Valley degeneracies in (111) silicon quantum wells

(111) silicon quantum wells have been studied extensively, yet no convincing explanation exists for the experimentally observed breaking of sixfold valley degeneracy into two- and fourfold degeneracies. Here, systematic sp(3)d(5)s(*) tight-binding and effective mass calculations are presented to show that a typical miscut modulates the energy levels, which leads to breaking of sixfold valley degeneracy into two lower and four raised valleys. An effective mass based valley-projection model is used to determine the directions of valley minima in tight-binding calculations of large supercells. Tight-binding calculations are in better agreement with experiments compared to effective mass calculations.