Influence of nonparabolicity on boundary conditions in semiconductor quantum wells

In this Letter we present precise derivation of the second boundary condition for the wavefunctions (the first boundary condition is the continuity of the wavefunctions) at the interface of two III–V compound semiconductors, starting from an accurate expression for the bulk conduction-band structure expanded up to fourth order in wavevector. The obtained boundary condition is valid for all states (both bound and continuous) of the quantum well, and follows directly from constantness of the probability current along the quantum well and does not conflict with the double integrating of the Schrödinger equation around the interface.