Essentials of Semiconductor Device Physics

An introductory semiconductor device physics textbook that is accessible to readers without a background in statistical physics

I wish this book had been available when I needed to make a Semiconductor class myself a few years ago [...] A very nice aspect is that some concepts (e.g. density of states) are explained in a way that I have not seen elsewhere. These types of unconventional approaches are very valuable for a teacher. (Bjorn Maes, University of Mons, Belgium)

[...] the author offers an accessible description of statistical analysis and adopts it to explain the core properties of semiconductors. [...] [He] uses interesting metaphors and analogies to exemplify some of the most difficult notions, in an innovative and engaging way. (Andrea di Falco, University of St. Andrews, UK)

The subject of this book is the physics of semiconductor devices, which is an important topic in engineering and physics because it forms the background for electronic and optoelectronic devices, including solar cells. The author aims to provide students and teachers with a concise text that focuses on semiconductor devices and covers the necessary background in statistical physics.

This text introduces the key prerequisite knowledge in a simple, clear, and friendly manner. It distills the key concepts of semiconductor devices down to their essentials, enabling students to master this key subject in engineering, physics, and materials. The subject matter treated in this book is directly connected to the physics of p-n junctions and solar cells, which has become a topic of intense interest in the last decade. Sample topics covered within the text include:

• Chemical potential, Fermi level, Fermi-Dirac distribution, drift current and diffusion current.
• The physics of semiconductors, band theory and intuitive derivations of the concentration of charge carriers.
• The p-n junction, with qualitative analysis preceding the mathematical descriptions.
• A derivation of the current vs voltage relation in p-n junctions (Shockley equation).
• Important applications of p-n junctions, including solar cells
• The two main types of transistors: Bipolar Junction Transistors (BJT) and Metal Oxide Semiconductor Field Effect Transistors (MOSFET)

For students and instructors, it may be used as a primary textbook for an introductory semiconductor device physics course and is suitable for a course of approximately 30-50 hours. Scientists studying and researching semiconductor devices in general, and solar cells in particular, will also benefit from the clear and intuitive explanations found in this book.

Emiliano R. Martins obtained his PhD in 2014 from the University of St. Andrews (UK) in the field of photonics, which deals with the interaction between light and matter in semiconductor devices. His research field involves solar cells and other optoelectronic devices and he has been teaching a course on semiconductor device physics since 2016 at the University of São Paulo in Brazil. He has written unpublished books for other undergraduate disciplines that he teaches, including signals and systems and digital signal processing.

Preface 2

About the Author

Acknowledgement

About the Companion Website

1– Concepts of Statistical Physics 6

1.1 Introduction 6

1.2 Thermal Equilibrium 20

1.3 Partition function - Part I 27

1.4 Diffusive equilibrium and the chemical potential 34

1.5 The partition function, Part II 47

1.6 Example of application: energy and number of elements of a system 50

1.7 The Fermi-Dirac distribution 56

1.8 Analogy between the systems “box” and “coins” 72

1.9 Concentration of electrons and Fermi level 73

1.10 Transport 74

1.11 Relationship between current and concentration of particles (continuity equation) 84

1.12 Suggestions for further reading 92

1.13 Exercises 93

2 – Semiconductors 98

2.1 Band Theory 98

2.2 Electrons and holes 106

2.3 Concentration of free electrons 108

2.4 Density of states 116

2.5 Concentration of holes and Fermi level 125

2.6 Extrinsic semiconductors (doping) 129

2. 7 Exercises 137

3 – Introduction to semiconductor devices: the p-n junction 140

3.1 p-n junction in thermodynamical equilibrium – qualitative description 140

3.2 p-n junction in thermodynamical equilibrium – quantitative description 146

3.3 Systems outside thermodynamical equilibrium: the quasi-Fermi levels. 158

3.4 Qualitative description of the relationship between current and voltage in a p-n junction. 161

3.5 The current vs voltage relationship in a p-n junction (Shockely’s equation) 170

3.6 Suggestions for further reading 183

3.7 Exercises 183

4 – Photovoltaic devices (mainly solar cells) 186

4.1 Solar cells and photodetectors 186

4.2 Physical principles 186

4.3 The equivalent circuit 188

4.4 The I x V curve and the fill-factor 191

4.5 Efficiency of solar cells and the theoretical limit 195

4.6 Connections of solar cells 199

4.7 Suggestions for further reading 200

4.8 Exercises 200

5 - Transistors 202

5.1 The Bipolar Junction Transistor (BJT) 202

5.1.1 Physical principles of the BJT 202

5.1.2 The β parameter and the relationship between emitter, collector and base currents 207

5.1.3 Relationship between IC and VCE and the Early effect 209

5.1.4 The BJT as an amplifier 210

5.2 The MOSFET 215

5.2.1 Physical principles 215

5.2.3 Examples of applications of MOSFETS: logic inverters and logic gates 218

5.3 Suggestions for further reading 222

5.4 Exercises 222

Appendix : geometrical interpretation of the chemical potential and free energy 225

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