Ionization potentials of semiconductors from first-principles.

The ionization potential is the key to determine the absolute positions of valence and conduction bands of a semiconductor with respect to the vacuum level, which play a crucial role in physical and chemical properties of surfaces and interfaces. In spite of its far-reaching significance, theoretical determination of ionization potentials has not attained as much attention as that of band gaps. In this work, a set of prototypical semiconductors are considered to establish the performance of the state-of-the-art first-principles approaches. We have shown that in general Kohn-Sham density functional theory with local density approximation or generalized gradient approximation (LDA/GGA) significantly underestimates the ionization potentials of semiconductors. When the quasi-particle correction from many-body perturbation theory in the GW approximation is taken into account, the agreement between theory and experiment can be greatly improved. We have made a critical comparison between two GW correction schemes, one taking into account the GW correction to the valence band maximum (VBM) of the bulk system, and the other based on the assumption that the LDA/GGA gives correct band gap center (BGC). Our study shows that the VBM scheme is better founded theoretically and leads to closer agreement with experiment practically than the BGC scheme. For semiconductors with shallow semicore states, for which the band gaps from the GW approach also exhibit significant errors, there is still significant discrepancy between GW and experiment, indicating the necessity to go beyond the standard GW approach for these materials.