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Contents
3.2.2.3 Oxide-Trapped Charge .......................................... 91
3.2.2.4 Mobile Ionic Charge ............................................... 91
3.2.3 Flat Band Voltage ................................................................... 92
3.2.4 Effect of Band Bending on the Semiconductor Surface .... 93
3.3 MOS Capacitor under Applied Bias ................................................. 94
3.3.1 Accumulation ......................................................................... 96
3.3.2 Depletion ................................................................................. 97
3.3.3 Inversion .................................................................................. 97
3.4 MOS Capacitor Theory ....................................................................... 99
3.4.1 Formulation of Poisson’s Equation in Terms
of Band-  Bending Potential .................................................. 100
3.4.2 Electrostatic Potentials and Charge Distribution ............ 103
3.4.2.1 MOS Capacitor at Depletion: Depletion
Approximation ..................................................... 105
3.4.2.2 MOS Capacitor at Inversion ................................ 107
3.5 Capacitance of MOS Structure ........................................................ 114
3.5.1 Low Frequency C–V Characteristics ................................. 115
3.5.1.1 Accumulation ........................................................ 116
3.5.1.2 Flat Band ................................................................ 116
3.5.1.3 Depletion ............................................................... 117
3.5.1.4 Inversion ................................................................ 118
3.5.2 Intermediate and High Frequency C–V
Characteristics ................................................................... 119
3.5.3 Deep Depletion C–V Characteristics ................................. 119
3.5.4 Deviation from Ideal C–V Curves ..................................... 121
3.5.5 Polysilicon Depletion Effect on C–V Curves .................... 121
3.6 Summary ............................................................................................ 123
Exercises ........................................................................................................ 123
4. Large Geometry MOSFET Compact Models ........................................ 131
4.1 Introduction ....................................................................................... 131
4.2 Overview of MOSFET Devices........................................................ 132
4.2.1 Basic Features of MOSFET Devices ................................... 133
4.2.2 MOSFET Device Operation ................................................ 135
4.3 MOSFET Threshold Voltage Model ................................................ 135
4.4 MOSFET Drain Current Model ....................................................... 138
4.4.1 Drain Current Formulation ................................................ 139
4.4.2 Pao-Sah Model ...................................................................... 144
4.4.3 Charge-Sheet Model ............................................................ 146
4.4.3.1 Drift Component of Drain Current ................... 147
4.4.3.2 Diffusion Component of Drain Current ........... 148
4.4.4 Regional Drain Current Model .......................................... 150
4.4.4.1 Core Model ............................................................ 152
4.4.4.2 Bulk-Charge Model .............................................. 160