We present a theoretical study of Ge-core/Si-shell nanocrystals in a wide bandgap matrix and compare the results with experimental data obtained from the samples prepared by co-sputtering. The empirical tight-binding technique allows us to account for the electronic structure under strain on the atomistic level. We find that a Si shell as thick as 1 monolayer is enough to reduce the radiative recombination rate as a result of valley $L - X$ cross-over. Thin Si shell leads to a dramatic reduction of the optical bandgap from visible to near-infrared range, which is promising for photovoltaics and photodetector applications. Our detailed analysis of the structure of the confined electron and hole states in real and reciprocal spaces indicates that the type-II heterostructure is not yet achieved for Si shells with the thickness below 0.8 nm, despite some earlier theoretical predictions. The energy levels of holes are affected by the Si shell stronger than the electron states, even though holes are completely confined to the Ge core. This occurs probably due to a strong influence of strain on the band offsets.
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