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
Contents 6.JFET and MESFET 153 61. The JFET 153 6. 2. The MESFET Important Equations.... 163 7. The Mos Transistor 165 7.1. Introduction and basic principles……… 165 7.2. The Mos capacitor…… 170 7. 2.1. Accumulation 7.2.2. Depletion ,176 7. 2. 3. Inversion 178 73. Threshold voltage 183 7.3.1 Ideal threshold voltage. 183 7.3.2. Flat-band voltage 7.3.3. Threshold voltage. 187 7. 4. Current in the mos transistor 187 7.4.1. Influence of substrate bias on threshold voltage 192 7.4.2. Simplified model 194 7.5. Surface mobility.... 7.6. Carrier velocity saturation 199 77. Subthreshold current- Subthreshold slope………………201 7. 8. Continuous model 206 7.9. Channel length modulation 7.10. Numerical modeling of the mos transistor 210 711. Short-channel effect 213 7. 12. Hot-carrier degradation 7. 12.1. Scaling rules 216 7. 12.2. Hot electrons 218 7. 12.3. Substrate current 218 7.12.4. Gate current 219 7. 12.5. Degradation mechanism 7.13. Terminal capacitances…… 7. 14. Particular mosfet structures 224 7.14.1. Non-Volatile Memory MOSFETs 224 7. 14.2. SOI MOSFETS 228 7. 15. Advanced MOSFET concepts 7.15.1. Polysilicon depletion…… 230 7. 15.2. High-k dielectrics.. 231 7.15.3. Drain-induced barrier lowering dIBl) 231 7.154. Gate-induced drain leakage(GDL……………………232 7.15.5. Reverse short-channel effect 7.15.6. Quantization effects in the inversion channel .234 Important Equatio Problems
Contents vii 6. 6.1. 6.2. 7. 7.1. 7.2. 7.2.1. 7.2.2. 7.2.3. 7.3. 7.3.1 7.3.2. 7.3.3. 7.4. 7.4.1. 7.4.2. 7.5. 7.6. 7.7. 7.8. 7.9. 7.10. 7.11. 7.12. 7.12.1. 7.12.2. 7.12.3. 7.12.4. 7.12.5. 7.13. 7.14. 7.14.1. 7.14.2. 7.15. 7.15.1. 7.15.2. 7.15.3. 7.15.4. 7.15.5. 7.15.6. JFET and MESFET The JFET The MESFET Important Equations The MOS Transistor Introduction and basic principles The MOS capacitor Accumulation Depletion Inversion Threshold voltage Ideal threshold voltage Flat-band voltage Threshold voltage Current in the MOS transistor Influence of substrate bias on threshold voltage Simplified model Surface mobility Carrier velocity saturation Subthreshold current - Subthreshold slope Continuous model Channel length modulation Numerical modeling of the MOS transistor Short-channel effect Hot-carrier degradation Scaling rules Hot electrons Substrate current Gate current Degradation mechanism Terminal capacitances Particular MOSFET structures Non-Volatile Memory MOSFETs SOI MOSFETs Advanced MOSFET concepts Polysilicon depletion High-k dielectrics Drain-induced barrier lowering (DIBL) Gate-induced drain leakage (GIDL) Reverse short-channel effect Quantization effects in the inversion channel Important Equations Problems 153 153 159 163 165 165 170 170 176 178 183 183 184 187 187 192 194 196 199 201 206 208 210 213 216 216 218 218 219 220 221 224 224 228 230 230 231 231 232 233 234 235 236
8. The Bipolar Transistor……… 1. Introduction and basic principles 8. 1. Long-base device 252 8.1.2. Short-base device...,.,. 8.1.3. Fabrication process 8. 2. Amplification using a bipolar transistor 8.3. Ebers-Moll model 259 8.3. 1. Emitter efficiency 269 8.4. Regimes of operatic 272 8.5. Transport model 8.6. Gummel-Poon model 275 8.6.1. Current gai 280 8.6.1.1. Recombination in the base .... 280 8.6. 1 2. Emitter efficiency and current gain 282 erect 8.8. Dependence of current gain on collector current 8.8.1. Recombination at the emitter-base junction. 290 8. 8.2. Kirk effect 92 89. Base resistance 8.10. Numerical simulation of the bipolar transistor…………295 8.11. Collector junction breakdown…………………,298 8. 1. Common-base configuration 8.11. 2. Common-emitter configura 8.12. Charge- control model…… 812.1. Forward active mode 8.12. 2 Large-signal model 306 8. 12.3. Small-signal model Important Equations Problems∴ 309 9. Heterojunction Devices 315 9. 1. Concept of a heterojunction 1. Energy band diagram 9. 2. Heterojunction bipolar transistor(HBT) 320 9. 2. High electron mobility transistor (HEMT)..... 9.3. Photonic Devices 324 9.3. 1 Light-emitting diode (led) 324 9.3.2. Laser diode Problems 330
viii Contents 8. 8.1. 8.1.1. 8.1.2. 8.1.3. 8.2. 8.3. 8.3.1. 8.3.2. 8.4. 8.5. 8.6. 8.6.1. 8.6.1.1. 8.6.1.2. 8.7. 8.8. 8.8.1. 8.8.2. 8.9. 8.10. 8.11. 8.11.1. 8.11.2. 8.12. 8.12.1. 8.12.2. 8.12.3. 9. 9.1. 9.1.1. 9.2. 9.2. 9.3. 9.3.1. 9.3.2. The Bipolar Transistor Introduction and basic principles Long-base device Short-base device Fabrication process Amplification using a bipolar transistor Ebers-Moll model Emitter efficiency Transport factor in the base Regimes of operation Transport model Gummel-Poon model Current gain Recombination in the base Emitter efficiency and current gain Early effect Dependence of current gain on collector current Recombination at the emitter-base junction Kirk effect Base resistance Numerical simulation of the bipolar transistor Collector junction breakdown Common-base configuration Common-emitter configuration Charge-control model Forward active mode Large-signal model Small-signal model Important Equations Problems Heterojunction Devices Concept of a heterojunction Energy band diagram Heterojunction bipolar transistor (HBT) High electron mobility transistor (HEMT) Photonic Devices Light-emitting diode (LED) Laser diode Problems 251 251 252 253 256 258 259 268 269 272 273 275 280 280 282 286 290 290 292 295 295 298 298 299 300 301 306 307 309 309 315 315 316 320 321 324 324 326 330
Contents 10. Quantum-Effect Devices.. ,331 101. Tunnel Diode 331 10.1.1. Tunnel effect 10.1.2. Tunnel diode 333 10.2. Low-dimensional devices ,336 10.2. 1. Energy band .337 10.2. 2. Density of states. 343 10.2.3. Conductance of a ID semiconductor sample 10.2 4. 2D and ID Mos transistors 350 103. Single-electron transistor……… 353 10.3. 1. Tunnel junction. 10.3.2. Double tunnel junction 355 103.3. Single-electron transistor. Problems… 361 11. Semiconductor Processing 363 11. Semiconductor materials 363 11. 2. Silicon crystal growth and refining 11.3. 1. Ion implantation.... 367 11.3.2. Doping impurity diffusion.. 370 1133. Gas-phase diffusion…………… 11. 4. Oxidation .374 11.5. Chemical vapor deposition(CVD)…… 381 11.5. 1. Silicon deposition and epitaxy 381 115.2. Dielectric layer deposition……… 382 11.6. Photolithography 11.8. Metallization 391 1 1.8.2. Metal deposition ,391 11. 83. Metal silicide 11.9. CMOS process 11.10. NPn bipolar process.……… Problems∴ 405 12. Anne ,409 Al. Physical Quantities and Units 409 A2. Physical Constants ,410 A3. Concepts of Quantum Mechanics A4. Crystallography -Reciprocal Space. 414 A5. Getting Started with Matlab 418 A6. Greek alphabet 卡卡“·““ A7. Basic Differential Eq 427
Contents ix 10. 10.1. 10.1.1. 10.1.2. 10.2. 10.2.1. 10.2.2. 10.2.3. 10.2.4. 10.3. 10.3.1. 10.3.2. 10.3.3. 11. 11.1. 11.2. 11.3. 11.3.1. 11.3.2. 11.3.3. 11.4. 11.5. 11.5.1. 11.5.2. 11.6. 11.7. 11.8. 11.8.2. 11.8.3. 11.9. 11.10. 12. Al. A2. A3. A4. A5. A6. A7. Quantum-Effect Devices Tunnel Diode Tunnel effect Tunnel diode Low-dimensional devices Energy bands Density of states Conductance of a 1D semiconductor sample 2D and 1D MOS transistors Single-electron transistor Tunnel junction Double tunnel junction Single-electron transistor Problems Semiconductor Processing Semiconductor materials Silicon crystal growth and refining Doping techniques Ion implantation Doping impurity diffusion Gas-phase diffusion Oxidation Chemical vapor deposition (CVD) Silicon deposition and epitaxy Dielectric layer deposition Photolithography Etching Metallization Metal deposition Metal silicides CMOS process NPN bipolar process Problems Annex Physical Quantities and Units Physical Constants Concepts of Quantum Mechanics Crystallography – Reciprocal Space Getting Started with Matlab Greek alphabet Basic Differential Equations Index 331 331 331 333 336 337 343 348 350 353 353 355 358 361 363 363 364 367 367 370 373 374 381 381 382 384 388 391 391 392 393 399 405 409 409 410 411 414 418 426 427 431
PREFACE This Textbook is intended for upper division undergraduate and graduate courses. As a prerequisite, it requires mathematics through differential equations, and modern physics where students are introduced to quantum mechanics. The different Chapters contain different levels of difficulty. The concepts introduced to the Reader are first presented in a simple way, often using comparisons to everyday-life experiences such as simple fluid mechanics. Then the concepts are explained in depth, without leaving mathematical developments to the Reader's responsibility. It is up to the Instructor to decide to which depth he or she wishes to teach the physics of semiconductor devices. In the Annex, the reader is reminded of graphy and qu mechanics which they have seen in lower division materials and physic courses. These notions are used in Chapter I to develop the Energy band Theory for crystal structures An introduction to basic Matlab programming is also included in the Annex, which prepares the students for solving problems throughout the text. Matlab was chosen because of its ease of use, its powerful graphics capabilities and its ability to manipulate vectors and matrices. The problems can be used in class by the Instructor to graphically illustrate theoretical concepts and to show the effects of changing the value of parameters upon the result. We believe it is important for students to understand and experience a" hands-on"feeling of the consequences of changing variable values in a problem(for instance, what happens to the C-v characteristics of a MOs capacitor if the substrate doping concentration is increased?- What happens to the band structure of a semiconductor if the lattice parameter is increased?-What happens to he gain of a bipolar transistor if temperature increases? ) Furthermore
PREFACE This Textbook is intended for upper division undergraduate and graduate courses. As a prerequisite, it requires mathematics through differential equations, and modern physics where students are introduced to quantum mechanics. The different Chapters contain different levels of difficulty. The concepts introduced to the Reader are first presented in a simple way, often using comparisons to everyday-life experiences such as simple fluid mechanics. Then the concepts are explained in depth, without leaving mathematical developments to the Reader's responsibility. It is up to the Instructor to decide to which depth he or she wishes to teach the physics of semiconductor devices. In the Annex, the Reader is reminded of crystallography and quantum mechanics which they have seen in lower division materials and physics courses. These notions are used in Chapter 1 to develop the Energy Band Theory for crystal structures. An introduction to basic Matlab programming is also included in the Annex, which prepares the students for solving problems throughout the text. Matlab was chosen because of its ease of use, its powerful graphics capabilities and its ability to manipulate vectors and matrices. The problems can be used in class by the Instructor to graphically illustrate theoretical concepts and to show the effects of changing the value of parameters upon the result. We believe it is important for students to understand and experience a "hands-on" feeling of the consequences of changing variable values in a problem (for instance, what happens to the C-V characteristics of a MOS capacitor if the substrate doping concentration is increased? - What happens to the band structure of a semiconductor if the lattice parameter is increased? - What happens to the gain of a bipolar transistor if temperature increases?). Furthermore
Preface some Matlab problems make use of a basic numerical, finite-difference technique in which the "exact" numerical solution to an equation is compared to a more approximate analytical solution such as the solution of the Poisson equation using the depletion approximation Chapters 1 to 3 introduce the notion of energy bands, carrier transport and generation-recombination phenomena in a semiconductor. End-of- hapter problems are used here to illustrate and visualize quantum mechanical effects, energy band structure, electron and hole behavior, and the response of carriers to an electric field Chapters 4 and 5 derive the electrical characteristics of PN and metal semiconductor contacts. The notion of a space-charge region is introduced and carrier transport in these structures is analyzed. Special applications such as solar cells are discussed. Matlab problems are used to visualize charge and potential distributions as well as current components In Junctions Chapter 6 analyzes the JFET and the MEsFet, which are extensions the pn or metal-semiconductor junctions. The notions of source, gate, drain and channel are introduced. together with two-dimensional field effects such as pinch-off. These important concepts lead the reader up to the MosFet chapter Chapter 7 is dedicated to the MOSFET. In this important chapter the MOs capacitor is analyzed and emphasis is placed on the physical mechanisms taking place. The current expressions are derived for the MOS transistor. including second-order effects such as surface channel mobility reduction, channel length modulation and threshold voltage roll- off. Scaling rules are introduced, and hot-carrier degradation effects are discussed. Special MOSFET structures such as non-volatile memory and silicon-on-insulator devices are described as well. Matlab problems are used to visualize the characteristics of the Mos capacitor, to compare different MOSFET models and to construct simple circuits Chapter 8 introduces the bipolar junction transistor(BJT). The Ebers- Moll, Gummel-Poon and charge-control models are developed and second-order effects such as the Early and Kirk effects are described Matlab problems are used to visualize the currents in the bjt. Heterojunctions are introduced in Chapter 9 and several heterojunction devices, such as the high-electron mobility transistor
xii Preface some Matlab problems make use of a basic numerical, finite-difference technique in which the "exact" numerical solution to an equation is compared to a more approximate, analytical solution such as the solution of the Poisson equation using the depletion approximation. Chapters 1 to 3 introduce the notion of energy bands, carrier transport and generation-recombination phenomena in a semiconductor. End-ofchapter problems are used here to illustrate and visualize quantum mechanical effects, energy band structure, electron and hole behavior, and the response of carriers to an electric field. Chapters 4 and 5 derive the electrical characteristics of PN and metalsemiconductor contacts. The notion of a space-charge region is introduced and carrier transport in these structures is analyzed. Special applications such as solar cells are discussed. Matlab problems are used to visualize charge and potential distributions as well as current components in junctions. Chapter 6 analyzes the JFET and the MESFET, which are extensions of the PN or metal-semiconductor junctions. The notions of source, gate, drain and channel are introduced, together with two-dimensional field effects such as pinch-off. These important concepts lead the Reader up to the MOSFET chapter. Chapter 7 is dedicated to the MOSFET. In this important chapter the MOS capacitor is analyzed and emphasis is placed on the physical mechanisms taking place. The current expressions are derived for the MOS transistor, including second-order effects such as surface channel mobility reduction, channel length modulation and threshold voltage rolloff. Scaling rules are introduced, and hot-carrier degradation effects are discussed. Special MOSFET structures such as non-volatile memory and silicon-on-insulator devices are described as well. Matlab problems are used to visualize the characteristics of the MOS capacitor, to compare different MOSFET models and to construct simple circuits. Chapter 8 introduces the bipolar junction transistor (BJT). The EbersMoll, Gummel-Poon and charge-control models are developed and second-order effects such as the Early and Kirk effects are described. Matlab problems are used to visualize the currents in the BJT. Heterojunctions are introduced in Chapter 9 and several heterojunction devices, such as the high-electron mobility transistor