A self-consistent tight binding model for hydrocarbon systems: application to quantum transport simulation

Abstract

A self-consistent environment-dependent (SC-ED) tight binding (TB) method for hydrocarbons that was developed for quantum transport simulations is presented. The method builds on a non-self-consistent environment-dependent TB model for carbon (Tang et al 1996 Phys. Rev. B 53 979) with parameters added to describe hydrocarbon bonds and to account for self-consistent charge transfer. The SC-EDTB model assumes an orthogonal basis set. Orthogonality is a key element for adapting the SC-EDTB scheme to transport problems because it substantially increases the efficiency of the NewtonRaphson algorithm used to accelerate self-consistency convergence under nonequilibrium conditions. Compared to most existing TB schemes the SC-EDTB scheme is distinctive in two respects. First, self-consistency is added through the exact evaluation of Hartree and linear expansion of exchange integrals. All Hamiltonian elements belonging to the same atom are affected by charge transfer, not just the diagonal elements. The second distinction is the choice of SC-EDTB parameters; they were fitted to Mulliken populations and eigenvalue spectra rather than energies or elastic properties. The former are directly related to the conductivity and potential profile, which are essential for transport simulation. No two-centre repulsive term parametrization was performed. The functionality of the method is exemplified by computing I -V curves, nonequilibrium potential profiles and current density for a resonant tunnelling device.

Electron density and transport in top-gated graphene nanoribbon devices: First-principles Green function algorithms for systems containing a large number of atoms

“…The DFT part of our simulation, which constructs the Hamiltonian of the central region as an input for NEGF post-processing to obtain the device transport properties, is performed by using the SC-EDTB model. 57,58 This model accounts for atomic polarization and interatomic charge transfer in a standard DFT-like fashion while making it possible to use a minimal basis set of four Gaussian orbitals per carbon and one orbital per hydrogen atom. The usage of such minimal basis set allows us to reduce the size of matrices H i,i and H i,i+1 discussed in Sec.…”

Extensions of DFTB to investigate molecular complexes and clusters

“…In their simplest versions, TB models do not include any explicit electrostatic effects. In the case of charged particles or heterogeneous systems with strong charge transfer, atomic charges can be taken into account through electrostatic corrections of the Hamiltonian matrix elements, with either perturbative 83–85, or self‐consistent solution 57, 59, 86–89. The DFTB scheme 57, 59 belongs to the latter class.…”

“…Many TB developments and applications were essentially concerned with homogenous bulk and nanoparticles. However self‐consistent schemes now make elaborate applications possible, such as quantum electronic transport in hydrogen passivated carbon systems 88. Montagnon and Spiegelman 80 have parameterized a self‐consistent TB scheme for neutral and multiply charged clusters that is also suitable for fragmentation studies.…”

Density-functional tight-binding: basic concepts and applications to molecules and clusters

“…In the simplest version with no electrostatics and no self-consistency included, e V is supposed to account for electron screening. In the case of ionic or iono-covalent systems or systems with significant charge fluctuations, interactions between on-site charges can be taken into account, either perturbatively [42][43][44] or self-consistently [21,40,[45][46][47][48][49][50][51]. Tightbinding methods may also be considered according to the origin of their parametrization: either semi-empirical tight-binding, where simple functional forms are used for the matrix elements fitted to reproduce ab initio or experimental data, or ab initio tight-binding, where the formalism, functions and inputs are fully derived from first principles references [47].…”