A one-dimensional Fickian model to predict the Ga depth profiles in three-stage Cu(In,Ga)Se2

We present a one-dimensional Fickian model that predicts the formation of a double Ga gradient during the fabrication of Cu(In,Ga)Se2 thin films by three-stage thermal co-evaporation. The model is based on chemical reaction equations, structural data, and effective Ga diffusivities. In the model, the Cu(In,Ga)Se2 surface is depleted from Ga during the deposition of Cu-Se in the second deposition stage, leading to an accumulation of Ga near the back contact. During the third deposition stage, where In-Ga-Se is deposited at the surface, the atomic fluxes within the growing layer are inverted. This results in the formation of a double Ga gradient within the Cu(In,Ga)Se2 layer and reproduces experimentally observed Ga distributions. The final shape of the Ga depth profile strongly depends on the temperatures, times and deposition rates used. The model is used to evaluate possible paths to flatten the marked Ga depth profile that is obtained when depositing at low substrate temperatures. We conclude that inserting Ga during the second deposition stage is an effective way to achieve this.