Intersubband and intrasubband electronic scattering rates in semiconductor quantum wells

Results from calculations of temperature-dependent intrasubband and intersubband electron-electron scattering rates in two subbands in a quasi-two-dimensional quantum well are presented. The screening of the interaction between the electrons plays an important role in determining the magnitude of these scattering rates. In this work we compare the use of different screening models in calculations of electron-electron scattering rates. The screening of the interaction between the electrons, due to the surrounding electron gas, is modeled using the full dynamic, finite-temperature, multisubband dielectric function derived in the random-phase approximation (RPA). A comparison of the scattering rates calculated using the dynamic RPA dielectric function, and the static, long-wavelength approximation to the dielectric function, shows, when plasmon emission is present, the necessity of using the dynamic dielectric function to describe the enhancement of the intrasubband scattering rates due to this process. This point is further emphasized by the good agreement between our calculated scattering rates with experimental estimates of electron-electron scattering rates published in the literature [Kim et al., Phys. Rev. Lett. 68, 2838 (1992)]. An approximation that is sometimes used in evaluating the static, long-wavelength approximation to the dielectric function is to assume that all the electrons are in the lowest subband. We point out that the dielectric function derived with this assumption is invalid for interactions involving intersubband transitions. We derive and present the comet expression for the static, long-wavelength screening in this case, which is also analytic and equally simple to evaluate. We also present an analytic result for the dynamic, temperature-dependent, RPA dielectric function derived in the Boltzmann limit. Finally, we compare electron-electron scattering rates calculated with both the dynamic RPA dielectric function, and the dynamic lattice permittivity, allowing for the treatment of coupled plasmon-phonon modes.