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- W1975022857 abstract "A description of the envelope-function equation of the superlattice (SL) is presented and then a review on the variational procedure for calculating energies and envelope functions of the SL is presented. The SL wave function and corresponding effective-mass equation are formulated in terms of a linear combination of Bloch states of the material with a smaller band gap. In this formulation, the difference in bulk Bloch states and band parameters between constituent materials is transformed to be a SL potential in the larger band-gap material region, so that the effective-mass equation can be solved as a whole. The present description provides easier implementation of numerical computations, because it does not require the interface matching as required in most of the previous approaches, and, in many cases, band parameters are empirically known. On the other hand, Schlosser and Marcus's method has been used by Altarelli to include the interface-matching condition in the variational calculation for the SL structure in the multiband envelope-function approximation. This procedure is reexamined more thoroughly and corresponding variational equations are presented in both general and reduced forms. The reduced form shows a difference from Altarelli's result. As an illustration of the application of the present approach, numerical computations are performed both for nonstrained ${mathrm{G}mathrm{a}mathrm{A}mathrm{s}/mathrm{A}mathrm{l}}_{x}{mathrm{Ga}}_{1ensuremath{-}x}mathrm{As}$ and strained ${mathrm{In}}_{1ensuremath{-}x}{mathrm{Ga}}_{x}{mathrm{A}mathrm{s}/mathrm{I}mathrm{n}}_{1ensuremath{-}x}{mathrm{Ga}}_{x}{mathrm{As}}_{y}{mathrm{P}}_{1ensuremath{-}y}$ SL's, and the results are compared with those reported previously." @default.
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- W1975022857 date "1998-12-15" @default.
- W1975022857 modified "2023-09-24" @default.
- W1975022857 title "Envelope-function equation and variational method for superlattices" @default.
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- W1975022857 doi "https://doi.org/10.1103/physrevb.58.15766" @default.
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