Practical rule for trimming the DFT-1/2 self-interaction: Band gap, absolute band alignment, and defect properties of semiconductors

In recent years, density functional theory (DFT) for material design and discovery has gained significant interest. Traditional approximations with the DFT, like the local density approximation (LDA), tend to underestimate band gaps. On the other hand, the Heyd-Scuseria-Ernzerhof (HSE) method provides better accuracy for band gaps but at a high computational cost. In 2008, Ferreira et al. introduced the DFT-1/2 method, which improves band gap predictions at a computational cost similar to LDA. This method adjusts the valence band energy levels by applying Self-Interaction Correction at the local potential level. The extent of this correction is determined by a parameter called 'cutoff,' which must be self-consistently calculated. Although DFT-1/2 is computationally efficient, it requires extra effort in parameter tuning. Moreover, it may not accurately predict band gaps for certain materials, such as narrow-gap semiconductors. Variations like DFT-1/4 or shDFT-1/2 have been developed to address this issue, providing more accurate band gaps for these materials but reducing accuracy for others. Therefore, choosing the optimal method is essential and material-dependent. To overcome these empirical challenges, we introduce a novel parameter-free approach in the framework of DFT-1/2 (parameter-free DFT-1/2). Unlike the original DFT-1/2, which requires an additional self-consistent field (SCF) loop to determine the cutoff radius that maximizes the band gap, our proposed method calculates the cutoff radius directly from the crystal structure, thus eliminating the need for the extra SCF loop. We validated the performance of parameter-free DFT-1/2 by calculating key electronic properties such as band gaps, effective masses, ionization energies, and electron affinities. We also assessed defect levels in the charge transition states of a silicon point defect in silicon carbide (SiC) for the first time. The results demonstrate that parameter-free DFT-1/2 can reproduce spin density with accuracy comparable to HSE and that parameter-free DFT-1/2 is also effective for predicting charge transition levels in defects.