Ellipticity and the spurious solution problem of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="bold">k</mml:mi><mml:mo>∙</mml:mo><mml:mi mathvariant="bold">p</mml:mi></mml:mrow></mml:math>envelope equations

Veprek, Ratko G.; Steiger, Sebastian; Witzigmann, Bernd

doi:10.1103/physrevb.76.165320

Cited by 78 publications

(65 citation statements)

References 39 publications

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“…Its application to quantum wires can lead to spurious solutions, depending on the involved materials. The associated problems are caused by the lack of ellipticity due to wrong operator ordering, as it was already found for zinc-blende k · p models (Veprek et al 2007). The suggested complete asymmetric operator ordering reestablishes the ellipticity of the equation system and leads to stable and spurious solution free band structures.…”

Section: Resultsmentioning

confidence: 98%

“…If h kl i j has both eigenvalues with positive and negative signs, the equation system is non-elliptic. As outlined in Veprek et al (2007), the lack of ellipticity of the designated equations changes their mathematical nature, leading to an improperly-posed problem. Solutions of these equations then depend on the applied discretization method and may appear as being spurious.…”

Section: Ellipticity Analysis Of Wurtzite K · P Modelmentioning

confidence: 99%

“…The second order terms of the k · p 6 × 6 matrix decouple into two similar 3 × 3 blocks, hence only one block must be analyzed. The associated matrix h kl i j is given by To quantify the non-ellipticity of a given parameter set, one defines the ratio between positive and negative eigenvalues λ i of h kl i j by (Veprek et al 2007)…”

Section: Ellipticity Analysis Of Wurtzite K · P Modelmentioning

confidence: 99%

“…The bilinear form of the coupled equation system given by the EFT is in analogy to a scalar second order partial differential operator given by (Veprek et al 2007)…”

Section: Ellipticity Analysis Of Wurtzite K · P Modelmentioning

confidence: 99%

“…We then use the ellipticity analysis (as presented in Veprek et al (2007) for zinc-blende materials) to suggest a stable operator ordering.…”

Section: Introductionmentioning

confidence: 99%

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

2008

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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.

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Section: Resultsmentioning

confidence: 98%

Section: Ellipticity Analysis Of Wurtzite K · P Modelmentioning

confidence: 99%

Section: Ellipticity Analysis Of Wurtzite K · P Modelmentioning

confidence: 99%

“…The bilinear form of the coupled equation system given by the EFT is in analogy to a scalar second order partial differential operator given by (Veprek et al 2007)…”

Section: Ellipticity Analysis Of Wurtzite K · P Modelmentioning

confidence: 99%

“…We then use the ellipticity analysis (as presented in Veprek et al (2007) for zinc-blende materials) to suggest a stable operator ordering.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations