lntersubband Relaxation in Step Quantum Well Structures

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.