Operation and Modeling of

The MOS Transistor

Second Edition

Yannis Tsividis Columbia University

New York Oxford OXFORD UNIVERSITY PRESS

CONTENTS

Chapter 1 l.l 1.2 1.3

1.4 1.5 1.6

1.7

Chapter 2 2.1 2.2 2.3 2.4

Semiconductors, Junctions, and MOSFET Overview Introduction Semiconductors Conduction 1.3.1 Transit Time 1.3.2 Drift 1.3.3 Diffusion Contact Potentials The pn Junction Overview of the MOS Transistor 1.6.1 Basic Structure 1.6.2 A Qualitative Description of MOS Transistor Operation 1.6.3 A Fluid Dynamical Analog 1.6.4 MOS Transistor Characteristics A Brief Overview of This Book References Problems

The Two-Terminal MOS Structure Introduction The Fiat-Band Voltage Potential Balance and Charge Balance Effect of Gate-Substrate Voltage on Surface Condition 2.4.1 Fiat-Band Condition 2.4.2 Accumulation

1 1 1 8 8 9

15 18 26 34 34 39 41 44 46 48 49

50 50 51 56 58 59 59

XV

XVI CONTENTS

2.5

2.6 2.7

Chapter 3 3.1 3.2 3.3 3.4

3.5

Chapter 4 4.1 4.2 4.3

4.4 4.5

4.6 4.7

2.4.3 Depletion and Inversion 2.4.4 General Analysis Inversion 2.5.1 General Relations and Regions of Inversion 2.5.2 Strong Inversion 2.5.3 Weak Inversion 2.5.4 Moderate Inversion Small-Signal Capacitance Summary of Properties of the Regions of Inversion References Problems

The Three-Terminal MOS Structure Introduction Contacting the Inversion Layer The Body Effect Regions of Inversion 3.4.1 Approximate Limits 3.4.2 Strong Inversion 3.4.3 Weak Inversion 3.4.4 Moderate Inversion A "VCB Control" Point of View 3.5.1 Fundamentals 3.5.2 "Pinchoff' Voltage 3.5.3 Expressions in Terms of the "Pinchoff Voltage References Problems

The Four-Terminal MOS Transistor Introduction Transistor Regions of Operation General Charge Sheet Models 4.3.1 Complete Charge Sheet Model 4.3.2 Simplified Charge Sheet Models 4.3.3 Model Based on Quasi-Fermi Potentials Regions of Inversion in Terms of Terminal Voltages Strong Inversion 4.5.1 Complete Symmetrie Strong-Inversion Model 4.5.2 Simplified Symmetrie Strong-Inversion Model 4.5.3 Simplified, Source-Referenced, Strong-Inversion Model 4.5.4 Model Origin Summary Weak Inversion Moderate Inversion

59 62 64 64 71 74 78 79 87 87 88

91 91 92

101 103 103 106 109 113 113 113 117 120 122 123

125 125 128 131 131 140 146 147 150 150 156 158 169 170 175

CONTENTS X V Ü

4.8 Interpolation Models 176 4.9 Source-Referenced vs. Body-Referenced Modeling 179

4.10 Effective Mobility 181 4.11 Temperature Effects 189 4.12 Breakdown 191 4.13 The /^-Channel MOS Transistor 192 4.14 Enhancement-Mode and Depletion-Mode Transistors 194 4.15 Model Parameter Values, Model Accuracy, and Model Comparison 195

References 197 Problems 203

Chapter 5 MOS Transistors with lon-Implanted Channels 207 5.1 Introduction 207 5.2 Enhancement nMOS Transistors 208

5.2.1 Preliminaries 208 5.2.2 Charges and Threshold Voltages 212 5.2.3 Drain-to-Source Current Model for Strong Inversion 219 5.2.4 Simplified Model for Strong Inversion 222 5.2.5 Weak Inversion 225

5.3 Depletion nMOS Transistors 225 5.3.1 The Need for an «-Type Implant 225 5.3.2 Charges and Threshold Voltage 227 5.3.3 Transistor Operation 234

5.4 Enhancement pMOS Transistors 240 5.4.1 Surface-Channel Enhancement-Mode pMOS 240 5.4.2 Buried-Channel Enhancement-Mode pMOS 241 References 241 Problems 245

Chapter 6 Small-Dimension Effects 248 by D. Antoniadis, Massachusetts Institute of Technology

6.1 Introduction 248 6.2 Channel Length Modulation 249 6.3 Barrier Lowering, Two-Dimensional Charge Sharing,

and Threshold Voltage 257 6.3.1 Introduction 257 6.3.2 Short-Channel Devices 257 6.3.3 Narrow-Channel Devices 270 6.3.4 Summary and Comments 277

6.4 Punchthrough 277 6.5 Carrier Velocity Saturation 280 6.6 Hot Carrier Effects—Substrate Current, Gate Current,

and Breakdown 286 6.7 Scaling 290

XV1I1 CONTENTS

6.8 Effect of Surface and Drain Series Resistances 296 6.9 Effects due to Thin Oxides and High Doping 298

References 301 Problems 309

Chapter 7 The MOS Transistor in Dynamic Operation— Large-Signal Modeling 312

7.1 Introduction 312 7.2 Quasi-Static Operation 313 7.3 Terminal Currents in Quasi-Static Operation 317 7.4 Evaluation of Charges in Quasi-Static Operation 325

7.4.1 Introduction 325 7.4.2 Strong Inversion 325 7.4.3 Moderate Inversion 331 7.4.4 Weak Inversion 332 7.4.5 General Charge Sheet Model 333 7.4.6 Depletion 335 7.4.7 Accumulation 336 7.4.8 Plots of Charges versus VGS 336 7.4.9 Use of Charges in Evaluating Terminal Currents 337

7.5 Transit Time under DC Conditions 339 7.6 Limitations of the Quasi-Static Model 340 7.7 Non-Quasi-Static Modeling 347

7.7.1 Introduction 347 7.7.2 The Continuity Equation 347 7.7.3 Non-Quasi-Static Analysis 348 References 354 Problems 358

Chapter 8 Small-Signal Modeling for Low and Medium Frequencies 359

8.1 Introduction . 359 8.2 A Low-Frequency Small-Signal Model for the Intrinsic Part 360

8.2.1 A Two-Path View 360 8.2.2 A Small-Signal Model for the Channel Path 361 8.2.3 A Small-Signal Model for the Drain-to-Substrate Path 365 8.2.4 Strong Inversion 367 8.2.5 Weak Inversion 378 8.2.6 Moderate Inversion 380 8.2.7 General Models 381

8.3 A Medium-Frequency Small-Signal Model for the Intrinsic Part 384 8.3.1 Introduction 384 8.3.2 Intrinsic Capacitances 385

CONTENTS X i X

8.4 8.5

8.6

Chapter 9 9.1 9.2

9.3 9.4

9.5 9.6

Chapter 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7

10.8 10.9

Small-Signal Modeling for the Extrinsic Part Noise 8.5.1 Introduction 8.5.2 White Noise 8.5.3 Flicker Noise 8.5.4 Small-Dimension Effects 8.5.5 Equivalent-Circuit Model General Models References Problems

High-Frequency Small-Signal Models Introduction A Complete Quasi-Static Model 9.2.1 Complete Description of Capacitance Effects 9.2.2 Small-Signal Equivalent Circuit Topologies 9.2.3 Evaluation of Capacitances 9.2.4 Frequency Region of Validity j-Parameter Models Non-Quasi-Static Models 9.4.1 Introduction 9.4.2 A Non-Quasi-Static Strong-Inversion Model 9.4.3 Other Approximations and Higher-Order Models 9.4.4 Model Comparison High-Frequency Noise Considerations in MOSFET Modeling for RF Applications References Problems

MOSFET Modeling for Circuit Simulation Introduction Types of Models Combining Several Effects into One Physical Model Parameter Extraction Accuracy Properties of Good Models Considerations and Choices 10.7.1 General Considerations 10.7.2 Considerations Related to Computer Implementation Benchmark Tests Nontechnical Considerations References Problems

405 410 410 414 422 424 425 426 428 438

440 440 440 440 445 451 458 460 467 467 469 490 491 492 495 504 508

513 513 514 516 519 528 529 530 530 533 534 543 543 553

Appendices A Energy Bands and Related Concepts 557 B Basic Laws of Electrostatics in One Dimension 566 C Charge Density, Electric Field, and Potential in the pn Junction 572 D Energy Band Diagrams for the Two-Terminal MOS Structure 574 E Charge Density, Electric Field, and Potential in the Two-

Terminal MOS Structure 578 F General Analysis of the Two-Terminal MOS Structure 580 G Careful Definitions for the Limits of Moderate Inversion 584 H Energy Band Diagrams for the Three-Terminal MOS Structure 587 I General Analysis of the Three-Terminal MOS Structure 591 J Drain Current Formulation Using Quasi-Fermi Potentials 594

K Results of a Detailed Formulation for the Drain Current and Drain Small-Signal Conductance in the Saturation Region 598

L Evaluation of the Intrinsic Transient Source and Drain Currents 600 M Charges for the Accurate Strong-Inversion Model 603 N Quantities Used in the Derivation of the Non-Quasi-Static

y-Parameter Model 606

Index 609