Self-Consistent Environment-Dependent Tight-Binding. Methodology and Applications.

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Title: Self-Consistent Environment-Dependent Tight-Binding. Methodology and Applications.
Author: Areshkin, Denis Alexeyevich
Advisors: Dr. Dieter P. Griffis, Committee Member
Dr. Donald W. Brenner, Committee Chair
Dr. Jerzy Bernholc, Committee Member
Dr. Klaus J. Bachmann, Committee Member
Abstract: In the last several years dramatic advances have been demonstrated in the area of quantum electronic transport. A large part of transport methodology is borrowed from quantum chemistry methods. Many studies in this field use well-established general-purpose ab-initio computer codes, which are sometimes not well suited for transport problems. The present research is motivated by a need for a tool that meets specific re-quirements essential for quantum transport simulation techniques. These requirements include: (a) self-consistency, (b) a minimal and (c) orthogonal basis set. Self-consistency is necessary for simulations involving charge transfer and applied fields. A minimal ba-sis set is desirable because non-equilibrium charge density evaluation requires massive O(N 3) operations. The orthogonality constraint is imposed because popular energy minimization techniques can not be used to accelerate self-consistency convergence in non-equilibrium cases. The choice for a convergence acceleration algorithm is limited to the class of methods that evaluate the derivatives of the output charge density with re-spect to input density. The size of the matrices involved in these techniques is propor-tional to the number of non-zero overlap matrix elements and becomes prohibitively large for non-orthogonal basis sets. We developed a hybrid scheme for hydrocarbons based on Density Functional Theory, which is the self-consistent extension of the Environment Dependent Tight Bind-ing (EDTB) method for carbon. The EDTB model refers to an orthogonal minimal basis set tight-binding (TB) method with two-center hopping matrix integrals that depend not only on the mutual arrangement of the two atoms on which the basis functions are cen-tered, but also on the arrangement of neighboring atoms as well. The EDTB model effec-tively includes the dependence of hopping integrals on the surrounding electron density. This feature makes the EDTB approach highly transferable compared to standard TB, and in many cases this method can produce even better results than DFT with the same num-ber of basis functions per atom. We used a conventional LCAO DFT approach to add charge transfer to the origi-nal EDTB model by including exact Hartree and linear expansion of exchange integrals. C-H bond parameterization consistent with the original EDTB model was also added. In the equilibrium case self-consistent EDTB (SC-EDTB) employs the variant of Newton-Raphson algorithm for self-consistency convergence acceleration. The scaling of the Newton-Raphson algorithm with system size was improved from O(N 4) to O(N 3). The convergence acceleration technique makes the SC-EDTB approach very robust with re-spect to the starting electron density and applied fields; convergence is achieved even when the potential variation along the system is larger than the system spectral energy range. The usual number of iterations required to achieve convergence is 2-3 for semi-conducting systems, and 7-10 for metallic systems. Adaptation of the convergence accel-eration algorithm for non-equilibrium cases is in progress. Currently the non-equilibrium density is obtained by scalar charge mixing with strong damping, which requires several hundred iterations to achieve self-consistency. Equilibrium and non-equilibrium exam-ples are used to demonstrate the functionality of SC-EDTB method.
Date: 2002-12-03
Degree: PhD
Discipline: Materials Science and Engineering

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