Nonequilibrium Green function modelling of transport in mesoscopic systems

A generalized Landauer formula, derived with the methods due to Keldysh, and Baym and Kadanoff, is gaining widespread use in the modeling of transport in a large number of different mesoscopic systems. We review some of the recent developments, including transport in semiconductor superlattices, calculation of noise, and nanoelectromechanical systems.Comment: Contribution to "Progress in Nonequilibrium Green Functions", Dresden, Germany, 19-22 August, Editor: Michael Bonit

Time-dependent transport in interacting and non-interacting mesoscopic systems

We consider a mesoscopic region coupled to two leads under the influence of external time-dependent voltages. The time dependence is coupled to source and drain contacts, the gates controlling the tunnel- barrier heights, or to the gates which define the mesoscopic region. We derive, with the Keldysh nonequilibrium Green function technique, a formal expression for the fully nonlinear, time-dependent current through the system. The analysis admits arbitrary interactions in the mesoscopic region, but the leads are treated as noninteracting. For proportionate coupling to the leads, the time-averaged current is simply the integral between the chemical potentials of the time-averaged density of states, weighted by the coupling to the leads, in close analogy to the time-independent result of Meir and Wingreen (PRL {\bf 68}, 2512 (1992)). Analytical and numerical results for the exactly solvable non-interacting resonant-tunneling system are presented.Comment: 42 pages, 13 figures (available either as ps-files, or as FAX, upon request), RevTex 3.

Density functional calculations of nanoscale conductance

Density functional calculations for the electronic conductance of single molecules are now common. We examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradient-corrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, XC corrections to the current are missed by the standard methodology. For finite bias, a new methodology for performing calculations can be rigorously derived using an extension of time-dependent current density functional theory from the Schroedinger equation to a Master equation.Comment: topical review, 28 pages, updated version with some revision

Interface Roughness Effects in Ultra-Thin Tunneling Oxides

Advanced MOSFET for ULSI and novel silicon-based devices require the use of ultrathin tunneling oxides where non-uniformity is often present. We report on our theoretical study of how tunneling properties of ultra-thin oxides are affected by roughness at the silicon/oxide interface. The effect of rough interfacial topography is accounted for by using the Planar Supercell Stack Method (PSSM) which can accurately and efficiently compute scattering properties of 3D supercell structures. Our results indicate that while interface roughness effects can be substantial in the direct tunneling regime, they are less important in the Fowler-Nordheim regime

Exploration of the memory effect on the photon-assisted tunneling via a single quantum dot: A generalized Floquet theoretical approach

The generalized Floquet approach is developed to study memory effect on electron transport phenomena through a periodically driven single quantum dot in an electrode-multi-level dot-electrode nanoscale quantum device. The memory effect is treated using a multi-function Lorentzian spectral density (LSD) model that mimics the spectral density of each electrode in terms of multiple Lorentzian functions. For the symmetric single-function LSD model involving a single-level dot, the underlying single-particle propagator is shown to be related to a 2 x 2 effective time-dependent Hamiltonian that includes both the periodic external field and the electrode memory effect. By invoking the generalized Van Vleck (GVV) nearly degenerate perturbation theory, an analytical Tien-Gordon-like expression is derived for arbitrary order multi- photon resonance d.c. tunneling current. Numerically converged simulations and the GVV analytical results are in good agreement, revealing the origin of multi- photon coherent destruction of tunneling and accounting for the suppression of the staircase jumps of d.c. current due to the memory effect. Specially, a novel blockade phenomenon is observed, showing distinctive oscillations in the field-induced current in the large bias voltage limit

Theoretical Principles of Single-Molecule Electronics: A Chemical and Mesoscopic View

Exploring the use of individual molecules as active components in electronic devices has been at the forefront of nanoelectronics research in recent years. Compared to semiconductor microelectronics, modeling transport in single-molecule devices is much more difficult due to the necessity of including the effects of the device electronic structure and the interface to the external contacts at the microscopic level. Theoretical formulation of the problem therefore requires integrating the knowledge base in surface science, electronic structure theory, quantum transport and device modeling into a single unified framework starting from the first-principles. In this paper, we introduce the theoretical framework for modeling single-molecule electronics and present a simple conceptual picture for interpreting the results of numerical computation. We model the device using a self-consistent matrix Green's function method that combines Non-Equilibrium Green's function theory of quantum transport with atomic-scale description of the device electronic structure. We view the single-molecule device as "heterostructures" composed of chemically well-defined atomic groups, and analyze the device characteristics in terms of the charge and potential response of these atomic groups to perturbation induced by the metal-molecule coupling and the applied bias voltage. We demonstrate the power of this approach using as examples devices formed by attaching benzene-based molecules of different size and internal structure to the gold electrodes through sulfur end atoms.Comment: To appear in International Journal of Quantum Chemistry, Special Issue in memory of J.A. Pople. 13 pages, 9 figure