First-principles based matrix Green's function approach to molecular electronic devices: general formalism

Abstract

Transport in molecular electronic devices is different from that in semiconductor mesoscopic devices in two important aspects: (1) the effect of the electronic structure and (2) the effect of the interface to the external contact. A rigorous treatment of molecular electronic devices will require the inclusion of these effects in the context of an open system exchanging particle and energy with the external environment. This calls for combining the theory of quantum transport with the theory of electronic structure starting from the first-principles. We present a rigorous yet tractable matrix Green's function approach for studying transport in molecular electronic devices, based on the NonEquilibrium Green's Function Formalism of quantum transport and the density-functional theory of electronic structure using local orbital basis sets. By separating the device rigorously into the molecular region and the contact region, we can take full advantage of the natural spatial locality associated with the metallic screening in the electrodes and focus on the physical processes in the finite molecular region. This not only opens up the possibility of using the existing well-established technique of molecular electronic structure theory in transport calculations with little change, but also allows us to use the language of qualitative molecular orbital theory to interpret and rationalize the results of the computation. We emphasize the importance of the self-consistent charge transfer and voltage drop on the transport characteristics and describe the self-consistent formulation for both device at equilibrium and device out of equilibrium. For the device at equilibrium, our method provides an alternative approach for solving the molecular chemisorption problem. For the device out of equilibrium, we show that the calculation of elastic current transport through molecules, both conceptually and computationally, is no more difficult than solving the chemisorption problem.

Density functional theory method for non-equilibrium charge transport calculations: TRANSAMPA

“…The main goal of the present implementation, as in previous ones [3][4][5]12], is to devise a scheme to calculate the above Green's functions, and thus the current, from a fully ab initio method. We then use a DFT formalism.…”

“…1). This partitioning in different regions, and the possibility to work with finite size matrices to simulate an open, nonperiodic infinite system, is made possible by the use of localized basis sets [4]. Here we use all the developments that have already been implemented in the SIESTA code, in particular, localized atomic orbitals (which are strictly zero beyond certain cutoff radii).…”

“…Due to the fact that a localized set of basis functions is used, the matrices H and S can be written in tri-diagonal form. This makes it possible to obtain an expression for the retarded matrix Green's function for the central region [4]. Note that the left and right electrodes do not have a direct interaction, that is H L,R = S R,L = 0 [21].…”

“…Albeit with some drawbacks, as discussed later on, the Density Functional Theory Non-Equilibrium Green's Function (DFT-NEGF) approach [3][4][5] to charge transport calculations comes very close to satisfying a good number of these requirements.…”

Does molecular electronics compute?

“…Experiments with single-molecule junctions, for example, have become more robust, reliable and reproducible 2 . At the same time, theoretical methods based on Green's function theory have been developed and have allowed researchers to investigate the fundamental properties of single molecules under nonequilibrium conditions 3 . These advances have led to the discovery of a host of novel effects that have only recently been systematically investigated.…”