Predicting Ga and Cu Profiles in Co-Evaporated Cu(In,Ga)Se 2 Using Modified Diffusion Equations and a Spreadsheet

Cu(In,Ga)Se 2 (CIGS) photovoltaic absorbers frequently develop Ga gradients during growth. These gradients vary as a function of growth recipe, and are important to device performance. Prediction of Ga profiles using classic diffusion equations is not possible because In and Ga atoms occupy the same lattice sites and thus diffuse interdependently, and there is not yet a detailed experimental knowledge of the chemical potential as a function of composition that describes this interaction. We show how diffusion equations can be modified to account for site sharing between In and Ga atoms. The analysis has been implemented in an Excel spreadsheet, and outputs predicted Cu, In, and Ga profiles for entered deposition recipes. A single set of diffusion coefficients and activation energies are chosen, such that simulated elemental profiles track with published data and those from this study. Extent and limits of agreement between elemental profiles predicted from the growth recipes and the spreadsheet tool are demonstrated.