Choosing a basis that eliminates spurious solutions in<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>theory

Foreman, Bradley A.

doi:10.1103/physrevb.75.235331

Cited by 27 publications

(40 citation statements)

References 77 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Calculations reported elsewhere 18 show that similar results for ⌫ 15v can be obtained from a simpler 4-state ͕⌫ 15v , ⌫ 1c ͖ model. A 3-state ⌫ 15v model gave fairly good results over a more limited energy range ͑although it probably would not work as well in real In 0.53 Ga 0.47 As/ InP superlattices, since the energy gap of In 0.53 Ga 0.47 As in the model system was significantly greater than the experimental value͒.…”

Section: Discussionsupporting

confidence: 58%

“…As discussed in the Introduction, one can achieve a similar effect for L, N, and K by including ⌫ 1c in the set A. 18 For the case of GaAs/ AlAs ͑with Al 0.5 Ga 0.5 As as the reference crystal͒, the linear approximation is off by nearly 50% in some cases, while the quadratic approximation is accurate to within 13% for K and to within 8% for the other parameters. The quadratic approximation is more accurate for In 0.53 Ga 0.47 As/ InP, with a maximum error of less than 4%.…”

Section: Effective-mass Parametersmentioning

confidence: 98%

“…10 This theory is shown here to work well in a 3-state model for the ⌫ 15v valence states ͑i.e., neglecting spinorbit coupling͒ of a GaAs/ Al 0.2 Ga 0. 8 18 To test the limits of the single-band ͑⌫ 15v ͒ model, this paper also extends the theory of Ref. 1 to include terms of order 2 k and 2 k 2 , where denotes the heterostructure perturbation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Valence-band mixing in first-principles envelope-function theory

Foreman

2007

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

This paper presents a numerical implementation of a first-principles envelope-function theory derived recently by the author ͓B. A. Foreman, Phys. Rev. B 72, 165345 ͑2005͔͒. The examples studied deal with the valence subband structure of GaAs/ AlAs, GaAs/ Al 0.2 Ga 0.8 As, and In 0.53 Ga 0.47 As/ InP ͑001͒ superlattices calculated using the local-density approximation to density-functional theory and norm-conserving pseudopotentials without spin-orbit coupling. The heterostructure Hamiltonian is approximated using quadratic-response theory, with the heterostructure treated as a perturbation of a bulk reference crystal. The valence subband structure is reproduced accurately over a wide energy range by a multiband envelope-function Hamiltonian with linear renormalization of the momentum and mass parameters. Good results are also obtained over a more limited energy range from a single-band model with quadratic renormalization. The effective kinetic-energy operator ordering derived here is more complicated than in many previous studies, consisting in general of a linear combination of all possible operator orderings. In some cases, the valence-band Rashba coupling differs significantly from the bulk magnetic Luttinger parameter. The splitting of the quasidegenerate ground state of no-common-atom superlattices has non-negligible contributions from both short-range interface mixing and long-range dipole terms in the quadratic density response.

show abstract

Section: Discussionsupporting

confidence: 58%

Section: Effective-mass Parametersmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Valence-band mixing in first-principles envelope-function theory

Foreman

2007

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

show abstract

“…This is still a standing problem; different approaches and models have been proposed to eliminate them but each approach has its drawbacks. Such solutions may appear as highly oscillatory or strongly localized wave functions within the band gap or dispersion curves bending in the wrong direction [38][39][40]. Three main reasons have been identified for the source of the spurious solutions.…”

Section: Parabolicmentioning

confidence: 99%

Modeling Energy Bands in Type II Superlattices

Bennecer

Sengouga

2019

Crystals

View full text Add to dashboard Cite

We present a rigorous model for the overall band structure calculation using the perturbative k · p approach for arbitrary layered cubic zincblende semiconductor nanostructures. This approach, first pioneered by Kohn and Luttinger, is faster than atomistic ab initio approaches and provides sufficiently accurate information for optoelectronic processes near high symmetry points in semiconductor crystals. k · p Hamiltonians are discretized and diagonalized using a finite element method (FEM) with smoothed mesh near interface edges and different high order Lagrange/Hermite basis functions, hence enabling accurate determination of bound states and related quantities with a small number of elements. Such properties make the model more efficient than other numerical models that are usually used. Moreover, an energy-dependent effective mass non-parabolic model suitable for large gap materials is also included, which offers fast and reasonably accurate results without the need to solve the full multi-band Hamiltonian. Finally, the tools are validated on three semiconductor nanostructures: (1) the bound energies of a finite quantum well using the energy-dependent effective mass non-parabolic model; (2) the InAs bulk band structure; and (3) the electronic band structure for the absorber region of photodetectors based on a type-II InAs/GaSb superlattice at room temperature. The tools are shown to work on simple and sophisticated designs and the results show very good agreement with recently published experimental works.

show abstract

“…When working in a plane wave basis these spurious solutions may be avoided by simply restricting the values of k, however this cannot be done in a real-space formulation. Spurious gap-crossing states can be eliminated by modifying the basis [51,52], choosing different material parameters [53], or altering the differencing scheme to include higher powers of k that push the spurious solutions out of the gap [54]. The threat of gap-crossing bands is greater in the atomistic limit due to the larger (computational) Brillouin zone associated with the smaller computational grid, providing more space for the bands to turn over and cross the gap.…”

Section: Parameter Fittingmentioning

confidence: 99%

Atomistic k ⋅ p theory

Pryor

Pistol

2015

Journal of Applied Physics

View full text Add to dashboard Cite

Pseudopotentials, tight-binding models, and k · p theory have stood for many years as the standard techniques for computing electronic states in crystalline solids. Here we present the first new method in decades, which we call atomistic k · p theory. In its usual formulation, k · p theory has the advantage of depending on parameters that are directly related to experimentally measured quantities, however it is insensitive to the locations of individual atoms. We construct an atomistic k · p theory by defining envelope functions on a grid matching the crystal lattice. The model parameters are matrix elements which are obtained from experimental results or ab initio wave functions in a simple way. This is in contrast to the other atomistic approaches in which parameters are fit to reproduce a desired dispersion and are not expressible in terms of fundamental quantities. This fitting is often very difficult. We illustrate our method by constructing a four-band atomistic model for a diamond/zincblende crystal and show that it is equivalent to the sp 3 tight-binding model. We can thus directly derive the parameters in the sp 3 tight-binding model from experimental data. We then take the atomistic limit of the widely used eight-band Kane model and compute the band structures for all III-V semiconductors not containing nitrogen or boron using parameters fit to experimental data. Our new approach extends k · p theory to problems in which atomistic precision is required, such as impurities, alloys, polytypes, and interfaces. It also provides a new approach to multiscale modeling by allowing continuum and atomistic k · p models to be combined in the same system.

show abstract

Choosing a basis that eliminates spurious solutions ink∙ptheory

Cited by 27 publications

References 77 publications

Valence-band mixing in first-principles envelope-function theory

Valence-band mixing in first-principles envelope-function theory

Modeling Energy Bands in Type II Superlattices

Atomistic k ⋅ p theory

Contact Info

Product

Resources

About