Universal critical exponents in percolation systems with tunneling

Some specific dependence of micro-crystalline solar cells efficiency on the crystallite size was reported recently [R. Beserman, A. Chak, R. Weil, T. Roschek, in: Proceedings of the 19th European Photovoltaic Solar Energy Conference, Paris, 2004, p. 1520]. The simple explanation of this dependence is suggested in the framework of percolation phenomena for non-equilibrium carriers. Percolation problem for non-equilibrium carriers was solved in continuous space with tunnel coupling between conducting grains. It was shown that local micro-geometry is not essential if the inter-grains transition time is less than the lifetime of the non-equilibrium carriers inside the conducting grains. In this case the main parameter of the problem is the lifetime of the non-equilibrium carriers in the conducting grains. A new bonding criterion was formulated. An amorphous hydrogenated silicon (a-Si:H) matrix with a big number of crystalline silicon (c-Si) inclusions was investigated as an example of the system. It was shown that universal dependence exists for non-equilibrium conductivity on the mean crystalline size. This prediction was verified by experiments with real solar cells produced from a-Si:H with c-Si inclusions.