  Multi-valley effective mass theory for silicon quantum well structure is
studied taking into account the external fields and the quantum interfaces. It
is found that the phenomenological delta function potential, employed to
explain the valley splitting caused by the quantum well interface in the
previous work [Ref. 10], can be derived self-consistently from the multi-valley
effective mass theory. Finite element method is used to solve the multi-valley
effective equations. Theoretical predictions are in a reasonably good agreement
with the recent experimental observation of valley splitting in a
SiO_{2}/Si/SiO_{2} quantum well, which prove the validity of our approach.
