Confined phonon modes and hot-electron energy relaxation in semiconductor microstructures

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Abstract
The role of confined phonon modes in determining the energy relaxation of hot electrons in low-dimensional semiconductor microstructures is discussed within a dielectric continuum model for the LO phonon confinement and a long wavelength Frohlich model for the electron-phonon interaction. Numerical results are provided for the hot-electron relaxation rate as a function of electron temperature and density for GaAs quantum wells and quantum wires by taking into account emission of slab phonon modes. Comparison with existing experimental results shows some evidence for slab phonon emission in intersubband electronic relaxation in reasonably narrow quantum wells. It is argued that most experiments can be interpreted in terms of an electron-bulk phonon interaction model (i.e. by taking into account the effect of confinement only on the electrons and assuming the phonons to be the usual bulk three-dimensional phonons) because a number of important physical processes, such as screening, the hot phonon effect, phonon self-energy correction etc, make it difficult to distinguish quantitatively between various models for phonon confinement, except perhaps in the narrowest (<50 AA) wells and wires. Detailed numerical results for the calculated intra-subband relaxation rate in GaAs quantum wires are provided within the slab phonon and the electron temperature model, including the effects of dynamical screening, quantum degeneracy and nonequilibrium hot phonons.