Energy relaxation of hot electrons in Si-doped GaN

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 T_e, 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 T_e dependences of the power loss and the energy relaxation time τ_E 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 T_e. At high electron temperatures $(Te>1500 K)$⁠, the power loss increases slowly with T_e 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 T_e. 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-T_e regions.