Theory of magnetic-field-dependent alloy broadening of exciton-photoluminescence linewidths in semiconductor alloys

A theory is developed for the inhomogeneous photoluminescence line shape and, in particular, the linewidth of excitons due to alloy disorder in undoped semiconductor alloys in the presence of external magnetic fields. In contrast to previous theories, we find that both the linewidth and its field dependence depend not only on the exciton wave function for the electron-hole relative motion but also depend sensitively on the localization length ${\mathit{R}}_0$ of the center-of-mass wave function. In general, the line shape depends on the nature of the exciton localization. The linewidths arise from the fluctuations of the conduction- and valence-band edges in the localization region where there is significant amplitude of the total exciton wave function. The wave function for the relative motion is calculated numerically by reducing the Schrödinger equation to a difference equation at arbitrary fields, while the center-of-mass wave function is treated phenomenologically. The linewidth is calculated as a function of the magnetic field and the localization length ${\mathit{R}}_0$. The results yield good agreement with recent experimental data from ${\mathrm{In}}_{0.48}$ ${\mathrm{Ga}}_{0.52}$P.