Hydrodynamic theory for spatially inhomogeneous semiconductor lasers. II. Numerical results

Abstract

We present numerical results for the diffusion coefficients (DCs) in the coupled diffusion model derived [J. Li and C. Z. Ning, preceding paper, Phys. Rev. A 66, 023802 (2002)] for a semiconductor quantum well. These include self- and mutual-diffusion coefficients in the general two-component case, as well as density- and temperature-related DCs under the single-component approximation. The results are analyzed from the viewpoint of the free Fermi gas theory with many-body effects incorporated. We discuss in detail the dependence of these DCs on densities and temperatures in order to identify different roles played by the free-carrier contributions including carrier statistics and carrier--LO-phonon scattering, and many-body corrections including band-gap renormalization and electron-hole $(e\ensuremath{-}h)$ scattering. In the general two-component case, it is found that the self- and mutual-diffusion coefficients are determined mainly by the free-carrier contributions, but with significant many-body corrections near the transition density where carrier statistics changes from the Maxwell to the Fermi-Dirac distribution. Carrier--LO-phonon scattering is dominant at low density, whereas e-$h$ scattering becomes important in determining their density dependence above the electron transition density. In the single-component case, it is found that many-body effects decrease the density coefficients but enhance the temperature coefficients. The modification is on the order of $10%$ and reaches a maximum of over $20%$ [C. Z. Ning and J. Li, Phys. Rev. B $65,$ 201305(R) (2002)] for the density coefficients. Overall, temperature elevation enhances the diffusive capability of carriers (DCs) linearly, and such an enhancement grows with density. The complete data set of various DCs as functions of carrier densities and temperatures provides necessary ingredients for future applications of the model to various spatially inhomogeneous optoelectronic devices.