Europhys. Lett.
Volume 69, Number 2, January 2005
Page(s) 249 - 255
Section Condensed matter: electronic structure, electrical, magnetic, and optical properties
Published online 17 December 2004
Europhys. Lett., 69 (2), pp. 249-255 (2005)
DOI: 10.1209/epl/i2004-10340-1

Envelope-function theory without spurious real solutions

F. Szmulowicz

Air Force Research Laboratory, Materials & Manufacturing Directorate Wright-Patterson AFB, OH 45433-7707, USA

received 20 September 2004; accepted in final form 12 November 2004
published online 17 December 2004

Spurious real solutions $k_S\ge 1$ $\un{{\AA}^{-1}}$ of the bulk $\bm{k}\bullet\bm{p}$ Hamiltonian for semiconductors can lead to spurious bands and nonnormalizable wave functions in the envelope function approximation (EFA). Since physical observables cannot depend on layer width variations on the scale of 1 $\un{\AA}$ -less than a typical interface width or the precision of defining an interface- we form coherent superpositions of spurious real solutions that satisfy boundary conditions with interface boundaries varying on the scale of kS-1. The superposition leads to a total destructive interference, which demonstrates that real spurious solutions do not contribute to the envelope function away from interfaces. In the interfacial region, we show that real spurious solutions should be replaced with evanescent solutions that decay within kS-1. The present technique is demonstrated in a model case and in a superlattice calculation using the $8\times 8$ EFA.

73.21.-b - Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems.
73.21.Cd - Superlattices.
73.21.Ac - Multilayers.

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