Boundary condition for the interface between silicon and silicon oxide

A boundary condition is formulated for the interface of a quantum well embedded in a material of large energy barrier. Distinct differences are pointed out between a free-standing film and the quantum well. The boundary condition for the effective-mass and envelope-function approach includes the property of the transition layer between the well and the barrier in the form of an adjustable parameter. A full-zone k.p method is used along with the boundary condition to calculate the energy gap of the quantum well as a function of the well thickness. The model fits well the experimental data on multiple Si/SiO2 quantum wells.