Customizing PBE Exchange-Correlation functionals: A comprehensive approach for band gap prediction in diverse semiconductors

Accurate band gap prediction in semiconductors is crucial for materials science and semiconductor technology advancements. This paper extends the Perdew-Burke-Ernzerhof (PBE) functional for a wide range of semiconductors, tackling the exchange and correlation enhancement factor complexities within Density Functional Theory (DFT). Our customized functionals offer a clearer and more realistic alternative to DFT+U methods, which demand large negative U values for elements like Sulfur (S), Selenium (Se), and Phosphorus (P). Moreover, these functionals are more cost-effective than GW or Heyd-Scuseria-Ernzerhof (HSE) hybrid functional methods, therefore, significantly facilitating the way for unified workflows in analyzing electronic structure, dielectric constants, effective masses, and further transport and elastic properties, allowing for seamless calculations across various properties. We point out that such development could be helpful in the creation of comprehensive databases of band gap and dielectric properties of the materials without expensive calculations. Furthermore, for the semiconductors studied, we show that these customized functionals and the Strongly Constrained and Appropriately Normed semilocal density functional (SCAN) perform similarly in terms of the band gap.