Phase-shift analysis of two-dimensional carrier-carrier scattering in GaAs and GaN:: Comparison with Born and classical approximations

We study Markovian two-dimensional (2D) carrier-carrier (c-c) scattering in GaAs and GaN quantum well systems. We evaluate the phase shifts of scattered partial waves by numerically solving the Schrodinger equation for the 2D c-c collision problem. The output of this phase shift analysis is exact quantum results (in Markovian Limit) for the 2D c-e scattering cross section and 2D c-c scattering rate. We compare these results with the results of the Born approximation (with the ''Fenni-golden-rule based'' theory), and find that the Born approximation can strongly overestimate the exact results. In particular, the 2D c-e scattering rate is overestimated by a factor of 1 to 15 in the GaAs quantum well and by a factor of 2 to 100 in the GaN quantum well, if conditions typical for a quantum-well-laser device or for a quantum well excited by a short laser pulse are considered. Our study is performed for a statically screened intercarrier interaction, but we expect the dynamic screening to further deteriorate the Born approximation: We show that the weaker the screening the worse the Born approximation in a 2D system. We also analyze the 2D c-e collision as a classical event, and find a very good agreement with the phase-shift analysis in the case of weak screening. For unscreened 2D c-c collisions the hierarchy of exact, Born, and classical cross sections is derived analytically, and it is shown that the Born approximation breakdown is due to the carrier two dimensionality.