Phase-shift analysis of two-dimensional carrier-carrier scattering in GaAsand 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 scatter ed 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 sectio n 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 f ind 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 qu antum 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 pe rformed for a statically screened intercarrier interaction, but we expect t he dynamic screening to further deteriorate the Born approximation: We show that the weaker the screening the worse the Born approximation in a 2D sys tem. 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 scree ning. For unscreened 2D c-c collisions the hierarchy of exact, Born, and cl assical cross sections is derived analytically, and it is shown that the Bo rn approximation breakdown is due to the carrier two dimensionality.