Appendix A
Derivations, Expressions and Approximations in Gate Modeling

In this appendix some derivations, expressions and approximations used in considering band-gap-narrowing and Fermi-Dirac statistics in the gate are collected.

Carrier Concentrations:
Solution of the Poisson Equation for Fermi-Dirac Statistics:
Solution of the Poisson Equation for Maxwell-Boltzmann Statistics:
Semiconductor Capacitance in Cases of FD and MB Statistics:
Onset of Inversion for FD Statistics:
Approximations to the Fermi Integrals and their Inverse:
Model of the Band-gap Narrowing:

Martin Stiftinger
Sat Oct 15 22:05:10 MET 1994

Appendix A Derivations, Expressions and Approximations in Gate Modeling

Appendix A
Derivations, Expressions and Approximations in Gate Modeling