Hello everyone.
For n-type non- degenerate semiconductor materials, the work function can be given by :
∅= χ+kT/e ln(Nc/n)
Where ∅, χ, Nc, n, k and T are the work function, electon affinity, density of state of the conduction band, electrons density, Boltzmann constant and temperature, respectively. In this particular case, Nc should be greater than n.
Is this formula stay the same for the degenerate semiconductors materials? If not, can someone help me with a link or paper where I can find it?
Thank you in advance
Regards,
Christian
Hi Christian,
I'm not familiar with such formulas, and I suspect that they'll depend heavily of the shape of the band near it's edge. However, in some standard cases, where the density of states isn't too low - a good zero-order approximation would be to assume that the Fermi level is at the band edge.
Lior
Hi Christian,
The Nc here is the effective density of state, which we get by assuming E-EF>>KbT for non-degenerate case. You will have to use expression of degenerate DOS. for eg. http://ecee.colorado.edu/~bart/book/book/chapter2/ch2_4.htm
The work function W is the difference between the vacuum level and the Fermi level (F). If you know the electron affinity, you need the energy separation between the conduction band edge (Ec) and the Fermi level.
W = χ + (Ec - F)
For degenerate semiconductor (Ec - F) < 0. The values of (Ec - F) can be found from the electron concentration via the Fermi integral F_1/2.:
n = Nc*F_1/2.
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