Finite-temperature inelastic scattering in 2D doped polar semiconductors

We calculate the finite-temperature inelastic scattering rate for hot electrons injected parallel to an n-doed GaAs/GaAlas interface or quantum well for various doping densities n, temperature T and injection energies. We use the born approximation and a T-dependent two-pole Pade approximation to the full finite T, frequency ω and wavevector q dependent RPA expression for the dielectric function ε(q, ω, T), which contains the screening of the 2D electron gas and the 3D polar LO phonons treated equally. We calculate the mean free path length and average energy loss for a hot electron scattering form the plasmon-coupled LO phonon and single-particle excitation modes. We find that these quantities are very dependent upon T, n and the energy of the hot carrier. We also find that 2D plasmon and polar LO phonons mutually screen each other so that the modes must be considered together. We will show that this high-T, low-n approximation, which incorporates Maxwell-Boltzmann statistics, is valid for GaAs systems at n