Warping in the valence band of silicon

Helmholz, Dirk; Voon, L. C. Lew Yan

doi:10.1103/physrevb.65.233204

Cited by 4 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Previous authors have attempted to provide measures of band warping, using certain methods of band structure calculations and ad hoc definitions for certain materials or considering limited sections of the BZ. 28,30 Our angular effective mass approach enables a more general formulation in all those respects.…”

Section: Quantitative Measures Of Band Warpingmentioning

confidence: 99%

“…[25][26][27] Since then, other authors have dealt with band warping in various ways. 12,[28][29][30] .…”

Section: Introductionmentioning

confidence: 99%

“…[25][26][27] Since then, other authors have dealt with band warping in various ways. 12,[28][29][30] . It turns out that energy bands that become degenerate at extrema in the BZ are almost invariably warped.…”

Section: -21mentioning

confidence: 99%

See 2 more Smart Citations

Theory of band warping and its effects on thermoelectronic transport properties

et al. 2014

View full text Add to dashboard Cite

Optical and transport properties of materials depend heavily upon features of electronic band structures in proximity of energy extrema in the Brillouin zone (BZ). Such features are generally described in terms of multi-dimensional quadratic expansions and corresponding definitions of effective masses. Multi-dimensional quadratic expansions, however, are permissible only under strict conditions that are typically violated when energy bands become degenerate at extrema in the BZ. Even for energy bands that are non-degenerate at critical points in the BZ there are instances in which multi-dimensional quadratic expansions cannot be correctly performed. Suggestive terms such as "band warping", "fluted energy surfaces", or "corrugated energy surfaces" have been used to refer to such situations and ad hoc methods have been developed to treat them. While numerical calculations may reflect such features, a complete theory of band warping has not hitherto been developed. We define band warping as referring to band structures that do not admit second-order differentiability at critical points in k-space and we develop a generally applicable theory, based on radial expansions, and a corresponding definition of angular effective mass. Our theory also accounts for effects of band non-parabolicity and anisotropy, which hitherto have not been precisely distinguished from, if not utterly confused with, band warping. Based on our theory, we develop precise procedures to evaluate band warping quantitatively. As a benchmark demonstration, we analyze the warping features of valence bands in silicon using first-principles calculations and we compare those with previous semi-empirical models. As an application of major significance to thermoelectricity, we use our theory and angular effective masses to generalize derivations of tensorial transport coefficients for cases of either single or multiple electronic bands, with either quadratically expansible or warped energy surfaces. From that theory we discover the formal existence at critical points of transport-equivalent ellipsoidal bands that yield identical results from the standpoint of any transport property. Additionally, we illustrate with some basic multi-band models the drastic effects that band warping and anisotropy can induce on thermoelectric properties such as electronic conductivity and thermopower tensors.

show abstract

Section: Quantitative Measures Of Band Warpingmentioning

confidence: 99%

“…[25][26][27] Since then, other authors have dealt with band warping in various ways. 12,[28][29][30] .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Theory of band warping and its effects on thermoelectronic transport properties

et al. 2014

View full text Add to dashboard Cite

show abstract

“…The fitting process is difficult on two levels: ͑i͒ the determination whether or not a particular tightbinding model can indeed properly reproduce some critical material properties, and ͑ii͒ the mapping of the large number of orbital coupling parameters onto the set of observables. The development of analytic expressions for effective masses for various tight-binding models, [6][7][8][9][10] along with automated fitting procedures, 11 has addressed some of these difficulties in tight binding.…”

Section: Introductionmentioning

confidence: 99%

Valence band effective-mass expressions in thesp3d5s*empirical tight-bin

2004

View full text Add to dashboard Cite

Exact, analytic expressions for the valence band effective masses in the spin-orbit, sp 3 d 5 s* empirical tight-binding model are derived. These expressions together with an automated fitting algorithm are used to produce improved parameter sets for Si and Ge at room temperature. Detailed examinations of the analytic effective-mass expressions reveal critical capabilities and limitations of this model in reproducing simultaneously certain gaps and effective masses. The ͓110͔ masses are shown to be completely determined by the ͓100͔ and ͓111͔ masses despite the introduction of d orbitals into the basis.

show abstract

“…The “forbidden” energy levels now appear as merged “forbidden” levels and are termed “bandgaps”. Bands and bandgaps can be identified and analyzed by spectroscopical methods (Helmholz and Voon 2002 ). The number of bands depends on both temperature and on the lattice size.…”

Section: Quantum Aspects Of Mattermentioning

confidence: 99%

Molecular imaging with nanoparticles: the dwarf actors revisited 10 years later

Thurner

Debbage

2018

Histochem Cell Biol

View full text Add to dashboard Cite

We explore present-day trends and challenges in nanomedicine. Creativity in the laboratories continues: the published literature on novel nanoparticles is now vast. Nanoagents are discussed here which are composed entirely of strongly photoluminescent materials, tunable to desired optical properties and of inherently low toxicity. We focus on “quantum nanoparticles” prepared from allotropes of carbon. The principles behind strong, tunable photoluminescence are quantum mechanical: we present them in simple outline. The major industries racing to develop these materials can offer significant technical guidance to nanomedicine, which could help to custom-design strongly signalling nanoagents specifically for stated clinical applications. Since such agents are small, they can be targeted easily, making active targeting possible. We consider it timely now to study the interactions nanoparticles undergo with tissue components in living animals and to learn to understand and overcome the numerous barriers the organism interposes between the blood and targets in or on parenchymal cells. As the near infra-red spectrum opens up, detection of glowing nanoparticles several centimeters deep in a living human subject becomes calculable and we present a simple way to do this. Finally, we discuss the slow-fuse and resource-inefficient entry of nanoparticles into clinical application. A first possible reason is failure to target across the body’s barriers, see above. Second, in the sparse translational landscape funding and support gaps yawn widely between academic research and subsequent development. We consider the agendas of the numerous “stakeholders” participating in this sad landscape and point to some faint glimmers of hope for the future.

show abstract

Warping in the valence band of silicon

Abstract: The origin of warping in the valence band of silicon is studied using tight-binding and k•p calculations. A number of new analytical expressions for the dispersion and effective masses are given. A measure of warping is also proposed.

Cited by 4 publications

References 12 publications

Theory of band warping and its effects on thermoelectronic transport properties

Theory of band warping and its effects on thermoelectronic transport properties

Valence band effective-mass expressions in thesp3d5s*empirical tight-bin

Molecular imaging with nanoparticles: the dwarf actors revisited 10 years later

Contact Info

Product

Resources

About