Multi-intermediate-band character of Ti-substituted ${\mathrm{CuGaS}}_2$: Implications for photovoltaic applications

Intermediate-band (IB) photovoltaic materials are designed to absorb a wider range of the solar spectrum by dividing the gap with a set of bands that plays a mediating role in two-step absorption processes. Thus far, the conventional model of IB absorbers has been focused on a single half-filled IB. We show that a multiple-IB picture with filled and empty bands provides a more convincing explanation of the experimental findings in some cases, and it should be considered as a possible scenario in understanding and engineering IB solar cells. Toward that end, we report the formation of two sets of IBs in a Ti-substituted ${\mathrm{CuGaS}}_2$ compound. Using hybrid functional calculations within the density functional theory framework, we show that the lower IBs are occupied and mainly derive from the Ti $3d_{x^2-y^2}$ states, while the higher ones originate from the Ti $3d_{z^2}$ states and are unoccupied. The positions of the IBs within the gap are found to depend weakly on the dopant concentration and the relative distances of the dopant ions. In addition, for a more pertinent comparison to real materials, we present a practical way to combine and analyze the densities of states resulting from the energetically most probable microscopic structures. This multi-intermediate-band picture provides a platform to comprehend unexplained features of the recent experimental study on the material [X. Lv et al., Solar Energy 103, 480 (2014)].

Figure 1

Schematic view of the energy-level positions for pristine and three differently doped structures.

Figure 2

(a) The element-specific projected DOS for the 2Ti-L spin-polarized structure and (b) combined DOS made of the DOS of three different configurations, namely the 2Ti-M spin-polarized and spin-compensated configurations, as well as the 2Ti-L spin-polarized configuration, mixed with their corresponding weight factors. Note that an additional broadening of $0.05$ eV has been applied.

Figure 3

Cu , Ga , S , Ti . Spatial distribution of DOS for the (a) lower and (b) upper IBs of the 2Ti-L structure. Titanium atoms and their sulfur ligands are shown in bright colors while other atoms are shown in dull colors. The $z$ axis is normal to the plane. Notice that Ga atoms carry no DOS in this particular isosurface, although it might seem so in the two-dimensional view.