共价半导体的高效密度泛函带隙修正

It is a common problem that the band gaps in semiconductors are systematically underestimated using the LDA/GGA of density functional theory. The LDA-1/2 method, proposed by Ferreira, does self-energy correction for the holes in real space. Hence it is very efficient and predicts satisfactory band structures for ionic semiconductors. Nevertheless, the method is not working well for covalent semiconductors, besides the fact that its operation principle is obscure for covalent semiconductors. This project aims at improving LDA-1/2 by using shell-like self-energy potential instead of spherical self-energy potential, in order to fit the location of holes in covalent semiconductors. Moreover, the project will also fix the standard operation principle for LDA-1/2, and resolve the intrinsic contradiction stemming from the LDA-1/2 theory. For the distinct purposes of material design and engineering, two modes of the new calculation method will be proposed: shLDA-1/2 and shLDA-x-y, respectively. They are both designed for accurate band structure calculation for covalent semiconductors at the computational cost of LDA. Dozens of bulk covalent semiconductors and six classes of 2D covalent semiconductors will be tested for their band structures. Moreover, shLDA-1/2 will be utilized to systematically study the variation of band structures in GeSn with respect to the doping concentration of Sn as well as the applied strain. Such application helps to demonstrate the power of the new method in frontier problems. In addition, the rule of assigning self-energy potentials to adjacent atoms forming the chemical bonds will be derived, so as to set up a quantitative identification of the extent of ionic bonding. Finally, the intelligent prediction algorithm for best self-energy cutoff radii will be developed, with software implementation, in order to popularize the application of these new methods.

密度泛函LDA/GGA近似会系统地低估半导体的带隙。Ferreira的LDA-1/2方法在实空间中进行空穴的自能修正，能快速准确地计算离子型半导体的能带，但对共价半导体效果差，且规则不明晰。本项目改进LDA-1/2，提出以球壳型自能势代替球形自能势以适应共价半导体的空穴位置，并解决LDA-1/2操作规范的问题和理论内在的矛盾。针对材料设计和工程计算，分别提出从头算的shLDA-1/2以及含有参数的shLDA-x-y方法，以期在LDA的运算量下准确计算共价半导体的能带。针对数十种体相共价半导体和六大类二维共价半导体展开能带结构的全面测试。使用shLDA-1/2解决GeSn体系在不同Sn掺杂浓度和应变下的能带变化规律，展示方法在前沿问题中的应用价值。在shLDA-x-y中通过掌握自能势划分的规律，建立标记化学键离子性程度的定量方法。实现截断半径智能预测的加速算法与软件，为方法的推广奠定基础。

对半导体带隙的系统性低估是密度泛函理论应用于光电子、微电子领域的主要问题之一。器件级别的第一原理计算要求能带计算方法速度、精度兼备。本项目推广了巴西学者Ferreira等人提出的DFT-1/2能带计算方法，通过引入双变分的球壳型截断函数，提出了新型shell DFT-1/2算法，能够同时适合于离子半导体和共价半导体的能带计算。特别是关于半导体Ge的能带计算结果与实验高度符合，对该半导体计算的速度、精度均优于HSE06杂化泛函。对于III-V族半导体如GaAs，虽然DFT-1/2与shell DFT-1/2都能给出满意的直接带隙值，但新方法在能带结构细节上与实验结果更匹配。新方法应用于超晶格红外探测材料等领域，取得了良好的效果，具有实用价值。Shell DFT-1/2算法发表后两年之内，已经被引入到WIEN2k、QuantumATK两款国际著名的第一原理计算软件中，并在ALKEMIE等高通量计算平台上获得了应用。项目研究成果发表期刊论文10篇，培养博士1名，硕士4名，产出一款Habit软件。