Defect calculations in Ga-based semiconductors using optimal hybrid functionals

半导体的功能与其点缺陷密切相关，点缺陷控制着材料的电子和光学行为。近年来，缺陷物理的研究重点已经从微电子转向光电子学和光伏学，即从传统的禁带宽度较窄的元素和二元半导体材料转向结构更为复杂的宽带隙材料。这些材料的电子结构计算表明，密度泛函理论(DFT)的局域和半局域近似是不可信的：部分原因是带隙宽度的较大误差，但也是因为缺陷态的人为离域(这使缺陷能级变浅，并阻止了小极化子态的重现)。虽然超越(半)局部密度泛函的第一性原理总能量计算还不能对超晶胞进行，但我们已经表明，HSE06筛选的杂化泛函对C、Si、SiC、Ge和TiO2中的缺陷产生了非常准确的结果。我们认为，这一成功与这些材料中的HSE06以适当的分段线性函数形式提供总能量有关，这是因为半局域交换和Hartree-Fock交换之间的误差补偿。镓基半导体具有巨大的技术重要性：除了GaN LED之外，Ga2O_3还具有作为功率MOSFET的紫外光透明电极和半导体的巨大潜力，而Ga基黄铜矿(CuGaS_2，CuGaSe_2)被认为是光伏领域的重要材料。HSE06低估了这些材料的带隙，我们最近已经证明，简单地调整混合参数来纠正这一点(像文献中通常的那样)并不能导致正确的缺陷能级。调整混合和屏蔽参数，重现能隙并满足广义Koopman定理，使我们能够获得总能量随占位数的正确的分段线性行为，从而准确地描述缺陷态。当然，此过程会产生特定于材料的参数。这个项目的目的有两个：一方面，我们想要调查上面提到的镓基半导体(也包括CuInS2和CuInSe2)的最佳参数的趋势，以便建立为一类材料寻找筛选的杂化材料的一般规则，另一方面，执行准确的计算以确定这些材料中的重要缺陷中心。

The functionality of semiconductors is closely connected to their point defects, which control the electronic and optical behavior of the material. The emphasis of defect physics has shifted in recent years from micro- to optoelectronics and photovoltaics, i.e., from the traditional elemental and binary semiconductors, with relatively narrow gap, to wide band gap materials of more complicated structures. Electronic structure calculations in these materials have revealed that local and semi-local approximations to density functional theory (DFT) cannot be trusted: partly because the bigger error in the width of the band gap but also because of the artificial delocalization of defect states (which, make the defect level shallower and preclude the reproduction of small polaron states). While first-principles total energy calculations beyond (semi)local DFT cannot yet be carried out for supercells, we have shown that the HSE06 screened hybrid functional yields very accurate results for defects in C, Si, SiC, Ge and TiO2. We have suggested that the success is connected to the fact that HSE06 in these materials provides the total energy as an appropriate piece-wise linear function of the occupation numbers, because of error compensation between semi-local and Hartree-Fock exchange.Gallium based semiconductors have immense technological importance: besides the GaN LEDs, Ga2O3 has also great potential for application as UV-transparent electrode and se-miconductor for power MOSFETs, and Ga-based chalcopyrites (CuGaS2, CuGaSe2) are considered in photovoltaics. HSE06 underestimates the band gap of these materials and we have recently shown that simple tuning of the mixing parameter to correct that (as usual in the literature), does not lead to correct defect levels. Tuning the mixing and the screening parameters, to reproduce the gap and to fulfill the generalized Koopman theorem, has allowed us to achieve the correct piece-wise linear behavior of the total energy as a function of the occupation numbers and, consequently, the accurate description of defect states. Of course, this procedure leads to material specific parameters. The aim of this project is twofold: on the one hand we would like to investigate the trends in the optimal parameters across the Ga-based semiconductors mentioned above (but also for CuInS2 and CuInSe2), in order to establish general rules for finding a screened hybrid for a class of materials and, on the other, perform accurate calculations to identify important defect centers in these materials.