Subscript p denotes the local matrix (CdTe, CdS, etc.) in which Cu is diffusing, and the number of sites per plane is n, . The Cu and matrix mole fractions in plane i are x6u and x~, respectively. For simplicity, the ideal-solution model is used for Jl6u and Jl~. Now a chemical potential, Jlbu-p' is defined for plane i that accounts for both species, subject to the complementarity condition X6u + X~= 1. Differentiating Eq. (1) with respect to the amount of Cu in plane i leads toABSTRACT An impurity migration model for systems with material interfaces is applied to Cu migration in CdTe solar cells. In the model, diffusion fluxes are calculated from the Cu chemical potential gradient. Inputs to the model include Cu diffusivities, solubilities, and segregation enthalpies in CdTe, CdS and contact materials. The model yields transient and equilibrium Cu distributions in CdTe devices during device processing and under field-deployed conditions. Preliminary results for Cu migration in CdTe photovoltaic devices using available diffusivity and solubility data from the literature show that Cu segregates in the CdS, a phenomenon that is commonly observed in devices after back-contact processing and/or stress conditions. A = Llhxbu~bu +hx~~~j.
;(1) Distance (lattice constants) Figure 1. Schematic illustration of the ideal-solution Cu migration potential near a hypothetical material interface.; 8 A ;xbu Jlcu-p = r;: 8 1 v ; = i1H cu_ p + kT I n ;(2) ,~cu
1-X Cu(3) 10 5 o -5 -10