MOSFET Models for VLSI Circuit Simulation : Theory and Practice

Metal Oxide Semiconductor (MOS) transistors are the basic building block ofMOS integrated circuits (I C). Very Large Scale Integrated (VLSI) circuits using MOS technology have emerged as the dominant technology in the semiconductor industry. Over the past decade, the complexity of MOS IC's has increased at an astonishing rate. This is realized mainly through the reduction of MOS transistor dimensions in addition to the improvements in processing. Today VLSI circuits with over 3 million transistors on a chip, with effective or electrical channel lengths of 0. 5 microns, are in volume production. Designing such complex chips is virtually impossible without simulation tools which help to predict circuit behavior before actual circuits are fabricated. However, the utility of simulators as a tool for the design and analysis of circuits depends on the adequacy of the device models used in the simulator. This problem is further aggravated by the technology trend towards smaller and smaller device dimensions which increases the complexity of the models. There is extensive literature available on modeling these short channel devices. However, there is a lot of confusion too. Often it is not clear what model to use and which model parameter values are important and how to determine them. After working over 15 years in the field of semiconductor device modeling, I have felt the need for a book which can fill the gap between the theory and the practice of MOS transistor modeling. This book is an attempt in that direction.

1 Overview.- 1.1 Circuit Design with MOSFETs.- 1.2 MOSFET Modeling.- 1.3 Model Parameter Determination.- 1.4 Interconnect Modeling.- 1.5 Subjects Covered.- References.- 2 Review of Basic Semiconductor and pn Junction Theory.- 2.1 Energy Band Model.- 2.2 Intrinsic Semiconductor.- 2.2.1 Fermi level.- 2.3 Extrinsic or Doped Semiconductor.- 2.3.1 Generation-Recombination.- 2.3.2 Quasi-Fermi Level.- 2.4 Electrical Conduction.- 2.4.1 Carrier Mobility.- 2.4.2 Resistivity and Sheet Resistance.- 2.4.3 Transport Equations.- 2.4.4 Continuity Equation.- 2.4.5 Poisson’s Equation.- 2.5 pn Junction at Equilibrium.- 2.5.1 Built-in Potential.- 2.5.2 Depletion Width.- 2.6 Diode Current-Voltage Characteristics.- 2.6.1 Limitation of the Diode Current Model.- 2.6.2 Bulk Resistance.- 2.6.3 Junction Breakdown Voltage.- 2.7 Diode Dynamic Behavior.- 2.7.1 Junction Capacitance.- 2.7.2 Diffusion Capacitance.- 2.7.3 Small Signal Conductance.- 2.8 Real pn Junction.- 2.9 Diode Circuit Model.- 2.10 Temperature Dependent Diode Model Parameters.- 2.10.1 Temperature Dependence of Is.- 2.10.2 Temperature Dependence of ?bi.- 2.10.3 Temperature Dependence of Cj0.- References.- 3 MOS Transistor Structure and Operation.- 3.1 MOSFET Structure.- 3.2 MOSFET Characteristics.- 3.2.1 Punchthrough.- 3.2.2 MOSFET Capacitances.- 3.2.3 Small-Signal Behavior.- 3.2.4 Device Speed.- 3.3 MOSFET Scaling.- 3.4 Hot-Carrier Effects.- 3.5 VLSI Device Structures.- 3.5.1 Gate Material.- 3.5.2 Nonuniform Channel Doping.- 3.5.3 Source-Drain Structures.- 3.5.4 Device Isolation.- 3.5.5 CMOS Process.- 3.6 MOSFET Parasitic Elements.- 3.6.1 Source-Drain Resistance.- 3.6.2 Source/Drain Junction Capacitance.- 3.6.3 Gate Overlap Capacitances.- 3.7 MOSFET Length and Width Definitions.- 3.7.1 Effective or Electrical Channel Length.- 3.7.2 Effective or Electrical Channel Width.- 3.8 MOSFET Circuit Models.- References.- 4 MOS Capacitor.- 4.1 MOS Capacitor with No Applied Voltage.- 4.1.1 Work Function.- 4.1.2 Oxide Charges.- 4.1.3 Flat Band Voltage.- 4.2 MOS Capacitor at Non-Zero Bias.- 4.2.1 Accumulation.- 4.2.2 Depletion.- 4.2.3 Inversion.- 4.3 Capacitance of MOS Structures.- 4.3.1 Low Frequency C-V Plot.- 4.3.2 High Frequency C-V Plot.- 4.3.3 Deep Depletion C-V Plot.- 4.4 Deviation from Ideal C-V Curves.- 4.5 Anomalous C-V Curve (Polysilicon Depletion Effect).- 4.6 MOS Capacitor Applications.- 4.7 Nonuniformly Doped Substrate and Flat Band Voltage.- 4.7.1 Temperature Dependence of V?b.- References.- 5 Threshold Voltage.- 5.1 MOSFET with Uniformly Doped Substrate.- 5.2 Nonuniformly Doped MOSFET.- 5.2.1 Enhancement Type Device.- 5.2.2 Depletion Type Device.- 5.3 Threshold Voltage Variations with Device Length andWidth.- 5.3.1 Short-Channel Effect.- 5.3.2 Narrow-Width Effect.- 5.3.3 Drain Induced Barrier Lowering (DIBL) Effect.- 5.3.4 Small-Geometry Effect.- 5.4 Temperature Dependence of the Threshold voltage.- References.- 6 MOSFET DC Model.- 6.1 Drain Current Calculations.- 6.2 Pao-Sah Model.- 6.3 Charge-Sheet Model.- 6.4 Piece-Wise Drain Current Model for EnhancementDevices.- 6.4.1 First Order Model.- 6.4.2 Bulk-Charge Model.- 6.4.3 Square-Root Approximation.- 6.4.4 Drain Current Equation with Square-RootApproximation.- 6.4.5 Subthreshold Region Model.- 6.4.6 Limitations of the Model.- 6.5 Drain Current Model for Depletion Devices.- 6.6 Effective Mobility.- 6.6.1 Mobility Degradation Due to the Gate Voltage.- 6.6.2 Mobility Degradation Due to the Drain Voltage.- 6.7 Short-Geometry Models.- 6.7.1 Linear Region Model.- 6.7.2 Saturation Voltage.- 6.7.3 Saturation Region—Channel Length Modulation.- 6.7.4 Subthreshold Model.- 6.7.5 Continuous Model.- 6.8 Impact of Source-Drain Resistance on Drain Current.- 6.9 Temperature Dependence of the Drain Current.- 6.9.1 Temperature Dependence of Mobility.- References.- 7 Dynamic Model.- 7.1 Intrinsic Charges and Capacitances.- 7.1.1 Meyer Model.- 7.1.2 Drawbacks of the Meyer Model.- 7.2 Charge-Based Capacitance Model.- 7.3 Long-Channel Charge Model.- 7.3.1 Capacitances.- 7.4 Short-Channel Charge Model.- 7.4.1 Capacitances.- 7.5 Limitations of the Quasi-Static Model.- 7.6 Small-Signal Model Parameters.- References.- 8 Modeling Hot-Carrier Effects.- 8.1 Substrate Current Model.- 8.2 Gate Current Model.- 8.3 Correlation of Gate and Substrate Current.- 8.4 Mechanism of MOSFET Degradation.- 8.5 Measure of Degradation—Device Lifetime.- 8.6 Impact of Degradation on Circuit Performance.- 8.7 Temperature Dependence of Device Degradation.- References.- 9 Data Acquisition and Model Parameter Measurements.- 9.1 Data Acquisition.- 9.1.1 Data for DC Models.- 9.1.2 Data for AC Models.- 9.1.3 MOS Capacitor C-V Measurement.- 9.2 Gate-Oxide Capacitance Measurement.- 9.2.1 Optical Method—Ellipsometry.- 9.2.2 Electrical Method.- 9.3 Measurement of Doping Profile in Silicon.- 9.3.1 Capacitance-Voltage Method.- 9.3.2 DC Method.- 9.4 Measurement of Threshold Voltage.- 9.5 Determination of Body Factor ?.- 9.6 Flat Band Voltage.- 9.7 Drain Induced Barrier Lowering (DIBL) Parameter.- 9.8 Determination of Subthreshold Slope.- 9.9 Carrier Inversion Layer Mobility Measurement.- 9.9.1 Split-CV Method.- 9.10 Determination of Effective Channel Length and Width.- 9. 10.1 Drain Current Methods of Determination ?L.- 9.10.2 Capacitance Method of Determining ?L.- 9.10.3 Methods of Determining ?W.- 9.11 Determination of Drain Saturation Voltage.- 9.12 Measurement of MOSFET Intrinsic Capacitances.- 9.12.1 On-Chip Methods.- 9.12.2 Off-Chip Methods.- 9.13 Measurement of Gate Overlap Capacitance.- 9.14 Measurement of MOSFET Source/Drain Diode JunctionParameters.- 9.14.1 Diode Saturation or Reverse Current Is.- 9.14.2 Junction Capacitance.- References.- 10 Model Parameter Extraction Using Optimization Method.- 10.1 Model Parameter Extraction.- 10.2 Basics Definitions in Optimization.- 10.3 Optimization Methods.- 10.3.1 Constrained Optimization.- 10.3.2 Multiple Response Optimization.- 10.4 Some Remarks on Parameter Extraction Using OptimizationTechnique.- 10.5 Confidence Limits on Estimated Model Parameter.- 10.5.1 Examples of Redundant Parameters.- 10.6 Parameter Extraction Using Optimizer.- 10.6.1 Drain Current Model Parameter Extraction.- 10.6.2 MOSFET AC Model Parameter Extraction.- References.- 11 SPICE Diode and MOSFET Models and Their Parameters.- 11.1 Diode Model.- 11.2 MOSFET Level 1 Model.- 11.2.1 DC Model.- 11.2.2 Capacitance Model.- 11.3 MOSFET Level 2 Model.- 11.3.1 DC Model.- 11.3.2 Capacitance Model.- 11.4 MOSFET Level 3 Model.- 11.4.1 DC Model.- 11.5 MOSFET Level 4 Model.- 11.5.1 DC Model.- 11.5.2 Capacitance Model.- 11.6 Comparison of the Four MOSFET Models.- References.- 12 Statistical Modeling and Worst-Case Design Parameters.- 12.1 Methods of Generating Worst Case Parameters.- 12.2 Model Parameter Sensitivity.- 12.2.1 Principal Factor Method.- 12.3 Statistical Analysis with Parameter Correlation.- 12.3.1 Principal Component Analysis.- 12.4 Factor Analysis.- 12.4.1 Factor Rotation.- 12.4.2 Regression Models.- 12.5 Optimization Method.- References.- Appendix A. Important Properties of Silicon, Silicon Dioxide and Silicon Nitride at 300 K.- Appendix B. Some Important Physical Constants at 300 K.- Appendix C. Unit Conversion Factors.- Appendix D. Magnitude Prefixes.- Appendix F. Charge Based MOSFET Intrinsic Capacitances.- Appendix G. Linear Regression.- Appendix H. Basic Statistical and Probability Theory.- Appendix I. List of Widely Used Statistical Package Programs.