A 3-dimensional numerical model of grain boundaries was developed in order to simulate the electrical properties of polycrystalline Si with doping densities greater than about 5 x 1017/cm3. It was shown that 3-dimensional effects played an important role in quantifying the minority-carrier properties of polycrystalline Si. The simulations reproduced the open-circuit voltage of a wide range of published experiments on thin-film Si p-n junction solar cells, choosing a velocity parameter for recombination at the grain boundaries, S, in the order of 105 to 106cm/s. The simulations indicate that, although S was reduced by one order of magnitude over the last two decades, improvements in the open-circuit voltage have mainly been achieved by increasing the grain size.

Development of a Three-Dimensional Numerical Model of Grain Boundaries in Highly Doped Polycrystalline Silicon and Applications to Solar Cells. P.P.Altermatt, G.Heiser: Journal of Applied Physics, 2002, 91[7], 4271-4