Rate of intersubband transitions of charge carriers in semiconductor quantum wells as a result of their Coulomb interaction

Abstract

621.315.592The intersubband scattering of charge carriers in semiconductor quantum wells as a result of their Coulomb interaction has been theoretically investigated. Analytical expressions for the rate of intersubband transitions in the process of electron-electron and electron-hole collisions have been derived in the Born approximation. The theoretical and experimental data on the photoluminescence decay time, obtained for the case of a nondegenerate distribution of charge carriers, were in qualitative agreement.Introduction. The active region of the now quantum-cascade lasers operating in the medium infrared spectral range [1] consists of narrow quantum wells, where the energy gap between the upper and lower laser states is larger than the energy of longitudinal optical photons. Among the processes of intersubband scattering of charge carriers, the emission of optical photons (which have been much studied by now) is dominant. To broaden the radiation wavelength range of quantum-cascade lasers toward the far-infrared region, it is necessary to use broad quantum wells with a transition energy lower than the energy of an optical photon. Under these conditions as well as in the case of high concentrations of charge carriers, the carrier-carrier (c-c) scattering is of great importance [2][3][4][5].In the present work, we investigated the carrier-carrier scattering in a semiconductor quantum well and analyzed the dependence of the rate of intersubband scattering of charge carriers on the parameters of this well.Calculation of the Carrier-Carrier Scattering Rate. We considered charge particles, whose movement along the z axis is limited by an infinitely deep quantum well of width d. Let a particle α with a two-dimensional wave vector k 1 be in the energy subband i and a particle β with wave vector k 2 be in the subband j (α, β    e, h    ). As a result of the Coulomb interaction, the particle α is scattered to the subband f with a wave vector k 1 ′ and the particle β is scattered to the subband m with a wave vector k 2 ′ . This transition will be denoted by ijfm. In this case, on con-

Two-period model for calculation of level populations in subbands of multi-period quantum-cascade superlattice structures

“…For QCLs operating in the far IR range, we need to also take into account electron-electron scattering with transition rate [15] R ijfm ee = (2π)…”