Paula Havu

Three real-space discretization techniques in electronic structure calculations

A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.

Conductance oscillations in metallic nanocontacts

We examine the conductance properties of a chain of Na atoms between two metallic leads in the limit of low bias. Resonant states corresponding to the conductance channel and the local charge neutrality condition cause conductance oscillations as a function of the number of atoms in the chain. Moreover, the geometrical shape of the contact leads influences the conductivity by giving rise to additional oscillations as a function of the lead opening angle.

Interfacial oxide growth at silicon∕high-k oxide interfaces: First principles modeling of the Si–HfO2 interface

We have performed first principles calculations to investigate the structure and electronic properties of several different Si–HfOx interfaces. The atomic structure has been obtained by growing HfOx layer by layer on top of the Si(100) surface and repeatedly annealing the structure using ab initio molecular dynamics. The interfaces are characterized via their geometric and electronic properties, and also using electron transport calculations implementing a finite element based Green’s function method. We find that in all interfaces, oxygen diffuses towards the interface to form a silicon dioxide layer. This results in the formation of dangling Hf bonds in the oxide, which are saturated either by hafnium diffusion or Hf–Si bonds. The generally poor performance of these interfaces suggests that it is important to stabilize the system with respect to lattice oxygen diffusion.

Nonequilibrium electron transport in two-dimensional nanostructures modeled using Green's functions and the finite-element method

We use the effective-mass approximation and the density-functional theory with the local-density approximation for modeling two-dimensional nanostructures connected phase coherently to two infinite leads. Using the nonequilibrium Greens-function method the electron density and the current are calculated under a bias voltage. The problem of solving for the Greens functions numerically is formulated using the finite-element method (FEM). The Greens functions have nonreflecting open boundary conditions to take care of the infinite size of the system. We show how these boundary conditions are formulated in the FEM. The scheme is tested by calculating transmission probabilities for simple model potentials. The potential of the scheme is demonstrated by determining nonlinear current-voltage behaviors of resonant tunneling structures.

Electron transport through quantum wires and point contacts

We have studied quantum wires using the Greens function technique within density-functional theory, calculating electronic structures and conductances for different wire lengths, temperatures, and bias voltages. For short wires, i.e., quantum point contacts, the zero-bias conductance shows as a function of the gate voltage and at a finite temperature a plateau at around

Spin-dependent electron transport through a magnetic resonant tunneling diode

0.7{G}_{0}

Finite-element implementation for electron transport in nanostructures

. (

Effects of chemical functionalization on electronic transport in carbon nanobuds

{G}_{0}=2{e}^{2}∕h

Modeling of electronic transport in nanostructures

is the quantum conductance.) The behavior, which is caused in our mean-field model by spontaneous spin polarization in the constriction, is reminiscent of the so-called 0.7 anomaly observed in experiments. In our model the temperature and the wire length affect the conductance\char21{}gate-voltage curves similarly as in experiments.

Large-scale surface reconstructions from first principles: Au(100) and Pt(100) by all-electron DFT

Electron-transport properties in nanostructures can be modeled, for example, by using the semiclassical Wigner formalism or the quantum-mechanical Green’s function formalism. We compare the performance and the results of these methods in the case of magnetic resonant-tunneling diodes. We have implemented the two methods within the self-consistent spin-density-functional theory. Our numerical implementation of the Wigner formalism is based on the finite-difference scheme whereas for the Green’s function formalism the finiteelement method is used. As a specific application, we consider the device studied by Slobodskyyet al. fPhys. Rev. Lett. 90, 246601 s2003dg and analyze their experimental results. The Wigner and Green’s function formalisms give similar electron densities and potentials but, surprisingly, the former method requires much more computer resources in order to obtain numerically accurate results for currents. Both of the formalisms can be used to model magnetic resonant tunneling diode structures.