We consider a compound semiconductor possessing a slowly varying position-dependent chemical composition. We derive an effective-mass equation governing the dynamics of electron (or hole) motion using the Kohn-Luttinger representation and canonical transformations. We show that, as long as the variation in chemical composition may be treated as a perturbation, the effective masses become constant, position-independent quantities. The effective-mass equation derived here is identical to the effective-mass equation derived previously by von Roos, using a Wannier representation.

• Received 17 September 1984

DOI:https://doi.org/10.1103/PhysRevB.31.2294