Recombination velocities at grain boundaries in solar-cell absorbers : revisited

The present work revisits the recombination velocities (sGB) of minority-charge carriers determined at grain boundaries in polycrystalline absorber materials for solar cells. The equations describing sGB as well as the barriers for electrons and holes were derived. It is shown that for given net-doping density and absolute temperature, the experimentally determined recombination velocity of a specific grain boundary can be described by sGB ¼ sn GB,0 exp ΦGB(NGB,charge)=(kBT) , where ΦGB is the band bending induced by the excess-charge density NGB,charge at the grain boundary, and kB as well as T are the Boltzmann constant and the absolute temperature; i.e., sGB depends only on the excess-charge density at this planar defect as well as on the prefactor sn GB,0 describing the nonradiative recombination. Value ranges for these two quantities can be determined for any measured sGB value. When analyzing sGB datasets acquired on various (Ag,Cu)(In,Ga)Se2 and microcrystalline Si absorbers, it is apparent that both the excess-charge density and the prefactor sn GB,0 remain within about the same orders of magnitude for all grain boundaries analyzed in a specific absorber. The broad range of the recombination velocities over several orders of magnitude indicates upward as well as downward band bending, and the band-bending values are on the order of several +10 meV for all materials analyzed.