Atomistic Models of In and Ga Diffusion in Cu(In,Ga)Se₂

To improve the performance of Cu(In,Ga)Se₂ (CIGS) thin-film photovoltaic devices, a robust understanding of the dominant diffusion pathways of the alloy species In and Ga is needed. For example, because the bandgap of CIGS varies significantly between pure CuInSe₂ (CIS) and pure CuGaSe₂ (CGS), knowledge and control of In/Ga interdiffusion in the system is necessary to optimize the spatial bandgap tuning. This in turn is necessary to produce the highest-quality devices. Here, we identify the most probable defects and mechanisms for mediating In and Ga diffusion by reviewing previous experimental and computational literature. We determine that defect complexes comprised of In_Cu and Ga_Cu antisites and V_Cu vacancies are the primary drivers of diffusion. With the aid of density functional theory software packages, we calculate the binding energies and migration barriers of these complexes in bulk CIS and CGS. We find that the binding between In_Cu, Ga_Cu, and V_Cu defects can be modeled as simple electrostatic interactions between point charges. We also find that the migration barriers for Ga_Cu are much higher than those for In_Cu, explained by a larger lattice distortion arising during Ga_Cu migration than during In_Cu migration. Using these results, we develop rate expressions for the different atomistic processes and incorporate them into analytic models and kinetic lattice Monte Carlo (KLMC) simulations, which are employed to predict the diffusivity of In and Ga in CIS under variations in composition and temperature. The activation energy of In diffusion in CIS from our KLMC simulations is 1.24 eV, and for Ga it is 1.54 eV. We show that In diffusion is dominated by correlated hops, where most In_Cu-V_Cu exchanges quickly reverse. Consequently, very few hops contribute to net long-range diffusion. In contrast, Ga diffusion is dominated by uncorrelated hops, which show little to no memory of the previous state and move in a random walk. We develop an analytic model for In and Ga diffusion, suitable for use in a continuum simulation, and show that it predicts complex formation and diffusivity as seen in our KLMC simulations with great accuracy. We find our models produce results that match well with experiment. The methods used here are highly transferable and can be applied to understand diffusion of both native and extrinsic species in many different materials.