# Influence of the temperature on the ionization energies for impurities in silicon

Is there any dependence of the impurities ionization energy on temperature in silicon? I mean if there are any interactions between localized electron and phonons which leads to renormalization of electron binding energy.

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By the equipartition theorem, temperature makes additional energy on the order of $k_B T$ available, which can effectively reduce such things as ionization energies. Note, however, that $k_B T \approx 25$ meV for $T = 300$ K is small compared with e.g. the bandgap of Si, which is $\sim 1.1$ eV. Whether or not this will contribute to the ionization of impurities depends on the binding energies of the valence electrons in those impurities.