The screened exchange (sX) hybrid functional can give good band structures for simple sp bonded semiconductors and insulators, charge transfer insulators, Mott-Hubbard insulators, two dimensional systems and defect systems. This is particularly attributed to the sX hybrid scheme fixing the self-interaction problem associated with local functionals. We investigate the effect of varying the screening parameter of the exchange potential on various material properties such as the band gap. The Thomas Fermi screening scheme in which the screening parameter varies with an average valence electron density leads to a weak dependence of the band gap on valence electron density, so that a fixed screening parameter could be applied to heterogeneous systems like surfaces, interfaces and defects.