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 ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$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 ${\mathit{T}}_{\mathit{l}}$ between 0.3 and 20 K. For a given heating power per electron, the electron temperature ${\mathit{T}}_{\mathit{e}}$ in a quantum wire can be greater or smaller than that in the corresponding quantum well, depending on the electron density ${\mathit{n}}_{\mathit{s}}$, while the energy relaxation in quantum dots with significant quantization energies is always slower than in the corresponding wells and wires.