Büttiker probes and the recursive Green's function: An efficient approach to include dissipation in general configurations

Abstract

An efficient and compact approach to the inclusion of dissipative effects in Non-Equilibrium Green's Function (NEGF) simulations of electronic systems is introduced. The algorithm is based on two well known methods in the literature, firstly that of the so-called Recursive Green's Function (RGF) and secondly that of Büttiker probes. Numerical methods for exact evaluation of the Jacobian are presented by a direct extension to RGF which can be modularly included in any codebase that uses it presently. Then using both physical observations and numerical methods, the computation time of the Büttiker probe Jacobian is improved significantly. An improvement to existing phonon models within Büttiker probes is then demonstrated in the simulation of fully atomistic graphene nanoribbon based field effect transistors in n-i-n and p-i-n operation.

Taylor series of Landauer conductance

“…Taylor series could improve the analysis of tight-binding structures, by increasing its computational efficiency, avoiding the calculation of the transmission function at too many energies. Moreover, they can be used to speed up the determination of Büttiker conductance in multiterminal devices, where the Newton-Raphson root-finder method could be employed to find the chemical potential such that the total current through each probe is zero [23].…”

“…Alternatively, a Taylor series may provide further information about the behavior of conductance in the neighborhood of each energy. By means of perturbation theory, firstorder Taylor expansions of Landauer conductance have been useful to analyze Büttiker probes [23], transition voltage spectroscopy [24], inelastic electron tunneling spectra [25], electromagnetic induced transparency and reflection [13], and quantum pumping [26]. These studies could be improved with higher-order Taylor expansions.…”

Nonequilibrium Green’s function method for phonon heat transport in quantum system

“…It provide a heuristic but efficient way to introduce scattering in NEGF method. The method is original developed for modeling inelastic electron scattering in the framework of NEGF [112][113][114][115]. Miao et al [100] extended this method into the phonon system to model anharmonic phonon scattering.…”

The effect of magnetic impurity scattering on transport in topological insulators

“…In previous works [31,32] it was shown that for certain models the in-scattering function may be replaced with some simpler form corresponding to Büttiker probes. We have found in this work that simple replacement with a Fermi-Dirac distribution (or sum thereof) -though able to reproduce effects with the correct order of magnitude -was insufficient to fully describe the physics related to magnetization, and led to an additional resistance term for collinear spins, in contradiction to the full in-scattering function.…”