Effective diffusion length of multicrystalline solar cells

Previous definitions of effective diffusion length L-e of a multicrystalline semiconductor are reviewed. A new definition is proposed, which is based on the comparison of the current collected from the base of a multicrystalline solar cell and a single-crystal cell for uniform carrier generation, and holds for any sample thickness. An analytical expression for L-e is obtained from the solution of the three-dimensional equation for the charge collection probability cp inside a grain with square cross section. This expression is used to numerically study the dependence of L-e on the bulk diffusion length, grain size and grain boundary recombination velocity, and to make a comparison with previous specifications of L-e. The results indicate, in particular, that L-e is the value that would be determined by the surface photovoltage method. The case of a cell with grains of different properties is briefly discussed and an average L-e is defined. It is also shown that phi can be used to calculate the contribution of the base to the reverse saturation current of the cell.