BSIM3v3.2.2 MOSFET Model - The University of Texas at Dallas

Charge-Thickness Capacitance Modelpronounced in thinner T ox devices due to the assumption of inversion andaccumulation charge being located at the interface. The charge sheet model or theband-gap(E g )-reduction model of quantum effect [31] improves theand thusthe V th modeling but is inadequate for CV because they assume zero chargethickness. Numerical quantum simulation results in Figure 4-1 indicate thesignificant charge thickness in all regions of the CV curves [32].This section describes the concepts used in the charge-thichness model (CTM).Appendix B lists all charge equations. A full report and anaylsis of the CTM modelcan be found in [32].Φ BNormalized Charge Distribution0.150.100.050.00EDCgg (µF/cm 2 )1.0E0.8 A0.60.4B DC0.2C -4 -3 -2 -1 0 1 2 3Vgs (V)ATox=30ANsub=5e17cm -3B0 20 40 60Depth (A)Figure 4-1. Charge distribution from numerical quantum simulations show significantcharge thickness at various bias conditions shown in the inset.CTM is a charge-based model and therefore starts with the DC charge thicknss,X DC . The charge thicknss introduces a capacitance in series with C ox as illustratedin Figure 4-2, resulting in an effective C ox , C oxeff . Based on numerical selfconsistentsolution of Shrodinger, Poisson and Fermi-Dirac equations, universaland analytical X DC models have been developed. C oxeff can be expressed asBSIM3v3.2.2 Manual Copyright © 1999 UC Berkeley 4-15