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Contents
4.4.4.3 Square Root Approximation of Bulk-Charge
Model ..................................................................... 161
4.4.4.4 Subthreshold Region Drain Current Model ..... 163
4.4.4.5 Limitations of Regional Drain Current
Model .................................................................. 169
4.5 Summary ............................................................................................ 171
Exercises ........................................................................................................ 171
5. Compact Models for Small Geometry MOSFETs ................................ 175
5.1 Introduction ....................................................................................... 175
5.2 Threshold Voltage Model ................................................................. 175
5.2.1 Effect of Nonuniform Channel Doping on Threshold
Voltage ................................................................................... 176
5.2.1.1 Threshold Voltage Modeling for
Nonuniform Vertical Channel Doping
Profile .................................................................. 177
5.2.1.2 Threshold Voltage Modeling for
Nonuniform Lateral Channel Doping
Profile ............................................................... 180
5.2.2 Small Geometry Effect on Threshold Voltage Model ..... 183
5.2.2.1 Threshold Voltage Model for Short Channel
MOSFET Devices .................................................. 183
5.2.2.2 Threshold Voltage Modeling for Narrow
Channel MOSFET Devices .................................. 186
5.3 Drain Current Model ........................................................................ 190
5.3.1 Surface Mobility Model ....................................................... 190
5.3.2 Subthreshold Region Drain Current Model ..................... 197
5.3.3 Linear Region Drain Current Model ................................. 197
5.3.4 Saturation Region Drain Current Model .......................... 200
5.3.5 Bulk-Charge Effect ............................................................... 201
5.3.6 Output Resistance ................................................................ 202
5.3.7 Unified Drain Current Equation ........................................ 204
5.3.8 S/D Parasitic Series Resistance .......................................... 205
5.3.9 Polysilicon Gate Depletion .................................................. 205
5.3.10 Temperature Dependence ................................................... 208
5.4 Substrate Current Model .................................................................. 210
5.4.1 Gate-Induced Drain Leakage Body Current Model ........ 218
5.4.2 Gate Current Model ............................................................. 219
5.5 Summary ............................................................................................ 221
Exercises ........................................................................................................ 221
6. MOSFET Capacitance Models .................................................................225
6.1 Introduction .......................................................................................225
6.2 Basic MOSFET Capacitance Model ................................................. 226