Reporting Effective Lifetimes at Solar Cell Relevant Injection Densities

Precise quantitative assessment of c-Si wafer quality is of crucial importance for the development and manufacturing of high efficiency solar cells. For this purpose, lifetime samples are typically fabricated with very well cleaned and passivated surfaces. Under those conditions the measured effective lifetime τeff is almost equal to the silicon bulk wafer lifetime τwafer, i.e. a material related quality parameter. Those lifetime measurements are typically carried out with a photo-conductance decay method (PCM) e.g. with a Sinton-WCT tool. The measurement result is an effective excess carrier lifetime τeff which typically exhibits a strong dependence on the excess carrier injection density Δn within the wafer. Stating τeff -values thus necessitates to specifiy Δn. The PV community typically reports at a fixed Δn in the range of 1×1014 cm-3 to 1×1016 cm-3 or for varying wafer doping density Ndop at Δn = Ndop/10. The latter allows for a comparison from the point of view of the Shockley-Read-Hall (SRH) formalism. Unfortunately, the impact of a certain lifetime for device performance changes with Ndop, due to the law of mass action. In this paper a wafer doping density dependent Δn which is relevant for the injection density at maximum power point (MPP) is derived. This Δn@MPP shows a contrary behaviour compared to the often used and accepted reporting method to set Δn = Ndop/10. Additionally, a wafer doping density independent material quality parameter, called material saturation current density j0,mat at MPP, is proposed to improve the comparability of measured effective lifetimes of differently doped wafers.