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Using the dielectric continuum (DC) and three-dimensional phonon (3DP)models, energy relaxation of the hot electrons in the quasi-two-dimensionalchannel of lattice-matched InAlN/AlN/GaN heterostructures is studiedtheoretically. The electron power dissipation and energy relaxation time due toboth half-space and interface phonons are calculated as functions of theelectron temperature $T_e$ using a variety of phonon lifetime values fromexperiment, and then compared with those evaluated by the 3DP model. The 3DPmodel yields very close results to the DC model: with no hot phonons orscreening the power loss calculated from the 3DP model is 5% smaller than theDC power dissipation, whereas slightly larger 3DP power loss (by less than 4%with a phonon lifetime from 0.1 to 1 ps) is obtained throughout the electrontemperature range from room temperature to 2500 K after including both thehot-phonon effect (HPE) and screening. Very close results are obtained also forenergy relaxation time with the two phonon models (within a 5% of deviation).However the 3DP model is found to underestimate the HPE by 9%. The Mori-Andosum rule is restored by which it is proved that the power dissipation valuesobtained from the DC and 3DP models are in general different in the pure phononemission process, except when scattering with interface phonons is sufficientlyweak, or when the degenerate modes condition is imposed, which is alsoconsistent with Register's scattering rate sum rule. Our calculation with bothphonon models has obtained a great fall in energy relaxation time at lowelectron temperatures ($T_e<$ 750 K) and slow decrease at the hightemperatures. The calculated temperature dependence of the relaxation time andthe high-temperature relaxation time $\sim$0.09 ps are in good agreement withexperimental results.

journal of applied physics

Hot electron energy relaxation in lattice-matched InAlN/AlN/GaN  heterostructures: the sum rules for electron-phonon interactions and  hot-phonon effect