Electron-Optical-Phonon Scattering Rates In Cubic Group Iii-Nitride Crystals: Path-Integral Corrections To Fermi Golden Rule Matrix Elements

III-nitride semiconductors with a cubic crystal structure have shown promise in enhancing efficiency in photonic and optoelectronic applications. The recent interest in cubic III-nitrides has arisen due to the inability to realize enhanced efficiency in optoelectronic applications of the wurtzite phase due to spontaneous polarization effects, crystal defects due to growth on lattice mismatched substrates, and also due to the requirement to fabricate normally-off transistors for high-mobility transistors. Cubic III-nitride materials are characterized by the strong coupling of carriers to optical phonons in which the standard perturbative approach-based on first order perturbation theory-breaks down. In this paper we determine the necessary corrections to the Fermi golden rule electron-optical-phonon matrix elements for selected cubic III-nitrides via the nonperturbative Thornber-Feynman path-integral techniques. Specifically, we report electron transport parameters such as the threshold electric field, threshold velocity, mobility and runaway length for BN, AlN, GaN and InN. 72.10.Di, 72.15.Lh, 72.80.Ey.