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

Zhang, J. -Z.; Dyson, A.; Ridley, B. K.


J. -Z. Zhang

A. Dyson

B. K. Ridley


Using the dielectric continuum (DC) and three-dimensional phonon (3DP) models, energy relaxation of the hot electrons in the quasi-two-dimensional channel of lattice-matched InAlN/AlN/GaN heterostructures is studied theoretically, taking into account non-equilibrium polar optical phonons, electron degeneracy, and screening from the mobile electrons. The electron power dissipation and energy relaxation time due to both half-space and interface phonons are calculated as functions of the electron temperature Te using a variety of phonon lifetime values from experiment, and then compared with those evaluated by the 3DP model. Thereby particular attention is paid to examination of the 3DP model to use for the hot-electron relaxation study. The 3DP model yields very close results to the DC model: with no hot phonons or screening the power loss calculated from the 3DP model is 5% smaller than the DC 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 electron temperature range from room temperature to 2500 K after including both the hot-phonon effect (HPE) and screening. Very close results are obtained also for energy 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-Ando sum rule is restored by which it is proved that the power dissipation values obtained from the DC and 3DP models are in general different in the pure phonon emission process, except when scattering with interface phonons is sufficiently weak, or when the degenerate modes condition is imposed, which is also consistent with Register’s scattering rate sum rule. The discrepancy between the DC and 3DP results is found to be caused by how much the high-energy interface phonons contribute to the energy relaxation: their contribution is enhanced in the pure emission process but is dramatically reduced after including the HPE. Our calculation with both phonon models has obtained a great fall in energy relaxation time at low electron temperatures (Te < 750 K) and slow decrease at the high temperatures with the use of decreasing phonon lifetime with Te. The calculated temperature dependence of the relaxation time and the high-temperature relaxation time ∼0.09 ps are in good agreement with experimental results.


Zhang, J. -., Dyson, A., & Ridley, B. K. (2015). Hot electron energy relaxation in lattice-matched InAlN/AlN/GaN heterostructures: The sum rules for electron-phonon interactions and hot-phonon effect. Journal of applied physics, 117(2), Article ARTN 025701.

Journal Article Type Article
Acceptance Date Dec 1, 2014
Online Publication Date Jan 8, 2015
Publication Date Jan 14, 2015
Deposit Date Nov 30, 2015
Publicly Available Date Nov 23, 2017
Journal Journal of applied physics
Print ISSN 0021-8979
Electronic ISSN 1089-7550
Publisher American Institute of Physics
Peer Reviewed Peer Reviewed
Volume 117
Issue 2
Article Number ARTN 025701
Keywords Phonon-electron interactions; Layered systems; III-V semiconductor-to-semiconductor contacts, p-n junctions, and heterojunctions
Public URL
Publisher URL
Additional Information The following article appeared in Journal of applied physics, 2015, v.117, and may be found at


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