Path integral Monte Carlo simulations of bound states in semiconductor quantum wells: Excitons, trions and biexcitons

We present first-principle path integral Monte-Carlo (PIMC) studies of strongly correlated electron-hole complexes such as excitons, trions (charged excitons) and biexcitons in AlxGa1-xAs quantum-well structures. The correlation and binding energies are calculated as function of quantum well width and compared with available experimental (1,2,3,4) and theoretical (5,6) data, The only approximation made is the separation of particle motion parallel and perpendicular to the quantum well plane. The obtained very accurate PIMC results for experimentally measured binding energies validates the applicability of our approximation in a wide range of quantum well widths 10 angstrom <= L <= MA. As in the experiments, we observe a maximum of the binding energies in GaAs/AlGaAs quantum well samples around L = 40 angstrom. We clearly show that the physical reason is non-monotonic dependence of the electron (hole) confinement on the well width. The developed method is a powerful tool for further investigation of temperature and many-body effects on bound states in heterostructures (e.g. depedence on finite exciton, biexciton densities or disorder).