Statistical model explaining the fine structure and interface preference of localized excitons in type-II GaAs/AlAs superlattices

Raman scattering experiments have allowed the determination of the spatial distribution of the thicknesses of GaAs and AlAs layers in a gradient GaAs/AlAs superlattice. A statistical model is developed which is consistent with all the data and ways to improve interface quality are suggested. The fine structures of XΓ and ΓΓ excitons observed in photoluminescence and differential reflection are found to be governed by the fractional parts of the average thickness of the layer (in monolayers). We conclude that each structure has two scales of fluctuations which form the relief of the AlAs surface. The largest fluctuations repeat the relief of the GaAs surface. The second scale has the size of a typical XΓ exciton Bohr radius. The smaller fluctuations disappear when the thickness of the AlAs layer is equal to an integer number of monolayers, which provide interfaces of the quality. The correlation of macro-rough fluctuations on the surface of AlAs and GaAs causes an asymmetry in the densities of states of type II excitons located at either AlAs-on-GaAs or GaAs-on-AlAs interfaces. Hence the lowest PL line is formed by excitons localized across the AlAs-on-GaAs interface. On the other hand, in structures with micro-rough but uncorrelated AlAs surfaces, the lowest energy state is expected to be occupied by excitons localized across the GaAs-on-AlAs interface.