First principles electron transport: finite-element implementation for nanostructures

We have modeled transport properties of nanostructures using the Green's function method within the framework of the density-functional theory. The scheme is computationally demanding so that numerical methods have to be chosen carefully. A typical solution to the numerical burden is to use a special basis-function set, which is tailored to the problem in question, for example, the atomic orbital basis. In this paper we present our solution to the problem. We have used the finite element method (FEM) with a hierarchical high-order polynomial basis, the so-called p-elements. This method allows the discretation error to be controlled in a systematic way. The p-elements work so efficiently that they can be used to solve interesting nanosystems described by non-local pseudopotentials. We demonstrate the potential of the implementation with two different systems. As a test system a simple Na-atom chain between two leads is modeled and the results are compared with several previous calculations. Secondly, we consider a thin hafnium dioxide (HfO2) layer on a silicon surface as a model for a gate structure of the next generation of microelectronics.