First Principles Prediction of Electronic Material Properties with Unprecedented Accuracy

背景和目的在考虑任何材料的电子特性时，带隙的存在和大小是两个最重要的参数。在半导体行业尤其如此，在半导体行业，无论是简单的led还是现代晶体管，材料中带隙的大小和偏移量的知识在新电子设备的设计中都是必不可少的。目前有很大的动力使用所谓的“高通量计算材料设计”（HTCMD） （Curtarolo et al., 2013）。使用这种设计方法，我们计算模拟大量候选材料，以筛选某些理想的特性。随着实验物理变得越来越复杂和昂贵，使用HTCMD提供了分析数百万种可能结构的机会，以产生候选结构的简短列表以进行实验分析。HTCMD层次的量子力学级别使用一套高度复杂的方法来精确和计算高效地确定材料特性。这个项目关注的是HTCMD层次结构的这一层。密度泛函理论（DFT） （Kohn & Sham, 1965）三十多年来一直是ab初始电子结构计算的标准，并且在此期间已经实现了系统基态特性（例如晶格常数，键角等）的严格理论与理论比较（Lejaeghere等人，2016）。然而，在Kohn-Sham方案中，DFT一直是失败的，激发态计算尚未达到相同的严格程度，其中确定带隙和带对准是最重要的一些。该项目的目标是开发所谓的后Kohn-Sham方法，用于HTCMD层次结构的量子力学水平，该方法将在激发态计算中达到与目前在基态计算中看到的相同水平的严密性和可靠性。研究计划研究将从Kohn-Sham方案中DFT的一维实现开始，使用Hedin的GW近似（Hedin, 1965）。我们相信，所有基本的物理和数值收敛都可以用一维模型进行初步的深入研究。该模型中的库仑势将使用伪势来模拟，并将包括所有电子能力。在分析了后科恩-深方案中使用的各种一维近似的准确性和收敛性后，该模型将被纳入现有的三维代码中，并利用并行计算资源，以利用高性能计算设施。这个三维代码最终将被用来构建一个完全收敛的基准计算的黄金标准集，与之竞争的DFT实现可以相互比较。如果时间允许，还可以研究狭义相对论产生的效应。

Background and AimsThe 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 ProposalResearch 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.