Indium-Gallium Segregation in ${\mathrm{CuIn}}_x{\mathrm{Ga}}_{1-x}{\mathrm{Se}}_2$: An Ab Initio–Based Monte Carlo Study

Thin-film solar cells with ${\mathrm{CuIn}}_x{\mathrm{Ga}}_{1-x}{\mathrm{Se}}_2$ (CIGS) absorber are still far below their efficiency limit, although lab cells already reach 20.1%. One important aspect is the homogeneity of the alloy. Large-scale simulations combining Monte Carlo and density functional calculations show that two phases coexist in thermal equilibrium below room temperature. Only at higher temperatures, CIGS becomes more and more a homogeneous alloy. A larger degree of inhomogeneity for Ga-rich CIGS persists over a wide temperature range, which contributes to the observed low efficiency of Ga-rich CIGS solar cells.

Figure 1

(a) CIGS unit cells with In and Ga atoms on Wyckoff position 4b. (b) Snapshot of a system of periodic unit cells. (c) Snapshot of the Ga-rich system at 348 K. (d) Snapshot of the Ga-rich system at 406 K. Ga atoms are yellow; In atoms are blue. Cu and Se are not displayed in the snapshots, and the size of the spheres is arbitrary.

Figure 2

Histograms showing the number of cubic segments in the simulation box that contain 1–16 atoms of a certain type. Blue is the distribution of In atoms in Ga-rich CIGS, and yellow is the distribution of Ga atoms in In-rich CIGS at temperatures of (a) 290 and (b) 406 K. A perfectly ordered In-rich or Ga-rich system would have 4 $\mathrm{Ga}/\mathrm{In}$ atoms in every segment. The histogram would have all entries in bin 4.

Figure 3

Average number of clusters (a) and size of clusters (b) for Ga-rich and In-rich CIGS. Data points are the average value of all data sets of an MC run, and error bars are the standard deviation. The blue lines give the limit for simulations with infinite temperature. The considered clusters are connected In atoms in Ga-rich CIGS and connected Ga atoms in In-rich CIGS.