Order-disorder transition in Cu2ZnSnS4 solar cells from Monte Carlo simulations

<pre>Kesterite-structured Cu2ZnSnS4 (CZTS) is an earth-abundant and non-toxic semiconductor that is being studied for use as the absorber layer in thin-film solar cells. Currently, the power-conversion efficiencies of this technology fall short of the requirements for commercialisation. Disorder in the Cu-Zn sub-lattice has been observed and is proposed as one explanation for the shortcomings of CZTS solar cells. Cation site disorder averaged over a macroscopic sample does not provide insights into the microscopic cation distribution that will interact with photogenerated electrons and holes. To provide atomistic insight into Cu-Zn disorder, we have developed a Monte Carlo (MC) model based on pairwise electrostatic interactions. Substitutional disorder amongst Cu and Zn ions in Cu-Zn (001) planes on the 2\textit{c} and 2\textit{d} Wyckoff sites -- 2D disorder -- has been proposed as the dominant form of Cu/Zn disorder in near-stoichiometric crystals. We use our model to study the Cu/Zn order-disorder transition in 2D but also allow Zn to substitute onto the Cu 2\textit{a} site -- 3D disorder -- including Cu-Sn (001) planes. We find that defects are less concentrated in Cu-Sn (001) planes but that Zn ions readily substitute onto the Cu 2\textit{a} site and that the critical temperature is lowered for 3D disorder.