Effect of random well-width fluctuations on the exciton optical absorptionspectrum in single quantum wells

The optical density function is calculated in a single quantum well for two -dimensional excitons moving in a random potential in the interfacial plane generated by fluctuations of the quantum-well thickness. Assuming Gaussian statistics far the random potential distribution, we have applied the path -integral approach and obtained in the adiabatic approximation two asymptot ic analytical expressions for the low- and high-energy tails of the optical absorption spectrum. The high-energy tail of the exciton absorption line i s also calculated using the perturbation theory. In order to obtain the spe ctrum across the whole energy range an analytical interpolation formula is found between the asymptotic expressions in the two cases, taking into acco unt the proper normalization of the spectral function. The calculated optic al density function is asymmetrically broadened, the magnitude of the peak is reduced, and the maximum is shifted to lower energy in both cases consid ered, as the disorder increases, in agreement with other theoretical result s. Using the fitting parameters to the time-resolved photoluminescence data of Zimmermann [Nuovo Cimento D 17, 1801 (1995)], we find that the path-int egral method leads to results for the spectral widths (full widths at half maximum) that are closer to those experimentally observable, as compared wi th results inferred from the perturbation theory approach. This can be attr ibuted to the additional contribution of the localized exciton states from the Kane band tail in the former method. The effect of varying the correlat ion length (at a fixed depth of the random potential fluctuations) on the o ptical density function is also studied.