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

The present work revisits the recombination velocities ($s_{\mathrm{GB}}$) of minority-charge carriers determined at grain boundaries in polycrystalline absorber materials for solar cells. The equations describing $s_{\mathrm{GB}}$ 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 depends only on the excess-charge density at this planar defect as well as on the prefactor $s_{\mathrm{GB,0}}$ describing the nonradiative recombination. Value ranges for these two quantities can be determined for any measured $s_{\mathrm{GB}}$ value. When analyzing $s_{\mathrm{GB}}$ datasets acquired on various (Ag,Cu)(In,Ga)Se$_2$ and microcrystalline Si absorbers, it is apparent that both, the excess-charge density and the prefactor $s_{\mathrm{GB,0}}$, 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 magnitude indicate upward as well as downward band bending, and the band-bending values are on the order of several $\pm$10 meV for all materials analyzed.