Performance of the modified Becke-Johnson potential

Abstract

Very recently, in the 2011 version of the Wien2K code, the long standing shortcome 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 forty one 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. These authors suggest that a LDA or a GGA optimization procedure is used previous to a band structure calculation and the resulting lattice parameter introduced into the 2011 code. This choice is important since small percentage differences in the lattice parameter can give rise to quite higher percentage deviations from experiment in the predicted band gap value. We found that by using the average of the two lattice parameters (LDA and GGA) a better agreement with the band gap experimental value is systematically obtained. As a rule, the LDA optimization underestimates the lattice parameter while the GGA one overestimates it. Also we found that using the experimental lattice parameter instead, surprisingly high deviations of the predicted band gap value from experiment, occur. This is an odd result since, in general, the quality of the LDA and GGA obtained lattice parameters are judged to be as good as their proximity to the experimental lattice parameter value. This judgment implies the idea that the best result for the predicted band gap value is obtained when the closest-to-experiment lattice parameter is used. On the other hand, the band structure calculated with the mBJLDA potential seems, at first sight, a simple rigid displacement of the conduction bands towards higher energies. A closer look reveals that, in some cases, important differences occur that might not be negligible in certain systems containing a semiconductor as it might happen at interfaces. So, in some systems containing a semiconductor, neither the direct use of the Wien2k previous version nor its use with a rigid displacement of the conduction bands added so as to reproduce the band gap value, are totally reliable. 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 as the GW approximation which give better results and a...