  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.
