Temperature Dependence of Donor Ionization Energies

[Lacan]

Donor ionization energies are calculated via the hydrogen-like model and use the static dielectric constant and effective mass to modify the screening between the electron and the donor. Nice and simple, I get it. But in a material the ionized electron needs to go someplace - presumably the bottom states of the conduction band. Given this, does the temperature dependence of the conduction band's bandwidth affect the donor ionization energy?

If so, I can see how this effect would may be small enough to be ignored when the saturation temperature is low (donor ionization energy is small and the concentration of donors is small), but what about when one is closer to the degenerate regime in a material doped with deep donors? In other words, what if the saturation temperature doesn't occur until, say, 1000K+? Does anyone have any examples of when the donor ionization energy get convoluted with the Varshni equation (if that occurs)?

Thanks!
~Lacan

 

[Useful nucleus]

Regardless of the changes in the band gap, temperature will certainly change the vibrational free energy of the lattice surrounding the dopant which can change the ionization "free" energy. In many applications this change is neglected. But there is still on going research to compute the temperature effect on dopants in semiconductors starting from quantum mechanical considerations. I think you could also find some simple formulations in literature based on Debye model for lattice vibrations.