| Issue |
Europhys. Lett.
Volume 69, Number 2, January 2005
|
|
|---|---|---|
| Page(s) | 249 - 255 | |
| Section | Condensed matter: electronic structure, electrical, magnetic, and optical properties | |
| DOI | https://doi.org/10.1209/epl/i2004-10340-1 | |
| Published online | 17 December 2004 | |
Envelope-function theory without spurious real solutions
Air Force Research Laboratory, Materials & Manufacturing Directorate Wright-Patterson AFB, OH 45433-7707, USA
Received:
20
September
2004
Accepted:
12
November
2004
Spurious real solutions 
of the bulk
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
—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 
. 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 . The
present technique is demonstrated in a model case and in a
superlattice calculation using the 
EFA.
PACS: 73.21.-b – Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems / 73.21.Cd – Superlattices / 73.21.Ac – Multilayers
© EDP Sciences, 2005
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