Energy relaxation of hot electrons in Si-doped GaN

Abstract

Energy relaxation of the hot electrons in Si-doped bulk GaN 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 are calculated as functions of the electron temperature Te, the hot-phonon effect (HPE) is examined by varying the optical phonon lifetime values, and the results are compared with previous calculations for typical GaN-based heterostructures. Particular attention is paid to the distinct temperature Te dependences of the power loss and the energy relaxation time τE at the low and high electron temperatures. At low electron temperatures (Te<500 K), the exponential rise of phonon generation number, fast weakened screening and HPE result in a rapid increase of power loss and sharp drop of relaxation time with Te. At high electron temperatures (Te>1500 K), the power loss increases slowly with Te due to the decrease in phonon generation rate, and the temperature-dependence of the energy relaxation time depends on the polar optical phonon lifetime—saturation in energy relaxation occurs when the phonon lifetime increases or varies little with Te. Our calculated temperature dependences of the energy relaxation time are in good agreement with experimental findings [Liberis et al., Appl. Phys. Lett. 89, 202117 (2006); Matulionis et al., Phys. Status Solidi C 2, 2585 (2005)]. With no HPE, the electron energy relaxation is much faster in bulk GaN (τE∼ several tens femtoseconds) than in the GaN-based heterostructures. However, stronger hot-phonon re-absorption occurs in bulk GaN due to rapid polar-optical phonon emission compared to phonon decay. Therefore, including HPE yields very close power loss and energy relaxation times in bulk and heterostructures with similar densities of electrons (τE∼ several tenths of a picosecond). Transparent expressions for energy relaxation are obtained in the Boltzmann approximation, which are very useful for resolving the temperature dependences of the energy relaxation in the low- and high-Te regions.