Multi-Valley Effective Mass Theory

Abstract

An effective mass theory for explaining valley splittings is formulated in the representation where kinetic parts are diagonalized. The theory is applied to n-channel inversion layers of Si. When intervalley matrix elements of the inversion layer potential are correctly included, the theory is shown to be the same as the Ohkawa and Uemura theory, which takes the representation where potential parts are diagonalized. It is also shown that other previous effective mass theories for valley splittings include only a part of intervalley matrix elements given by the present paper. Application of the present theory to donor states in Si is briefly discussed.