The screening effect on the Hartree-Fock (HF) exchange term plays a key role in the investigation of solid-state materials by first-principles electronic structure calculations. We recently proposed a novel screened HF exchange potential, in which the inverse of the dielectric constant represents the fraction of the HF exchange term incorporated into the potential. We demonstrated that this approach can be used to reproduce the energy band structure of diamond well [T. Shimazaki and Y. Asai, J. Chem. Phys. 130, 164702 (2009)]. In the present paper, we report that the screened HF exchange method is applicable to other semiconductors such as silicon, AlP, AlAs, GaP, and GaAs.