Atomistic k ⋅ p theory

doi:10.1063/1.4936170

Title: Atomistic k ⋅ p theory

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Abstract

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{sup 3} tight-binding model. We can thus directly derive the parameters in the sp{sup 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 structuresmore »« less

Authors:

Pryor, Craig E., E-mail: craig-pryor@uiowa.edu ^[1]; Pistol, M.-E., E-mail: mats-erik.pistol@ftf.lth.se ^[2]

Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242 (United States)
NanoLund and Solid State Physics, Lund University, P.O. Box 118, 221 00 Lund (Sweden)

Publication Date:: Mon Dec 14 00:00:00 EST 2015

OSTI Identifier:: 22493039

Resource Type:: Journal Article

Journal Name:: Journal of Applied Physics

Additional Journal Information:: Journal Volume: 118; Journal Issue: 22; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-8979

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; ACCURACY; ATOMIC MODELS; BORON; CRYSTAL LATTICES; CRYSTALS; DIAMONDS; EXPERIMENTAL DATA; IMPURITIES; MATRIX ELEMENTS; NITROGEN; POTENTIALS; SEMICONDUCTOR MATERIALS; SIMULATION; WAVE FUNCTIONS; ZINC SULFIDES

Citation Formats


                    Pryor, Craig E., E-mail: craig-pryor@uiowa.edu, and Pistol, M.-E., E-mail: mats-erik.pistol@ftf.lth.se. Atomistic k ⋅ p theory.  United States: N. p., 2015. 
        Web.  doi:10.1063/1.4936170.

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                    Pryor, Craig E., E-mail: craig-pryor@uiowa.edu, & Pistol, M.-E., E-mail: mats-erik.pistol@ftf.lth.se. Atomistic k ⋅ p theory.  United States.  https://doi.org/10.1063/1.4936170

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                    Pryor, Craig E., E-mail: craig-pryor@uiowa.edu, and Pistol, M.-E., E-mail: mats-erik.pistol@ftf.lth.se. 2015.  
        "Atomistic k ⋅ p theory".  United States.  https://doi.org/10.1063/1.4936170.

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@article{osti_22493039,

  title        = {Atomistic k ⋅ p theory},

  author       = {Pryor, Craig E., E-mail: craig-pryor@uiowa.edu and Pistol, M.-E., E-mail: mats-erik.pistol@ftf.lth.se},

  abstractNote = {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{sup 3} tight-binding model. We can thus directly derive the parameters in the sp{sup 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.},

  doi          = {10.1063/1.4936170},

  url          = {https://www.osti.gov/biblio/22493039},
  journal      = {Journal of Applied Physics},

  issn         = {0021-8979},

  number       = 22,

  volume       = 118,

  place        = {United States},

  year         = {Mon Dec 14 00:00:00 EST 2015},

  month        = {Mon Dec 14 00:00:00 EST 2015}

}

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