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.
B-Splines and NURBS Based Finite Element Methods for Strained Electronic Structure Calculations
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.
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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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