Valley splitting in the silicon inversion layer: Misorientation effects

Abstract

The valley splitting is calculated with the use of the electric breakthrough formalism in $n$-channel inversion layers on slightly misoriented silicon (001) surfaces. The result of Ohkawa and Uemura on the exact (001) surface can be obtained by a simple formula without a tedious numerical calculation and is shown to be essentially equivalent to the result of the surface scattering mechanism recently proposed by Sham and Nakayama. Misorientation effects are enormous and greatly reduce the valley splitting especially in weak magnetic fields, which explains the strange behavior of the valley splitting that it is observed only in strong magnetic fields and disappears in weak fields.