  Despite of its huge successes in vast amount of applications, the Kohn-Sham
scheme of density functional theory (DFT-Kohn-Sham) has not been able to get
reliable ionization potentials (IP) for semiconductors, due to self-interaction
error in the local density approximation (LDA) and generalized gradient
approximations (GGA), and the difficulty of using asymptotically long-ranged
potentials for surface calculations. An approximate optimize effective
potential (OEP), the Becke-Johnson'06 exchange, is used to explore the
capability of OEP to calculate semiconductor IP with a surface technique
suitable for both short- and long-ranged potentials. Combined with the LDA
correlation, the approximate OEP has achieved an IP accuracy for 17
semiconductors which is similar to the much more sophisticated $GW$
approximation (GWA), with the computational cost of only LDA/GGA. For the first
time, this opens the way for systematic calculation of semiconductor IP's by
the DFT-Kohn-Sham scheme. The long-range part of the $v_{xc}$ is not as
important for solid surface as for atoms and molecules since the wave functions
are mainly bound to the slab while less exposed to the asymptotic region.
Nevertheless, it contributes significantly to the total IP and therefore shall
not be simply ignored. Without including its effects, it is unlikely that the
same GWA procedure could achieve universally accurate band gaps and accurate
IP's at the same time, as is indeed seen in practical calculations.
