Electron Transmission across an interface of Different One- Dimensional Crystals.

An exact solution is obtained for the quantum-mechanical reflection and transmission coefficients for the electronic motion across the boundary of two different one-dimensional crystals, each described by a Kronig-Penney model. The result is compared with those obtained in the envelope-function (plane-wave) approximations with different degrees of refinement. It turns out that, in general, neither the simplest such approximation, corresponding to a continuous envelope function PHI and a discontinuous gradiant PHI' (with a single-parameter matching of the electron flux m sup (-1) PHI' across the interface), nor the refined procedure, originally proposed by Harrison (corresponding to a two-parameter matching of discontinuous PHI and PHI' subject to the flux- continuity condition), produce an adequate description.