ECN publication
A multiscale model of the aluminium layer at the rear side of a solar cell
Amstel, T. van; Popovich, V.A.; Bennett, I.J.
Published by: Publication date:
ECN Solar Energy 21-9-2009
ECN report number: Document type:
ECN-M--09-026 Conference Paper
Number of pages: Full text:
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Presented at: 24th European Photovoltaic Solar Energy Conference and Exhibition, Hamburg, Germany, 21-25 september 2009.

In order to achieve faster time to market for new innovations and to optimize existing manufacturing processes it is becoming increasingly important to develop models that allow for the design and optimization of new cells and modules. In this article a thermo-mechanical bowing model of a solar cell after firing is described. The model integrates the thermo-mechanical behaviour of the layers at the rear of the cell to allow bowing of the cell to be predicted. Most commercially manufactured solar cells consist, apart from a p-type silicon bulk, of a number of layers: silver, silicon-nitride, BSF and rear-side aluminium. The silicon, silver, silicon-nitride, BSF and eutectic Al-silicon rear-side layers can be accurately described using standard modelling techniques. The Al bulk layer can best be modelled as a composite material. A Mori-Tanaka homogenisation method was used in combination with detailed finite element models of the Al microstructure to predict the mechanical response of the Al layer. This composite modelling approach allows the mechanics of the Al microstructure to be related to the effect of Al on cell bowing. Microstructural features include morphology, inclusion size, aspect ratio distribution and mechanical properties of the inclusions in the Al layer. The model can also be used to predict the Al microstructure based on measurements of cell bowing. Furthermore it is shown that when plastic behaviour is incorporated that final bowing is determined by the flow stress and hardening behaviour of the eutectic and Al bulk layer. The Young’s modulii of the eutectic and Al bulk layer, thermal expansion coefficients and temperature change during the firing process do not directly affect final bowing.

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