Electron momentum and energy relaxation rates in GaN and AlN in the high-field transport regime

Momentum and energy relaxation characteristics of electrons in the conduction band of GaN and AlN are investigated using two different theoretical approaches corresponding to two high electric-field regimes, one up to 1-2 MV/cm values for incoherent dynamics, and the other at even higher fields for coherent dynamics where semiballistic and ballistic processes become important. For the former, ensemble Monte Carlo technique is utilized to evaluate these rates as a function of electron energy up to an electric-field value of 1 MV/cm (2 MV/cm) for GaN (AlN). Momentum and energy relaxation rates within this incoherent transport regime in the presence of all standard scattering mechanisms are computed as well as the average drift velocity as a function of the applied field. Major scattering mechanisms are identified as polar optical phonon (POP) scattering and the optical deformation potential (ODP) scattering. Roughly, up to fields where the steady-state electron velocity attains its peak value, the POP mechanism dominates, whereas at higher fields ODP mechanism takes over. Next, aiming to characterize coherent dynamics, the total out-scattering rate from a quantum state (chosen along a high-symmetry direction) due to these two scattering mechanisms are then computed using a first-principles full-band approach. In the case of POP scattering, momentum relaxation rate differs from the total out-scattering rate from that state; close to the conduction-band minimum, momentum relaxation rate is significantly lower than the scattering rate because of forward-scattering character of the intravalley POP emission. However, close to the zone boundary the difference between these two rates diminishes due to isotropic nature of intervalley scatterings. Finally, a simple estimate for the velocity-field behavior in the coherent transport regime is attempted, displaying a negative differential mobility due to the negative band effective mass along the electric-field direction.