# 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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## 1 Answer

I don't know about your specific example of impurities in Si, but in general temperature does effect electronic excitations and energy levels.

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.

There are also indirect effects of temperature on electronic structure. In particular, increased temperature typically causes materials such as Si to expand. Changes in bond lengths are necessarily accompanied by changes in the probability density of the electrons. Thus, expanding and contracting bond lengths give an indirect dependence of electronic structure with temperature. This, however, is also typically a "small" effect, unless the material in question goes through a phase transition.

Temperature dependence as a whole is very often neglected in electronic structure calculations, which typically focus on the ground-state configuration.

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Thank you for the answer. All mechanisms of the temperature dependence described above are true, but in the case of impurity, the bangap does not play much role for the ionization energy. What could play role is the dependence of the effective mass on the temperature since it enters most of equations concerning the ionization energy according to Luttinger-Kohn hydrogenic model for the shallow impurity potentials. And, of course, I am still curious about phonons and their role. – freude Apr 19 '13 at 20:48