Origin of localization in Ti-doped Si

Intermediate band semiconductors hold the promise to significantly improve the efficiency of solar cells but only if the intermediate impurity band is metallic. We apply a recently developed first principles method to investigate the origin of electron localization in Ti doped Si, a promising candidate for intermediate band solar cells. We compute the critical Ti concentration and compare it against the available experimental data. Although Anderson localization is often overlooked in the context of intermediate band solar cells, our results show that in Ti doped Si it plays a more important role in the metal insulator transition than Mott localization. To this end we have devised a way to gauge the relative strengths of these two localization mechanisms that can be applied to study localization in doped semiconductors in general. Our findings have important implications for the theory of intermediate band solar cells.

Figure 1

Schematic of an intermediate band solar cell (adapted from Ref. [4]). Intermediate band states can dramatically improve the efficiency of solar cells by enabling two-photon processes which leads to the increase of photocurrent in a system.

Figure 2

Density of states (DOS) and typical density of states (TDOS) of Ti doped Si for various Ti concentrations: $x=1\%$, 0.4%, 0.2%, 0.1%. Two sets of results are presented based on the impurity potentials from supercell calculations with two difference sizes: ${\mathrm{TiSi}}_8$ and ${\mathrm{TiSi}}_{216}$. VB, CB, and IB correspond to the valence, conduction, and intermediate band, respectively. The chemical potentials are indicated by dashed lines.

Figure 3

Density of states (DOS) of Ti doped Si for Ti concentration $x=0.2\%$ based on the impurity potential derived from the ${\mathrm{TiSi}}_{216}$ supercell. (a) Orbital resolved contributions. (b) DOS when hybridization between Ti-$t_{2g}$ and Si-$s$, Si-$p$ is removed. The dashed line indicates the chemical potential.