SelfConsistent EnvironmentDependent TightBinding. Methodology and Applications.
Title:  SelfConsistent EnvironmentDependent TightBinding. 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 wellestablished generalpurpose abinitio 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 requirements essential for quantum transport simulation techniques. These requirements include: (a) selfconsistency, (b) a minimal and (c) orthogonal basis set. Selfconsistency is necessary for simulations involving charge transfer and applied fields. A minimal basis set is desirable because nonequilibrium 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 selfconsistency convergence in nonequilibrium 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 respect to input density. The size of the matrices involved in these techniques is proportional to the number of nonzero overlap matrix elements and becomes prohibitively large for nonorthogonal basis sets. We developed a hybrid scheme for hydrocarbons based on Density Functional Theory, which is the selfconsistent extension of the Environment Dependent Tight Binding (EDTB) method for carbon. The EDTB model refers to an orthogonal minimal basis set tightbinding (TB) method with twocenter hopping matrix integrals that depend not only on the mutual arrangement of the two atoms on which the basis functions are centered, but also on the arrangement of neighboring atoms as well. The EDTB model effectively 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 number of basis functions per atom. We used a conventional LCAO DFT approach to add charge transfer to the original EDTB model by including exact Hartree and linear expansion of exchange integrals. CH bond parameterization consistent with the original EDTB model was also added. In the equilibrium case selfconsistent EDTB (SCEDTB) employs the variant of NewtonRaphson algorithm for selfconsistency convergence acceleration. The scaling of the NewtonRaphson algorithm with system size was improved from O(N 4) to O(N 3). The convergence acceleration technique makes the SCEDTB approach very robust with respect 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 23 for semiconducting systems, and 710 for metallic systems. Adaptation of the convergence acceleration algorithm for nonequilibrium cases is in progress. Currently the nonequilibrium density is obtained by scalar charge mixing with strong damping, which requires several hundred iterations to achieve selfconsistency. Equilibrium and nonequilibrium examples are used to demonstrate the functionality of SCEDTB method. 
Date:  20021203 
Degree:  PhD 
Discipline:  Materials Science and Engineering 
URI:  http://www.lib.ncsu.edu/resolver/1840.16/3023 
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