Intersubband relaxation due to electron interactions with the localized phonon modes
plays an important role for population inversion in quantum well laser structures
designed for intersubband lasers operating at mid-infrared to submillimeter wavelengths.
In this work, intersubband relaxation rates between subbands in step quantum
well structures are evaluated numerically using Fermi's golden rule, in which the
localized phonon modes including the asymmetric interface modes, symmetric interface
modes, and confined phonon modes and the electron – phonon interaction Hamiltonians
are derived based on the macroscopic dielectric continuum model, whereas the
electron wave functions are obtained by solving the Schrödinger equation for the
heterostructures under investigation. The sum rule for the relationship between the form
factors of the various localized phonon modes and the bulk phonon modes is examined
and verified for these structures. The intersubband relaxation rates due to electron
scattering by the asymmetric interface phonons, symmetric interface phonons, and
confined phonons are calculated and compared with the relaxation rates calculated
using the bulk phonon modes and the Fröhlich interaction Hamiltonian for step
quantum well structures with subband separations of 36 meV and 50meV, corresponding
to the bulk longitudinal optical phonon energy and interface phonon energy,
respectively. Our results show that for preferential electron relaxation in intersubband
laser structures, the effects of the localized phonon modes, especially the interface
phonon modes, must be included for optimal design of these structures.
lntersubband Relaxation in Step Quantum
Well Structures