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- 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?
I think page 152 of ashcroft is about electron-ion interaction.But my question is about chapter 17 of this book.
Thera are two fundamentals reasons why the strong interaction of conduction electrons with each other and with the positive ions can have the net effect of a weak potentials...
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})}##