Electron–interface phonon interaction in multiple quantum well structures

Intersubband relaxation rates due to electron interactions with the interface phonons are evaluated for multiple quantum well structures designed for step quantum well lasers operating at mid-infrared to submillimetre wavelengths. The interface phonon modes and electron–phonon interaction Hamiltonians for the structures are derived using the transfer matrix method, based on the macroscopic dielectric continuum model, whereas the electron wavefunctions are obtained by solving the Schrödinger equation. Fermi’s golden rule is employed to calculate the electron relaxation rates between the subbands in these structures. The relaxation rates for two different structures are examined and compared with those calculated using the bulk phonon modes and the Fröhlich interaction Hamiltonian. The sum rule for the relationship between the form factors of the various localized phonon modes and the bulk phonon modes is verified. The results obtained in this work illustrate that the transfer matrix method provides a convenient way for deriving the properties of the interface phonon modes in different structures of current interest and that, for preferential electron relaxation in intersubband laser structures, the effects of the interface phonon modes are significant and should be considered for optimal design of these laser structures.