Front Metal Finger Inhomogeneity: Its Influence on Optimization and on the Cell Efficiency Distribution in Production Lines

A model is developed for simulating the inhomogeneity of front metal fingers and its influence on the performance of mass-produced crystalline silicon solar cells. First, it is shown by numerical device simulations that, in modern cell design, the optimal number of fingers will be increasingly determined by the emitter sheet resistivity and to a lesser extent by other geometries of the metallization (such as finger width, their cross-sectional area A, and the number of bus bars). An example from production shows that the relationship between finger width and the amount of screen-printing paste can be inferred from the data cloud containing short-circuit current and fill factor values of fabricated cells. A logistic function is introduced to fit a broad range of cross-sectional finger shapes. With all this as input, spice simulations are preformed to elucidate the dynamics of cell efficiency in dependency of cross-sectional finger area A. The model for finger inhomogeneity is illustrated with a failure analysis. Then, it is shown that finger inhomogeneity contributes only to a small extent to the observed variations in mass production, so the metal fingers can be designed with considerably smaller A to save silver without causing a too large spread in efficiency. Finally, a desirable near-future target of A ≈ 300μm2 is derived from a combination of modeling and a literature collection of metallization data. It will not be necessary in future cell design to increase the number of fingers beyond about 155 (equivalent to a finger pitch of about 1mm), regardless of the number of bus bars or of a multi-bus bar design. Comparing the simulations with the trend in literature data suggests that screen-printing will be the moving target in metallization for some time to come. Mainly economic pain due to high silver prices may favor a transition to (near) silver-free printing techniques.