This paper presents B-splines and nonuniform rational B-splines (NURBS)-based finite element method for self-consistent solution of the Schrödinger wave equation (SWE). The new equilibrium position of the atoms is determined as a function of evolving stretching of the underlying primitive lattice vectors and it gets reflected via the evolving effective potential that is employed in the SWE. The nonlinear SWE is solved in a self-consistent fashion (SCF) wherein a Poisson problem that models the Hartree and local potentials is solved as a function of the electron charge density. The complex-valued generalized eigenvalue problem arising from SWE yields evolving band gaps that result in changing electronic properties of the semiconductor materials. The method is applied to indium, silicon, and germanium that are commonly used semiconductor materials. It is then applied to the material system comprised of silicon layer on silicon–germanium buffer to show the range of application of the method.
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September 2018
Research-Article
B-Splines and NURBS Based Finite Element Methods for Strained Electronic Structure Calculations
Arif Masud,
Arif Masud
Fellow ASME
3129-E Newmark Civil Engineering Laboratory,
University of Illinois at Urbana-Champaign,
205 N. Mathews Avenue,
Urbana, IL 61801
e-mail: amasud@illinois.edu
3129-E Newmark Civil Engineering Laboratory,
University of Illinois at Urbana-Champaign,
205 N. Mathews Avenue,
Urbana, IL 61801
e-mail: amasud@illinois.edu
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Ahmad A. Al-Naseem,
Ahmad A. Al-Naseem
3103 Newmark Civil Engineering Laboratory,
University of Illinois at Urbana-Champaign,
205 N. Mathews Avenue,
Urbana, IL 61801
e-mail: alnasee2@illinois.edu
University of Illinois at Urbana-Champaign,
205 N. Mathews Avenue,
Urbana, IL 61801
e-mail: alnasee2@illinois.edu
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Raguraman Kannan,
Raguraman Kannan
Mechanical Engineering Department,
Prince Mohammad Bin Fahd University,
e-mail: ragu2.kannan@gmail.com
Prince Mohammad Bin Fahd University,
e-mail: ragu2.kannan@gmail.com
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Harishanker Gajendran
Harishanker Gajendran
University of Illinois at Urbana-Champaign,
2112 Newmark Civil Engineering Laboratory,
205 N. Mathews Avenue,
Urbana, IL 61801
e-mail: harishankerg@gmail.com
2112 Newmark Civil Engineering Laboratory,
205 N. Mathews Avenue,
Urbana, IL 61801
e-mail: harishankerg@gmail.com
Search for other works by this author on:
Arif Masud
Fellow ASME
3129-E Newmark Civil Engineering Laboratory,
University of Illinois at Urbana-Champaign,
205 N. Mathews Avenue,
Urbana, IL 61801
e-mail: amasud@illinois.edu
3129-E Newmark Civil Engineering Laboratory,
University of Illinois at Urbana-Champaign,
205 N. Mathews Avenue,
Urbana, IL 61801
e-mail: amasud@illinois.edu
Ahmad A. Al-Naseem
3103 Newmark Civil Engineering Laboratory,
University of Illinois at Urbana-Champaign,
205 N. Mathews Avenue,
Urbana, IL 61801
e-mail: alnasee2@illinois.edu
University of Illinois at Urbana-Champaign,
205 N. Mathews Avenue,
Urbana, IL 61801
e-mail: alnasee2@illinois.edu
Raguraman Kannan
Mechanical Engineering Department,
Prince Mohammad Bin Fahd University,
e-mail: ragu2.kannan@gmail.com
Prince Mohammad Bin Fahd University,
e-mail: ragu2.kannan@gmail.com
Harishanker Gajendran
University of Illinois at Urbana-Champaign,
2112 Newmark Civil Engineering Laboratory,
205 N. Mathews Avenue,
Urbana, IL 61801
e-mail: harishankerg@gmail.com
2112 Newmark Civil Engineering Laboratory,
205 N. Mathews Avenue,
Urbana, IL 61801
e-mail: harishankerg@gmail.com
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 23, 2018; final manuscript received May 25, 2018; published online June 18, 2018. Editor: Yonggang Huang.
J. Appl. Mech. Sep 2018, 85(9): 091009 (11 pages)
Published Online: June 18, 2018
Article history
Received:
March 23, 2018
Revised:
May 25, 2018
Citation
Masud, A., Al-Naseem, A. A., Kannan, R., and Gajendran, H. (June 18, 2018). "B-Splines and NURBS Based Finite Element Methods for Strained Electronic Structure Calculations." ASME. J. Appl. Mech. September 2018; 85(9): 091009. https://doi.org/10.1115/1.4040454
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