Behavior of $\mathrm{\Sigma }3$ Grain Boundaries in ${\mathrm{CuInSe}}_2$ and ${\mathrm{CuGaSe}}_2$ Photovoltaic Absorbers Revealed by First-Principles Hybrid Functional Calculations

The inconclusive results of the previous first-principles studies on the $\mathrm{\Sigma }3$ grain boundaries (GBs) in ${\mathrm{CuInSe}}_2$ reveal the importance of employing a method that can correctly describe the electronic structure of this solar-cell material. We employ hybrid functional calculations to study the $\mathrm{\Sigma }3(112)$ and $\mathrm{\Sigma }3(114)$ GBs in ${\mathrm{CuInSe}}_2$ and ${\mathrm{CuGaSe}}_2$. The electronic structure changes introduced by the formation of GBs are threefold: the creation of gap states, a shift in band edges, and the alteration of band-gap sizes. Gap states commonly behave as recombination centers, but the band alignment and the change in the band-gap size induced by GBs mitigate the destructive effect of these states in ${\mathrm{CuInSe}}_2$. That means that $\mathrm{\Sigma }3$ GBs are not detrimental for the carrier transport in devices based on ${\mathrm{CuInSe}}_2$. Conversely, these GBs are destructive for the carrier transport in ${\mathrm{CuGaSe}}_2$. The different behaviors of the $\mathrm{\Sigma }3$ GBs in CISe and CGSe might be considered by experimentalists to optimize the device fabrication to achieve high-performance solar cells.

Figure 1

Band offset between system “1” and “2”. The common reference level is the average electrostatic potential of the periodic bulk.

Figure 2

Atomic structure of the (a) cation-Se-terminated (type I) and (b) Se-Se-terminated (type II) $\mathrm{\Sigma }3(112)$ GB. (c) and (d) depict the atomic structures of type I and type II of the $\mathrm{\Sigma }3(114)$ GB. The Cu, In, and Se atoms are shown as brown spheres, light gray (large) spheres, and dark gray (small) spheres, respectively.

Figure 3

Partial DOS calculated for GBs in ${\mathrm{CuInSe}}_2$. Panels (a), (b), (c), and (d) shows the partial DOS for $\mathrm{\Sigma }3(112)\text{-I}$, $\mathrm{\Sigma }3(112)\text{−}\mathrm{II}$, $\mathrm{\Sigma }3(114)\text{-I}$, and $\mathrm{\Sigma }3(114)\text{−}\mathrm{II}$ GB, respectively. Black and red lines show the projected DOS for the bulk atoms and the atoms close to the GBs, respectively. The zero of the energy is set at the bulk VBM. Vertical dashed lines show the VBM and CBM.

Figure 4

Schematic band offset and gap states of GBs for ${\mathrm{CuInSe}}_2$ (top panel) and ${\mathrm{CuGaSe}}_2$ (bottom panel). The occupied and unoccupied single-particle levels are represented as black and white rectangles. Horizontal dashed lines show the band gap of the bulk ${\mathrm{CuInSe}}_2$ ($E_g=1.0\mathrm{eV}$) and ${\mathrm{CuGaSe}}_2$ ($E_g=1.6\mathrm{eV}$), respectively. The distance between tics is 0.2 eV.