Boundary Conditions in the Envelope Function Approximation as Applied to Semiconductor Heterostructures: The Multi-Band Case

Abstract

We have found the equations that determine the self-adjoint extensions, and thus the boundary conditions, of the differential operator used in the multi-band k·p-theory, when the coefficients in the Kane-matrix are piecewise constant. Both the one-dimensional and the three-dimensional case have been investigated. A numerical calculation shows that the choice of boundary conditions affects the energy eigenvalues for a quantum well.