Band structures of Ge and InAs: A 20 <b>k.p</b> model

Radhia, S. Ben; Ridene, Saïd; Boujdaria, K.; Bouchriha, H.; Fishman, G.

doi:10.1063/1.1505990

Cited by 20 publications

(13 citation statements)

References 22 publications

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“…Such a representation where all the relevant quantities are slowly varying continuous functions may lead one to believe that the model is a continuous one and that it cannot capture the full symmetry of the nanostructure. 31 The multiband kÁp Hamiltonians [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] are capable of reproducing the bulk band structure more accurately than the standard 8-band Hamiltonian. Some of these, that include a large number of bands (Z15 or 30 after incorporation of the spin degree of freedom), are even capable of reproducing the bulk band structure throughout the whole Brillouin zone.…”

Section: Introductionmentioning

confidence: 99%

Symmetry reduction in multiband Hamiltonians for semiconductor quantum dots: The role of interfaces and higher energy bands

Tomić¹,

Vukmirović²

2011

Journal of Applied Physics

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The role of interfaces and higher bands on the electronic structure of embedded semiconductor quantum dots (QDs) was investigated. The term in the multiband kÁp Hamiltonian that captures the effect of interface band mixing was derived starting from the microscopic theory. It was shown, analytically and numerically, that, with such a term included, the right symmetry of the QD system can be captured. It leads to splitting of otherwise degenerate energy levels of the order of several meV. The inclusion of additional higher bands beyond the ones from the standard eight-band model also leads to the reduction of symmetry from an artificially high one to the true atomistic symmetry of the system, however their quantitative effect is weaker. These results prove that the multiband kÁp Hamiltonians are fully capable of describing the correct symmetry of a QD.

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Section: Introductionmentioning

confidence: 99%

Symmetry reduction in multiband Hamiltonians for semiconductor quantum dots: The role of interfaces and higher energy bands

Tomić¹,

Vukmirović²

2011

Journal of Applied Physics

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“…An exact diagonalization of the Hamiltonian has also been performed (originally by M. Cardona and F. H. Pollak [28], more recently by other authors [29][30][31][32]), extending the number of considered bands (and thus the number of involved parameters) to reproduce the band structure all over the Brillouin zone to a reasonable degree of accuracy (for example, in their original paper M. Cardona and F. H. Pollak consider 15 bands, with 10 parameters, to reproduce the energy band structure of germanium and silicon).…”

Section: If We Define (18)mentioning

confidence: 99%

“…The k • p method allows to extrapolate the band structure of materials from the knowledge of a restricted set of parameters (a limited number of energy gaps and of momentum matrix elements between band lattice functions), evaluated in correspondence of a single point k 0 of the reciprocal space, which are generally treated as fitting parameters, that can be obtained from experiments or ab initio calculations. Even though, considering quite a large number of bands and thus of parameters, the k • p method can be used to obtain the band structure all over the Brillouin zone of the material [28][29][30][31][32], its primary use is to explore with great detail the dispersion relations around the considered point k 0 . In particular, it allows to obtain the band structure of materials in the regions of the reciprocal space near the band extrema, expanding the eigenvalues and eigenvectors of the single-electron Hamiltonian as a function of k around the wave vector k 0 corresponding to the band maximum or minimum.…”

Section: -Introductionmentioning

confidence: 99%

The k.p method and its application to graphene, carbon nanotubes and graphene nanoribbons: the Dirac equation

Marconcini,

Macucci

2011

Preprint

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The k • p method is a semi-empirical approach which allows to extrapolate the band structure of materials from the knowledge of a restricted set of parameters evaluated in correspondence of a single point of the reciprocal space. In the first part of this review article we give a general description of this method, both in the case of homogeneous crystals (where we consider a formulation based on the standard perturbation theory, and Kane's approach) and in the case of nonperiodic systems (where, following Luttinger and Kohn, we describe the single-band and multi-band envelope function method and its application to heterostructures). The following part of our review is completely devoted to the application of the k • p method to graphene and graphene-related materials. Following Ando's approach, we show how the application of this method to graphene results in a description of its properties in terms of the Dirac equation. Then we find general expressions for the probability density and the probability current density in graphene and we compare this formulation with alternative existing representations. Finally, applying proper boundary conditions, we extend the treatment to carbon nanotubes and graphene nanoribbons, recovering their fundamental electronic properties.

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“…The reference provides parameters for the usual 6×6 (Luttinger-Kohn [37]) and 8×8 (Kane [17] and Rashba-Sheka-Pikus [38]) band models. As we go further into the k•p models, there exist only few reliable sources of parameters for models with a higher number of bands, e.g., for 14×14 [39,40], 20×20 [41], 24×24 [42], 34×34 [43] and 40×40 [44] bands.…”

Section: Introductionmentioning

confidence: 99%

Stability and accuracy control of k · p parameters

Bastos

Sabino

Faria

et al. 2016

Semicond. Sci. Technol.

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The k·p method is a successful approach to obtain band structure, optical and transport properties of semiconductors, and it depends on external parameters that are obtained either from experiments, tight binding or ab initio calculations. Despite the widespread use of the k·p method, a systematic analysis of the stability and the accuracy of its parameters is not usual in the literature. In this work, we report a theoretical framework to determine the k·p parameters from state-of-the-art hybrid density functional theory including spin-orbit coupling, providing a calculation where the gap and spin-orbit energy splitting are in agreement with the experimental values. The accuracy of the set of parameters is enhanced by fitting over several directions at once, minimizing the overall deviation from the original data. This strategy allows us to systematically evaluate the stability, preserving the accuracy of the parameters, providing a tool to determine optimal parameters for specific ranges around the Γ-point. To prove our concept, we investigate the zinc blende GaAs that shows results in excellent agreement with the most reliable data in the literature.

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Band structures of Ge and InAs: A 20 k.p model

Cited by 20 publications

References 22 publications

Symmetry reduction in multiband Hamiltonians for semiconductor quantum dots: The role of interfaces and higher energy bands

Symmetry reduction in multiband Hamiltonians for semiconductor quantum dots: The role of interfaces and higher energy bands

The k.p method and its application to graphene, carbon nanotubes and graphene nanoribbons: the Dirac equation

Stability and accuracy control of k · p parameters

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