  Intra and intersubband scattering rates and electron capture rates are
considered when mediated by hybrid optical phonons in an AlAs/GaAs/AlAs double
heterostructure confined between two outer metallic barriers. In evaluating
scattering rates we concentrate first on an infinite quantum well for the
electrons and show that the presence of the outer metal barriers results in
reductions of the intra and intersubband scattering rates due to the
suppression of the interface-like modes. For a quantum well (QW) with a finite
depth we find that the outer barriers are responsible for the existence of a
discrete energy spectrum above the well. The electron capture process under
these circumstances is defined as the electron transition from the first
electron subband above the well to all possible subbands inside the well by the
emission of hybrid phonons. Explicit calculations reveal that the capture rates
are characterized by sharp peaks, referred to as electron resonances which
arise when a new electron state is generated on increasing the quantum well
width. Other sharp peaks are identified as phonon resonances and arise when the
energy of the initial state differs by a phonon energy from an electron state
at the bottom of a quantum well subband.
