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 Inₓ{Ga}_{1{{-}}x}$As/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 Tₗ between 0.3 and 20 K. For a given heating power per electron, the electron temperature Tₑ in a quantum wire can be greater or smaller than that in the corresponding quantum well, depending on the electron density nₛ, while the energy relaxation in quantum dots with significant quantization energies is always slower than in the corresponding wells and wires.