Effective-mass approximation in the presence of an interface

For an electron in an inhomogeneous system such as a junction with an interface, the validity of including a sharply varying interface potential in the effective-mass equation is questioned. A new scheme is presented where the electron wave function is expressed in terms of eigenfunctions of the junction system including the interface. An effective-mass equation with accompanying boundary conditions is then derived to account for a slowly varying external potential. The various results, depending on the different types of interface reflections, are categorized. The theory is applied here mainly to the space-charge layer in a MOSFET, in particular to the splitting of the valley degeneracy in the n inversion layer of Si(100)-SiO₂