PHYSICS OF SEMICONDUCTOR DEVICES Jean-Pierre Colinge Cynthia A. Colinge KLUWER ACADEMIC PUBLISHERS
PHYSICS OF SEMICONDUCTOR DEVICES
PHYSICS OF SEMICONDUCTOR DEVICES
PHYSICS OF SEMICONDUCTOR DEVICES J. P Colinge Department of electrical and Computer Engineering University of california, Davis C. A. Colinge Department of Electrical and Electronic Engineering California State University KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSToN, DORDRECHT, LONDON, MOSCO
PHYSICS OF SEMICONDUCTOR DEVICES by J. P. Colinge Department of Electrical and Computer Engineering University of California, Davis C. A. Colinge Department of Electrical and Electronic Engineering California State University KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
CONTENTS Preface I. Energy Band Theory 1. 1. Electron in a crystal 1. 1. 1. Two examples of electron behavior. L1.1. Free electron 1. 2. The particle-in-a-box approach.. 1. 1. 2. Energy bands of a crystal (intuitive approach) 6 1.3. Kronig-Penney model 1 14. Valence band and conduction band 1. 5. Parabolic band approximation 1. 1.6. Concept of a hole 20 1.1.7. Effective mass of the electron in a crystal 1.1.8. Density of states in energy bands…………,25 1. 2. Intrinsic semiconductor 1. 3. Extrinsic semiconductor. 1.3. 1. lonization of impurity atoms. 1.3.2. Electron-hole equilibrium. 1.3.3. Calculation of the Fermi Level 1.3.4. Degenerate semiconductor……… 1. 4. Alignment of Fermi levels Important Equations Problems 2. Theory of Electrical Conduction,…,…,… 2.1. Drift of electrons in an electric field 2.2. Mobility 2.3. Drift current 2.3.1. Hall effect 2,4. Diffusion current 2.5. Drift-diffusion equations 2.5.1. Einst 2.6. Transport equations 2.7. Quasi-Fermi levels 65 Important equations Problems
CONTENTS Preface 1. Energy Band Theory 1.1. Electron in a crystal 1.1.1. Two examples of electron behavior 1.1.1.1. Free electron 1.1.1.2. The particle-in-a-box approach 1.1.2. 1.1.3. 1.1.4. 1.1.5. 1.1.6. 1.1.7. 1.1.8. Energy bands of a crystal (intuitive approach) Krönig-Penney model Valence band and conduction band Parabolic band approximation Concept of a hole Effective mass of the electron in a crystal Density of states in energy bands 1.2. 1.3. Intrinsic semiconductor Extrinsic semiconductor 1.3.1. 1.3.2. 1.3.3. 1.3.4. Ionization of impurity atoms Electron-hole equilibrium Calculation of the Fermi Level Degenerate semiconductor 1.4. Alignment of Fermi levels Important Equations Problems 2. Theory of Electrical Conduction 2.1. 2.2. 2.3. Drift of electrons in an electric field Mobility Drift current 2.3.1. Hall effect 2.4. 2.5. 2.5.1. 2.6. 2.7. Diffusion current Drift-diffusion equations Einstein relationships Transport equations Quasi-Fermi levels Important Equations Problems xi 1 1 1 1 3 6 7 15 19 20 21 25 29 31 34 35 37 39 40 43 44 51 51 53 56 57 59 60 60 62 65 67 68
ontents 3. Generation/Recombination Phenomena., 31. Introduction 3.2. Direct and indirect transitions. 74 3.3. Generation/recombination centers 3.4. Excess carrier lifetime 3.5. SRH recombination 82 3.5.1. Minority carrier lifetime 3.6. Surface recombination Important Equations……………,… Problems 4. The pn Junction Diode ∴95 41. Introduction 4.2. Unbiased PN junction. 4.3. Biased PN junction... 103 44. Current-voltage characteristics 4.4 1. Derivation of the ideal diode model 107 4.4.2. Generation/recombination current 4.3. Junction breakdown....... 4.4.4. Short-base diode 118 4.5. PN junction capacitance. 4.5.1. Transition capacitance 120 4.5.2. Diffusion capacitance…… 4.5.3. Charge storage and switching time 123 4.6. Models for the PN junction 4.6. 1. Quasi-static, large-signal model 4.6.2. Small-signal, low-frequency model 4.6.3. Small-signal, high-frequency model 47. Solar cell 128 4. 8. pin diode .133 5. Metal-semiconductor contacts 5.1. Schottky diode 139 5.1.1. Energy band diagram.. 5.1.2. Extension of the depletion region 5.1.3. Schottky effect 143 5.1.4. Current-voltage characteristics 145 5.1.5. Influence of interface states 146 5.1.6. Comparison with the PN junction. 147 5.2. Ohmic contact Important Equations……… Problems 151
vi Contents 3. 3.1. 3.2. 3.3. 3.4. 3.5. 3.5.1. 3.6. 4. 4.1. 4.2. 4.3. 4.4. 4.4.1. 4.4.2. 4.4.3. 4.4.4. 4.5. 4.5.1. 4.5.2. 4.5.3. 4.6. 4.6.1. 4.6.2. 4.6.3. 4.7. 4.8. 5. 5.1. 5.1.1. 5.1.2. 5.1.3. 5.1.4. 5.1.5. 5.1.6. 5.2. Generation/Recombination Phenomena Introduction Direct and indirect transitions Generation/recombination centers Excess carrier lifetime SRH recombination Minority carrier lifetime Surface recombination Important Equations Problems The PN Junction Diode Introduction Unbiased PN junction Biased PN junction Current-voltage characteristics Derivation of the ideal diode model Generation/recombination current Junction breakdown Short-base diode PN junction capacitance Transition capacitance Diffusion capacitance Charge storage and switching time Models for the PN junction Quasi-static, large-signal model Small-signal, low-frequency model Small-signal, high-frequency model Solar cell PiN diode Important Equations Problems Metal-semiconductor contacts Schottky diode Energy band diagram Extension of the depletion region Schottky effect Current-voltage characteristics Influence of interface states Comparison with the PN junction Ohmic contact Important Equations Problems 73 73 74 77 79 82 86 87 89 89 95 95 97 103 105 107 113 116 118 120 120 121 123 125 126 126 128 128 132 133 133 139 139 139 142 143 145 146 147 149 150 151