  The performance of density functional theory depends largely on the
approximation applied for the exchange functional. We propose here a novel
screened exchange potential for semiconductors, with parameters based on the
physical properties of the underlying microscopic screening and obeying the
requirements for proper asymptotic behavior. We demonstrate that this
functional is Koopmans-compliant and reproduces a wide range of band gaps. We
also show, that the only tunable parameter of the functional can be kept
constant upon changing the cation or the anion isovalently, making the approach
suitable for treating alloys.
