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## Summary:

- Electron-electron interaction in metals vs semiconductors

What is the difference between Electron-electron interaction in metals and semiconductors? And for which one it is stonger?

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## Summary:

- Electron-electron interaction in metals vs semiconductors

What is the difference between Electron-electron interaction in metals and semiconductors? And for which one it is stonger?

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Astronuc

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dRic2

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dRic2

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You can read at page 152

Chapter 17 is about e-e interaction, it shows you how to deal with it. You should always try to include interactions in your model. Sometimes you can save yourself the trouble and neglect them, but that you can not say that in advance without proper evidence. It is true that in the high density limit the interaction potential in the hamiltonian of the electron gas becomes small and you can treat it using standard perturbation theory. That is however not a reason to fully neglect it: there could be a pretty big difference from a free theory and an interacting theory even if the interactions are small.Thera are two fundamentals reasons why the strong interactionof conduction electrons with each otherand with the positive ions can have the net effect of a weak potentials...

This is all I really have in mind, but I'm not an expert so...

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Thanks so much.

But I didn't know how we consider e-e interaction in metals and semiconductor? Is the relation 17.50 in ashcroft use for both?

As in wikipedia:

The Thomas–Fermi wavevector (in Gaussian-cgs units) is[1]

##{\displaystyle k_{0}^{2}=4\pi e^{2}{\frac {\partial n}{\partial \mu }}}##,

where μ is the chemical potential (Fermi level), n is the electron concentration and e is the elementary charge.

Under many circumstances, including semiconductors that are not too heavily doped, n∝eμ/kBT, where kB is Boltzmann constant and T is temperature. In this case,

##{\displaystyle k_{0}^{2}={\frac {4\pi e^{2}n}{k_{\rm {B}}T}}}##,

i.e. 1/k0 is given by the familiar formula for Debye length. In the opposite extreme, in the low-temperature limit T=0, electrons behave as quantum particles (fermions). Such an approximation is valid for metals at room temperature, and the Thomas–Fermi screening wavevector kTF given in atomic units is

##{\displaystyle k_{\rm {TF}}^{2}=4\left({\frac {3n}{\pi }}\right)^{1/3}}##.

If we restore the electron mass ##{\displaystyle m_{e}}m_{e} and the Planck constant {\displaystyle \hbar }\hbar##, the screening wavevector in Gaussian units is ##{\displaystyle k_{0}^{2}=k_{\rm {TF}}^{2}(m_{e}/\hbar ^{2})}##

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dRic2

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I'm sorry but I don't know the answer.

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Thanks. Your answers help me to think about the question more precisely.

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