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Title: Localization landscape theory of disorder in semiconductors. I. Theory and modeling

Abstract

Here, we present here a model of carrier distribution and transport in semiconductor alloys accounting for quantum localization effects in disordered materials. This model is based on the recent development of a mathematical theory of quantum localization which introduces for each type of carrier a spatial function called localization landscape. These landscapes allow us to predict the localization regions of electron and hole quantum states, their corresponding energies, and the local densities of states. We show how the various outputs of these landscapes can be directly implemented into a drift-diffusion model of carrier transport and into the calculation of absorption/emission transitions. This creates a new computational model which accounts for disorder localization effects while also capturing two major effects of quantum mechanics, namely, the reduction of barrier height (tunneling effect) and the raising of energy ground states (quantum confinement effect), without having to solve the Schrödinger equation. Finally, this model is applied to several one-dimensional structures such as single quantum wells, ordered and disordered superlattices, or multiquantum wells, where comparisons with exact Schrödinger calculations demonstrate the excellent accuracy of the approximation provided by the landscape theory.

Authors:
 [1];  [1];  [2];  [2];  [3];  [4]
+ Show Author Affiliations
  1. Ecole Polytechnique, Univ. Paris-Saclay, Palaiseau (France). Lab. of Condensed Matter Physics
  2. National Taiwan Univ., Taipei (Taiwan). Graduate Inst. of Photonics and Optoelectronics and Dept. of Electrical Engineering
  3. Ecole Polytechnique, Univ. Paris-Saclay, Palaiseau (France). Lab. of Condensed Matter Physics; Univ. of California, Santa Barbara, CA (United States). Dept. of Materials
  4. Univ. of Minnesota, Minneapolis, MN (United States). School of Mathematics
Publication Date:
Research Org.:
Univ. of California, Santa Barbara, CA (United States)
Sponsoring Org.:
USDOE Office of Energy Efficiency and Renewable Energy (EERE), Energy Efficiency Office. Building Technologies Office; French National Research Agency (ANR); Ministry of Science and Technology (MOST), Taipei (Taiwan); Alfred P. Sloan Foundation; National Science Foundation (NSF)
OSTI Identifier:
1429093
Alternate Identifier(s):
OSTI ID: 1352103
Grant/Contract Number:  
EE0007096; DMS-1056004
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B
Additional Journal Information:
Journal Volume: 95; Journal Issue: 14; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING; Anderson localization; local density of states; localization; disordered systems; semiconductor compounds

Citation Formats

Filoche, Marcel, Piccardo, Marco, Wu, Yuh-Renn, Li, Chi-Kang, Weisbuch, Claude, and Mayboroda, Svitlana. Localization landscape theory of disorder in semiconductors. I. Theory and modeling. United States: N. p., 2017. Web. doi:10.1103/physrevb.95.144204.
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Filoche, Marcel, Piccardo, Marco, Wu, Yuh-Renn, Li, Chi-Kang, Weisbuch, Claude, & Mayboroda, Svitlana. Localization landscape theory of disorder in semiconductors. I. Theory and modeling. United States. https://doi.org/10.1103/physrevb.95.144204
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Filoche, Marcel, Piccardo, Marco, Wu, Yuh-Renn, Li, Chi-Kang, Weisbuch, Claude, and Mayboroda, Svitlana. Tue . "Localization landscape theory of disorder in semiconductors. I. Theory and modeling". United States. https://doi.org/10.1103/physrevb.95.144204. https://www.osti.gov/servlets/purl/1429093.
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@article{osti_1429093,
title = {Localization landscape theory of disorder in semiconductors. I. Theory and modeling},
author = {Filoche, Marcel and Piccardo, Marco and Wu, Yuh-Renn and Li, Chi-Kang and Weisbuch, Claude and Mayboroda, Svitlana},
abstractNote = {Here, we present here a model of carrier distribution and transport in semiconductor alloys accounting for quantum localization effects in disordered materials. This model is based on the recent development of a mathematical theory of quantum localization which introduces for each type of carrier a spatial function called localization landscape. These landscapes allow us to predict the localization regions of electron and hole quantum states, their corresponding energies, and the local densities of states. We show how the various outputs of these landscapes can be directly implemented into a drift-diffusion model of carrier transport and into the calculation of absorption/emission transitions. This creates a new computational model which accounts for disorder localization effects while also capturing two major effects of quantum mechanics, namely, the reduction of barrier height (tunneling effect) and the raising of energy ground states (quantum confinement effect), without having to solve the Schrödinger equation. Finally, this model is applied to several one-dimensional structures such as single quantum wells, ordered and disordered superlattices, or multiquantum wells, where comparisons with exact Schrödinger calculations demonstrate the excellent accuracy of the approximation provided by the landscape theory.},
doi = {10.1103/physrevb.95.144204},
journal = {Physical Review. B},
number = 14,
volume = 95,
place = {United States},
year = {Tue Apr 18 00:00:00 EDT 2017},
month = {Tue Apr 18 00:00:00 EDT 2017}
}
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Journal Article:
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https://doi.org/10.1103/physrevb.95.144204
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Figures / Tables:

FIG. 1 FIG. 1: The localization landscape theory: (a) 3D representation of the original 2D disordered potential V ; (b) 3D representation of the landscape u solving Eq. (2). (c) The valley lines of the landscape u (black lines) delimit the various localization regions. (d) Effective localization potential W ≡ $u$ −1more » . The localization subregions outlined in (c) are also the basins of W .« less
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Works referenced in this record:

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    Works referencing / citing this record:

    Universality of fold-encoded localized vibrations in enzymes
    journal, September 2019

    Optical absorption edge broadening in thick InGaN layers: Random alloy atomic disorder and growth mode induced fluctuations
    journal, January 2018

    • Butté, Raphaël; Lahourcade, Lise; Uždavinys, Tomas Kristijonas
    • Applied Physics Letters, Vol. 112, Issue 3
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    Three dimensional simulation on the transport and quantum efficiency of UVC-LEDs with random alloy fluctuations
    journal, October 2018

    • Chen, Hung-Hsiang; Speck, James S.; Weisbuch, Claude
    • Applied Physics Letters, Vol. 113, Issue 15
    • DOI: 10.1063/1.5051081

    Compensation between radiative and Auger recombinations in III-nitrides: The scaling law of separated-wavefunction recombinations
    journal, November 2019

    • David, Aurelien; Young, Nathan G.; Lund, Cory
    • Applied Physics Letters, Vol. 115, Issue 19
    • DOI: 10.1063/1.5123743

    Application of localization landscape theory and the k · p model for direct modeling of carrier transport in a type II superlattice InAs/InAsSb photoconductor system
    journal, January 2020

    • Tsai, Tsung-Yin; Michalczewski, Krystian; Martyniuk, Piotr
    • Journal of Applied Physics, Vol. 127, Issue 3
    • DOI: 10.1063/1.5131470

    Resonant photoluminescence studies of carrier localisation in c-plane InGaN/GaN quantum well structures
    journal, April 2018

    • Blenkhorn, W. E.; Schulz, S.; Tanner, D. S. P.
    • Journal of Physics: Condensed Matter, Vol. 30, Issue 17
    • DOI: 10.1088/1361-648x/aab818

    Kinetic Monte Carlo simulations of the dynamics of a coupled system of free and localized carriers in AlGaN
    journal, January 2020

    • Kravcov, O.; Mickevičius, J.; Tamulaitis, G.
    • Journal of Physics: Condensed Matter, Vol. 32, Issue 14
    • DOI: 10.1088/1361-648x/ab61cb

    Impact of alloy disorder on Auger recombination in single InGaN/GaN core-shell microrods
    journal, December 2019

    Many-body localization landscape
    journal, January 2020

    Electronic structure of semiconductor nanostructures: A modified localization landscape theory
    journal, January 2020

    Switching of exciton character in double InGaN/GaN quantum wells
    journal, October 2018

    Resonant photoluminescence studies of carrier localisation in c-plane InGaN/GaN quantum well structures.
    text, January 2018

    • Blenkhorn, We; Schulz, S.; Tanner, Dsp
    • Apollo - University of Cambridge Repository
    • DOI: 10.17863/cam.25432

    Universality of fold-encoded localized vibrations in enzymes
    preprint, January 2019

    Many-Body Localization Landscape
    text, January 2019

    The landscape law for the integrated density of states
    journal, October 2021

    Localization of eigenfunctions via an effective potential
    journal, July 2019

    • Arnold, Douglas N.; David, Guy; Filoche, Marcel
    • Communications in Partial Differential Equations, Vol. 44, Issue 11
    • DOI: 10.1080/03605302.2019.1626420

    Computing the eigenstate localisation length at very low energies from Localisation Landscape Theory
    journal, June 2021

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      Figures / Tables found in this record:

      FIG. 1 (p. 4)figure
      FIG. 2 (p. 5)figure
      FIG. 3 (p. 8)figure
      FIG. 4 (p. 8)figure
      FIG. 5 (p. 10)figure
      FIG. 6 (p. 11)figure
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      FIG. 8 (p. 12)figure
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      FIG. 10 (p. 13)figure
      FIG. 11 (p. 13)figure
      FIG. 12 (p. 13)figure
      FIG. 13 (p. 14)figure
      FIG. 14 (p. 14)figure
      FIG. 15 (p. 15)figure
      FIG. 16 (p. 15)figure
      FIG. 17 (p. 16)figure
      FIG. 18 (p. 16)figure
      TABLE I (p. 17)table
      TABLE II (p. 17)table
      TABLE III (p. 17)table
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