Resolution of the out-of-zone solution problem in envelope-function theory

• Published in: Superlattices and microstructures Vol. 23; no. 2; pp. 531 - 534
• Main Author: Burt, M.G.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-02-1998; Elsevier
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems; Electron states and collective excitations in thin films, multilayers, quantum wells, mesoscopic and nanoscale systems; Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures; Exact sciences and technology; Physics; quantum wells; superlattices, envelope functions, spurious solutions, out-of-zone solutions; superlattices, envelope functions, spurious solutions, out-of-zone solutions; quantum wells; Theoretical study; Band structure; Electronic structure; Envelope function; Superlattices; Heterostructures
• ISSN: 0749-6036; 1096-3677
• DOI: 10.1006/spmi.1996.0214

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 one-dimensional 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\break approach.