Ab-Initio and Machine-Learning Methods to Study Defects in Complex Materials

Defects are present in all materials and are essential for many applications. However, defects can also reduce device performances, and understanding their properties is therefore crucial to further push the boundaries of solar-cell efficiency.
In this context, chalcopyrites (Cu(In,Ga)Se2/Cu(In,Ga)S2) have emerged as an alternative to silicon-based solar cells. They are intrinsically doped and inherit a tunable band gap depending on the ratio of indium and gallium. This broad range of band gaps makes them a well-suited candidate for tandem-solar cells.
We want to understand the defect properties in CuInS2 and CuGaS2 by conducting a detailed study of the most common intrinsic defects in these materials. We use the Heyd, Scuseria and Ernzerhof (HSE) hybrid functional and investigate the impact of the two HSE parameters, α and ω, on the band gap and compliance with the general Koopmans' theorem. With the optimized HSE parameters, we calculate the thermodynamic charge transition levels to access the electronic properties. We further investigate the optical transition levels, by considering that optical transitions are vertical within a configuration coordinate diagram. Our results emphasize that for comparison with photoluminescence measurements, this difference (corresponding to a Franck-Condon shift) should not be neglected. We further calculate optical transitions with a ∆-SCF approach in which we constrain an electron to an unoccupied state enabling a charge neutral excited state.
A comparison with the available photoluminescence measurements in the literature reveals multiple candidates for the experimentally observed deep defect transitions. For indium-rich Cu(In,Ga)S2, we find candidates for both deep defect transitions, namely Cu_In/Ga, V_In, V_Cu, Cu_i and In_Cu. Furthermore, our results suggest three defects, V_Cu, Cu_Ga, and Cu_i as possible candidates that could be involved in a broad defect peak around 2.15 eV observed in measurements on CuGaS2.
The complexity of these materials and the need for supercells to compute defect properties limit us to total energy evaluations. Thus, calculations of macroscopic properties of defects remains difficult. One possible solution is to use semi-empirical methods like tight-binding that are capable of calculating the properties of large super cells with many more atoms than density functional theory (DFT) is capable of.
Fitting such a semi-empirical tight-binding model to a pristine crystal via the band structure is common practice. However, the fit to the defective band structure become difficult because the increase of the cell in real space results in a folding in reciprocal space. We therefore present a workflow that uses the atom- and orbital-projected density of states instead. Additionally, introducing defects into the crystal perturbs its structure. The fit of the large number of different parameters for these defective systems presents a considerable challenge. We reduce the number of fitting parameters to a minimum by introducing two distance dependencies for the tight-binding parameters. This allows a neural network to learn the impact of defects on the host material within the tight-binding approximation.
We investigate carbon substitutions (monomer and dimer) in hexagonal boron nitride and demonstrate the capability of the workflow to predict tight-binding parameters for deep defect states. To address transferability of the tight-binding model, we show that it can describe defects under strained conditions and that it maintains DFT accuracy for different distances between neighboring defects. The method opens a path to understanding complicated defect landscapes using a computationally affordable semi-empirical approach without sacrificing accuracy, thereby enabling investigations of macroscopic defect properties.