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A systematic development is given for the construction, at any energy in the conduction or valence bands, of all of the solutions to the coupled second-order equations describing electron, light hole, and spin-orbit split-off envelope functions, for arbitrary superlattice grading profile of direct gap materials, retaining all coupling parameters. While some solutions achieve a clear physical significance, attention is also given to those functions which, on their own, are of questionable significance. The procedures are easy to use, and are applied to the case of a sawtooth superlattice of composition Gal-xAlxAs.

Envelope Function Theory for Direct-gap Semiconductor Superlattices of Arbitrary Grading Profile