First Principles Prediction of Electronic Material Properties with Unprecedented Accuracy

Background and Aims
The presence and size of a band gap are two of the most important parameters when considering the electronic properties of any material. This is especially true in the semiconductor industry, where knowledge of the size and offset of band gaps in materials is essential in the design of new electronic devices, whether these are simple LEDs or modern transistors.

There is currently a large drive to use what is termed 'high throughput computational materials design' (HTCMD) (Curtarolo et al., 2013). Using this method of design, we computationally simulate large sets of candidate materials to screen for certain desirable properties. As experimental physics becomes more complex and expensive, use of HTCMD gives the opportunity to analyse millions of possible structures to produce a short-list of candidate structures to analyse experimentally.

The quantum mechanical level of the HTCMD hierarchy uses a set of highly sophisticated methods for the accurate and computationally efficient determination of material properties. It is this level of the HTCMD hierarchy that is the concern of this project.

Density functional theory (DFT) (Kohn & Sham, 1965) has been the standard for ab-initioelectronic-structure calculations for over three decades, and in that time has achieved rigorous theory to theory comparisons for ground state properties of systems (e.g. lattice constants, bond angles etc) (Lejaeghere et al., 2016). It has been a constant failing of DFT in the Kohn-Sham scheme, however, that the same level of rigour has not yet been achieved for excited state calculations, of which determining band-gaps and band-alignments are some of the most important.

The goal of this project then, is to develop so called post Kohn-Sham methods to be used in the quantum mechanical level of the HTCMD hierarchy that will achieve the same level of rigour and reliability in excited state calculations as is currently seen in ground state calculations.

Research Proposal
Research will begin with a one-dimensional implementation of DFT in the Kohn-Sham scheme, using the Hedin's GW approximation (Hedin, 1965). It is believed that all the essential physics and numerical convergence can be studied in some depth initially using only a one-dimensional model.

The Coulomb potential in this model will be mimicked using pseudopotentials and all electron capability will be included.

After analysing the accuracy and convergence of various approximations used in post Kohn-Sham schemes in one dimension, the model will be incorporated into a pre-existing three dimensional code and make use of parallel computational resources so as to utilise high performance computing facilities. This three-dimensional code will finally be used to construct a gold standard set of fully converged benchmark calculations, against which competing DFT implementations can compare themselves.

Time permitting, the inclusion of effects arising from special relativity may also be investigated.