Electrothermal Finite-Element Modeling for Defect Characterization in Thin-Film Silicon Solar Modules

We present and validate a finite-element model for coupled charge and heat transport in monolithically interconnected thin-film solar modules. Using measured current-voltage (I-V) and lock-in thermography (LIT) measurements of amorphous silicon minimodules, we experimentally validate our model. The entire module volume is represented by two planes (front and back electrodes) which are coupled in vertical direction using 1-D models, leading to a large reduction of the degrees of freedom in the numerical model and contributing to an efficient solution approach. As compared to 3-D models, the vertical coupling of the charge transport is represented by local temperature-dependent I-V curves. These can be obtained by drift-diffusion calculations, single-cell measurements or, as presented here, by an analytical solar cell diode model. Inhomogeneous heat sources such as Joule's heating in the electrodes lead to nonuniform temperature distributions. The explicit temperature dependence in the local I-V curve, therefore, mediates the feedback of the thermal transport on the local electrical cell characteristics. We employ measured I-V curves under partial illumination and analytical solutions for the potential distribution to validate this approach. Further, with LIT measurements of the same modules with and without artificially induced electrical shunts, we verify the computed temperature distributions.