Chapter 8 The gDFTB tool for molecular electronics

Abstract

The gDFTB approach for transport computations is based on the density functional tight-binding (DFTB) method, extended to the non-equilibrium Green's functions (NEGF) for the self-consistent computation of charge density and electronic transport. The gDFTB method allows a nearly first-principle treatment of systems comprising a large number of atoms. The Green's function technique enables the computation of the tunneling current flowing between two contacts in a manner consistent with the open boundary conditions that naturally arise in transport problems. The NEGF formalism allows computing the charge density consistently with the non-equilibrium conditions in which a molecular device is driven when biased by an external field. The key ingredient of the self-consistent loop is the solution of the Hartree potential needed in the density functional Hamiltonian. The Hartree potential is calculated by solving the three-dimensional Poisson's equation, for the corresponding non-equilibrium charge density computed via the NEGF formalism.