Theoretical optoelectronic analysis of ${\text{MgIn}}_2{\text{S}}_4$ and ${\text{CdIn}}_2{\text{S}}_4$ thiospinels: Effect of transition-metal substitution in intermediate-band formation

We analyzed and compared two families of intermediate-band materials derived from indium thiospinels: ${\text{MgIn}}_2{\text{S}}_4$, having an inverse spinel structure, and ${\text{CdIn}}_2{\text{S}}_4$, a direct spinel. First-principles studies of the electronic structures of these two parent semiconductors were carried out to understand the nature of their band gaps. Optical properties were also analyzed and we found good agreement with experiments. As derivatives of these semiconductors, alloys where transition metals ($M=\text{Ti}$ and V) substitute for In atoms at octahedral sites are presented as a class of intermediate-band materials. First, the effect of the substitution on structural parameters is assessed. Then, electronic structures are determined for ${\text{Mg}}_{2}M{\text{In}}_3{\text{S}}_8$ and ${\text{Cd}}_{2}M{\text{In}}_3{\text{S}}_8$ to show that the $t_{2g}$ $d$ states of the transition metal form a partially filled localized band within the band gap of the host semiconductor. The suitability of these compounds as photovoltaic high-efficiency absorbers is discussed. An increase in absorption is assessed by studying the contribution of the transition-metal band toward their optical properties, in the range of higher solar emission, and comparing them with those of the host semiconductors. An analysis of transmittance spectra is carried out to predict the range of optimum thicknesses for samples of this type of thin film absorber. We compare, by means of structural, electronic, and optical behavior, Ti and V as substituents, to evaluate the resulting alloys for potential photovoltaic applications.

Figure 1

(Color online) Projection of the band diagram of ${\text{CdIn}}_2{\text{S}}_4$, where the circles size is proportional to the orbital projections of the (a) In $5s$, (b) Cd $5s$, and (c) S $3p$ states divided by the number of atoms of each species. The contribution of other orbitals is comparatively negligible in this energy range. As a guide to the eye, the band diagram containing all the states is represented as a thin dashed line.

Figure 2

(Color online) Projection of the band diagram of ${\text{MgIn}}_2{\text{S}}_4$, where the circles size is proportional to the orbital projections of the (a) In $5s$, (b) Mg $3s$, and (c) S $3p$ states divided by the number of atoms of each species. The contribution of other orbitals is comparatively negligible in this energy range. As a guide to the eye, the band diagram containing all the states is represented as a thin dashed line.

Figure 3

(Color online) Total (solid line) and transition-metal projected (dotted line) densities of states (DOS) of the (a) ${\text{MgIn}}_2{\text{S}}_4$ semiconductor, (b) Ti-substituted alloy and (c) V-substituted compound (up and down spins), aligned at the valence-band maximum. Black vertical lines indicate the Fermi energy.

Figure 4

(Color online) The same as Fig. 3, but for the ${\text{CdIn}}_2{\text{S}}_4$ derivatives.

Figure 5

(Color online) (a) Spin-up and (b) spin-down band diagrams of ${\text{Cd}}_2{\text{TiIn}}_3{\text{S}}_8$. The size of the red circles is proportional to the orbital projection of the Ti $d$ states.

Figure 6

(Color online) (a) Spin-up and (b) spin-down band diagrams of ${\text{Cd}}_2{\text{VIn}}_3{\text{S}}_8$. The size of the red circles is proportional to the orbital projection of the V $d$ states.

Figure 7

(Color online) (a) Absorption coefficient and (b) reflectance of the two host semiconductors.

Figure 8

(Color online) Absorption coefficient of the Ti-substituted ${\text{MgIn}}_2{\text{S}}_4$ intermediate-band compound, compared to that of the host semiconductor. Interpretation of the main peaks through the transitions involving the intermediate band. The AM1.5G solar spectrum in the background is shown as a reference.

Figure 9

(Color online) The same as Fig. 8, but for the V-substituted ${\text{MgIn}}_2{\text{S}}_4$ alloy.

Figure 10

(Color online) Absorption coefficient of the Ti-substituted ${\text{CdIn}}_2{\text{S}}_4$ intermediate-band compound compared to that of the host semiconductor. Interpretation of the main peaks through the transitions involving the intermediate band. The AM1.5G solar spectrum in the background is shown as a reference.

Figure 11

(Color online) The same as Fig. 10, but for the V-substituted ${\text{CdIn}}_2{\text{S}}_4$ alloy.

Figure 12

(Color online) Transmittance of the intermediate-band derivatives of ${\text{MgIn}}_2{\text{S}}_4$ as a function of the width of the sample $w$.

Figure 13

(Color online) The same as Fig. 12, but for the derivatives of ${\text{CdIn}}_2{\text{S}}_4$.