Performance of the modified Becke-Johnson potential for semiconductors

Very recently, in the 2011 version of the wien2k code, the long-standing shortcoming of the codes based on density functional theory, namely, its impossibility to account for the experimental band-gap value of semiconductors, was overcome. The novelty is the introduction of a new exchange and correlation potential, the modified Becke-Johnson potential (mBJLDA). In this paper, we report our detailed analysis of this recent work. We calculated using this code, the band structure of 41 semiconductors and found an important improvement in the overall agreement with experiment as Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] did before for a more reduced set of semiconductors. We find, nevertheless, within this enhanced set, that the deviation from the experimental gap value can reach even much more than 20$%$, in some cases. Furthermore, since there is no exchange and correlation energy term from which the mBJLDA potential can be deduced, a direct optimization procedure to get the lattice parameter in a consistent way is not possible as in the usual theory. We analyze the consequences of this problem. Furthermore we found that using the experimental lattice parameter as input, surprisingly high deviations of the predicted band-gap value from experiment occur. This is an odd result. A closer look at the obtained band structures reveals that, in some cases, important differences occur that might not be negligible. The overall implementation of the calculation of the band structure of semiconductors with the wien2k code using this new potential is quite empirical, although it mimics well the results obtained by other methods, such as the GW approximation, which give better results and are theoretically well founded. We conclude that, in spite of the very important improvement in the band-gap agreement with experiment using the mBJLDA potential, there are issues that point to the fact that this problem is not yet totally closed.