Bound-polaron model of effective-mass binding energies in GaN

We have calculated thermal binding energies in the effective-mass limit for GaN based on the theory of bound polarons developed by Buimistrov and Pekar and modified by Brandt and Brown. In the process we have verified that at least some shallow donors $\left(\sim 30\mathrm{meV}\right)$ are well described in terms of simple effective-mass theory with a static dielectric constant. However, the results of semicontinuum potential calculations suggest that if shallower isolated donors exist, either they are not effective-mass like or they are associated with more complex defects. In the case of acceptors, an experimental hole polaron mass of ${0.75m}_e$ leads to a predicted thermal binding energy in the effective-mass limit of $\sim 100–125\mathrm{meV}.$ We provide in tabular form alternative binding energies for different band masses, as well as for different parameters corresponding to the zinc-blende and wurtzite phases of GaN.