How does lattice vibration affect electron mobility in semiconductor?

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Aria James
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Hi everyone,
I'm currently studying how temperature impacts electron mobility in semiconductors, particularly in relation to lattice vibrations (phonons). I understand that as temperature increases, phonon scattering increases, which reduces mobility but I’m trying to get a more detailed understanding of how this is modeled or measured in real-world materials like silicon or GaAs.
Has anyone worked on this topic or can point me to a reliable experimental method or dataset? Also, does this effect vary significantly between crystalline and amorphous materials?
Would appreciate any thoughts, resources, or experiences!
References:
Thanks in advance!
 
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One way to model and measure the impact of thermal lattice vibrations for crystalline materials is the
https://en.wikipedia.org/wiki/Debye–Waller_factor (edit: there are better references than wikipedia for the measurements and empirical models, but I am too lazy at the moment)
It damps higher (spatial) frequency correlations (edit: maybe I should describe this differently, but I am too lazy at the moment), and thereby effectively reduces the range of the spatial crystal order. So the crystalline material behaves increasingly similar to a polycrystalline or amorphous material. But note that room temperature is often a quite low temperature from the perspective of insulating or semiconducting materials, so take this only as an indication of the trend.
 
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From the BCS theory of superconductivity is well known that the superfluid density smoothly decreases with increasing temperature. Annihilated superfluid carriers become normal and lose their momenta on lattice atoms. So if we induce a persistent supercurrent in a ring below Tc and after that slowly increase the temperature, we must observe a decrease in the actual supercurrent, because the density of electron pairs and total supercurrent momentum decrease. However, this supercurrent...
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