Amorphous Silicon Thin-Film Transistors: Operation, Modelling and Applications 3031247922, 9783031247927

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Synthesis Lectures on Engineering, Science, and Technology

Zoubeida Hafdi

Amorphous Silicon Thin-Film Transistors Operation, Modelling and Applications

Synthesis Lectures on Engineering, Science, and Technology

The focus of this series is general topics, and applications about, and for, engineers and scientists on a wide array of applications, methods and advances. Most titles cover subjects such as professional development, education, and study skills, as well as basic introductory undergraduate material and other topics appropriate for a broader and less technical audience.

Zoubeida Hafdi

Amorphous Silicon Thin-Film Transistors Operation, Modelling and Applications

Zoubeida Hafdi Département du Tronc Commun en Sciences et Technologie, Faculty of Technology Batna 2 University Batna, Algeria

ISSN 2690-0300 ISSN 2690-0327 (electronic) Synthesis Lectures on Engineering, Science, and Technology ISBN 978-3-031-24792-7 ISBN 978-3-031-24793-4 (eBook) https://doi.org/10.1007/978-3-031-24793-4 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To the memory of my Parents To Noureddine Nabti; inspiring husband, good friend and source of perpetual patience

Preface

Amorphous silicon material has imposed itself as a basic part of a mature technology for several years to date. Amorphous silicon technology facilitated to the highest degree the control of amorphous silicon-based thin-film transistor electronic characteristics. This improvement is due to the fabrication reproducibility and uniformity over large area of amorphous silicon components and display backplanes which acted in favor of the expanding of this technology. This is also owed to the low-cost fabrication and the scalability to larger-sized substrates. At the device level and in parallel to manufacturing issues, models are to be developed and implementation means are to be thought in such a way that the transistor can overcome the challenges associated to the new and nontraditional future applications, namely those related to flexible electronics. The book fits into this context. It is the essence of several years of work on thinfilm transistors based on amorphous silicon from the material level to the circuit one. Effort was focused on basics for physical fundamentals, modeling and simulations as a bridge to practical applications that may extend beyond active matrices and the associated peripheral circuits. It tries, as far as possible, to help rapidly building ideas from targeted concepts by an emphasis on acquisition of basic, general and technical knowledge. It also recalls modeling and simulation as important concerns for integrated circuit design. It exposes at what extent simulation may reveal the implemented model accuracy and its aptitude to predict devices and circuits behavior before the manufacturing phase. Besides, some optimization design practices and strategies to build reliable circuits are highlighted. The book is at the same time introductory, undergraduate, graduate and continuing education textbook since it provides information at many levels beginning by basics and fundamentals at the material level to advanced information for device and circuit design. It has the objective to give the basic principles that the reader needs to know about amorphous silicon material and amorphous silicon-based transistors. It is appropriate for undergraduate and graduate students, circuit simulators developers, integrated circuits designers and manufacturers, as well as everyone engaged in work on large area integrated circuit technologies, photovoltaics and low-cost applications and would like to have introductory concepts in amorphous silicon technology.

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Preface

The required background falls under the theme of component and integrated circuit physics, design and fabrication. This involves knowledge on advances and design of application-specific circuits, semiconductor technology and characterization, and design aids for the control of the design flows for amorphous silicon-based circuit implementation. Along with principles, the proposed book is thought to be a vehicle of simplicity as it enhances simple and expressive modeling of a-Si:H TFTs. Effort is made to make the content clear and simple enough to be understood by the reader. Model fundamentals are first detailed to allow accurate and fast device simulation and characterization, and then, some basic a-Si:H TFT applications for digital and high-voltage generation circuit design are covered. Constantine, Algeria 2022

Zoubeida Hafdi

Acknowledgements

The author is very thankful to the following organizations for their permission obtained for material she has previously published: Organization

Journals, Proceedings…

Elsevier B.V. Open access

Physics Procedia

IDOSI Publications

World Applied Sciences Journal

Institute of Electrical and Electronics Engineers (IEEE)

IEEE Proceedings

The Japan Society of Applied Physics

Japanese Journal of Applied Physics

The Society of Digital Information and Wireless Communications (SDIWC)

International Conference on Digital Information: Processing, Electronics, and Wireless Communications, Proc.

The author is also grateful to Doctor Nelva Nely Almanza Ortega from the Tecnológico Nacional de México/IT de Tlalnepantla for her constant support. Constantine, Algeria 2022

Zoubeida Hafdi [email protected]

ix

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 8

2 Hydrogenated Amorphous Silicon Thin-Film Transistors . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Amorphous Silicon and a-Si:H TFTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Silicon Nitride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Thin-Film Transistor Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Thin-Film Transistor Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 a-Si:H TFTs Performance Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 a-Si:H TFT Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.1 Subthreshold or Weak Accumulation Regime . . . . . . . . . . . . . . . . . 2.7.2 Above Threshold or High Accumulation Regime . . . . . . . . . . . . . 2.7.3 Transitional Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.4 Crystalline-Like Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11 11 12 14 14 15 16 17 18 18 18 19 19

3 Amorphous Silicon-Based MIS Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Density of States in the Amorphous Silicon . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Band Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Charge Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Density of Free Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Charge Density in the Deep Localized States . . . . . . . . . . . . . . . . . 3.4.3 Charge Density in Tail Localized States . . . . . . . . . . . . . . . . . . . . . 3.5 MIS Structure DC Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Assumptions and Calculation Principle . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Poisson Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3 Potential Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23 23 24 25 26 26 26 28 29 29 29 30

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3.6

Quantitative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Bulk Charge Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Electrostatic Field and Electrostatic Potential . . . . . . . . . . . . . . . . . 3.6.3 Induced Charge in the Semiconductor . . . . . . . . . . . . . . . . . . . . . . . 3.6.4 Localized Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.5 Free Electron Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Profiles Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.1 Potential Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.2 Charge Densities Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31 31 31 31 32 32 32 32 35 36 37

4 Hydrogenated Amorphous Silicon Thin-Film Transistor: A DC Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Model Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Drain Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 General Expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Potential Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Weak Accumulation Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Poisson Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Potential Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Conduction Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 Drain Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.5 Simplified Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Strong Accumulation Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Poisson Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Potential Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 Conduction Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.4 Drain Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.5 Simplified Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Field Effect Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Mobility Ratio in Weak Accumulation . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Mobility Ratio in Strong Accumulation . . . . . . . . . . . . . . . . . . . . . . 4.7 Blocking State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Model Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.1 Weak Accumulation (V g < V t ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.2 Strong Accumulation (V g ≥ V t ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10 Current–Voltage Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.11 Threshold Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39 39 40 41 41 42 43 43 44 45 46 47 48 49 50 51 51 52 54 54 54 55 55 56 56 57 57 58

Contents

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4.12 On-to-Off Current Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.13 Field Effect Mobility-to-Band Mobility Ratio . . . . . . . . . . . . . . . . . . . . . . . 4.14 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59 61 63 64

5 Interface States in Amorphous Silicon Thin-Film Transistors . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Current–Voltage Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Lower Threshold Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Upper Threshold Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Field Effect Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Subthreshold Swing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Surface States Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67 67 69 71 72 73 74 74 77 78

6 Hydrogenated Amorphous Silicon Thin-Film Transistor: A Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Some Dynamic Model Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Capacitance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Calculation of the Charges in Source and Drain Sides . . . . . . . . . 6.3.2 Source Side Charge Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Drain Side Charge Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.4 Total Charge Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.5 Intrinsic Gate-to-Source Capacitance Calculation . . . . . . . . . . . . . 6.3.6 Intrinsic Gate-to-Drain Capacitance Calculation . . . . . . . . . . . . . . 6.4 Total Capacitances Analysis for Transistor Operational Regimes . . . . . . 6.4.1 Blocking State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Below Threshold Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3 Above Threshold Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Model Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79 79 80 86 86 87 88 88 88 89 89 89 90 90 91 94 95

7 Amorphous Silicon Thin-Film Transistors for Digital Circuits . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 a-Si-based Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 a-Si-based Logic Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 a-Si:H TFT Model Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Design Considerations for a-Si Logic Gates . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97 97 99 100 101 102 105 109

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8 Amorphous Silicon Thin-Film Transistors for Charge Pump Circuits . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 The Dickson Charge Pump: Some Considerations . . . . . . . . . . . . . . . . . . . 8.3 a-Si:H TFT-Based Charge Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Charge Pump Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Transient Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.2 Steady-State Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

111 111 114 115 117 117 117 124 125

Abbreviations

3D AM AMOLED a-Si a-Si:H a-Si:H TFT CAD CMOS CP CVD DC DOS FET IC IoT LCD LTspice MIS MOS MOSFET NMOS PECVD PTL rf SNM TFT

Three dimensions Active matrix Active matrix organic light emitting diode Amorphous silicon Hydrogenated amorphous silicon Hydrogenated amorphous silicon thin film transistor Computer-aided design Complementary MOS Charge pump Chemical vapor deposition Direct current Density of states Field effect transistor Integrated circuit Internet of Things Liquid crystal display Linear technology simulation program with IC emphasis Metal–insulator–semiconductor Metal–oxide–semiconductor Metal–oxide–semiconductor FET n-type MOS transistor Plasma-enhanced chemical vapor deposition Pass transistor logic Radio frequency Static noise margin Thin-film transistor

xv

Symbols

A a Cgd Cgdi Cgdo Cgs Cgsi Cgso Ci Css q d Dss Ec EF Ev fd f(E) ft g gd gd (E) gm gt gt (E) I0d I0t I(0, t) I(L, t) I(y, t)

Constant Unitless factor, a-Si:H TFT applied voltages dependent Gate-to-drain capacitance Intrinsic gate-to-drain capacitance Overlap gate-to-drain capacitance Gate-to-source capacitance Intrinsic gate-to-source capacitance Overlap gate-to-source capacitance Insulator capacitance per unit area Surface states capacitance Elementary electron charge Gate insulator thickness Density of interface states Conduction band edge Fermi level energy Valance band edge Constant Fermi–Dirac carrier distribution function a-Si:H TFT cut-off frequency Degenerescence factor of the acceptor-like states Deep states density at Ec Deep states energy distribution a-Si:H TFT transconductance Tail states density at Ec Tail states energy distribution Constant Constant I(y, t) at the source Transient drain current at the drain side Current flowing from the drain to source at a location y xvii

xviii

Id Idl Ids (t) Idt Ist k K L Lod Los Nc Nf Nlocd Nloct Qd (t) Qf Qg (t) Qlocd Qloct Qs (t) Qsc Qss Rl S T Td tt Tt V(y) Vdd Vfb Vg Vgd Vgs V1d V1t V2d V2t Vi Vout Vs

Symbols

Drain current Leakage drain current Transient drain current Drain transient current Source transient current Boltzmann’s constant Constant a-Si channel length Drain side overlap space Source side overlap space a-Si effective density of states Free carrier density Density of the deep states Density of the tail states Transient drain charge Insulator fixed interface charge per unit area Transient gate charge Charge localized on deep states Charge localized on tail states Transient source charge a-Si charge per unit area Surface states charge per unit area Leakage sheet resistance Subthreshold swing Absolute temperature Deep states characteristic temperature Carrier transit time Tail states characteristic temperature a-Si channel voltage at a location y Bias voltage Flat-band voltage MIS external applied voltage Gate-to-drain voltage Gate-to-source voltage Constant Constant Constant Constant Insulator voltage drop Output voltage Source voltage taken as reference

Symbols

Vsc Vsc (0, t) Vsc (L, t) Vt X W ε εi ϕm χsc εSiN μfet μn xeff ξ ξs ξt ρ σ χs ψ(x) ψs ψs0 ψsd ψst

xix

a-Si channel voltage Channel voltage in the source side Channel voltage in the drain side Threshold voltage Constant Channel width a-Si:H dielectric constant Insulator dielectric constant Metal work function a-Si:H electron affinity Silicon nitride dielectric constant Field effect mobility Band mobility a-Si channel effective depth Electric field Surface electric field Tail states electric field Space charge density Conductivity a-Si electronic affinity Electrostatic potential at a location x Surface potential Interface band bending in the absence of voltage Deep states surface potential Tail states surface potential

1

Introduction

The idea that one-day amorphous silicon (a-Si) will be used for large-scale manufacturing of complex integrated circuits (ICs) was too ambitious to be realized because of its immaturity due to the degraded performance of the material. Remarkable progress has been made since 1975, when Spear, Lecomber and Madan of the University of Dundee in Scotland [1] showed that the amorphous silicon conductivity could be controlled. It turned out at that time that the issue was familiar to only a few physicists in the scientific community who had not yet realized the importance of this emerging technology. Historically, amorphous silicon was used in photovoltaic components. In 1976, Carlon and Wronski manufactured a p-i-n hydrogenated amorphous silicon (a-Si:H) solar cell on a glass substrate [1]. The active area of the cell was 5.10–3 cm2 , and its conversion efficiency was 2.4%. Enormous progress was made since then, and values comprised between 5.3 and 6.3% have been reported [2, 3]. In 1979, Lecomber, Spear and Gaith manufactured the first thin-film transistor based on hydrogenated amorphous silicon (a-Si:H TFT). These authors suggested the component as an electronic switch for addressing active matrices (AM) in liquid crystal display (LCD) panels. Many years later, several companies, most of them were Japanese, developed these kinds of transistors for color flat screens, and many other applications have been deployed especially in the electronics domain [4–10]. As indicated by its name, amorphous silicon is disordered in nature. It has an amorphous network which, although has a local order, is constituted by atoms that form a continuous network in a random manner where the bonds are dangling and not connected, without extended range order. These dangling bonds cause a poor electrical behavior of the material, namely the conductivity, though optical properties and absorption are also affected. Hydrogenated amorphous silicon is an improved version of amorphous silicon where atoms of hydrogen are intentionally incorporated for passivation and consequently higher electronic performance. The density of defects is effectively reduced, and conductivity is improved so that a-Si:H is now acknowledged as a low-cost material in the

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 Z. Hafdi, Amorphous Silicon Thin-Film Transistors, Synthesis Lectures on Engineering, Science, and Technology, https://doi.org/10.1007/978-3-031-24793-4_1

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1 Introduction

industry for several applications. Despite this improvement, defects still remain and introduce electronics states in its gap. These states act as trapping and/or recombination centers that impact the optical and the electrical properties of the material. As will be expounded later, the density of states (DOS) influences profoundly the properties of the amorphous silicon leading to an unusual behavior of the devices manufactured with this material. Comparing to crystalline silicon-based electronic devices, electronic properties of those based on amorphous silicon are not suitable for applications requiring high functioning speeds. a-Si:H TFTs are thus acquiring more importance in applications where strict frequency specificities are not critical. They are now established as forming a part of a low-cost technology for a significant domain of applications in the microelectronics domain especially photovoltaics, large area electronics, sensors and currently flexible electronics. In flat panel displays, these transistors are particularly suitable in the design of switching elements in the matrices forming these panels because of their low off-state current. The applications extend from digital imaging applications [11], to active matrix liquid crystal displays [4] and active matrix organic light emitting diodes (AMOLEDs) [12], a-Si:H gate drivers for LCD applications [13] and X-ray detection [14]. Several approaches have been used to understand the amorphous silicon technology. Some of them have investigated the amorphous silicon at the material level [15], while others focused on the fabrication process of amorphous silicon layers by optimizing their characteristics. The process parameters cover reactive gases, power, temperature, dangling bonds, hydrogen content, photosensitivity or mechanical and electrical stress. Other investigations have targeted the hydrogenated amorphous silicon at the level of the device for thin-film transistor fabrication either as a sequence of deposited layers, or as a model to be implemented in a circuit simulator. Several studies have pointed out the different structures susceptible to be manufactured and the issues that give better reliability and yield [16, 17]. Owing to thin-film technology improvement over the past years [18–21], thin-film transistors have known a great development in terms of electronic applications. Several enhancements were made according to the fact that deposited materials by thin-film technology processes and techniques showed a large controllability of their conductance. This is particularly important since almost every parameter was controlled so that the performance of the obtained devices, namely transistors, is refined over time. The parameters include not only material uniformity and instabilities but also the gate insulator and interface effects as well. Stability issues in thin-film transistors concern actually on-current, off-current, commonly called leakage, and carrier mobility. The later defines the operation speed of the circuits fabricated with these TFTs. The hydrogenated a-Si material offers a viable technological alternative for improved imaging of optical signals because it has a high optical absorption, a low temperature deposition ( V t , • off state regime: V gs < V fb . It is necessary to recall that V gs , V gd , V fb and V t are the gate-to source, gate-to-drain, flat-band and threshold voltages, respectively. Besides the fact that this structure is simple to manufacture, the choice of the structure is based on two specifics: the first one is the fact that the hydrogenated amorphous silicon thin-film surface is not as defective as in the bulk [2, 3], and thin-film transistors based on this structure have a higher carrier mobility and a threshold voltage lower than those in the other structures. Before we proceed with the development of the theoretical study, let us consider a number of hypotheses that are necessary for the description of the hydrogenated amorphous silicon-based transistor operation. The following assumptions are thus considered: – Only the acceptor localized states in the upper half of amorphous silicon gap are taken into account (n-channel TFT). – Only carriers in the conduction band are susceptible to participate in conduction operation. – The free carrier density follows a Boltzmann type law, that means a non-degenerated material is considered. Fig. 4.1 Structure of the a-Si:H TFT under study. Reproduced from [1]

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Drain Current

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– Localized states occupation in the amorphous silicon gap is governed by the Fermi– Dirac statistics (DC operation). – The amorphous silicon film is homogenous and of infinite thickness. – Electrons current is null in x and z directions. – In non-pinched off channel regime, the hypothesis of gradual channel holds so that: ∂2V ∂2V