In this paper we give a mathematical derivation of how luminescence images of silicon solar cells can be calibrated to local junction voltage. We compare two different models to extract spatially resolved physical cell parameters from voltage images. The first model is the terminal connected diode model, where each pixel is regarded as a diode with a certain dark saturation current, which is connected via a series resistance with the terminal. This model is frequently used to evaluate measurement data of several measurement techniques with respect to local series resistance. The second model is the interconnected diode model, where the diode on one pixel is connected with the neighbor diodes via a sheet resistance. For each model parameter at least one image is required for a coupled determination of the parameters. We elaborate how also the voltage calibration can be added as an unknown parameter into the models, and how the resulting system of equations can be solved analytically. Finally the application of the models and the different ways of voltage calibration are compared experimentally
The reduction of wafer thickness requires an improved quality control of the wafer strength, which is significantly influenced by cracks. We introduce a machine learning framework to establish photoluminescence (PL) imaging as an optical inspection technique for the detection of cracks in multi-crystalline silicon wafers. The specially derived algorithm enables reliable crack detection in spite of similar background structures in the PL image from grain boundaries and dislocations. Within an experiment on thin wafers with artificially induced cracks we evaluate our approach by comparing the PL detection results to the findings of an infrared-transmission system and fractographical reference data. Based on the optical detection result, we derive a description of the crack structure. Since wafer strength may change after etching and thermal processes, wafer strength is analyzed during cell production and correlated to the optical detection results
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