# Doping of semiconductors

by Niles
Tags: doping, semiconductors
 P: 1,863 Hi all It can be shown that the product of the hole and electron concentration is constant at a given temperature in a semiconductor, as long as the Fermi level is in the ~middle of the gab. When we dope semiconductors, do we use the above argument? I.e., does doping work because of this argument?
 P: 1,863 If my question is unclear, I can explain it in a new way.
 Emeritus Sci Advisor PF Gold P: 29,238 It is puzzling because of your last statement in the OP. When you dope a semiconductor, the Fermi level (or more precisely, the chemical potential) is no longer in the middle of the band gap. So I'm not sure how using "the above argument" would explain doping, i.e I'm not sure what you're getting at. Zz.
 P: 1,863 Doping of semiconductors My book says (and I am quoting): "Because the product of the electron and hole concentration is a constant independent of impurity concentration at a given temperature, the introduction of a small proportion of a suitable impurity to increase n, say, must decrease p." Here n is the concentration of electrons, and p is the concentration of holes. And the correct assumption in the OP is: The distance of the Fermi level (i.e. the chemical potential, since we are dealing with semiconductors) from the edge of both bands is large in comparision with T. I am using Kittel (it's page 207). What I don't understand is, when we have a donor atom in a semiconductor, then the extra electron gets thermally excited to the conduction band. But that still brings down a hole to the donor energy level, right?
 Emeritus Sci Advisor PF Gold P: 29,238 I still don't see how that passage that you quoted implied that the chemical potential doesn't change with doping. The fact that you now have more charge carriers in the conduction band when you n-doped means that the statistical count of charge carriers that determines the chemical potential has changed. Zz.
 P: 1,863 You make a good point. When we have a donor atom in a semiconductor, then the extra electron gets thermally excited to the conduction band. Does that bring down a hole to the donor energy level?
Emeritus