Localized excitons in II-VI semiconductor alloys: Density-of-states model and photoluminescence line-shape analysis

A simple but tractable model of the density of exciton states associated with potential fluctuations in semiconductor alloys is proposed. It consists of minimizing the fluctuation entropy related to the composition fluctuation Δx averaged over a volume V, for a given localization energy ɛ. A critical volume ${\mathit{V}}_{\mathit{c}}$(Δx), defined as the smallest volume in which the fluctuation Δx can occur, is introduced. This model leads to a density-of-states tail of the form exp[-(ɛ/${\mathrm{\varepsilon }}_0$ ${)}^{3/2}$]. The characteristic energy ${\mathrm{\varepsilon }}_0$ depends on the manner an exciton can be localized: as a whole or through electron and/or hole confinement. It is shown that the most probable event is determined by two physical parameters of the system: the electron-hole mass ratio and the ratio between the coefficients of variation with composition of the conduction- and valence-band edges. The density of states is used to model the exciton photoluminescence line shape of three representative alloys ${\mathrm{Zn}}_{0.97}$ ${\mathrm{Hg}}_{0.03}$Te, ${\mathrm{CdS}}_{0.36}$ ${\mathrm{Se}}_{0.64}$, and ${\mathrm{Cd}}_{0.92}$ ${\mathrm{Hg}}_{0.08}$Te in which exciton localization occurs, respectively, via the electron, via the hole, or by electron-hole confinement. In each case a good agreement with the experimental results is obtained.