Theory of neutral and charged exciton scattering with electrons in semiconductor quantum wells

Electron scattering on both neutral ($X$) and charged ($X^-$) excitons in quantum wells is studied theoretically. A microscopic model is presented, taking into account both elastic and dissociating scattering. The model is based on calculating the exciton-electron direct and exchange interaction matrix elements, from which we derive the exciton scattering rates. We find that for an electron density of $10^9 {\rm cm}^{-2}$ in a GaAs QW at $T=5K$, the $X^-$ linewidth due to electron scattering is roughly twice as large as that of the neutral exciton. This reflects both the $X^-$ larger interaction matrix elements compared with those of $X$, and their different dependence on the transferred momentum. Calculated reflection spectra can then be obtained by considering the three electronic excitations of the system, namely, the heavy-hole and light-hole 1S neutral excitons, and the heavy-hole 1S charged exciton, with the appropriate oscillator strengths.