Solution of the Poisson Equation for Fermi-Dirac Statistics:



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Solution of the Poisson Equation for Fermi-Dirac Statistics:

The Poisson equation reads

 

in one dimension, -type gate and constant doping case. Routinely transforming we get

 

where . Finally, the relationship between the surface electric field and the surface potential becomes

 

In deriving A.11, we exploited the peculiarity of the normalized Fermi integrals

 

which is valid when these integrals are defined by

 



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