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 tau(eff) is almost equal to the silicon bulk wafer lifetime tau(wafer), 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 tau(eff) which typically exhibits a strong dependence on the excess carrier injection density Delta n within the wafer. Stating tau(eff)-values thus necessitates to specifiy Delta n. The PV community typically reports at a fixed Delta n in the range of 1x10(14) cm(-3) to 1x10(16) cm(-3) or for varying wafer doping density N-dop at Delta n = N-dop/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 Delta n which is relevant for the injection density at maximum power point (MPP) is derived. This Delta n@MPP shows a contrary behaviour compared to the often used and accepted reporting method to set Delta n = N-dop/10. Additionally, a wafer doping density independent material quality parameter, called material saturation current density j(0, mat) at MPP, is proposed to improve the comparability of measured effective lifetimes of differently doped wafers. (C) 2016 The Authors. Published by Elsevier Ltd.