Why the mass action law is not valid for very low temperatures?

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SUMMARY

The mass action law is not valid for very low temperatures in semiconductors due to the breakdown of the non-degeneracy condition, where the energy gap (E_g) is not significantly greater than the thermal energy (k_B T). At low temperatures, the behavior of electrons in the lattice becomes increasingly significant, leading to deviations from the predictions of the mass action law. This phenomenon is critical for understanding semiconductor behavior in low-temperature environments.

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  • Understanding of semiconductor physics
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  • Basic principles of statistical mechanics
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why the mass action law is not valid for very low temperatures??

Hi,
In the context of semiconductors, I was asked why the mass action law is not valid for very low temperatures. I thought that it was valid, since for very low temperature it holds the non-degeneracy condition E_g >> k_B T (I think so...). But maybe for some other reason it breaks. Does someone know why? Thanks!
 
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I am not sure, but perhaps it is related to the behavior of electrons in the lattice, which becomes more prominent at lower temperatures (or low energies)?
 

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