# Impurity scattering temperature dependence

Is there any temperature dependence of relaxation time in impurity scattering of conducting electrons? It seems to me that there is none. But, some people claim that there is.

So if you could explain, how temperature dependence comes into play if it does at all?

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Might want to emphasise 'impurity scattering' in the title, since this is the key part to this question ... – Brendan Dec 2 '12 at 0:07
Ok, thanks for the tip, but since this problem is driving me crazy, might want to give me some answer? – Zarko Dec 2 '12 at 8:21
I don't know the answer :-) Pretty much all I know about the impurity term is that it has a zero temperature contribution to resistivity. Actual impurities in a material should not increase with T but the effects could potentially increase with T. As far as I am aware, most 'textbook' models leave the impurity contribution as a constant but these are simplified and only reflect current established theory. The likely answer is that temperature dependence of the impurity contribution in most metals etc. is slight but in some cases it may be important ... Sorry I can't give a definitive answer! – Brendan Dec 2 '12 at 15:25
Yes, that is what I know, too. I am actually wondering, if you exclude lattice and electron-electron collisions, what of temperature dependence is left? Just the average energy of carriers coming from temperature dependence of Fermi-Dirac distribution, because, after all, impurity scattering is very much affected by kinetic energy of carriers, meaning, it is small for high energies..so, one way of increasing energy is by increasing temperature...anyone? – Zarko Dec 2 '12 at 22:07

## 1 Answer

Ok, so, since nobody is answering, let me try. If we neglect everything but electrons we can write for conductivity an integral with derivative of fermi dirac function under it. So, there it is. This derivation is a delta f at T=0, but it gets fuzzier while temperature increases. So in that change lies T dependence, I guess. But, why then Ziman in his book on transport says that there is no impurity scattering temperature dependence?

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