentration is reconstructed based on its contribution to the device capacitance, when the trap states are filled by an AC signal. The thermal emission of charges from trap states happens with a specific time constant, τt . Therefore, the maximum frequency f t at which trapped charges can respond to the applied signal can be determined as 1/τt . We can write f t in terms of the angular frequency of the AC modulation:   Et , (4.14) ωt = 2ν0 exp − kB T where E t is the trap energy with respect to the transport energy and ν0 is the attemptto-scape frequency [35]. Equation (4.14) relates the trap energy to the modulation frequency of the signal. Different trap energies can be probed as each trap energy corresponds to a transition in the C- f spectrum. The attempt-to-scape frequency is

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4 Materials and Experimental Methods

also related to the thermal velocity, v th , and capture cross-section for electrons and holes (σn , σp ), via [48]: ν0 = Nn,p vth σn,p = Nn,p βn,p ,

(4.15)

which serves an approximation for the recombination rate βSRH , used in the simu−1 ) is not expected lations presented in Chap. 5. An exact agreement (βSRH = ν0 Nn,p here, as Nn,p is unknown. The trap contribution to the capacitance has been derived based on the Boltzmann occupation of trap states with respect to the Fermi level (E F ) and can be written as:     E − EF E F − E −1 2 + exp − + exp − Nt d E, kB T kB T −∞ (4.16) where u˜ n,p and u˜ ext are the local shift in the quasi-Fermi level and the external perturbation, respectively. According to Eq. (4.16), when the frequency of the external perturbation is low enough, trap states crossed by the Fermi-level contribute more strongly to the capacitance. As the distance of trap states from E F increases, their contribution decreases exponentially. An analytic expression can be derived from Eq. (4.16), assuming that the trap distribution is constant in the interval E F ± 2kB T , which reads: Ct =

q 2 u˜ n,p kB T u˜ ext



+∞



Ct = q 2

u˜ n,p Nt (E F ). u˜ ext

(4.17)

Considering u˜ n,p and u˜ ext constant and integrating Eq. (4.17) in the depletion region, an analytic expression for Nt can be derived: Nt (E) = −

Vbi ω dC , qW kB T dω

(4.18)

where Vbi is the built-in voltage and W is the space charge width region. Using Eq. (4.18), the trap distribution can be determined from the derivative of the capacitance spectra and the trap energy from Eq. (4.14) with the right choice of ν0 . As discussed in the case of equivalent circuits, one single temperature does not allow for the determination of E t , as ν0 is unknown. Instead, ν0 can be determined from . Alternatively, the Nt spectra at different the Arrhenius plot of the maxima of −ω dC dω temperature can be matched in the plot of Nt versus E t by the appropriated choice of ν0 [41]. The latter approach is used in this thesis.

4.3 Characterization Methods

4.3.8.6

111

Experimental Details of Impedance Spectroscopy Measurements

IS measurements are performed with a potentiostat/galvanostat module36 connected to the cryostat described in Sect. 4.3.1. A sinusoidal signal with 20 mV amplitude is sent to the device and the Z (ω) is measured at different frequencies, from 0.1 to 106 Hz. Most measurements performed within this investigation are conducted at 0 V in dark conditions. Otherwise, the voltage is indicated. By biasing the device, different effects can be probed, which helps to distinguish different physical phenomena [30, 31].

4.3.9 Transient Photocurrent Measurements Transient photocurrent measurements were performed by Łukasz Baisinger.37 To record current transients, the measured device was held at short-circuit, connected to the low impedance (50 ) input of an oscilloscope.38 100 Hz square waveform from a signal generator39 was used to control a MOSFET40 driving the high-power white LED.41 The pulse length was set to 5 ms, allowing device to reach a steady state before switching off the light. The signal from the device was pre-amplified42 prior to being recorded by the oscilloscope.

4.3.10 Spectroscopic Ellipsometry Measurements Variable-angle spectroscopic ellipsometry measurements were performed by Dr. Eva Bittrich43 with the aid of an ellipsometer.44 The uniaxial optical dispersion of a thin-films was obtained using an optical model (Si/SiO2 (1 µm)/thin-film(100 nm,

36

Autolab PGSTAT302N, Metrohm AG, Switzerland. IAPP, TU Dresden, KRO 2.03. Nöthnitzerstraße 61, Dresden, Germany. 38 DPO7354C, Tektronix, USA. 39 Agilent 33600A Series, USA. 40 IRF630N, Infineon, Germany. 41 LED Engin, Osram Sylvania Inc., USA. 42 DHPCA-100, FEMTO Messtechnik GmbH, Germany. 43 Leibniz-Institut für Polymerforschung Dresden e.V., Hohe Str. 10, 01069 Dresden, Germany. 44 M2000, J.A. Woollam Co., Inc., USA. 37

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4 Materials and Experimental Methods

1 Tauc-Lorentz and 5 Gaussian oscillators, energy positions coupled z to x y) with sharp interfaces and additional effective medium approximation (EMA) (50% void, 50% thin-film) roughness top-layer [49].

4.4 Drift-Diffusion J V -Simulation 1D-Drift-diffusion simulations were preformed by Andreas Hofacker.45 The set of coupled differential equation describing the dynamics of charges in the device were solved numerically in Python programming language, using Cython bindings to solve integrals and improve the performance of the code. Equations (4.19) and (4.20) are the continuity equations for electron (n) and holes ( p), which, besides including the generation and recombination rates, also accounts for changes in the electrical current. Electron and holes currents (Eqs. (4.21) and (4.22)) depend on the drift current caused by the electric field and on the diffusion current, which is proportional to the diffusion coefficient, Dn , Dp , see Eq. (2.44), and to charge carrier concentration. Equation (4.23) is the Poisson equation to account for electrostatic effects of the carriers as well as ionized dopants. ∂n 1 ∂ Jn =G−R+ = fn, ∂t q ∂x ∂p 1 ∂ Jp =G−R− = fp, ∂t q ∂x ∂n Jn = qnμn F + q Dn , ∂x ∂p Jp = qnμp F − q Dp , ∂x

∂ 2φ q p − n + ND+ − NA− . =− 2 ∂x εε0

(4.19) (4.20) (4.21) (4.22) (4.23)

Additionally to the set of equations presented above, we included a modification in the generation-recombination dynamics, according to the SRH theory and Poole-Frenkel effect for charge detrapping. This will be discussed in more details in Chap. 5, where the model and results will be presented. To solve the system of equation, the 1D sample is spatially discretized into N points. As the processes in the device are also time-dependent, a time discretization is also necessary. Steady state condition are required to simulate J V characteristics. An initial state is defined and the system is let to evolve until a termination criterion is met. The solution is achieved by the following an iterative procedure [50]. 45

[email protected], IAPP, TU Dresden, KRO 2.28. Nöthnitzerstraße 61, Dresden, Germany.

4.4 Drift-Diffusion J V -Simulation

113

1. Choose a guess for the densities of charge carriers at time ti+1 . 2. Calculate F either from Eq. (4.23) or via Gauss law at a given x and ti+1 . 3. Evaluate the spatial finite differences at time ti+1 either by integration of Eqs. (4.19) and (4.20) or by the approach described by Scharfetter and Gummel [51]. 4. Evolve the charge carrier densities in time. 5. Check for consistency by comparing the evolved densities with the guessed densities: εn = (n guess − n i ) − f n (n i+1 , ...)(ti+1 − ti ) εp = (n guess − pi ) − f p ( pi+1 , ...)(ti+1 − ti ),

(4.24) (4.25)

and modify the values with the new guesses εn,p . 6. Repeat steps 2 to 5 until they are below a tolerance threshold, and accept the final guess as the new state. A complete description of the solution can be found in the thesis of Andreas Hofacker [50].

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Chapter 5

Reverse Dark Current in Organic Photodetectors: Generation Paths in Fullerene Based Devices

OPDs have promising applications in low-cost imaging, health monitoring and near infrared sensing. Recent research on OPDs based on donor-acceptor systems has already resulted in narrow-band, flexible and biocompatible devices, with the best reaching photovoltaic external quantum efficiencies of almost 100%. However, the high noise spectral density (Sn ) of these devices limits their specific detectivity to around 1013 Jones in the visible and several orders of magnitude lower in the NIR, severely reducing the performance. Here, we show that the shot noise, proportional to the dark current (J D ), dominates Sn , demanding a comprehensive understanding of J D . We demonstrate that, in addition to the intrinsic saturation current generated via charge-transfer (CT) states, J D contains a major contribution from trap-assisted generated charges and decreases systematically with decreasing concentration of traps. By modeling J D of several donor-acceptor systems, we reveal the interplay between traps and CT states as source of dark current and show that traps dominate the generation processes, thus being the main limiting factor of the OPDs detectivity. This chapter is adapted from work published in J. Kublitski, A. Hofacker, B. K. Boroujeni, J. Benduhn, V. C. Nikolis, C. Kaiser, D. Spoltore, H. Kleemann, A. Fischer, F. Ellinger, K. Vandewal, and K. Leo, “Reverse Dark Current in Organic Photodetectors and the Major Role of Traps as Source of Noise”, Nature Communications, vol. 12, p. 551, 2021 [1].

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Kublitski, Organic Semiconductor Devices for Light Detection, Springer Theses, https://doi.org/10.1007/978-3-030-94464-3_5

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5.1 Introduction As discussed in Chap. 1, OPDs offer several advantages in comparison to inorganic PDs. However, OPDs still suffer from a high Sn , resulting in rather low detectivities. Among the many sources of noise, the shot noise, proportional to the dark current, has been suggested to play a major role [2], especially because PDs are usually operated in reverse bias voltages, where the measured reverse dark current (JD ) strongly deviates from its ideal value. Dark current suppression in organic diodes has been the subject of several reports in the literature [3]. Most frequently used approaches are charge selective layers [4, 5], contact alignment [6, 7], prevention of shunt paths via layer thickness increase [8] and interlayers to smooth the bottom contact [9, 10], as well as charge transport layer structuring [11]. While the above mentioned JD suppression approaches lead to an improved OPD performance, a comprehensive understanding of the intrinsic and extrinsic sources of dark current is still missing, which would provide insights for future device optimization using improved materials or architectures. In an ideal diode, in addition to the diffusion current, the dark saturation current (J0 ) embraces a thermally activated component, the result of thermal generation of charges over the gap of the material, if intra-gap states are absent [12]. However, in organic diodes formed by a D-A structure, CT states are present at the interface [13, 14]. Being usually lower than the gap of the single components, the effective gap of the blend is the characteristic charge-transfer state energy (E CT ). Therefore, the activation energy of the ideal dark current of organic diodes, based on D-A blends, is determined by E CT .

5.2 The Role of Dark Current on the Specific Detectivity The specific detectivity is proportional to the E Q E and inversely proportional to Sn , as shown in Eq. (2.92). The best organic systems show E Q Es approaching 100%, narrowing the room for improvement by increasing E Q E. Despite these high E Q Es, D ∗ is limited to around 1013 Jones [8, 15–22], far below the background limited infrared photodetection limit, the so-called BLIP limit, which assumes E Q E of 100% and the background radiation as the only source of noise, see Sect. 2.3.6. This discrepancy is a consequence of the high Sn observed in OPDs and represents the main limiting factor for this device class to approach the BLIP limit. In Fig. 5.1, this issue is visualized for two of the systems studied in this chapter: the role of E Q E and Sn are compared for P4-Ph4-DIP:C60 and ZnPc:C60 , which, besides having representative CT energies, better represent the current state-of-art of E Q E (see Sect. 4.2 for details about the materials and Fig. 4.3a for the device structure). The BLIP limit is shown as a black dot-dashed line. Symbols indicate D ∗ given in literature, which are typically many orders of magnitude below this limit. The real D ∗ of the P4-Ph4-DIP:C60 device (solid line) would improve only by one order of magnitude if an E Q E maximum of 100% would be reached. On the other hand, if Sn is assumed to be dominated by the shot noise and is calculated in the non-radiative limit, D ∗ can be improved by six

5.2 The Role of Dark Current on the Specific Detectivity

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Fig. 5.1 The role of external quantum efficiency and JD on the specific detectivity | D ∗ of two donor:C60 (6 mol%) material systems assuming shot noise at −1 V and E Q E as measured (solid lines), shot noise at −1 V and normalized E Q E at the maximum of the spectrum (hatched region), and shot noise in the non-radiative limit and E Q E as measured (dashed lines). Symbols show data from literature [8, 15–22]. (*) Hamamatsu K1713-05 [23]

Fig. 5.2 Spectral noise density | a and b show the Sn of seven donor:C60 (6 mol%) material systems. Dashed colored lines represent the shot noise of each device calculated at reverse Ibias , as indicated in the legend. Black dashed lines show the fit according to Eq. (2.88) for b = 1. The noise corner frequency, f c , is determined from the interception of the shot and 1/ f component

orders of magnitude, considering the real E Q E. A similar behavior is also shown for ZnPc:C60 . From these examples, it is clear that there is large room for improvement, and the noise current has to be significantly improved in order to achieve a higher detectivity.

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The measured Sn embraces several unknown sources. However, a comparison of Sn to the shot noise contribution (colored dashed lines in Fig. 5.2) reveals that, for frequencies larger than the noise corner, f c , i.e. the frequency at which the noise assumes a 1/ f dependence, the dark current represents the dominant noise source in OPDs. As shown in Fig. 5.2, Sn approaches the theoretical shot level, calculated as √ 2q Ibias , where Ibias represents the current driven through the device, equivalent to around −0.8 V. This highlights the importance of studying dark currents in OPDs. Because Sn is mainly determined by JD , suppressing JD translates directly into higher D ∗ . In order to approach any possible intrinsic limit of JD , we need to ensure that extrinsic effects are minimized. Therefore, in the next section, we describe a series of optimization methods which guarantee that the observed JD is not a result of inappropriate device engineering.

5.3 Device Optimization for Dark Current Studies Many processes can lead to an increased JD . Such processes can hide possible physical phenomena that would help us to describe the high JD of OPDs. In order to minimize these processes, we fabricate a series of devices and optimize their properties to reduce JD . The device structure used in each of the following sections is depicted in Table 5.1. After optimization, the final structure of OPD 8 is used within this chapter to study intrinsic properties of JD .

5.3.1 Contact Selectivity and Blocking Layers When biasing the device in reverse direction, the selectivity of the contacts is very important. Selectivity means how efficiently the injection of the wrong charge carriers (electrons into the anode and holes into the cathode) is blocked. Generally, this property can be controlled by the energy levels of the employed materials. However, in some cases, different effects can also play a role. In Fig. 5.3a and b, we show J V characteristics of OPDs comprising ZnPc and TPDP as donors, respectively. Using n-HATNA-Cl6 in ZnPc:C60 BHJ reduces JD considerably. This effect is caused by a better selectivity of the n-doped layer, in comparison to BPhen. Interestingly, the same is not true for the TPDP BHJ. This indicates that, in the case of TPDP, another mechanism dominates JD and the minor effect of selectivity is no longer observed. Moreover, because HAT(CN)6 has a very low HOMO (see Table 4.4), which should express a better selectivity, it was also employed as n-doped layer as further comparison. Once more, no improvements are observed confirming the secondary character of the selectivity for this material system. Comparing the HOMOs of HATNA-Cl6 and BPhen, −7.20 eV and −6.46 eV [24, 25], respectively, one can already conclude that the selectivity should be better for HATNA-Cl6 . In addition, BPhen should cause an extraction barrier in forwards bias,

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Table 5.1 Structures used to study different aspects of JD in the following sections | The devices were produced by thermal evaporation on a glass substrate coated with structured ITO. The final device structure reads: ITO/ pin/C60 (20 nm, buffer layer)/Al (100 nm) (Kurt J. Lesker Co. Ltd.). See Sect. 4.2 for the chemical structure of the materials

Fig. 5.3 Dark current with different electron transport layers and for different donors | In a ZnPc is used as donor blended with C60 (50 wt%), in b TPDP (5 wt%) is the donor, also blended with C60

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Fig. 5.4 Dark currents of devices with different blocking layers thickness | a MeO-TPD is used as EBL and varied from 0 to 20 nm. b HATNA-Cl6 is employed as HBL using different thicknesses. JD is reduced for both cases but due to the lower conductivity of these undoped layers, the forward region is also affected

when used with C60 , as its LUMO is shallower in energy. However, this effect is not observed for thin layers (≤8 nm). Therefore, it is reasonable to assume that a thin BPhen layer gets doped by the metal [26] or that trap states are formed within its gap, allowing not only electron extraction in forward direction but also hole injection in reverse bias, explaining the bad selectivity observed in Fig. 5.3a. Similarly to the selectivity property, another commonly used strategy to reduce JD is the use of blocking layers. For blocking electron (holes) injection in reverse direction, the material should have as low (high) as possible LUMO (HOMO) level. This relies once more on the energy levels of these materials. By itself, the energy levels of n-HATNA-Cl6 and p-MeO-TPD should comply this role. Besides, we inserted a further layer of neat HATNA-Cl6 and MeO-TPD as HBL and EBL, respectively. The results shown in Fig. 5.4 indicate that the insertion of a further blocking layer slightly improves the dark current, in both sides of the device. These layers, however, can also affect the behavior in forward bias, as can be seen for thicker layers of neat HATNA-Cl6 and MeO-TPD. As our goal is to minimize JD , the thickness of 20 nm of MeO-TPD will be used in the final device structure. Since the improvement in JD for 5 and 10 nm of HATNA-Cl6 is not significant, we use 5 nm in the final device structure, as this also preserves a low resistance, as indicated by the higher saturation current in Fig. 5.4b, see region above 0.5 V. Please, note that the curves indicated as “0 nm” still contain the doped layers, which also presents blocking properties, as discussed above.

5.3.2 Shunt Paths in OPDs The presence of shunt paths in thin-film devices is well-known in the literature [27, 28]. Shunt usually refers to ohmic metallic paths formed between the top and bottom

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123

contact, but it may also be understood as an easier path that might be followed by charge carriers than the rectifying diode path [29]. Since the active layer is sandwiched between buffer and/or blocking layers in our device, the latter is assumed to be very unlikely. Moreover, pin devices using doped layers should also contribute in this sense, due to the good selectivity of the contacts achieved by doping [30]. Hence, we mainly investigate the presence of metallic paths, which could lead to high dark currents, especially in reverse bias. In Fig. 5.5a we show J V characteristics for four different active layer thicknesses using the same optimized structure and TPDP:C60 as BHJ. The thickness of the active layer is varied from 50 to 200 nm. If shunts would be present in the device, it is likely that JD would decrease upon thickness increase. As can be seen, JD does not show any trend within this range and the lowest value is achieved for 50 nm. Figure 5.5a supports the fact that shunts are not responsible for high JD observed in these devices.

5.3.3 Device Structuring The last topic investigated within this optimization is the influence of the lateral leakage current, as discussed by Zheng et al. [11]. The doped layers, namely n-HATNACl6 and p-MeO-TPD, were structured following the same approach discussed by the authors. The devices discussed in this work are formed by organic materials sandwiched between two crossed-like electrodes: a pre-structured ITO layer as anode and a metal layer cathode. The organic materials are deposited over a larger area than that of the actual device area, see Fig. 4.2. Due to the high conductivity of doped layers, lateral leakage current might flow from the surroundings and be collected as dark current. This means that in fact the real device area could be larger than 6.44 mm2 and undefined. By structuring the doped layers using shadow masks, Zheng et al. were able to reduce the dark current of OLEDs by at least two orders of magnitude. More details about the structuring procedure can be found in Ref. [11]. Our results employing this approach are shown in Fig. 5.5b. Interestingly, the effect of structuring can be clearly observed for TAPC:C60 devices, however, for TPDP:C60 this is not the case, where JD remain unaffected. This result shows that lateral currents become important when the intrinsic JD is low (high E CT as predicted by Eq. (3.21)). In the scope of Zheng et al.’s work, the authors used mostly large gap materials such that this effect was clearly observed. For low E CT BHJs, the intrinsic JD is much higher than the lateral contribution such that its effect becomes irrelevant. Summarizing the optimizations that have been performed, JD is affected by selectivity of the contacts, blocking layers usage and device structuring. However, the low E CT BHJ TPDP:C60 seems to be unaffected by any of these optimization proceedings, including a thickness variation. Thus, we have strong indications that other effects than device optimization are causing high JD .

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Fig. 5.5 Dark currents versus active layer thicknesses and the role of device structuring | a Four different thicknesses are used, varying from 50 to 200 nm. b Dark J V curves for devices with TPDP as donor using structured (solid) and unstructured (dashed lines) are drawn in black. Likewise, TAPC is drawn in red. Upon structuring JD remains unchanged in reverse bias for TPDP and considerably decrease for TAPC

5.4 Diode Saturation Current Generated via Charge-Transfer States In order to understand the origin of the dark current, we have reviewed the present perspective on how JD is generated. The dark current as well as the open-circuit voltage (VOC ) have been shown to relate to the energy difference between the HOMO of the donor and the LUMO of the acceptor [31, 32]. In fact, at open-circuit conditions, free charge carriers recombine through CT states, connecting VOC and E CT [33]. While E CT is linked to the energy levels of donor and acceptor, a direct relation cannot be drawn as it hides polarization effects and binding energies, which can strongly modify the energy value, depending on the materials and mixing ratios [34]. In an ideal diode, the saturation current (J0 ) is linked to E CT by

J0 

  2π f CT q E CT , (E − λ ) exp − CT CT E Q E EL h 3 c2 kB T

which is also connected to VOC :   q VOC kB T , for VOC  J0  exp − . kB T q

(3.21 revisited)

(5.1)

In Sect. 3.2.2, a derivation of Eq. (3.21), which relates VOC and E CT , is given [35]. Such a relation has already been successfully employed to explain the dependence of VOC on CT state properties, including the often observed correlation between VOC and E CT [33, 35], the dependence of VOC on D-A interface area [36] and non-radiative recombination [37].

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While Eq. (5.1) successfully explains VOC in organic solar cells, it is not clear whether J0 corresponds to the measured dark current at negative bias voltages (JD ). To investigate this, we fabricated a series of devices following the optimization methods described above, which led us to the final structure OPD 8, see Table 5.1. The devices are based on different donors blended with C60 at 6 mol%, where lowdonor-content BHJ have been chosen to ensure a comparable morphology, which is known to depend on D-A mixing ratio [34, 38], miscibility [39] and aggregation properties [40]. Details about the series of donors and materials used to fabricate the devices can be found in Sect. 4.2. In Fig. 5.6a, the experimental dark J V characteristics of seven different devices employing different donor molecules combined with C60 are shown. In this series, E CT is increased from 0.85 eV (TTDTP:C60 ) to 1.58 eV (P4-Ph4:DIP:C60 ), as indicated in the legend. At reverse voltages, the dark current indeed decreases with increasing E CT , however, not as predicted by Eq. (3.21), from which an exponential dependence is expected. For the blend with the highest E CT (P4-Ph4-DIP:C60 ), dark currents as low as 10−7 mA cm−2 at −1 V bias were achieved, which is among the lowest values reported for state-of-the-art OPDs [3]. Such low dark currents rely on the correct device optimization as described above, also reflected in the remarkably low noise corner achieved in these devices, in the range of 0.3–150 Hz, c.f. Fig. 5.2, which are lower than that for recently reported high performance OPDs [41, 42]. For the sake of comparison, we kept the same structure for all devices shown in Fig. 5.6. This implies that for low E CT combinations, an extraction barrier is formed between donor and EBL, MeO-TPD, while for high E CT combinations, an injection barrier can be formed at the same position. The latter affects mainly the forward regime of the J V curves up to the space-charge limited current region, where the saturation current is determined by the mobility of the blend. The extraction barrier, however, might affect both forward and reverse regions. This is also reflected in the results shown in Fig. 5.6 and will be discussed later in this chapter.

Fig. 5.6 Experimental dark J V characteristics versus ECT | a Experimental dark J V characteristics of different donor:C60 (6 mol%) blends with different E CT . b Device stack used

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Fig. 5.7 CT state properties of donor:C60 | a Sensitively measured E Q E spectra (solid line) and the corresponding fits of the CT state absorption (dashed line) for the donor:C60 BHJs. The black curve represents ZnPc:C60 (50 wt%). b JD extracted from Fig. 5.6a at −1 V (black left y-axis) and ideal J0 , calculated through Eqs. (3.21) and (5.1) (red right y-axis). For the calculation of J0 , E CT , λCT and f CT were extracted from sensitively measured E Q E spectra by fitting the CT state feature with a Gaussian function as shown in Fig. 5.7a and E Q E el was estimated from the non-radiative voltage losses, both as described in Ref. [43]. Legend from (a) is also valid in (b). Dash-dotted lines in b are guides to the eye Table 5.2 Fitting parameters extracted from sE Q E spectra shown in Fig. 5.7a Donor E CT λCT f CT (meV) (meV) (µ(eV)2 ) TTDPT TPDP m-MTDATA Spiro-MeO-TPD ZnPc TAPC P4-Ph4-DIP

851 903 1029 1106 1195 1426 1585

172 178 453 207 425 196 159

6.7 9.4 148.9 59.4 2037.8 709.4 1272.4

For a meaningful analysis of JD and its relation to E CT , it is useful to estimate its lower limit, i.e., J0 according to Eq. (3.21) and compare it with the experimental results shown in Fig. 5.6a. In order to do so, we need to determine the CT properties and the E Q E el for each blend. The former can be achieved by sensitively measuring (s-) the E Q E and fitting the CT region to Eq. (3.18), while the latter can be estimated from the non-radiative voltage losses using Eq. (3.22). In Fig. 5.7a, the s-E Q E measurements and each respective fit for the seven blends are shown. The fitting parameters are summarized in Table 5.2. With the aid of the values listed in Table 5.2 and estimated non-radiative losses, as shown in Table 5.3, J0 can be determined. For comparison, in Fig. 5.7b we plot both JD (−1 V) and J0 as function of CT state energy. Despite the low dark currents

5.4 Diode Saturation Current Generated via Charge-Transfer States

127

Table 5.3 Ideal value of the saturation current | J0 was calculated using Eq. (3.21). The parameters used in the calculation were extracted from Table 5.2 and E Q E el was estimated following Ref. [43] in accordance to the typical voltage losses analyses for OSCs. For ZnPc:C60 (50 wt%), f CT and λCT are 288.0 meV and 4.0 m(eV)2 , respectively Donor molecule E CT VOC ΔVrec ΔVrad ΔVnonrad E Q E el J0 (eV) (mV) (mV) (mV) (mV) (1) (mA cm−2 ) TTDPT TPDP m-MTDATA Spiro-MeO-TPD ZnPc TAPC P4-Ph4-DIP ZnPc (50 wt%)

0.85 0.90 1.04 1.10 1.19 1.42 1.58 1.15

307 309 434 496 583 836 949 555

543 591 596 614 607 594 631 595

124 137 181 223 278 257 344 220

419 454 415 391 329 337 287 375

6 × 10−8 2 × 10−8 8 × 10−8 2 × 10−7 2 × 10−6 3 × 10−6 1 × 10−5 4 × 10−7

4 × 10−6 3 × 10−6 4 × 10−8 5 × 10−10 4 × 10−11 3 × 10−15 3 × 10−18 3 × 10−9

and the observed scaling of JD with E CT , there are two main issues that need to be pointed out: (i) JD at reverse voltages of all OPDs is at least three orders of magnitude higher than the diode dark saturation current (see Fig. 5.7b). (ii) Equations (3.21) and (5.1) do not account for any field dependence of the dark current at reverse bias. However, the experimental data presented in Fig. 5.6a clearly shows an increasing dark current upon increasing the absolute reverse voltage. Considering that the BHJ results shown in Fig. 5.6a are acquired by means of the aforementioned optimization and, more importantly, rely on the same device structure and material combination, except for the chosen donor, it is reasonable to assume that the high JD is an intrinsic property of each material combination. The experimental JD cannot be explained solely by thermal excitation through CT states. In the following sections, we address fundamental characteristics of organic diodes based on the fullerene C60 that help us to clarify the two aforementioned points and understand why the experimentally measured JD deviates from J0 calculated via Eqs. (3.21) and (5.1).

5.5 Traps as the Main Source of Reverse Dark Current in OPDs Trap states with intra-gap energies are commonly observed in organic materials and devices due to their disordered nature [44], structural defects, and the presence of impurities [45]. Several publications address the limitations on charge transport [45– 47], increase of recombination rates [48] and change of recombination dynamics [49]

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Fig. 5.8 CT state properties in TPDP:C60 devices at different donor concentrations | a Sensitively measured E Q E spectra. b E CT and λCT extracted from (a). Note that E CT increases only about 20 meV when the donor concentration varies from 6.0 to 26.7 mol%

caused by these states. However, only very few studies investigated the influence of trap states on JD [50]. Drift-diffusion models with band-tail [51] and mid-gap [52] trap states were employed to reproduce the experimental J V characteristics of organic solar cells and OPDs, respectively. However, the trap density of states was not characterized and thus it is unclear whether the number of traps assumed corresponds to that of the real device. Moreover, the field dependence was either ignored or described by an electronic band structure model, making its application for organic materials questionable. A consistent experimental observation of the impact of traps on JD , supported by a theoretical modeling, is still missing. The microscopic properties of a D-A system are related to the electronic characteristics of the device, e.g., donor concentration usually affects VOC , because the number of CT states and their energy change. This gives us also insight into trap states, which could likewise arise from the D-A interaction and depend, therefore, on the D-A mixing ratio. If a correlation between mixing ratio and concentration of traps exists, also the impact on JD can be investigated. From Fig. 5.6, we know that E CT strongly influences JD , which means that a D-A system and a range of mixing ratio has to be found in which E CT is constant. A careful analysis of the material systems shown in Fig. 5.6 revealed that in the TPDP:C60 system, from 6 mol% to around 27 mol%, this condition is fulfilled. sE Q E spectra and the rather constant E CT are shown in Fig. 5.8. The fitting parameters are summarized in Table 5.4. Given that E CT is constant within these concentrations, we can use the TPDP:C60 system to enlighten the relation among mixing ratios, trap and JD . Therefore, we fabricated devices comprising different concentrations of TPDP:C60 using the same device architecture as shown in Fig. 5.6b. As the concentration of TPDP in C60 decreases from 26.7 to 6.0 mol%, JD also decreases by approximately one order of magnitude, as shown in Fig. 5.9a, which according to Eqs. (3.21) and (5.1) cannot explain the significant decrease of JD . In addition to the improved JD , this result raises the question whether a correlation with the amount of traps can be found.

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Table 5.4 CT state properties of TPDP:C60 devices extracted from fits of the spectra shown in Fig. 5.8 TPDP concentration E CT λCT f CT (mol%) (meV) (meV) (µ(eV)2 ) 6.0 10.5 13.3 16.1 18.8 21.5 24.1 26.7

904 900 897 895 898 897 890 887

139 147 154 162 155 160 179 186

1.7 2.3 2.0 1.7 1.6 1.4 1.1 1.1

Measuring traps in organic solids is a rather difficult task due to the lack of simple techniques able to access their concentration and energetic characteristics. Nonetheless, a widely applied method was proposed by Walter et al. based on the capacitive response of these states, whose occupation depends on the modulation of the signal [53]. On the one hand, this enables the characterization of defects by a straightforward technique, such as impedance spectroscopy (IS). On the other hand, such technique probes many effects in the device, especially in organic ones, which can show identical capacitive spectra to those generated by traps, inspiring discussion in the community whether such measurements can in fact reveal the trap characteristics in organic devices [54–56]. Particular caution should be taken when using this method in low mobility materials and in devices where energetic transport barriers are present. As both are the case for our devices, in Appendix A, we discuss the limitations of the method and show that for these devices, IS can show meaningful results. We can neglect the range below 10 Hz, as in this region the capacitance spectra is dominated by resistance of the layer, which, as expected, increases for lower concentrations. In addition, above 10 kHz the geometric capacitance and the series resistance of the contacts controls the spectra. Therefore, this region can also be excluded of the analyses. The remaining part of the spectra presented in Fig. 5.9b shows an increase in the capacitance, which we attribute to traps. By measuring the capacitance at different temperatures (cf. Fig. 5.10) and overlapping the reconstructed temperature-dependent trap densities by the appropriate choice of ν0 , the full description of the trap density of states is achieved, where Nt and E t are calculated using Eqs. (4.18) and (4.14), respectively. This analysis is shown in Fig. 5.11. For clarity, in Fig. 5.9d the reconstructed Nt is plotted only at 293.15 K, which allows to identify the scaling of Nt as a function of concentration. The trap densities of every concentration have been fitted with a single Gaussian distribution function from which Nt , E t , and the broadness of the Gaussian, σ , were extracted, which are listed in the insets of Fig. 5.11. Nt is summarized in Fig. 5.9c and compared to the

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5 Reverse Dark Current in Organic Photodetectors: Generation …

Fig. 5.9 Increasing the trap density in TPDP:60 device | a Dark J V curves, b normalized capacitance and c Nt (left black y-axis) compared to |JD (−1.0)|V (right red y-axis) versus donor concentration of TPDP:C60 blends with different D-A mixing ratios. d Distribution of traps at 293.15 K at different at D-A mixing ratios. Due to the small capacitive contribution of the traps at very low concentrations, the method fails in reconstructing the trap density of states for these cases. Therefore, the results of the 6.0 mol% device are not shown in (c–d). Trap energies represents the energy difference from C60 LUMO (LUMOC60 − E t ) [57]. The hatched areas in (b) show the frequency ranges excluded from the trap analyses as discussed in the text. Cgeom. refers here to the capacitance at 100 kHz, where the geometric capacitance dominates

absolute value of JD (−1.0 V). The increase of JD with increasing Nt suggests that the generation of charges producing extra dark current proceeds via trap states. With decreasing TPDP concentration in the blend, the amount of trap states becomes lower, as shown in Fig. 5.9d. For concentrations below 10.5 mol%, the sensitivity limit of the measurement is reached and the method fails in reconstructing the density of traps states for this material system. Nevertheless, the presence of traps cannot be excluded. While from Fig. 5.9 it is clear that traps are connected to JD , we can also model the thermal generations of charges contributing to JD via these traps to reveal their role on D ∗ . This can be done in the framework of the Shockley–Read–Hall (SRH) theory [59], as it will be discussed in the next section.

5.5 Traps as the Main Source of Reverse Dark Current in OPDs

131

Fig. 5.10 Capacitance for TPDP:C60 at different donor concentrations. For all D-A systems, the temperature and the concentration are varied from 243.15 K to 323.15 K and 6 mol% to 26.7 mol%, respectively

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Fig. 5.11 Trap analysis for TPDP:C60 at different donor concentrations | Trap concentration measured for all devices comprising TPDP:C60 as active layer at temperatures varying from 243.15 to 323.15 K. For 6.0 mol%, a fitting was not achieved and no parameters could be extracted. In Eq. (4.18), Vbi is assumed to be 1.0 V, calculated according to Mantri et al. [58]. The frequency range is chosen accordingly to avoid effects of contact and layer resistances

5.6 Generation-Recombination Statistics Due to a Distribution …

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5.6 Generation-Recombination Statistics Due to a Distribution of Traps and Drift-Diffusion Modeling 5.6.1 Trap-Assisted JD Generation Model When recombination centers, such as the ones measured in the previous section, are found within the energy gap of semiconductors, they contribute to the generation and recombination processes. This is a consequence of the occupation statistics of these states, which happens through the excitation of charges carriers. Shockley–Read– Hall (SRH) theory was firstly derived for a single trap level and is based on four rates of capture (energy absorption) and release (energy emission) of charges [59], as schematically represented in Fig. 5.12. In order to obtain the rates shown in Fig. 5.12, one assumes a Fermi–Dirac occupation function f (E, T ) for the probability that a trap at energy E t is occupied. The rates can then be written as [60]: r1 = nvth σn Nt [1 − f (E, T )] r2 = en Nt f (E, T ) r3 = pvth σp Nt f (E, T )

(5.2) (5.3) (5.4)

r4 = ep Nt [1 − f (E, T )].

(5.5)

In Eq. (5.5), n and p are the electron and hole concentration defined by Eqs. (2.14) and (2.15), respectively. σn (σp ) and en (ep ) are the capture cross-section and the emission coefficient for electrons (holes). The product σn en can be estimated from the trap analyses via Eq. (4.15). Because Nn and Np are unknown, a direct input via Eq. (4.15) was not considered and the value was adjusted to achieve a good agreement with the experimental curve. In thermal equilibrium, the capture and emission rates for electrons and holes must be equal (r1 = r2 , r3 = r4 ). With this assumption, using the set of equations

Fig. 5.12 Rates of capture and release of charges in the SRH framework. r1 and r2 represents capture and emission of electrons, respectively. r3 and r4 are the equivalent for holes. E t represents a discrete trap energy in the trap distribution Nt . E i is the mid-gap energy

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5 Reverse Dark Current in Organic Photodetectors: Generation …

above, en and ep can be found. We define the net generation/recombination efficiency as: ηG,R = r1 − r2 = r3 − r4 .

(5.6)

Once more, using the set of equation above and Eq. (5.6), we can derive the occupation function (solving Eq. (5.6) for f (E, T )) and generation/recombination rate, which can be written as: ηG,R = vth σn σp

np − n 2i · nvth σn + pvth σp + en + ep

(5.7)

By multiplying Eq. (5.7) by Nt , we can obtain the rates of generation (G) and recombination (R), which are related as G = −R. We are interested in the reverse region of the J V curve, because photodetectors are mainly operated at negative bias. Considering that, we can make some approximations to understand the behavior of Eq. (5.7). Firstly, under reverse conditions, the concentration of free charges in the device is very small because they are extracted by the drift-applied field. Moreover, the capture rates are proportional to the number of free charges, making these processes irrelevant for the device. This also allows considering σn = σp = σ0 . At reverse bias, the important processes are the emission of electron and holes assisted by the trap states. These electrons (holes) are then emitted to the LUMO (HOMO), increasing the dark current value. Applying the aforementioned considerations/assumptions and expressing en and ep in terms of appropriated variables, Eq. (5.7) can be written in the form of Eq. (2.62): G SRH =

σ0 vth Nt  ni.  i 2 cosh Ekt B−E T

(2.62 revisited)

Equation (2.62) describes, as observed experimentally, that the generation increases linearly with Nt and is more efficient when E t = E i , i.e. mid-gap traps are more relevant for JD . This is a consequence of the trapping/detrapping probability of a charge in a two-step process: An electron is firstly excited from the HOMO to the trap state, followed by a second excitation, which releases it to the LUMO. A charge contributes to JD only after a double thermal excitation and the final rate depends on both activation energies. As schematically shown in Fig. 5.12, if r2 increases as E t approaches the conduction band, r4 decreases concomitantly. In fact, the highest generation rate is achieved around E i , decreasing exponentially towards valence and conduction band. The experimental reverse current densities are generally not constant, but increase with the magnitude of the reverse voltage. This behavior is not reproduced by the simple models of SRH generation or thermal generation over the effective gap, which do not contain a field dependence. However, in thin-film devices, i.e. vertical dimensions, at −1 V, electric fields of around 105 V cm−1 can be achieved. In this electric field

5.6 Generation-Recombination Statistics Due to a Distribution …

135

regime, it is reasonable to assume that, due to energy level bending, the trap energy depth is lowered by the applied electric field. The Poole–Frenkel model describes field-dependent generation of a carrier bound in a trap state with the energy landscape bent by an external field such that the effective energy necessary for escaping the trap is diminished. For a trap of zero-field depth E t , an approximation for this effective depth E t,eff is:  q3 F E t,eff = E t − , (5.8) π εε0 with the absolute value of the electric field (F) and the relative and vacuum permittivity, ε and ε0 , respectively [61]. Since the devices measured show a distribution of traps that could be approximated by a Gaussian distribution, we model the SRH generation in the drift-diffusion simulation by integrating the product of Eq. (5.7) by the measured distribution over the entire electrical gap (see Fig. 5.13f) assuming that E t is lowered as described by Eq. (5.8):  LUMOA Nt (E)ηG,R d E. (5.9) G= HOMOD

5.6.2 Modeling Trap-Assisted JD Generation in OPDs In Fig. 5.13a, we show the results of these simulations and compare them with the experimental data. Using the trap parameters extracted from the trap distribution as input in the simulation, the model describes the increase in JD upon increase of the amount of traps, achieving a good agreement in the voltage dependency and magnitude of the dark current. At low forward voltages, the simulated current densities are higher than the experimental values, which is a consequence of the extraction barrier for holes in these devices, see the schematic energy diagram in Fig. 5.13e. This barrier arises from the difference of HOMO level of the donor TPDP [15] and the EBL, MeO-TPD [62]. The effect vanishes when the EBL thickness is decreased to 5 nm, as shown also in Fig. 5.13c, indicating that holes can be extracted, possibly because the underneath layer is not completely covered. However, this also affects the blocking property of the layer, which ultimately precludes the study of JD versus trap concentration, as a larger amount of electrons are injected under reverse bias. Because the MeOTPD layer is not doped, the field drops across the layer. As the MeO-TPD thickness increases, the electric field becomes weaker, which reduces the electric current, as shown in Fig. 5.13c, where different thicknesses of MeO-TPD are compared. Besides causing S-shapes on J V curves of organic solar cells [63], the extraction barrier modifies the onset of the forward current [64]. The voltage at which current starts to flow depends on the built-in field which is determined by MeO-TPD in this device. This

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Fig. 5.13 Simulated J V characteristics of different D-A systems | Simulated (dashed lines) compared to experimental (symbols and solid lines) for devices based on a TPDP:C60 at three representative concentrations and b ZnPc:C60 (50 wt%). Also shown in b are the J V characteristics for SRH process in the absence of Poole–Frenkel effect and bimolecular generation over E CT . Inset in a shows the reverse region in detail. Mobilities and recombination rates in the simulation were optimized to achieve a good agreement with the experimental data, see Table 5.5 for the list of parameters used in the simulation. c Increased effect of the extraction barrier in TPDP:C60 (13.7 mol%) devices for different MeO-TPD layer thicknesses. d Effect of the HOMO level of the EBL/HTL on J V characteristics of TPDP:C60 (13.7 mol%) devices. e Schematic representation of the energy level of the different energy configuration presented in this chapter. f Schematic representation of a mid-gap trap distribution in a donor-acceptor system

5.6 Generation-Recombination Statistics Due to a Distribution …

137

Table 5.5 Parameters used in the drift-diffusion simulation shown in Fig. 5.13a–b ZnPc:C60 TPDP:C60 Unit Trap distribution a βSRH = vn σn = ν0 Nn−1 βbimolecular Effective thicknessb μn , μp

Vbi = φcathode − φanode

As measured (see Fig. 5.14) 1 × 10−11 5 × 10−12 50 + 50 + 50 9 × 10−5 5 0.97

As measured (see Fig. 5.11) 2 × 10−11 5 × 10−13 50 + 50 + 50 2 × 10−5 5 0.60

See parameters cm3 s−1 cm3 s−1 nm cm2 V−1 s−1 V

a

See discussion about the accuracy of this approximation in Appendix A. An equivalent relation can be written for holes b EBL + active layer + HBL. The simulation is performed for a single-layer device with ohmic contacts and an effective thickness, which accounts for the field drop along undoped EBL, active layer and HBL. The generation is limited within the active layer. As suggested by the experimental data, traps are found only in this region supporting this approach

can be visualized in Fig. 5.13d, where different EBLs are compared: note that the forward current depends on the HOMO of the EBL. As the HOMO decreases from −5.0 to −5.25 eV, the forward region becomes increasingly S-kinked. The extraction barrier also affects the reverse region. By increasing the barrier height by ∼250 meV, when comparing ZnPc (HOMO = −5.0 eV) [65] to BFDPB (−5.25 eV) [66] in Fig. 5.13d, a decrease of JD by one order of magnitude is observed. This suggests that JD of TPDP:C60 devices, which use MeO-TPD (HOMO = −5.10 eV) [67], could be higher in the absence of barriers. However, the scaling of JD with the trap concentration remains valid, as the barrier is kept constant. Moreover, the LUMO of the EBL/HTL can also affect JD , as it represents the injection barrier for electrons under reverse bias, which should be as high as possible. The extraction limitation in TPDP:C60 devices also becomes evident when simulating a barrier-free device, such as the well-studied ZnPc:C60 (50 wt%) system, shown in Fig. 5.13b. The model (red dashed line) is able to describe entire experimental dark J V curve with good agreement (see Fig. 5.14 for the characterization of the trap density of this system). Since only the D-A system was changed, it explains the deviation observed in Fig. 5.13a. The extraction barrier affects also the reverse region in the low-regime field as shown in the inset of Fig. 5.13a, where the experimental current density is lower than the simulated one, due to the barrier faced by holes. However, as the magnitude of reverse bias increases, the effect vanishes as a result of the increased electric field. At higher voltages, the J V curves eventually reach the space-charge-limitedcurrent regime, where the current density is primarily determined by the carrier mobility and the device thickness [61]. In this regime, our simulations match the

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Fig. 5.14 Trap analysis for ZnPc:C60 (50 wt%) | a C-f spectra and b trap density measured at different temperatures

experiments for both the ZnPc and the TPDP device, confirming that the mobilities assumed for the simulations are adequate. The importance of the energy level bending and the traps can be visualized in Fig. 5.13b. In the absence of traps, only charge carriers thermally excited over the effective gap, i.e. E CT , contribute to current in reverse bias. This leads to values of around 10−9 mA cm−2 , similarly to the J0 estimated from the quantum efficiency measurements of this device, see Table 5.3. By including SRH generation through the measured trap states, the simulated JD increases almost three orders of magnitude, however, still not fully reproducing the experimental data, as both magnitude and field dependence are not reached solely by the SRH generation. Ultimately, the experimental data can be reproduced by including the Poole–Frenkel effect.

5.6.3 Ideality Factor in Trap-Assisted JD It is common to associate the ideality factor, i.e., the slope of the exponential region of the J V curve (n id ) to recombination processes. It should approach n id = 2 when trap-assisted recombination dominates. From a first analysis, one could conclude that as the trap concentration increases, Fig. 5.9a, n id decreases. However, because of the extraction barrier, the information given by n id is misleading and its analysis nontrivial. In fact, by locally accessing n id at different temperatures, we can define a more meaningful region where it can be characterized [68, 69]. As shown in Fig. 5.15, n id is between 1.7 and 1.8 for all devices, indicating that trap-assisted recombination is the dominant processes. However, no clear trend with the amount of traps could be observed, which can still be a result of the extraction barrier, whose effect seems to get more pronounced for high concentration devices. This is in agreement with Fig. 5.8, where E CT slightly decreases with TPDP concentration, indicating that the extraction barrier increases.

5.6 Generation-Recombination Statistics Due to a Distribution …

139

Fig. 5.15 Ideality factor for TPDP devices | a For 24.1 mol% at different temperatures. A common value of n id is found for all temperatures, namely around 1.8, in agreement with trap assisted recombination process. At room temperature, n id can be analyzed at around 10−1 mA cm2 . This is done for all concentration in (b)

5.6.4 Arrhenius Activation Energy of Trap States The simulations and the experimental data suggest that activation energy for charge detrapping is field-dependent. This energy E a can also be accessed via temperaturedependent measurements of the dark current. In Fig. 5.16a, the Arrhenius analysis of E a for TPDP:C60 at different voltages reveals that its magnitude decreases when higher fields are applied to the device. This is a direct consequence of the Poole– Frenkel effect: the higher the applied voltage, the lower the barrier and, therefore, the lower the activation energy. Note also that E a is very similar to E t measured via impedance spectroscopy, which is consistent with the model developed here.

Fig. 5.16 Arrhenius analysis for TPDP:C60 devices | a Activation energy for TPDP:C60 extracted from temperature dependent J V measurements. The current was measured at temperatures varying from 223.15 to 303.15 K with ΔT = 10 K. For each bias, the logarithm of the current was plotted versus 1/T and E a was extracted from the slope of the curve. b Exemplary fit at V = −1.5 V

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5 Reverse Dark Current in Organic Photodetectors: Generation …

A quantitative agreement of the absolute E a values is however not possible, since the experimental values are affected by other thermally activated processes that were not taken into account in the simulations, such as charge transport and overcoming energy barriers. We speculate that charge transport is also responsible for the decrease of the activation energy in low-bias regime for low concentrations devices.

5.6.5 The Impact of the Trap Distribution Characteristics on JD Traps increase JD by thermally generating charges. However, it also important to understand the influence of the trap distribution characteristics on JD . While we know that increasing Nt leads to an increased JD , the role of the broadness of the trap distribution, as well as the exact trap energy are still unclear. In order to investigate that, we simulate JD for varying E t and σ . The results are shown in Fig. 5.17. As predicted from Eq. (2.62), traps are more important when close to the midgap. This can be seen in Fig. 5.17a, where JD strongly depends on the energetic distance from the E i . For E i − E t = −140 meV, the trapping process is more efficient, but the detrapping becomes less probable, see r4 and r2 in Fig. 5.12. The opposite can be observed when E i − E t = 260 meV, where trapped charges are more likely detrapped, but the amount of trapped charges is decreased. Figure 5.17b shows the influence of σ on JD . Within the simulated range, σ indeed plays a minor role. In fact, it is not possible to correlate JD with σ . It is thus not excluded that a constant trap density of states, i.e. a very large σ , could be used

Fig. 5.17 Influence of Et and σ on the dark current of TPDP:C60 (26.7 mol%) | a Simulated for different positions of the trap level in relation to the mid-gap energy for this system, the latter here defined as −4.45 eV. The curve 60 meV away from mid-gap represents E t at −4.51 eV, as measured for this system. As E t is moved away from mid-gap, the contribution of traps to the dark current decreases, as predicted by Eq. (2.62). b Simulated for different widths of the trap density of states. Within the studied range, this width plays a minor role, and a strong trend is not observed when varying this parameter

5.6 Generation-Recombination Statistics Due to a Distribution …

141

Fig. 5.18 Simulated dark J V curves | Dark current simulated for different E CT . Nt , E t and βSRH were kept constant as described in Table 5.5

to obtain a similar value of JD , similar to what was already shown by Fallahpour et al. for a Gaussian trap distribution centered at mid-gap [52]. However, our trap distributions have been independently obtained from the IS measurements, and we use those as input to simulate both magnitude and field-dependence of JD as shown for three TPDP:C60 concentrations in Fig. 5.13.

5.6.6 The Interplay Between CT States and Trap States Besides quantitatively describing the dark current of ZnPc and TPDP donors, by a variation of E CT , our model is also able to reproduce the entire range of experimental JD , depicted in Fig. 5.6a. This variation is shown in Fig. 5.18, where E CT is increased from 0.9 to 1.3 eV. Here, we targeted the effect of E CT versus traps, therefore all parameters are kept constant, except for E CT , explaining the deviation of the absolute value of JD versus E CT . Nonetheless, it is clear that including traps in the model, the experimental JD can be reproduced. To support this finding, the trap concentration of all devices was characterized as shown in Figs. 5.19 and 5.20. For all of them, Nt ranges1 from 1015 to

1

In organic devices, the voltage drops over the organic intrinsic layers. Therefore, the space charge width (W ) is assumed to be 90 nm, which corresponds to the device thickness minus the doped layer thicknesses. According to Eq. (4.18), variations in Vbi and W lead to minor errors in Nt , which does not affect the main outcome of this chapter.

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1016 cm−3 , obtained from the fit of the measured spectra to a Gaussian distribution,2 as shown in the insets of Fig. 5.20. These measurements indicate a rather general trend for donor:C60 BHJs. While many reports describe exponential trap density of states, for the materials investigated within this chapter and the energy range probed by IS, the measured spectra resemble a Gaussian distribution, in agreement with previous investigations in organic systems based on different techniques [70–73]. Given that traps have been observed not only in small molecule fullerene based BHJs, but also in many polymer-based D-A structures [47, 74] and non-fullerene-based devices

Fig. 5.19 Capacitance for donor:C60 (6 mol%) devices | The data of TPDP:C60 is shown in Fig. 5.10

2

The fitting range in Fig. 5.20 is further adjusted, depending on the material system and the effect of the blend resistance of that specific material system. For Spiro-MeO-TPD and P4-Ph4-DIP, for example, it seems that another type of distribution starts to appear at higher energies. However, we neglect it since within the frequency range where a reliable result can be obtained and the temperature range we studied, these features could not be properly resolved.

5.6 Generation-Recombination Statistics Due to a Distribution …

143

Fig. 5.20 Trap analyses for donor:C60 (6 mol%) devices | Trap concentration of donor:C60 devices. The data of TPDP:C60 is shown in Fig. 5.11. For Nt determination with Eq. (4.18), Vbi was extracted according to Mantri et al. [58]

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5 Reverse Dark Current in Organic Photodetectors: Generation …

[73], it is reasonable to assume trap-assisted dark current generation as an important source of non-idealities in the experimental dark J V curves reported in literature. The final dark current is dominated by trap-assisted generation. These finding highlight that, in addition to optimization routines to reduce JD from a device engineering perspective, future research should also focus on understanding the origin of such states and parameters governing trap creation. We also want to point out that the trap states characterized above are not observed in sensitive optical measurements of the photocurrent or E Q E spectra as recently reported [75]. The sensitivity E Q E spectra measured in this thesis reveal only characteristic absorption peak attributed to CT states, see Fig. 5.7. These states are accounted for when calculating J0 as described above.

5.7 Conclusion In this chapter, we develop a comprehensive model which can quantitatively explain the reverse currents in bulk heterojunction photodiodes. JD follows the same trend with E CT as its theoretical value J0 but is orders of magnitude higher. This can be explained by trap-assisted generation in a field-dependent version of the SRH model. By characterizing the trap distribution of different materials and blend concentrations, we show that JD scales with the total trap density and forms the main generation path in the studied OPDs. The commonly observed voltage dependency can be understood as the enhancement of emission rates assisted by the energy barrier lowering caused by the reverse applied bias. By using different approaches, we reduce JD to around 10−7 mA cm−2 and demonstrate that shot noise dominates the noise current. The shot-like behavior can be attributed to the detrapping of charge carriers, where an energy barrier of E t must be overcome for generation of charge carriers. Although our results point to an interfacial interaction between donor and acceptor, the origin of trap states is still unknown and further research needs to be done to clarify this aspect. Detectivity is limited by high noise currents, especially in the NIR regime. Understanding the molecular and morphological parameters ruling the formation of trap states is essential to pave a path towards its suppression and, therefore, a significant increase in detectivity.

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Chapter 6

Enhancing Sub-Bandgap External Quantum Efficiency by Photomultiplication in Narrowband Organic Near-Infrared Photodetectors

Detection of electromagnetic signals for applications such as health, product quality monitoring or astronomy requires highly responsive and wavelength selective devices. Photomultiplication-type organic detectors (PM-OPDs) have shown to achieve high efficiencies mainly in the visible range. Much less research has been focused on realizing near-infrared narrowband PM-OPDs. Here, we demonstrate fully vacuum-processed narrow- and broadband PM-OPDs. Devices are based on enhanced hole injection leading to an maximum external quantum efficiency (EQE) of almost 2000% at −10 V for the broadband device. The enhancement is also observed in the charge-transfer (CT) state absorption region, which we use to demonstrate a tunable narrowband PM-OPDs operated in the CT region, with EQEs superior to those of pin-devices. The presented concept can further improve state-of-art CT-OPDs, which were so far limited by the low EQE provided by these devices. This chapter is adapted from work published in J. Kublitski, A. Fischer, S. Xing, L. Baisinger, E. Bittrich, J. Benduhn, D. Spoltore, K. Vandewal, K. Leo, “Enhancing Sub-Bandgap External Quantum Efficiency by Photomultiplication for Narrowband Organic Near-Infrared Photodetectors”, Nature Communications, vol. 12, p. 4259, 2021 [1].

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Kublitski, Organic Semiconductor Devices for Light Detection, Springer Theses, https://doi.org/10.1007/978-3-030-94464-3_6

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6.1 Introduction From simple automatic lights in the halls of our building to the cruise control of cars, PDs are playing a major role in everyday life [2]. Often, fast detection of faint signals is required, which is currently provided by inorganic avalanche photodiodes [3]. As the automotive industry is moving toward self-driving cars [4], properties like lower cost, higher sensitivity, wavelength selectivity and form-free devices are required [5, 6]. PDs made from organic semiconductors can offer these properties but further research is needed to optimize these devices for low intensity signals [7]. PM-OPDs are capable of amplifying small photocurrents without requiring external/additional circuit components. This can be achieved by a photo-induced enhanced injection via energy level bending caused by charge accumulation near the injecting electrode [8, 9]. Following its observation in single material active layers [10] and D-A heterojunctions [11], different strategies have been introduced to achieve such charge accumulation and thereby the required energy level bending through a lack of percolation path for one charge carrier type [12–15], energetic barriers via interfacial layers [16, 17] as well as intentionally inserted trap states [18, 19]. All of these strategies include an accumulation of one carrier type near the contact, such that the electrical field caused by these charges bends the energy level, enabling the opposite charge to be injected via tunneling across the injection barrier [8]. If the transit time of injected charge carrier is lower than the lifetime of the accumulated, photo-generated charges, an E Q E > 100% is observed. Here, we would like to stress that prior to the photomultiplication process the photon needs to be absorbed by the active layer. We therefore conclude that the minimum criteria for photomultiplication is that the IQE is larger than unity. The effect described above has been applied in organic and hybrid PDs, leading to outstanding EQEs as high as 105 % [20–22]. Nonetheless, D ∗ achieved by these devices, which takes into account not only EQE, but also the device noise current, ranges from 1010 to 1015 cm Hz1/2 W−1 (Jones) in the visible range [8], values comparable to those of diode-like OPDs. Guo et al. presented two different polymers blended with zinc-oxide nanoparticles, reaching D ∗ of 1015 Jones in the ultraviolet region [18]. In the NIR at 1200 nm, using colloidal lead sulfide (PbS) quantum dots, Lee et al. achieved D ∗ of 1013 Jones [23], while 1014 Jones was attained for polymer-based devices in the visible range [24]. Recently, imagers [25] and dual band [26] OPDs were also fabricated using photomultiplication, with D ∗ of 1014 and 1013 Jones, respectively. Moreover, photomultiplication has been also explored in perovskites [27], for which EQE of 4500% and D ∗ of 1013 Jones were demonstrated at around 600 nm [28]. Despite the remarkable performance achieved by PM-OPDs in terms of increased EQE, limitations are still present in these class of devices. PM-OPDs suffer from high noise, a result of field dependent dark currents observed in these devices. In fact, this represents the main limitation in PM-OPDs as the gain acquired by biasing the device can be suppressed by the high dark current. Photomultiplication has been extensively exploited in solution-processed organic/ hybrid devices. However, despite the many advantages offered by sublimable small

6.1 Introduction

153

molecules, fewer examples were demonstrated in fully vacuum-processed devices [11, 16, 29–31]. Huang et al. demonstrated EQE higher than 1000% in devices based on C60 . These values were attributed to the disordered structure of C60 and to interfacial traps at the interface C60 /HTL [32]. Similar results were achieved by interfacial blocking layers in hybrid (solution- and vacuum-processed) [19, 33] and fully vacuum-processed devices [17, 34], which are used to avoid charge extraction, thereby causing the necessary band bending. In general, the vacuum deposition provides the possibility of depositing a vertical gradient of donor or acceptor molecules in the blend, as well as fine-tuning the mixing ratio. Yet, such fine-tuning extensively used in solution-processed PM-OPDs has not been investigated in vacuum-processed devices. Besides that, vacuum deposition offers the possibility of sequentially stacking multiple layers, the well-established doping technology [35, 36], straightforward fabrication of matrices of individual pixels, and is for commercial organic optoelectronic devices the currently preferred manufacturing technique. Another aspect not considered in PM-OPDs concerns photomultiplication in the extended CT state absorption region. With the aid of a Fabry-Perot microcavity, this rather weak absorption region has been used in NIR narrowband organic photodetectors (CT-OPD) [37–39]. Such narrowband OPDs could significantly benefit from the increased IQE, if photomultiplication would take place also by direct excitation of CT states. However, it is unclear whether direct excitation of CT states can result in a photomultiplication process. Utilizing the intermolecular CT state absorption renders possible to detect NIR photons beyond 1700 nm meanwhile using rather small and sublimable organic semiconductors where the absorption profile can be easily tuned by the D-A system. On the other hand, the weak intermolecular absorption cross section [40, 41] challenges the overall performance and here the photomultiplication could improve the electrical performance by increasing the gain for every absorbed photon. Here, we report a fully vacuum-processed PM-OPD based on low-acceptor content (3 wt%) ZnPc:C60 material system, with a maximum EQE of almost 2000% achieved at −10 V. Additionally, an optimum operation regime maximizing EQE while keeping a low dark current is found, leading to a D ∗ of 2.2 × 1012 Jones at 670 nm. Sensitively measured EQE spectra reveal that direct excitation of CT states also results in photomultiplication, which is confirmed by an IQE higher than 100% over the entire absorption region. Under −5 V reverse bias, the EQE of the PMOPD surpasses that of an optimized pin-photodiode, demonstrating the potential for application in CT-OPD. Indeed, by exchanging the transparent ITO contact with semitransparent Ag mirrors, while varying the thicknesses of the optical microcavity from 355 nm to 400 nm, peaks in the NIR region originating from cavity enhanced CT absorption arise. Narrowband PM-OPDs show peak EQEs from 20% to 80% under −10 V with full width at half maximum (FWHM) from 17 nm to 33 nm, and D ∗ of around 1011 Jones for all the resonant wavelengths. These results are comparable with narrowband organic pin-photodiodes based on cavities [37, 39], and higher than that of narrowband photomultiplication type devices based on charge injection narrowing (CIN) [42]. The new concept presented here can be used to boost EQE of microcavity narrowband OPD based on the absorption of the CT band (CT-OPD),

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which so far was mainly limited by the low absorption cross section of CT states, the low internal quantum efficiency [39], and the parasitic absorption of the contacts and transporting layers.

6.2 Photomultiplication in ZnPc:C60 Devices Controlling the mixing ratio is essential for the working principle of reported PMOPDs. For enhanced hole injection in reverse bias, electrons must accumulate near the cathode: we designed our device based on a low acceptor content (3 wt%), such that few percolation paths are formed. The well-known ZnPc:C60 system is chosen given the LUMO energy offset between these materials. At this concentration, electron are intentionally trapped within the LUMO level of C60 and the bending caused by electron accumulation in the C60 phase leads to EQEs above 100%. Below, we describe how this can be achieved in this system and how this effect can be used in narrow-band PM-OPD.

6.2.1 Enhancing the External Quantum Efficiency The PM-OPD operation in dark and under light as well as the architecture are shown in Fig. 6.1a–c. The bulk heterojunction comprising low C60 content (3 wt%) is sandwiched between two contacts, top Aluminum and bottom ITO, from which light enters the device, as shown in Fig. 6.1c. Pristine HATNA-Cl6 is used as HBL in between active layer and Al electrodes to reduce the reverse dark current. However, the thickness of HATNA-Cl6 must be carefully controlled such that injection is enabled upon band bending. Under reverse bias in the dark, the high injection barriers (Fig. 6.1a) hinder holes and electrons to be injected into ZnPc and HATNACl6 , respectively. Under forward bias, electrons and hole are injected into the device, such that the device behaves similarly to a photodiode. When the device is exposed to illumination, excitons are formed and free charges are generated at D-A interface. Due to absence of percolation paths, electrons are trapped in the acceptor phase and their transport is further hindered by the low conductivity of the electrically undoped HATNA-Cl6 layer [43]. While n-doped HATNA-Cl6 has been already employed as an ETL, in this device, we intentionally use a pristine layer such that the electron extraction is hindered and slowed down, which helps the electron accumulation at the cathode. This accumulation of electrons upon illumination causes that the energy levels bend in the vicinity of the contact, enabling holes from the external circuit to tunnel through the energy barrier imposed by the HATNA-Cl6 layer into the donor phase, where they are efficiently transported together with the photo-induced holes towards the anode. From the process described above, a voltage dependent increase in EQE is expected, as higher reverse voltage further decreases the energy barrier for injection.

6.2 Photomultiplication in ZnPc:C60 Devices

155

Fig. 6.1 Operation, device structure and EQE of a PM-OPD | Schematic energy diagram a under dark at flat band condition and b negatively biased under illumination. c Schematic device structure. d Voltage-dependent EQE (solid lines) of the device shown in c comprising ZnPc blended with C60 at 3 wt%. Each line corresponds to one symbol in e. Dashed red line shows the absorption spectrum of the same blend. Additionally, in e, the relative enhancement factor as a function of applied reverse bias is presented. Symbols show the ratio between EQE at 670 nm at each voltage from d normalized by the EQE at 670 nm at 0 V. The blue line is a guide to the eye. Note that no saturation is observed, indicating that EQE can be further increased. The energy level values of ZnPc, C60 and HATNA-Cl6 in a are taken from the literature [44–46]

The black line in Fig. 6.1d shows the EQE measured at 0 V, for which a maximum of 0.5% is achieved. This rather low value can be explained by the interrupted percolation path for electrons and charge separation probability at this concentration as well as by the unoptimized device architecture for 0 V operation. Clearly, no photomultiplication is observed. To prove the described working mechanism, we increase the reverse applied bias from 0 V to −10 V. Indeed, the EQE rises accordingly, reaching almost 2000% at −10 V. Further increase is expected for higher negative bias, as can be seen from Fig. 6.1e, where no saturation in the relative enhancement is observed. However, as it will be discussed below, an optimum operation regime exists in the range of −2.5 V, where the highest D ∗ is achieved.

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In spite of the extensive work performed by different groups on similar device structures [11, 17], this effect has not yet been utilized to increase EQE in the spectral region of CT state absorption. In D-A systems, interaction between donor and acceptor results in an extended but weak absorption band related to an optical transition from the HOMO of the donor to the LUMO of the acceptor. Recently, CT-OPDs have been introduced [37–39], which could benefit from high gain for absorbed photons provided by photomultiplication. However, it is not clear whether photomultiplicative gain can be achieved for photons that directly excite CT states. Before investigating PM gain in the CT absorption band, we first determine the optimum D-A concentration to achieve PM, as well as the relation with dark current. Below, we investigate these issues in ZnPc:C60 based devices.

6.2.2 Effect of Acceptor Concentration on Photomultiplication In the previous section, we showed that EQE can be enhanced by a least three orders of magnitude by photomultiplication based on electron accumulation. In polymeric systems based on the same effect, it is well accepted that low concentration of one material type (D or A) is necessary for attaining photomultiplication, a condition which has not been investigated for small molecule based devices. Zhang et al. reported an efficient photovoltaic effect at around 5 wt% donor content, which suggests that at such concentrations, hole transport takes place efficiently [47]. The minimum acceptor concentration required for a BHJ to work as a D-A solar cell has not been established for low acceptor content systems. To investigate the concentration dependence, we fabricated devices comprising concentrations from 1 wt% to 4 wt%. The results are depicted in Fig. 6.2. Devices comprising 1 wt% and 2 wt% mixing ratios do not show any amplification and behave as an unoptimized photodiode. For these devices, EQE does not overcome 100% and is limited by the poor free charge carrier generation of the system, which explains the slightly higher EQE of the blend at 2 wt%, where more exciton dissociation centers are available. At 3 wt%, the photocurrent increases almost one order of magnitude at a given reverse voltage. This abrupt enhancement is a result of a sufficient accumulation of charges at the contact, leading to an increased injection. At 4 wt%, the device still shows amplification, but the performance of the device deteriorated, which we attribute to a more efficient extraction of electrons at this concentration. If the concentration is further increased, percolation paths are formed and efficient extraction of both charge carrier types takes place. The device will then behave as a typical organic photodiode. From these results, we infer that an optimum concentration exists (in our case, 3%), where sufficient charges are trapped to cause energy level bending while providing enough free charge carrier generation. At concentrations higher than

6.2 Photomultiplication in ZnPc:C60 Devices

157

Fig. 6.2 Electric characteristics of PM-OPD | a JV curves in dark (dashed lines) and under 100 mW cm−2 illumination (solid lines) of devices based on ZnPc:C60 at different concentrations. A clear increase of the light and dark current is observed for devices with concentration higher than 3 wt%. b EQE of the same devices shown in a, measured at −5 V. The observed increase in current under illumination results in an increased EQE over 100%, achieving maximum of 450%

that, the injection is reduced either because charges are extracted more efficiently or because the bimolecular recombination rate increases. The maximum amplification found at a very specific concentration demonstrates the importance of highly controlled mixing ratios and morphology achievable in vacuum-processed devices. The dark current of the 1 wt% device is lower than that of the 2 wt% device, which we attribute to the smaller amount of D-A interfaces as well as to an increased number of traps [48, 49]. However, comparing the dark current of 3 and 4 wt% devices, we see that the former has a higher dark current and therefore a different behavior than the devices comprising 1 and 2 wt%. Analyzing the four devices together, we observe that an enhanced photocurrent and thereby EQE, seems to be correlated with an increased dark current. Daanoune et al. suggested that this correlation is an intrinsic consequence of the working principle of devices based on enhanced injection by charge accumulation [50]. In the dark, charges are thermally activated over the bandgap of the system, which in a D-A heterojunction corresponds to the energy of CT states. In an ideal diode, this current corresponds to the saturation current, J0 . In PM-OPDs, charge carriers forming J0 accumulate in the same way that photogenerated carries do, leading to an enhanced injection, also of dark current. In the same study, the authors also correlate the rather slow speed of PM-OPDs to the slow trap dynamics. This not only explains the observed trend but also indicates that this dark current effect might be detrimental for the specific detectivity (D ∗ ) of PM-OPD. This aspect is addressed in the following section.

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6.2.3 The Role of Dark Current in PM-OPDs The specific detectivity D ∗ of photodetectors depends on the EQE, which can be enhanced by photomultiplication. However, it also depends on the noise of the device. We can express D ∗ in terms of the device spectral noise density, Sn , as: D∗ =

qλ E Q E . hc Sn

((2.92) revisited)

In the absence of a frequency dependent component of the noise, Sn reads:  Sn =

2q JD +

4kB T , Rsh

(6.1)

which takes into account the shot and thermal noise, the first and second term in Eq. (6.1), respectively. In Eq. (6.1), Rsh is the shunt resistance extracted from the inverse of the derivative of JV curve around 0 V. In most organic devices, however, the high reverse dark current makes the shot component the main source of noise, which represents a limitation also in diode-like organic photodetectors. In polymer based devices, different material systems have been reported to show extremely high EQE, however, the values of the dark current have not always been presented. As mentioned before, the increase in photocurrent is usually correlated with an increased dark current. Therefore, both parameters have to be analyzed concomitantly in order to identify whether photomultiplication can be used to indeed get an increased D ∗ as an equivalent pin-photodiode. In Fig. 6.3a, the dark current of the same devices shown in Fig. 6.2a is compared to that of a pin-photodiode comprising the same D-A concentration. While the photocurrent reaches values two orders of magnitude higher than that of the pin-photodiode at −10 V, the dark current is four orders of magnitude higher, see Fig. 6.3a. Therefore, in order to overcome the performance of a pin-photodiode in terms of signal detectivity, EQE has to be as high as possible to even compensate such an increase in dark current. We have already shown that EQEs over of almost 2000% can be achieved for small molecule devices. Now, we must investigate whether D ∗ is indeed higher than that of equivalent pin-photodiodes. In most well working pin-photodiodes, EQE is weakly dependent on applied bias, which can also be seen in Fig. 6.3a, where the photocurrent does not increase significantly with increasing reverse bias. Nonetheless, we measured the voltagedependent EQE (in Fig. 6.3b) and approximated its maximum value as function of voltage by a 5th order polynomial, which allows to have estimated values of EQE for every voltage. From the fit, together with the measured dark current and shunt resistance, the voltage dependent D ∗ can be calculated, according to Eqs. (2.92) and (6.1). The same procedure is used for the PM-OPD. The results are compared in Fig. 6.3b.

6.2 Photomultiplication in ZnPc:C60 Devices

159

Fig. 6.3 Comparison of a PM-OPD and an equivalent pi n-photodiode | a JV characteristics in dark and under 100 mW cm−2 illumination of a pin-photodiode and of a PM-OPD. b The EQE measured at different voltages is fitted with a polynomial function, from which the detectivity is predicted. The total noise is calculated from the shot and thermal noise, which are obtained from the dark current and the shunt resistance at room temperature, respectively. The PM-OPD shows a maximum D ∗ of 2.2 × 1012 Jones around −2.5 V, which is higher than D ∗ of the equivalent pin-photodiode over the entire range measured, besides the high dark current at high reverse bias. c J V curves of the pin-photodiode measured within an extended voltage range showing the efficient injection in forward bias region. d Structure of the pin-photodiode

From Fig. 6.3, it is obvious that increasing EQE only is not sufficient to achieve high specific detectivities. As the dark current usually changes by orders of magnitude as a function of applied bias, the latter dominates D ∗ . Given this trade-off, an optimum operation region has to be found, where the effect of the dark current does not overcome the enhancement in EQE. In the most favorable operation region, D ∗ of 2.2 × 1012 Jones is obtained for the PM-OPD device, comparable to results reported for PM-OPDs and higher than D ∗ provided by the equivalent pin-photodiode where D ∗ is in the order of 1011 Jones over the entire range measured. Whether the abrupt increase in dark current is indeed an intrinsic consequence of the photomultiplication process, as previously suggested, is still not clear. While it seems to be the case for most reported PM-OPDs, some examples combine a high EQE with low dark currents, leading to very high performance [18]. If the dark current of the PM-OPDs

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were comparable to the one obtained in the pin-photodiode, D ∗ could be improved by two orders of magnitude. This shows that further investigation is needed to understand the origin of dark current in this device class.

6.2.4 Enhancement of Charge-Transfer State Response in PM-OPDs We have shown that by controlling the D-A mixing ratio, photomultiplication can also be achieved in vacuum-processed organic blends in the visible range. Whether the same effect is present when exciting the device in the CT absorption region is an important and, so far unaddressed question, which is relevant for microcavity CTOPDs. However, the low acceptor concentration required for photomultiplication to take place decreases the amount of D-A interfaces, establishing a trade-off between enhanced EQE and absorption. In order to be useful, the amplified EQE in the CT absorption region should overcome the EQE of a standard photodiode-based device, in which a higher concentration of CT states is usually present. In Fig. 6.3b, we showed that the PM-OPD is superior the pin-photodiode based on the same blend ratio. However, ZnPc:C60 system was shown to produce maximum photocurrent when used in the in 50 wt% mixing ratio [51]. Therefore, in Fig. 6.4a, the sensitively measured EQE spectra of a PM-OPD at different bias are compared to that of a standard ZnPc:C60 (50 wt%) pin-photodiode at zero bias. The CT band is observed for wavelengths longer than 800 nm in the sensitively measured EQE spectra of both devices. In the pin-photodiode, the CT band is more pronounced due to the higher density of CT states provided by the larger amount of D-A interfaces. In the same region, the PM-OPD shows a lower absorption shoulder, but also extending to the near infrared region. As expected, at zero bias, the EQE of the PM-OPD is orders of magnitude lower than that of the pin-photodiode, as no enhanced injection takes place. When −5 V are applied to device, the entire EQE spectrum of the PMOPD surpasses that of the pin-photodiode, confirming that direct excitation of CT states can also trigger the photomultiplication process in these devices. While the PM effect is commonly accompanied by an EQE above 100%, it is the IQE which better defines the physical phenomenon behind this effect. In order to induce PM, free charge carriers must be firstly generated, requiring photons to be absorbed. As a means of quantifying whether absorbed photon induce enhanced injection in the sub-gap absorption region in our devices, we estimated their IQE, which accounts only for absorbed photons. To that end, we employ the TMM to simulate the absorption in our devices and adjust the IQE to reproduce the magnitude of the measured EQE spectra. This requires the refractive and extintion coefficients (n, k) of all layers in the device, which can be derived from ellipsometry spectra. However, the absorption in the CT state absorption region is very weak, hindering the modeling of k-values from spectroscopic ellipsometry. As we are mainly interested in this region, we derived k-values as described by Kaiser et al. [52]. Besides the n, k-

6.2 Photomultiplication in ZnPc:C60 Devices

161

Fig. 6.4 transfer matrix method (TMM) simulation of a broad and b narrowband devices | a Simulated EQE (solid lines) compared to experimental EQE measured at different biases (dashed lines). The absorption spectra is simulated by TMM and the simulated EQE spectra are matched to the experimental ones by assuming constant IQE values as indicated in the legend for different biases. Magenta dashed line with filled circles shows the EQE of a pin-photodiode comprising ZnPc:C60 (50 nm) at 50wt% at 0 V. b Normalized simulated EQE for four different thicknesses (d) of the optical microcavity, leading to four detection wavelengths (λdetec. )

values of all the other layers of the device, the method requires device parameters such as EQE spectrum. The latter is obtained from a pin-photodiode with the same structure shown in Fig. 6.3d, but with active layer thickness of 100 nm. Since the architecture of the pin-photodiode is not optimized, the EQE is measured at −10 V to ensure that all photogenerated charges are extracted. In Fig. 6.5a we compare the simulated k-values (red solid line) to the measured k-values (dashed line) in the visible range. A good agreement is achieved, indicating that the simulated k-values of ZnPc:C60 (3 wt%) are properly derived. The obtained n, k-values allows us to simulate the PM-OPD to calculate the internal quantum efficiency. This is shown in Fig. 6.4a. Under −10 V a constant IQE of 1750% over the full wavelength range, i.e. including CT absorption, is required to describe the experimental data. Figure 6.4a demonstrates the potential of combining such systems with optical cavities to accomplish high performance narrowband photodetectors. In order to test whether such devices could be achieved, we embedded the best performing PM-OPD, i.e. 3 wt%, into an optical microcavity, see Fig. 6.7b for the device structure. Due to the high Ag work function as compared to that of ITO, we inserted a 10 nm thick MeO-TPD layer to hinder hole injection in reverse bias. With aid of TMM, we simulate the optical photoresponse of a device comprising the same active layer thickness of 400 nm, which leads to a resonant peak around 880 nm. Different resonant peaks can be achieved by varying the thickness of the active layer, leading to tunable near infrared detection as shown in Fig. 6.4b. The JV and EQE characteristics of devices comprising thicknesses from 355 nm to 400 nm are shown in Fig. 6.7a, c, respectively. As predicted by the optical simulation, narrowband peaks arise in the EQE spectra. As a demonstration, we tune the response wavelength from

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Fig. 6.5 n, k-values of ZnPc:C60 (3 wt%) | a In-plane n-values are obtained from variable-angle spectroscopic ellipsometry. In the visible region up to 800 nm, k-values can be obtained by the same method. In the NIR, k-values are calculated from the EQE spectrum of a pin-photodiode. Red solid line shows the calculated values in the entire range compared to the ellipsometric derived values (red dashed line) in the visible range. b Measured EQE at −10 V of the pin-photodiode compared to the TMM simulated spectrum of the same device using the n, k-values from a

Fig. 6.6 EQE and IQE of narrowband devices | a EQE of narrowband devices measured at −15 V. b Estimated IQE at −15 V (dashed black line) and −10 V (dashed red line). In b, dashed lines are guide to the eye

830 nm to 880 nm, which under −10 V, reaches maximum EQE of 20% to 80%, with a FWHM varying from 17 nm to 33 nm. As to prove that photomultiplication also takes place in the narrowband devices, we estimate the IQE of these devices. Indeed, for the device with a detection wavelength of 828 nm, an IQE of 160% is achieved. The three other devices show IQE of around 40%, from which it is not possible to infer whether such values are a result of the PM effect or other phenomena. Therefore, to elucidate that, we increase the bias voltage to −15 V. This leads to EQEs and IQEs above 100% for all four devices, with peak values of 430% and 920%, respectively, as shown in Fig. 6.6. Also in the microcavity devices, the dark current plays an important role in the final D ∗ . Although in these devices a better on/off ratio is kept along the reverse bias

6.2 Photomultiplication in ZnPc:C60 Devices

163

Fig. 6.7 Photomultiplication in the CT state absorption region used in narrowband devices | a J V characteristics in the dark and under 100 mW cm−2 illumination of four different narrowband devices with varying resonant wavelength as indicated in the legend. b Device structure of narrowband devices. c EQE of cavities of the same devices shown in a at −10 V. As the active layer thickness increases from 355 nm to 400 nm, the resonant wavelength redshifts from around 830– 880 nm. Dashed lines show the fit to a Lorentzian function, from which the FWHM is extracted. d The EQE measured at different voltages is fitted with polynomial function, from which D ∗ is calculated. An optimum operation region is found around −3.5 V, where D ∗ of 6 × 1011 Jones is obtained

region as compared to those of Fig. 6.2, see Fig. 6.7a, the on/off ratio decreases as the reverse voltage increases, pointing to a decreased D ∗ at high reverse bias. Therefore, we also estimate an optimum operation regime, where the trade-off between EQE and dark current is maximized. As depicted Fig. 6.7d, we obtain D ∗ as high as 6 × 1011 Jones in narrowband devices, which is comparable to narrowband pindevices based on cavities [37, 38]. Moreover, it is superior than that of narrowband photomultiplication type devices based on CIN [42], where, in addition, excessively thick devices are demanded, which increases the operation voltage.

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6.2.5 Transient Photocurrent Another important figure-of-merit of photodetectors is the response speed. In PMOPDs, the temporal response is believed to be limited by the trapping/detrapping dynamics [18, 50], while other processes such as charge carrier transit time should be much shorter. In order to investigate the response speed of our devices, transient photocurrent measurements are performed, as shown in Fig. 6.8. The rise time (from 10% to 90% of the device saturated signal) and fall time (from 90% to 10% of the device off signal) are summarized in Table 6.1. The rise time of both broad- and narrowband devices ranges from 20 µs to 600 µs, corresponding to −3 dB cut-off frequencies of 19.5 kHz to 0.4 kHz. These values are comparable to the best performing PM-OPDs reported so far [8] and are suitable for health monitoring and video applications.

Fig. 6.8 Transient photocurrent of a broad- and b narrowband PM-OPDs | For all measurements, 100 Hz pulse signal was used to probe the white LED, except for the broadband device at −10 V, 50 Hz was used due to the long decay time. Switching-on and -off time constants are defined as the time the device response takes to rise from 10% to 90% (on) and to fall from 90% to 10% (off) of its maximum value. ton and toff are summarized in Table 6.1 −1 Table 6.1 Speed of broad- and narrowband PM-OPDs | The known relation f −3 dB  0.35ton is used to calculate the cut-off frequencies [53] Broadband Narrowband (843 nm)

Applied bias (V) −2.5 −5.0 −10.0

ton (µs) 63 541 556

f −3 dB  −1 0.35ton (kHz) 5.55 0.65 0.63

toff (µs)

ton (µs)

280 539 597

135 941 18

f −3 dB  −1 0.35ton (kHz) 2.59 0.37 19.44

toff (µs) 326 613 667

6.3 Dynamic Range of PM-OPDs

165

Fig. 6.9 Dynamic of PM-OPDs | a Broadband and b narrowband (843 nm) devices. Red crosses refer to calibrated measurements acquired in the setup described in Sect. 4.3.2, where the light intensity is directly measured. The remaining curves refer to uncalibrated measurements acquired in the setup described in Sect. 4.3.4 at 25 ◦C. The magnitude of the photocurrent measured by a reference Si diode is matched to the photocurrent of the calibrated measurement at around 100 mW cm−2 , by knowing the respective photocurrent of the PM-OPD at the same light intensity

6.3 Dynamic Range of PM-OPDs Besides a fast and sensitive response, detectors are expected to show a predictable and reproducible response to the light, which makes the calibration of the device easier. In order to analyze that, we measured the dynamic range of our devices under different biases, and calculated the dynamic range (DR) as described in Sect. 2.3.7. The results are shown in Fig. 6.9. Except for the broadband device biased at −10 V, a broad dynamic range is observed over four orders of magnitude. This corresponds to DR of 91 dB. Note that no saturation is observed up to 6 Suns, the strongest light intensity used, suggesting that a higher linear dynamic range could be achieved.

6.4 Conclusion In CT-OPDs, the thicknesses required are much smaller than those used in narrowband devices based on charge collection narrowing (CCN) [54, 55] or CIN [42, 56]. In the latter, for example, the thickness of the active layer must be much larger than the inverse of the absorption coefficient of the active layer, such that under illumination charges are generated close to the injecting contact, thereby causing the necessary band bending [56]. Moreover, in CT-OPDs the response can be further redshifted not only by increasing the thicknesses of the active layer but also by introducing well conducting spacer/transport layers, making the device electrically thin but optically thick [37–39]. By combining the concept used in CT-OPDs with photomultiplica-

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6 Enhancing Sub-Bandgap External Quantum Efficiency by Photomultiplication …

tion, we are able to achieve much thinner devices, as demonstrated in Fig. 6.7, where active layers of 355 nm were used for spectral response at 830 nm, compared to 2.5 µm reported for spectral response at 650 nm when using CIN combined with photomultiplication [42]. The new concept presented here can further benefit from the properties of microcavity devices while keeping enhanced EQE by photomultiplication at reasonable thicknesses and operation voltages. Moreover, in PM-OPDs, the position of the active layer can be placed in an optimized position, either near the contact to enhance injection or such that optical overtones are minimized. There are systems combining extremely low dark currents with enhanced EQE [18]. Together with our new concept, such systems can potentially overcome the performance of state-of-art near infrared narrowband photodetectors. In summary, we investigate the photomultiplication effect in fully vacuumprocessed organic photodetecting devices. At 3 wt% of C60 , a significant increase in EQE is observed under reverse bias, attributed to the accumulation of electrons caused by the lack of percolation paths. In the optimum operation regime, a specific detectivity D ∗ of  1012 Jones is achieved. In addition, sensitively measured EQE spectra reveal that the enhancement extends to the CT absorption region, which indicates that these states also trigger photomultiplication, making microcavity CTOPDs with photomultiplication possible. Indeed, by exchanging the bottom contact by a semitransparent mirror, narrowband NIR PM-OPDs with response from 830 nm to 880 nm are realized, achieving D ∗ of 1011 Jones and FWHM as low as 17 nm. The combination of optical microcavities with the photomultiplication effect can potentially boost NIR CT-OPDs, which so have been limited by the low EQE in the CT absorption region. Furthermore, much thinner devices are sufficient to achieve narrowband detection, as compared to the CIN approach. Additionally, the method presented here allows placing the active layer in different positions within the device or using gradients of D-A mixing ratio, thereby enhancing injection and diminishing the effect of optical overtones, a critical problem in CT-OPDs.

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Chapter 7

Summary and Outlook

The modern world is surrounded by devices designed to facilitate and automatize daily tasks. Most of these devices rely on the detection of the electromagnetic radiation. Organic photodetectors offer many new possibilities of use, however, their low performance still hampers the commercialization. In what follows, the findings towards high performance OPDs achieved within this entire work are summarized and the main outcomes are highlighted. Moreover, an outlook for the field of OPDs is given where the most important current challenges are presented.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Kublitski, Organic Semiconductor Devices for Light Detection, Springer Theses, https://doi.org/10.1007/978-3-030-94464-3_7

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7.1 Summary Certainly, the technological advances from the last decades have modified the way human beings interact to each other and to the world. So far, the inorganic semiconductor industry has provided the necessary technology for such developments, including photodetectors, which compose a significant part of this new automatized world. However, further extending the interaction of human body with technology depends on properties that cannot be provided by inorganic semiconductors. Instead, new and more versatile detecting devices are desired. Given the intrinsic properties of organic materials such as flexibility and low processing costs, OPDs have great potential to fulfill these needs. Apart from intrinsic properties of known organic materials, organic chemistry allows for the development of new materials designed for specific applications, widening the range in which OPDs can thrive. However, to bring OPDs into commercialization, many issues still need to be addressed. Among them is the high performance to detect faint light/signals, which depends on the efficiency with which an electric output is generated upon light absorption, namely the external quantum efficiency (EQE), and noise produced by the device in the absence of input signal. In this thesis both have been significantly improved. Below, the findings of Chaps. 5 and 6 are described.

7.1.1 On the Origin of the Dark Current of Organic Photodetectors In photovoltaic-type OPDs, EQE is physically limited to 100%. Given the vast knowledge acquired from the field of organic solar cells, many D-A systems show optimized EQEs approaching that limit, which leaves less room for improvements by increasing EQE. On the other hand, OPDs typically show a high noise at reverse bias, which is the most favorable operation regime. As this parameter was so far not well understood, in Chap. 5, the sources of noise in OPDs are studied, where it is found that the noise spectral density (Sn ) of OPDs is directly related to the dark current (JD ). For frequencies above the noise corner, i.e., f > f c , where f c is the frequency at which 1/ f appears, the device Sn can be well described by its shot noise contribution, which is proportional to JD , promoting the latter as one of the most important parameters for OPDs. Therefore, Chap. 5 is dedicated to elucidate the origin of JD , starting from its the fundamental limits. Similarly to organic solar cells, in organic photodetectors formed by a D-A systems, charge-transfer (CT) states play an important role, defining the upper limit for the device performance. As the recombination process is mediated by CT states, also the inverse process, i.e., generation, takes place via these states, whose energy is lower than the electrical gap of single D or A. Therefore, a minimum saturation current can be derived, representing the current thermally generated by the background radiation. Observing such a relation is not always straightforward, as many

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parameters can mask this dependence. By running an extensive optimization procedure, including contact selectivity, reduction of shunt paths and device structuring the influence of extrinsic effects could be minimized. Such an optimization allowed for a clear decrease of dark current with increasing the CT state energy (E CT ) to be observed. Moreover, as a result of the optimization procedure, a dark current as low as 10−7 mA cm−2 at −1 V is achieved for E CT of 1.58 eV, which is among the lowest values demonstrated for OPDs. However, in spite of observing a relation between CT states and JD , some aspects still remain intriguing. Firstly, the experimental values are much higher than the lower limit derived for J0 , suggesting that a different effect generates the experimental dark current. Secondly, JD shows a strong field dependence, which is not expected from the thermally generated charge carrier. Lastly, it is observed that low E CT systems are less sensitive to the optimization, pointing to an additional but also microscopic phenomena increasing JD . In the literature, trap states had been suggested to increase JD [1], but no robust experimental evidence was provided. Likewise, the density of traps (Nt ) was shown to scale with D-A mixing ratio [2]. The analyses of different D-A systems reveled that for TPDP:C60 , E CT remains constant upon varying the D-A mixing ratio. This is crucial to analyse any other influence on JD , as a strong dependence on E CT was shown. By increasing the mixing ratio and monitoring the characteristics of the trap distribution, Nt , the broadness (σ) and the trap depth (E t ), with the aid of impedance spectroscopy [3], a clear scalling of Nt with the mixing ratio is observed. Most importantly, JD increases concomitantly. These are strong evidences that the source of JD in that system are trap states and that they originate from the D-A interface. In order to quantify the effect of the measured trap distribution on the device characteristics, we simulated the trap assisted generation of JD by using a drift-diffusion model, where the experimentally obtained Nt , E t and σ served as input parameters. In addition to describing the dark charge carrier generation in the framework of SRH theory, the field dependence of JD is studied. The experimental JD can be better reproduced when assuming Poole-Frenkel effect, i.e., that E t is lowered by the applied electrical field. Such an assumption is reasonable in thin-film devices, where high electric field are achieved under typical operation biases. This comprehensive model does not only explain the field dependence but also reproduces the magnitude of JD . Furthermore, it is found that E t and Nt have a strong impact on the final JD , while σ is less important within the measured range. In total, seven D-A systems were investigated, with CT energies varying from 0.85 eV to 1.58 eV. For all of them, the trap analysis of impedance spectroscopy measurements revealed that trap states are present, which explains the high experimental JD . Despite the rather low concentration, ranging from 1015 cm−3 to 1016 cm−3 , trap states are harmful for OPD performance, especially if they are located close to the mid-gap, where the generation rate is most prolific. Moreover, the dark current of all systems can be reproduced when traps are taken into account in the drift-diffusion simulation. The take away message from the study performed on the origin of JD in OPDs is that J0 offers a measure of how far a D-A system is from its upper limit of detectivity. The discrepancy can be explained by trap states, which are the responsible for the high

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experimental dark currents observed in OPDs, especially when device engineering is shown to be at its limit. Moreover, D ∗ is limited by the noise produced by these states, which is detrimental for OPDs to surpass inorganic technology. As the microscopic origin of trap states is unknown, further research needs to be done in oder to maximize the performance of OPDs.

7.1.2 Enhancing EQE via Photomultiplication in Organic Photodetectors When targeting high D ∗ , also EQE is important. While photovoltaic-type OPDs are physically limited to an EQE of 100%, another class of devices exists for which this limit can be overcome. The so-called PM-OPDs were demonstrated for organic materials some time ago, but since then, much attention has been given to solution processed devices, in detriment of the vacuum processing technology. Given the efforts to tackle the reduced performance of OPDs, especially the CT-OPD, the photomultiplication (PM) effect in small molecule BHJs was investigated. It was found that PM can be achieved in these systems when a small concentration of acceptor molecules is embedded into a donor matrix. An optimum concentration exist for which less percolation paths are formed, leading to an accumulation of charges in the vicinity of the injecting contact. The induced electric field bends the energy level close to the cathode enhancing charge injection, which leads to an EQE of around 2000% at −10 V. For the device demonstrated in Chap. 6, the life-time of electrons is longer than the transit-time of injected hole. This means that within the life-time of the photogenerated charge carriers, more than one injected charge carrier with opposite charge crosses the devices. Although PM is an already known phenomenon, we showed that also the direct excitation of the CT band triggers the effect. This result enables the application of PM in CT-OPDs. By combining optical microcavities with the CT state absorption of BHJ blended at a small D-A mixing ratio, we developed the narrowband PM-type OPD. The performance of these devices is superior to that of narrowband OPDs based on CIN, besides requiring much thinners structures, which reduces production costs. Also from this study, it is evident that both EQE and JD must be optimized. As both parameters seem to be correlated in PM-OPDs, demonstrating extremely high EQEs at the cost of high dark currents is not sufficient for achieving high performance. Nonetheless, PM-OPDs devices have great potential to become an improved version of CT-OPDs, which are already in the market. In summary, improved D ∗ can be achieved either by means of noise reduction, which in OPDs translates into reduced JD , or by means of increased external quantum efficiencies. Identifying the microscopic origin of traps states in organic materials is essential to improve the performance of OPDs. Moreover, a deeper understanding of the working mechanism of PM-OPDs is desired, such that also in these devices the dark current can be minimized without affecting EQE. In that direction, the findings

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regarding JD in OPDs can give insights when dealing with PM-OPDs, as trapping of charges is thought to be necessary for PM-OPD operation. Even though the nature of the trap states is different, the physical mechanism behind dark current generation can take place via these states in both systems.

7.1.3 Related Topics Investigated Alongside with this Thesis (Not Shown) Apart from what is discussed in Chaps. 5 and 6, different topics were investigated during the development of this thesis, which are related to what is discussed here in a greater or lesser degree. Therefore, the main finding of these topics are also summarized below. As already discussed in Chap. 1, one requirement for material sensing is acquiring narrowband OPDs, enabling the detection of specific absorption regions in the spectra. For that, different aspects must be targeted such as high performance, NIR photoresponse as well as device engineering. In a recent work by Xing et al. [4], we combined the transmission spectra of optical microcavities with highly optimized OPDs to realize D ∗ higher than 1014 Jones in the visible range. In the same work, a miniaturized VIS-NIR spectrometer was demonstrated. While the photoresponse of these devices is limited to around 1000 nm, Kaiser et al. synthesized new absorbers, extending the photoresponse region to 1665 nm in CT-OPDs [5]. Thanks to the optimized device structure, our most red-shifted device reached D ∗ of around 108 Jones. In order to enhance the capability of distinguishing different components in the spectrum, we also investigated dual-band devices. Wang et al. fabricated a structure composed of two stacked microcavities, leading to a dual band response with peak D ∗ of 1011 in the range of 790–1180 nm and 108 in the range of 1020–1435 nm [6]. Most of these devices operate far from the non-radiative recombination limit, meaning that the extrinsic effects such as trap-assisted generation decreases the device performance as described in Chap. 5. However, Gielen and Kaiser et al. synthesized four new polymers which are limited by non-radiative recombination. In the same work, we calculated the intrinsic detectivity limits assuming that non-radiative recombination is also an intrinsic effect as pointed by Benduhn et al. for fullerene based OSCs [7]. Under this assumption, it has been suggested that OPDs cannot operate beyond 2000 nm, as a consequence of the high non-radiative recombination rates [8]. Given the similarity of photovoltaic-type OPDs and OSCs, different perspectives of charge generation [9–11], bandgap and energy level engineering [12, 13] as well as voltage losses [14, 15] were studied. Nikolis and Dong et al. investigated two different systems where charge generation happens efficiently, even though no heterojunction is intentionally formed. For α-sexithiophene (α-6T), the generation is attributed to the electrostatic energy offsets caused by different orientation in the active layer, leading to a driving force of around 0.4 eV [10]. Whereas for subnaph-

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thalocyanine (SubNc) free charge carrier generation happens due to a field-assisted exciton dissociation mechanism specific to the device configuration [9]. Interestingly, in both α-6T and SubNc system, charge carrier generation was believed to happen spontaneously without D-A interfaces and, therefore, with zero driving force. However, this is not the case for these systems. Nonetheless, in the work published by Zhong et al., we studied different non-fullerene D-A systems for which fast chargetransfer in the order of few hundred femtoseconds even at nearly zero driving force still takes place [11]. Although most OPDs still operate far from the non-radiative limit, the discussion held for OSCs regarding voltage losses is also valid for OPDs. Pranav et al. investigated non-radiative surface recombination in devices comprising molybdenum trioxide (MoO3 ) as HTL [15]. In this study, by using a thin layer of C60 between the MoO3 HTL and the D-A system, we showed that the thin C60 layer increases the built-in potential and reduces the presence of minority charges at the electrode, thereby, reducing the recombination. A different strategy to reduce voltage losses was proposed by Nikolis et al. using strong light-matter coupling [14]. Here, we embedded fullerene-free OSCs into optical microcavities, which results in a redshifted optical gap. As E CT and VOC remains unaffected, a decrease in non-radiative voltage losses is observed. For every optoelectronic device, the energy alignment between different layers controls many of the device parameters. Therefore, being able to manipulate energy levels and bandgaps opens a wide range of possibilities for device fabrication. Schwarze et al. showed that by blending ZnPc with its fluorinated derivatives, the energy levels of these systems can be tunned [12]. In the same work, we related the shifts in ionisation energy to molecular quadrupole moment along the π-π stacking. In a further study published by Ortstein et al., we demonstrated that blending two materials together can affect the energy gap as well, which is attributed to changes in the dielectric constant of the blend [13].

7.2 Outlook The relation involving JD , E CT and trap states elucidated within this work as well as the development of a new device structure, the PM-OPD, helps to define future strategies towards higher performance OPDs. However, different aspects still hampers their way to commercialization. Below, we list some open research topics which still need to be addressed in order to make OPDs more competitive in concrete applications. For convenience, the topics are divided into three categories related to photovoltaic-type OPDs, PM-OPDs and OPDs in general.

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7.2.1 Open Research Topics for Photovoltaic-Type OPDs • Unveil the origin of trap states: Elucidating the microscopic formation of trap states in organic systems is essential not only for OPDs but also for the entire field of organic electronics, as these states are detrimental for most organic devices. The power conversion efficiency of OSCs is reduced by the non-radiative recombination via trap states, which is also an issue for OLEDs. Likewise, in organic transistors shallow traps reduce charge carrier mobilities, leading to slower devices. From the results presented in Chap. 5, the traps identified here seem to be related to interfacial interactions, as they depend on the interfacial area. This suggests that a correlation with CT states might exist, see also Ref. [16]. • Reaching non-radiative limit in OPDs: For fullerene OSCs, it has been suggested that non-radiative recombination is an intrinsic characteristic of these systems [7]. However, in OPDs, this limit if often far from being reached such that very few examples are available were D ∗ is limited by non-radiative recombination [8]. Therefore, it is important to reduce JD to the point where the discussion of VOC in OSCs can also be applied to OPDs. From the results shown in Chap. 5, this means eliminating trap states. • Describe the effects of traps on device speed and linearity: It is common to observe that the recombination process depends on the charge carrier concentration, which is usually responsible for the non-linearities in OPDs. It is important to quantify how traps are related to the recombination order in organic systems. Besides that, traps are known for affecting device speed but no clear conclusions were given in that direction.

7.2.2 Open Research Topics for Photomultiplication-Type OPDs • Study novel D-A systems for application in PM-OPDs: In devices composed of ZnO nanoparticles blended with semiconducting polymers, high EQE and impressive low dark currents were demonstrated [17]. New D-A systems can be designed where low dark current and high EQEs can be achieved concomitantly. • Layer engineering in PM-OPDs: A major advantage of PM-OPDs is that the generation region can be optimized to the region close to the injecting contact. This can not only reduce parasitic absorption but also minimize optical overtones inside the microcavity. However, this topic has not been fully elucidated, yet. • Extending photoresponse into the NIR spectral range: The absorption of the system shown in Chap. 6, ZnPc:C60 , is limited to around 1200 nm. New material systems should be investigated for photomultiplication in order to amplify the detection range into the NIR. • Reveal the origin of the dark current: High JD was suggested to be intrinsically correlated to the working mechanism of PM-OPDs [18]. However, such conclusion

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is debatable, since low JD , while attaining high EQE, was already shown [17]. This topic deserves further research, given the direct relation to device performance.

7.2.3 Open Research Topics for OPDs in General • Fabrication of arrays: Imaging and many other applications require arrays of detectors to be built. Hence, embedding well performing devices into arrays is desired, which includes device engineering and structuring methods. • Integration with read out circuits: In the same direction of the previous topic, detectors need to be integrated with read out circuits. This can be done with organic transistors/circuits or with the inorganic technology. In both cases, so far only very little research and engineering has been done. • Studies with flexible and stretchable substrates: For certain applications, organic devices are ideal if their special mechanical properties can be used. But not as much is known for formless devices, since only a few examples can be found, where OPDs were built on flexible and/or stretchable substrates [19–22]. • Development of biocompatible materials and devices: OPDs are suitable for health/healing monitoring. Such application could reduce the number of surgical interventions, provide precise dosing of medication and early diagnosis, among many other applications. However, depending on the region of use, biocompatible and biodegradable devices/materials are required. This is also an alive research topic, which can be further addressed.

References 1. Fallahpour A, Kienitz S, Lugli P (2017) Origin of dark current and detailed description of organic photodiode operation under different illumination intensities. IEEE Trans Electron Devices 64(6):2649–2654. https://doi.org/10.1109/TED.2017.2696478 2. Sergeeva N, Ullbrich S, Hofacker A, Koerner C, Leo K (2018) Structural defects in donoracceptor blends: influence on the performance of organic solar cells. Phys Rev Appl 9(2):24039. https://doi.org/10.1103/PhysRevApplied.9.024039 3. Walter T, Herberholz R, Müller C, Schock HW (1996) Determination of defect distributions from admittance measurements and application to cu(in, ga)se2 based heterojunctions. J Appl Phys 80(8):4411–4420. https://doi.org/10.1063/1.363401 4. Xing S, Nikolis VC, Kublitski J, Guo E, Jia X, Wang Y, Spoltore D, Vandewal K, Kleemann H, Benduhn J, Leo K (2021) Miniaturized VIS-NIR spectrometers based on narrowband and tunable transmission cavity organic photodetectors with ultrahigh detectivity above 1014 Jones. Nat Photon 5. Kaiser C, Schellhammer KS, Benduhn J, Siegmund B, Tropiano M, Kublitski J, Spoltore D, Panhans M, Zeika O, Ortmann F et al (2019) Manipulating the charge transfer absorption for narrowband light detection in the near-infrared. Chem Mater 31(22):9325–9330. https://doi. org/10.1021/acs.chemmater.9b02700

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6. Wang Y, Siegmund B, Tang Z, Ma Z, Kublitski J, Xing S, Nikolis VC, Ullbrich S, Li Y, Benduhn J, Spoltore D, Vandewal K, Leo K (2020) Stacked dual-wavelength near-infrared organic photodetectors. Adv Opt Mater 2001784. https://doi.org/10.1002/adom.202001784 7. Benduhn J, Tvingstedt K, Piersimoni F, Ullbrich S, Fan Y, Tropiano M, McGarry KA, Zeika O, Riede MK, Douglas CJ, Barlow S, Marder SR, Neher D, Spoltore D, Vandewal K (2017) Intrinsic non-radiative voltage losses in fullerene-based organic solar cells. Nat Energy 2(6):17053. https://doi.org/10.1038/nenergy.2017.53 8. Gielen S, Kaiser C, Verstraeten F, Kublitski J, Benduhn J, Spoltore D, Verstappen P, Maes W, Meredith P, Armin A, Vandewal K (2020) Intrinsic detectivity limits of organic near-infrared photodetectors. Adv Mater 32:2003818. https://doi.org/10.1002/adma.202003818 9. Nikolis VC, Dong Y, Kublitski J, Benduhn J, Zheng X, Huang C, Yüzer AC, Ince M, Spoltore D, Durrant JR, Bakulin AA, Vandewal K (2020) Field effect versus driving force: charge generation in small-molecule organic solar cells. Adv Energy Mater 10:2002124. https://doi. org/10.1002/aenm.202002124 10. Dong Y, Nikolis VC, Talnack F, Chin Y-C, Benduhn J, Londi G, Kublitski J, Zheng X, Mannsfeld SC, Spoltore D, Muccioli L, Li J, Blase X, Beljonne D, Kim J-S, Bakulin AA, D’Avino G, Durrant JR, Vandewal K (2020) Orientation dependent molecular electrostatics drives efficient charge generation in homojunction organic solar cells. Nat Commun 11(1):4617. https://doi. org/10.1038/s41467-020-18439-z 11. Zhong Y, Moore GJ, Krauspe P, Xiao B, Günther F, Kublitski J, Shivhare R, Benduhn J, BarOr E, Mukherjee S, Yallum K, Réhault J, Mannsfeld Stefan C, Neher D, Richter LJ, DeLongchamp DM, Ortmann F, Vandewal K, Zhou E, Banerji N (2020) Sub-picosecond charge-transfer at near-zero driving force in polymer: non-fullerene acceptor blends and bilayers. Nat Commun 11(1):833. https://doi.org/10.1038/s41467-020-14549-w 12. Schwarze M, Schellhammer KS, Ortstein K, Benduhn J, Gaul C, Hinderhofer A, Toro LP, Scholz R, Kublitski J, Roland S, Lau M, Poelking C, Andrienko D, Cuniberti G, Schreiber F, Neher D, Vandewal K, Ortmann F, Leo K (2019) Impact of molecular quadrupole moments on the energy levels at organic heterojunctions. Nat Commun 10(1):2466. https://doi.org/10. 1038/s41467-019-10435-2 13. K. Ortstein, S. Hutsch, M. Hambsch, K. Tvingstedt, B. Wegner, J. Benduhn, J. Kublitski, M. Schwarze, S. Schellhammer, F. Talnack, A. Vogt, P. Bäuerle, N. Koch, S. C. B. Mannsfeld, H. K. F. Ortmann, and K. Leo, “Band Gap Engineering in Blended Organic Semiconductor Films Based on Dielectric Interactions,” Nature Materials, 2021, in revision 14. Nikolis VC, Mischok A, Siegmund B, Kublitski J, Jia X, Benduhn J, Hörmann U, Neher D, Gather MC, Spoltore D, Vandewal K (2019) Strong Light-Matter Coupling for Reduced Photon Energy Losses in Organic Photovoltaics. Nat Commun 10(1):3706. https://doi.org/10. 1038/s41467-019-11717-5 15. M. Venkataramani, J. Benduhn, M. Nyman, S. M. Hosseini, J. Kublitski, D. Neher, K. Leo, and D. Spoltore, “Enhanced Charge Selectivity via Anodic-C60 Layer Reduces Non-Radiative Losses in Organic Solar Cells,” ACS Applied Materials & Interfaces, vol. 13, pp. 12 603–12 609, 2021, DOI: 10.1021/acsami.1c00049 16. Zarrabi N, Sandberg OJ, Zeiske S, Li W, Riley DB, Meredith P, Armin A (2020) ChargeGenerating Mid-Gap Trap States Define the Thermodynamic Limit of Organic Photovoltaic Devices. Nat Commun 11(1):5567. https://doi.org/10.1038/s41467-020-19434-0 17. Guo F, Yang B, Yuan Y, Xiao Z, Dong Q, Bi Y, Huang J (2012) A Nanocomposite Ultraviolet Photodetector Based on Interfacial Trap-Controlled Charge Injection. Nat Nanotechnol 7(12):798–802. https://doi.org/10.1038/nnano.2012.187 18. Daanoune M, Clerc R, Flament B, Hirsch L (2020) Physics of Trap Assisted Photomultiplication in Vertical Organic Photoresistors. J Appl Phys 127(5):055502. https://doi.org/10.1063/1. 5126338 19. Siegmund B, Mischok A, Benduhn J, Zeika O, Ullbrich S, Nehm F, Böhm M, Spoltore D, Fröb H, Körner C, Leo K, Vandewal K (2017) Organic Narrowband Near-Infrared Photodetectors Pased on Intermolecular Charge-Transfer Absorption. Nat Commun 8:15421. https://doi.org/ 10.1038/ncomms15421

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20. Fuentes-Hernandez C, Chou W-F, Khan TM, Diniz L, Lukens J, Larrain FA, Rodriguez-Toro VA, Kippelen B (2020) Large-area low-noise flexible organic photodiodes for detecting faint visible light. Science 370(6517):698–701. https://doi.org/10.1126/science.aba2624 21. Lee Y, Oh JY, Xu W, Kim O, Kim TR, Kang J, Kim Y, Son D, Tok JB-H, Park MJ et al. (2018) Stretchable organic optoelectronic sensorimotor synapse. Sci Adv 4(11):EAAT7387. https:// doi.org/10.1126/sciadv.aat7387 22. Chow PCY, Someya T (2020) Organic photodetectors for next-generation wearable electronics. Adv Mater 32(15):1902045. https://doi.org/10.1002/adma.20190204

Appendix

Impedance Spectroscopy in Organic Blends

Using the method introduced by Walter et al. [1] to characterize trap states organic devices is debated in literature, especially when dealing with low mobility materials or devices where energy barriers are present. As both conditions apply for our devices, we exemplarily compare different devices and analyze the effects on the trap characterization to ensure that the results discussed within Chap. 5 can be accurately estimated. In order to do that, we analyze devices comprising different thicknesses and under different biasing conditions. In Fig. A.1, data for devices with different active layer thicknesses is shown. The trap density is not expected to vary with thickness. Indeed, from 50 to 150 nm, Nt remains constant. As mentioned above, the attempt-to-scape frequency (ν0 ) is obtained by overlapping Nt measured at different temperatures. For 150 nm, in order to achieve that, ν0 has to be set to a lower value. As pointed out by different research groups, thicker devices [2] and low mobility materials [3] lead to a wrong estimation of ν0 . This further explains why using Eq. 4.15 as a direct estimation of the recombination rate is not possible as ν0 can be underestimated. Therefore, the values of ν0 must be taken only as an approximation in our study, representing a limitation of the method. Also, E t can be slightly affected depending on the mobility of the blend. The results shown in Fig. A.1 were measured in devices fabricated in the same batch, but in a different batch than that of the samples presented in the previous sections, explaining the small deviations in the absolute amount of traps. Another important aspect when applying this method in devices is the presence of energy barriers, as they can produce the same signature in the capacitance spectra as those produced by traps. As argued by Siebentritt et al., the occupancy of trap states is governed by the crossing of the Fermi level with the trap level, therefore, any trap signature should disappear at high enough forward bias, since the Fermi level will no longer cross the trap level [4]. Following the same reasoning, a minority carrier trap signature should also disappear at high enough reverse bias. Indeed, measuring our device at different biases we can clearly observe this effect: the step in the capacitance spectra, observed at zero bias in the range from 10 Hz to 10 kHz, disappears when either forward or reverse bias are used. From this measurement, © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Kublitski, Organic Semiconductor Devices for Light Detection, Springer Theses, https://doi.org/10.1007/978-3-030-94464-3

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Fig. A.1 Trap analysis for TPDP:C60 (13.3 mol%) at different device thicknesses | a–c Capacitance and d–e calculated trap density

Appendix: Impedance Spectroscopy in Organic Blends

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Fig. A.2 Capacitance spectra at different biases for a device based on TPDP:C60 (13.3 mol%) | Note that the reconstruction of the trap density uses the derivative of the capacitance spectra. This implies that all spectra at bias below −0.3 V, as well as above 0.3 V, would lead to the same trap density, which tends to zero, given their rather constant shape

shown in Fig. A.2, we can infer that the step in the capacitance arises from traps and, more importantly, that these states are minority carrier traps [4].

References 1. Walter T, Herberholz R, Müller C, Schock HW (1996) Determination of defect distributions from admittance measurements and application to Cu(In,Ga)Se2 based heterojunctions. J Appl Phys 80(8):4411–4420. https://doi.org/10.1063/1.363401 2. Xu L, Wang J, Hsu JW (2016) Transport effects on capacitance-frequency analysis for defect characterization in organic photovoltaic devices. Phys Rev Appl 6(6):064020. https://doi.org/ 10.1103/PhysRevApplied.6.064020 3. Wang S, Kaienburg P, Klingebiel B, Schillings D, Kirchartz T (2018) Understanding thermal admittance spectroscopy in low-mobility semiconductors. J Phys Chem C 122(18):9795–9803. https://doi.org/10.1021/acs.jpcc.8b01921 4. Werner F, Babbe F, Elanzeery H, Siebentritt S (2019) Can we see defects in capacitance measurements of thin-film solar cells? Prog Photovolt: Res Appl 27(11):1045–1058. https://doi.org/ 10.1002/pip.3196

Curriculum Vitae

Jonas Kublitski 29 years old, Brazilian

Professional Experience 29/07/2021–present Postdoc fellow, Technische Universität Dresden, Dresden—Germany Physics Description: Research on organic optoelectronic devices, such as photodetectors and solar cells, and fundamental properties of organic semiconductors 01/06/2015–31/12/2015 Lecturer in Transport Phenomena, UNIFACEAR, Araucária—Brazil, Description: Lecturer in Transport Phenomena for different Engineering courses. 01/02/2013–10/12/2013 Physics teacher, Paraná Department of Education and Sport, Ponta Grossa—Brazil, Description: Physics teacher of 1st to 3rd grade of public high schools. 01/03/2013–01/02/2014 Tutor, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)/PIBID—Teaching Initiation Program, Ponta Grossa—Brazil, Description: Within this governmental project, Physics

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Kublitski, Organic Semiconductor Devices for Light Detection, Springer Theses, https://doi.org/10.1007/978-3-030-94464-3

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teaching bachelor students visit schools in peripheral region of the city to promote science/astronomy. My role consisted of giving tutorials on concepts such as stars, planets and constellations with the aid of a mobile planetary

Academic Projects ◦ ◦ ◦ ◦ ◦ ◦ ◦

Hole transport in low-donor content bulk heterojunctions Photomultiplication in organic devices. Investigation of dark current of Organic Photodetectors. Thermoelectricity in Poly (2,2’—Bithiophene). Seebeck coefficient measurements. Electrodeposition of Multiwalled Carbon Nanotubes (MWCNT). Electrochemical deposition of Sulfonated Polyaniline (SPAN).

Academic Education with Degree 01/10/2016–28/07/2021 Ph.D., Technische Universität Dresden, Dresden— Germany, Physics. Organic Semiconductor Devices for Light Detection 01/02/2014–01/02/2016 Master, Federal University of Paraná, Curitiba—Brazil, Physics. Organic photovoltaic and Thermoelectric devices based on poly (2, 2’–bithiophene) 01/02/2010–01/02/2014 Bachelor, State University of Ponta Grossa, Ponta Grossa—Brazil, Physics Teaching. Didactic Planning as Organization of the TeachingLearning Environment in Physics Teaching.

Non-academic Education 01/04/2016–30/10/2016 German language course, Carl Duisberg Centren, Berlin—Germany.

Curriculum Vitae

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Publications 1 Y. Wang, J. Kublitski, S. Xing, F. Dollinger, D. Spoltore, J. Benduhn, K. Leo “Narrowband Organic Photodetectors—Towards Miniaturized Spectrometers on a Single Chip”, vol. xx, p.xx, Materials Horizon, 2021. 2 S. Xing, J. Kublitski, H. Kleemann, J. Benduhn and K. Leo, “Vacuum-Processed Photomultiplication-Type Organic Photodetectors with High Detectivity Stability under Reverse Bias”, Advanced Science, 2021—accepted. 3 J. Kublitski, A. Fischer, S. Xing, J. Benduhn, D. Spoltore, K. Vandewal, K. Leo, “Enhancing sub-bandgap external quantum efficiency by photomultiplication for narrowband organic near-infrared photodetectors”, Nature Communications, vol. 12, p. 4259, 2021. 4 S. Xing, V. C. Nikolis, J. Kublitski, E. Guo, X. Jia, Y. Wang, D. Spoltore, K. Vandewal, H. Kleemann, J. Benduhn and K. Leo, “Miniaturized VIS-NIR Spectrometers based on Narrowband and Tunable Transmission Cavity Organic Photodetectors with Ultrahigh Detectivity above 1014 Jones”, Advanced Materials, p. 2102967, 2021. 5 K. Ortstein, S. Hutsch, M. Hambsch, K. Tvingstedt, B. Wegner, J. Benduhn, J. Kublitski, M. Schwarze, S. Schellhammer, F. Talnack, A. Vogt, P. Bäuerle, N. Koch, S. C. B. Mannsfeld, H. Kleemann, F. Ortmann, and K. Leo, “Band gap engineering in blended organic semiconductor films based on dielectric interactions”, Nature Materials, vol. 20, p. 1407, 2021. 6 M. Pranav, J. Benduhn, M. Nyman, S. M. Hosseini, J. Kublitski, D. Neher, Karl Leo, D. Spoltore, “Enhanced Charge Selectivity via Anodic-C60 Layer Reduces Non-Radiative Losses in Organic Solar Cells”, ACS Applied Materials & Interfaces, vol. 13, p. 12603, 2021. 7 J. Kublitski, A. Hofacker, B. K. Boroujeni, J. Benduhn, V. C. Nikolis, C. Kaiser, D. Spoltore, H. Kleemann, A. Fischer, F. Ellinger, K. Vandewal, and K. Leo, “Reverse Dark Current in Organic Photodetectors and the Major Role of Traps as Source of Noise”, Nature Communications, vol. 12, p. 551, 2021. 8 Y. Wang, B. Siegmund, Z. Tang, Z. Ma, J. Kublitski, S. Xing, V. C. Nikolis, S. Ullbrich, Y. Li, J. Benduhn, D. Spoltore, K. Vandewal, and K. Leo., “Stacked Dual-Wavelength Near-Infrared Organic Photodetectors”, Advanced Optical Materials, p. 2001784, 2020. 9 V. C. Nikolis, Y. Dong, J. Kublitski, J. Benduhn, X. Zheng, C. Huang, A. C. Yüzer, M. Ince, D. Spoltore, J. R. Durrant, A. A. Bakulin, and K. Vandewal, “Field effect versus driving force: Charge generation in small-molecule organic solar cells”, Advanced Energy Materials, p. 2002124, 2020. 10 S. Gielen, C. Kaiser, F. Verstraeten, J. Kublitski, J. Benduhn, D. Spoltore, P. Verstappen, W. Maes, P. Meredith, A. Armin, and K. Vandewal, “Intrinsic detectivity limits of organic near-infrared photodetectors”, Advanced Materials, p. 2003818, 2020. 11 Y. Dong, V. C. Nikolis, F. Talnack, Y.-C. Chin, J. Benduhn, G. Londi, J. Kublitski, X. Zheng, S. C. Mannsfeld, D. Spoltore, L. Muccioli, J. Li, X. Blase, D.

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Beljonne, J. S. Kim, A. A. Bakulin, G. D’Avino, J. R. Durrant, and K. Vandewal, “Orientation Dependent Molecular Electrostatics Drives Efficient Charge Generation in Homojunction Organic Solar Cells”, Nature Communications, vol. 11, p. 4617, 2020. Y. Zhong, G. J. Moore, P. Krauspe, B. Xiao, F. Günther, J. Kublitski, R. Shivhare, J. Benduhn, E. BarOr, S. Mukherjee, K. Yallum, J. Réhault, C. Mannsfeld Stefan, D. Neher, L. J. Richter, D. M. DeLongchamp, F. Ortmann, K. Vandewal, E. Zhou, and N. Banerji, “Sub-Picosecond Charge-Transfer at Near-Zero Driving Force in Polymer:Non-Fullerene Acceptor Blends and Bilayers”, Nature Communications, vol. 11, p. 833, 2020. C. Kaiser, K. S. Schellhammer, J. Benduhn, B. Siegmund, M. Tropiano, J. Kublitski, D. Spoltore, M. Panhans, O. Zeika, F. Ortmann, P. Meredith, A. Armin, and K. Vandewal, “Manipulating the Charge Transfer Absorption for Narrowband Light Detection in the Near-Infrared”, Chemistry of Materials, vol. 31, p. 9325, 2019. V. C. Nikolis, A. Mischok, B. Siegmund, J. Kublitski, X. Jia, J. Benduhn, U. Hörmann, D. Neher, M. C. Gather, D. Spoltore, and K. Vandewal, “Strong LightMatter Coupling for Reduced Photon Energy Losses in Organic Photovoltaics”, Nature Communications, vol. 10, p. 3706, 2019. M. Schwarze, K. S. Schellhammer, K. Ortstein, J. Benduhn, C. Gaul, A. Hinderhofer, L. P. Toro, R. Scholz, J. Kublitski, S. Roland, M. Lau, C. Poelking, D. Andrienko, G. Cuniberti, F. Schreiber, D. Neher, K. Vandewal, F. Ortmann, and K. Leo, “Impact of Molecular Quadrupole Moments on the Energy Levels at Organic Heterojunctions”, Nature Communications, vol. 10, p. 2466, 2019. J. Kublitski, A. C. Tavares, J. P. Serbena, Y. Liu, B. Hu, I. A. Hümmelgen, “Electrode material dependent p-or n-like thermoelectric behavior of single electrochemically synthesized poly (2, 2’-bithiophene) layer-application to thin film thermoelectric generator”, Journal of Solid State Electrochemistry, vol. 20, p. 2191, 2016. F. C. N. Borges, W. R. Oliveira, J. Kublitski, “Mechanical, structural and tribological properties of superaustenitic stainless steel submitted at solution heat treatment”, vol. 20, Matéria, 2015.

Attended Conferences 1 2021 MRS Spring Virtual Meeting—USA, April 17th to 23th, 2021—Oral presentation. 2 DPG 2020 Spring Meeting of the Condensed Matter (Dresden—Germany, March 15th to 20th, 2020.)—Participation. 3 2019 MRS Spring Meeting (Phoenix—USA, April 19th to 26th, 2018)—Oral presentation

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4 International Symposium on Flexible Organic Electronics (Thessaloniki—Greece, July 2nd to 5th, 2018)—Oral presentation. Young research award: Best oral presentation. 5 DPG 2017 Spring Meeting of the Condensed Matter (Dresden—Germany, March 19th to 24th, 2017.)—Participation. 6 XXXVIII National Meeting on Condensed Matter Physics (Foz do Iguaçu— Brazil, May 24th a 28th, 2015.)—Poster presentation. 7 XIII Brazilian MRS meeting (João Pessoa—Brazil, September 24th a 2nd, 2014.)—Poster presentation.

Prizes and Awards 1 Young research award: Best oral presentation—International Symposium on Flexible Organic Electronics, Thessaloniki—Greece 2 Meiss Prize: Most impressive publication of 2020—Dresden Integrated Center for Applied Physics and Photonic Materials, Dresden—Germany 3 Thesis publication in the Springer Theses collection—An international series of most outstanding thesis

Funding Received So Far 01/10/2020–31/12/2020 TU-Dresden—Ph.D. completion scholarship. 3-months allowance for Ph.D. students to complete their Ph.D. funded by the Technische Universität Dresden Graduate Academy. Awarded upon project analysis. 01/04/2016–30/09/2020 DAAD—Ph.D. scholarship. Monthly allowance for Ph.D. students funded by the German Academic Exchange Service. Awarded upon project analysis. In 2016, 50 scholarships were offered for the entire Brazil, including all research areas. The scholarship also supported the language curse described in the “Non-academic Education” section. 01/02/2014–01/02/2016 CAPES/Master scholarship. Monthly allowance for master students funded by the Brazilian government. Awarded according to selection criteria of the master program. 01/03/2013–01/02/2014 CAPES/PIBID scholarship—Teaching Initiation Program. Monthly allowance for bachelor students of physics teaching to promote educational projects in public high-schools.

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Awarded by the Brazilian government upon project analysis.

Supervising and Mentoring Activities 01/03/2021–present Co-supervisor of Master thesis. Co-supervison of Louis Conrad Winkler, master student at the Technische Universität Dresden. Topic: Development and characterization of narrowband near-infrared photomultiplication-type organic photodetectors. 01/06/2018–30/12/2018 Mentoring of Physics students. The activity consisted of assisting undergrad students of Physics at the Technische Universität Dresden on performing experiments, data analysis and discussion, as well as evaluation of the students.

Languages Portuguese English German Spanish

Native C2 C1 B2

Knowledge Area Programing Languages Python Experimental expertise Fabrication and characterization of optoelectronic devices, profilometry and MEV images. Optical measurements and electrochemical deposition of Polymers by oxidation of monomers in Galvanostatic and Potentiostatic mode. Use of thermal evaporation in high vacuum systems and Spin Coater equipment. Sensitive EQE measurements.

Referees Prof. Dr. Karl Leo, TU Dresden, Dresden, Germany. Institut für Angewandte Physik (IAP)

Curriculum Vitae

Chair for Optoelectronics [email protected] +49 351 463-34389 Prof. Dr. Ing. Koen Vandewal, Hasselt University, Hasselt, Belgium. Instituut voor Materiaalonderzoek (IMO) Full Professor [email protected] +3211268879

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