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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]
  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), Building Technologies Office (EE-5B); 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.
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. doi:10.1103/physrevb.95.144204.
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. doi:10.1103/physrevb.95.144204. https://www.osti.gov/servlets/purl/1429093.
@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 = {2017},
month = {4}
}

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Cited by: 6 works
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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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