Posted by MRH on February 24, 2014, 10:16 pm, in reply to "Re: Holes"
Another hole related question.
I am trying to calculate the number of holes and electrons liberated from their impurities at a temperature T, in a material with bandgap Eg.
The estimating procedure I have used is as follows:
Use the grand partition function. Write down the two neutral (spin degeneracy) and 1 ionised state (taken to be in the conduction or valence band), and ignore all other states. Treat the absence of electrons as holes, and use the same energy scale for both so that the chemical potential is on the same energy scale.
This gave results that disagreed with Kittel. Kittel thinks that as T tends to infinity, the no of holes and electrons released is 1/3 of the number of dopants. He seems to believe you can use the grand partition function for holes or electrons indiscriminately, for the same chemical potential (no extra minus signs).
I think that the number of released charge carriers as a fraction of dopants is 1/3 for electrons and 2/3 for holes. My result makes sense in terms of stat mech. As T goes to infinity, populations are randomly distributed. There is 1 ionised state for electrons but 2 ionised states for holes.
Who is correct?
Unfortunately I have not been able to find a satisfactory treatment of this elsewhere.
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