Solution of the Poisson Equation for Maxwell-Boltzmann Statistics:



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Solution of the Poisson Equation for Maxwell-Boltzmann Statistics:

When MB statistics apply to both carrier types the relationship between the surface field and the surface potential has the well known form

 

Note that the last term is negligible. This equation directly follows from A.11, when we remember that for MB statistics the normalized Fermi integrals reduce to for an arbitrary order . In common cases, holds. In A.14, the quantity is the effective Fermi barrier

 

The effective intrinsic concentration is given by A.7 for =0, because FD statistics is adopted for majorities. This effective Fermi barrier differs from the Fermi barrier introduced in 2.15 for the case of nonsymmetric band-gap narrowing, as it follows from the relationship

 

valid for MB statistics. However, the differences between and are not only small, but also of only academic importance, since we do not dispose of any experimental technique to measure the individual band shifts and separately from each other at present.



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