New envelope function for describing the electronic properties of semiconductor heterostructures
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A new representation of the envelope function has been introduced, and is used as a framework for a proposed simple and at the same time precise formulation of a method for determining the electronic states in microstructures. The applicability of this method is demonstrated not only for structures with perturbations of the potential which are smooth on the scale of the crystal lattice but also for structures with sharp potential changes. Conditions are found for matching of the envelopes in the approximation of sharp heteroboundaries, which can be used in the “complex band structure” method. Matching conditions are found for the envelopes in the effective mass approximation and used to determine the limits of applicability of the well-known matching conditions of Ben Daniel and Duke.
KeywordsBrillouin Zone Matching Condition Energy Eigenvalue Envelope Function Effective Mass Approximation
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