Cu-Zn disorder in stoichiometric and non-stoichiometric Cu2ZnSnS4/Cu2ZnSnSe4

Cu-Zn disorder is unavoidable but plays an important role in high-efficiency Cu2ZnSnS4 and Cu2ZnSnSe4 solar cells. Using the cluster expansion method along with Monte Carlo (MC) simulations, we study the Cu-Zn disorder, considering cases both with and without vacancies. We find that the 2a, 2c, and 2d Wyckoff sites all show order-disorder transitions for both cases, in agreement with recent experiments supporting disorder at all 2a, 2c and 2d sites, but, in contrast to early experiments, supporting Cu-Zn disorder only at 2c and 2d sites. Below the transition temperature in non-stoichiometric cases, we find that excess Zn prefers to occupy 2c over 2a sites due to the greater similarity of 2c sites to 2d sites. Such site preferences indicate that Cu-Zn occupations exhibit some new kind of ordering rather than randomly distributed at 2a and 2c sites. We find that while Cu-Zn disorder reduces the band gap, the site preferences in non-stoichiometric samples increase the band gaps by suppressing Cu-Zn disorder. Generally, lowering annealing temperatures, while increasing Zn and vacancies, will lead to larger band gaps