DFT plus U study of electrical levels and migration barriers of early 3d and 4d transition metals in silicon

Owing to their strong interaction with carriers, early 3d-row (Ti, V, and Cr) and 4d-row (Zr, Nb, and Mo) transition metals (TMs) are undesired contaminants in solar-and electronic-grade Si. The increasing stringent control of contamination levels is urging an accurate picture of their electronic structure. In the present work, the electrical levels and migration energies of these TMs are determined by means of standard density-functional theory (DFT) and a rotationally invariant formulation of DFT+U. The latter approach improves on the treatment of electronic correlations at the TM sites and relies on on-site Hubbard Coulomb and Hund's exchange parameters U and J, respectively. These are calculated self-consistently from linear-response theory without fitting to experimental data. The effect of correlation was found more pronounced for Ti and V, with a strong impact on the location of their electrical levels. In most cases, the agreement with the experimental data is satisfactory allowing the identification of the type and character of the levels. For Cr and Mo in particular, the results resolve longstanding controversies concerning the type and position of the levels. The obtained migration barriers display moderate charge-state and correlation dependency. High barriers were found for all metals studied, with the exception of Cr, confirming them as slow diffusers in silicon among the whole TM family.