Phonon scattering and energy relaxation in two-, one-, and zero-dimensional electron gases

We report on calculations of intrasubband and intersubband phonon scattering in quantum-confined electron gases based on lattice-matched In_xGa_1-xAs/InP quantum wells. Dimensionality effects on the emission of acoustic phonons are studied comparing the scattering times of two-, one-, and zero-dimensional electron gases as a function of the lateral confinement. Optical phonon scattering in quantum wells and wires is discussed using a phenomenological broadening of the one-dimensional density of states. The energy relaxation rates of heated electron gases due to phonon emission and absorption have been calculated for lattice temperatures T_l between 0.3 and 20 K. For a given heating power per electron, the electron temperature T_e in a quantum wire can be greater or smaller than that in the corresponding quantum well, depending on the electron density n_s, while the energy relaxation in quantum dots with significant quantization energies is always slower than in the corresponding wells and wires.