✍ Scribed by M.G. Burt
No coin nor oath required. For personal study only.
Envelope-function equations are widely used to model electron states in microstructures where single-band effective mass models are inappropriate. However, the presence of spurious out-of-zone solutions poses a serious problem for the method: the out-of-zone solutions appear unphysical yet including them is necessary to satisfy all the boundary conditions implied by the envelope-function equations. In an earlier publication, the author has suggested that the mathematically correct procedure is to use all solutions, including out-of-zone solutions, of the envelope-function equations and to apply all the boundary conditions implied by those equations at abrupt interfaces. This procedure is applied to a simple onedimensional model and it is shown that it generates the correct wavefunction and the role of the out-of-zone solutions is clarified. As a result of this work there is now a straightforward unambiguous procedure for applying the envelope-function method to microstructures, a procedure that removes uncertainty, but retains the simplicity of the envelope-function approach.
📜 SIMILAR VOLUMES
## Abstract We consider an interpolation problem of Nevanlinna–Pick type for matrix‐valued Carathéodory functions, where the values of the functions and its derivatives up to certain orders are given at finitely many points of the open unit disk. For the non‐degenerate case, i.e., in the particular