Simulation of Steady-State Characteristics of Dye-Sensitized Solar Cells and the Interpretation of the Diffusion Length

Abstract

Quantitative modeling of the photovoltaic response of the dye-sensitized solar cell (DSC) is an important subject for improving both the understanding of operation mechanisms and the device performance. A range of experimental techniques indicates that nonlinear recombination of the form <i>U</i>_<i>n</i> = <i>k</i>_r<i>n</i>^β, with β ≠ 1, is a property of DSCs. We show that the diffusion length <i>L</i>_<i>n</i> defined from the probability of collection is independent of the macroscopic perturbation for β≠1 only for a small perturbation, and in this case, it coincides with the value λ_<i>n</i> = (<i>D</i>_<i>n</i>τ_<i>n</i>)^1/2 that can be measured by impedance spectroscopy in homogeneous conditions. The increase of the diffusion length with the potential, usually observed experimentally, is attributed to the increase of the free carrier lifetime. We also discuss the modeling of real DSC devices under different conditions, and we conclude that the diffusion−recombination−generation equation based on <i>U</i>_<i>n</i> = <i>k</i>_r<i>n</i>^β is a fundamental ingredient of the simulation tools