Optical and Quantum Electronics

, Volume 40, Issue 14–15, pp 1169–1174 | Cite as

Operator ordering, ellipticity and spurious solutions in k · p calculations of III-nitride nanostructures

  • Ratko G. VeprekEmail author
  • Sebastian Steiger
  • Bernd Witzigmann


We analyze the ellipticity of the standard k · p wurtzite model for the symmetrized and the Burt–Foreman operator ordering. We find that for certain situations the symmetrized Hamiltonian is unstable, leads to unplausible results and can cause spurious solutions. We show that the operator ordering in wurtzite must be completely asymmetric to be stable. The asymmetric operator ordering is elliptic and consequently no spurious solutions are obtained. Therefore we recommend the use of a complete asymmetric operator ordering for nitride device simulation.


k · p Spurious solutions Finite element method Nanostructures Operator ordering Nitride Wurtzite 


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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  • Ratko G. Veprek
    • 1
    Email author
  • Sebastian Steiger
    • 1
  • Bernd Witzigmann
    • 1
  1. 1.Department of Information Technology and Electrical EngineeringIntegrated Systems LaboratoryZurichSwitzerland

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