Rules of Thumb for Industrial Solar Cells - Taylor Approximation of the One-Diode Model

The efficiency is the parameter of paramount interest for photovoltaic devices. Though an accurate determination for a specific device layout is possible with numerical tools, analytical approximations are desirable for many applications. In this paper we set up a model for an efficiency approximation for PERC-like devices, based on three input parameters: series resistance, photo induced current density and saturation current density. Applying Taylor's theorem, we find that the dependence of the efficiency can be expressed dominantly linear with respect to the first two parameters and logarithmically for the latter for PERC devices in the efficiency range of 21% and higher. A relative derivative of 2.5%/(mA/cm²) for the photo induced current density and 6.0%/(Ω cm²) for the series resistance are very useful and accurate in the vicinity of a center point (j<inf>ph</inf>^∗=0.0405 A/cm², j<inf>0</inf>^∗=76 fA/cm², R<inf>s</inf>^∗=0.50 Ω cm²) with η(j<inf>ph</inf>^∗, j<inf>0</inf>^∗, R<inf>s</inf>^∗)=23.1 %. Furthermore, the accuracy of the absolute efficiency value is still better than 1% relative for a variation within a reasonable range to cover all cell parameters of interest. The simplicity of the model and the acceptable accuracy make it a very useful approach for simple layout considerations of high-efficiency PERC devices.