Influence of Frohlich polaron coupling on renormalized electron bands in polar semiconductors: Results for zinc-blende GaN

We develop a simple method to study the zero-point and thermally renormalized electron energy epsilon(kn)(T) for kn the conduction band minimum or valencemaximum in polar semiconductors. We use the adiabatic approximation, including an imaginary broadening parameter i delta to suppress noise in the density-functional integrations. The finite delta also eliminates the polar divergence which is an artifact of the adiabatic approximation. Nonadiabatic Frohlich polaron methods then provide analytic expressions for the missing part of the contribution of the problematic optical phonon mode. We use this to correct the renormalization obtained from the adiabatic approximation. Test calculations are done for zinc-blende GaN for an 18 x 18 x 18 integration grid. The Frohlich correction is of order -0.02 eV for the zero-point energy shift of the conduction band minimum, and +0.03 eV for the valence band maximum; the correction to renormalization of the 3.28 eV gap is -0.05 eV, a significant fraction of the total zero point renormalization of -0.15 eV.