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Title: Advanced Electronic Structure Calculations For Nanoelectronics Using Finite Element Bases and Effective Mass Theory.

Abstract

This paper describes our work over the past few years to use tools from quantum chemistry to describe electronic structure of nanoelectronic devices. These devices, dubbed "artificial atoms", comprise a few electrons, con ned by semiconductor heterostructures, impurities, and patterned electrodes, and are of intense interest due to potential applications in quantum information processing, quantum sensing, and extreme-scale classical logic. We detail two approaches we have employed: nite-element and Gaussian basis sets, exploring the interesting complications that arise when techniques that were intended to apply to atomic systems are instead used for artificial, solid-state devices.

Authors:
 [1];  [1];  [1];  [1];  [1];  [1];  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1429801
Report Number(s):
SAND-2017-7107J
655084
DOE Contract Number:
AC04-94AL85000
Resource Type:
Program Document
Country of Publication:
United States
Language:
English

Citation Formats

Gamble, John King, Nielsen, Erik, Baczewski, Andrew David, Moussa, Jonathan Edward, Gao, Xujiao, Salinger, Andrew G., and Muller, Richard P. Advanced Electronic Structure Calculations For Nanoelectronics Using Finite Element Bases and Effective Mass Theory.. United States: N. p., 2017. Web.
Gamble, John King, Nielsen, Erik, Baczewski, Andrew David, Moussa, Jonathan Edward, Gao, Xujiao, Salinger, Andrew G., & Muller, Richard P. Advanced Electronic Structure Calculations For Nanoelectronics Using Finite Element Bases and Effective Mass Theory.. United States.
Gamble, John King, Nielsen, Erik, Baczewski, Andrew David, Moussa, Jonathan Edward, Gao, Xujiao, Salinger, Andrew G., and Muller, Richard P. Sat . "Advanced Electronic Structure Calculations For Nanoelectronics Using Finite Element Bases and Effective Mass Theory.". United States. doi:.
@article{osti_1429801,
title = {Advanced Electronic Structure Calculations For Nanoelectronics Using Finite Element Bases and Effective Mass Theory.},
author = {Gamble, John King and Nielsen, Erik and Baczewski, Andrew David and Moussa, Jonathan Edward and Gao, Xujiao and Salinger, Andrew G. and Muller, Richard P.},
abstractNote = {This paper describes our work over the past few years to use tools from quantum chemistry to describe electronic structure of nanoelectronic devices. These devices, dubbed "artificial atoms", comprise a few electrons, con ned by semiconductor heterostructures, impurities, and patterned electrodes, and are of intense interest due to potential applications in quantum information processing, quantum sensing, and extreme-scale classical logic. We detail two approaches we have employed: nite-element and Gaussian basis sets, exploring the interesting complications that arise when techniques that were intended to apply to atomic systems are instead used for artificial, solid-state devices.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sat Jul 01 00:00:00 EDT 2017},
month = {Sat Jul 01 00:00:00 EDT 2017}
}

Program Document:
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  • We present a method for electronic-structure calculations based on the finite-element method. In this method all the calculations are performed in real space and the use of nonuniform mesh is possible. As a result, localized systems such as transition metals can be treated with ease, and even all-electron calculations can be performed within the same framework as well as the pseudopotential calculations. We apply our method to the all-electron calculations of H{sub 2} and pseudopotential calculations of Si. Our method is also applicable to mesoscopic systems.
  • We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the method is completely general and its convergence can be controlled systematically. Because the basis functions are strictly local in real space, the method allows for variable resolution in real space; produces sparse, structured matrices, enabling the effective use of iterative solution methods; and is well suited to parallel implementation. The method thus combines the significant advantages of both real-space-grid and basis-oriented approaches and so promises to be particularlymore » well suited for large, accurate {ital ab initio} calculations. We develop the theory of our approach in detail, discuss advantages and disadvantages, and report initial results, including electronic band structures and details of the convergence of the method. {copyright} {ital 1999} {ital The American Physical Society}« less
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