Splitting of the excitonic peak in quantum wells with interfacial roughness

Excitons in a quantum well depend on the interfacial roughness resulting from its growth. The interface is characterized by islands of size $\xi$ separated by one monolayer steps across which the confining potential decreases by $V_0$ for wider wells. A natural length is the localization length ${\xi }_0=\pi ħ/\sqrt{{2MV}_0}$ characterizing the minimum size island to confine an exciton. For small islands $(\xi <{\xi }_0),$ the absorption spectrum has a single exciton peak. As the island size $\xi$ exceeds the localization length ${\xi }_0,$ the peak gradually splits into a doublet. Generally the spectra exhibit the following features: (1) the shape is very sensitive to $\xi /{\xi }_0$ and depends only weakly on the ratio of island size to exciton radius; (2) in the small island regime $\xi \ll {\xi }_0,$ the asymmetric shape of the exciton peak is correctly described by a model of white-noise potential, except for the position of the peak which still depends on the correlation length of the disorder.