Effects of confinement on the valley splitting of si quantum structures

Valley splitting in SiGe/Si/SiGe heterostructures is calculated with the multi-valley effective mass theory. By examining various quantum structures, such as wells, wires and dots, we show that the valley splitting exhibits an oscillating behavior as a function of geometrical size. The maximum value of the valley splitting is found to be on the order of meV for a typical well-width of about 5 nm, which is consistent with experimental values. We discuss the origins of the valley splitting and the confinement effects in the presence of an electric-field.