Effect of a random adiabatic potential on the optical properties of two-dimensional excitons

We investigate the absorption spectrum and the distribution of radiative decay times for two-dimensional excitons in semiconductor quantum wells, as affected by a random adiabatic in-plane excitonic potential. We limit our discussion to the case of a white-noise potential. Such a potential could arise as a result of fluctuations in the composition of an alloy semiconductor, or alternatively, fluctuations in quantum-well thickness. We find, in general, that the shortest radiative decay time is directly proportional to the inhomogeneous broadening of the exciton line in absorption, which in turn is proportional to the correlation parameter of the random potential. We calculate the magnitude of the correlation parameter for several cases of potential interest. The theory is in qualitative agreement with available experimental data.