Spatially varying band structures

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Abstract
Advances in technology have made possible the fabrication of rapidly varying heterostructures which hold the promise of important applications. We develop a set of approximate treatments of electron states in a variety of layered heterostructures. The approximations are all based on the concept of one-band generalized Wannier functions. Following a discussion of the validity of this representation, we apply it to an evaluation of the bound states in a narrow quantum well in GaAs, which clearly demonstrates the mixing of main and satellite valley states as well as the contribution of evanescent states, and of the states of a superlattice in a model structure of up to 20 quantum wells. As a final example we discuss the application of generalized Wannier functions to the matching of electronic states at a heterojunction between two model band structures with different effective masses, and compare the formalism with alternative approaches to this problem.