Shockley Equation Parameters of Organic Solar Cells derived by Transient Techniques

TL;DR

This study validates the Shockley equation for organic solar cells by comparing static and transient methods, revealing insights into recombination processes, and accurately determining key parameters like the ideality factor and band gap.

Contribution

It demonstrates the consistency of static and transient techniques for extracting Shockley parameters in OSCs and links these parameters to recombination mechanisms and material properties.

Findings

Shockley parameters are consistent across static and transient methods.

Reproduced photocurrent from recombination rates across temperatures.

Determined effective band gap aligning with literature values.

Abstract

The Shockley equation (SE), originally derived to describe a p--n junction, was frequently used in the past to simulate current--voltage (j/V) characteristics of organic solar cells (OSC). In order to gain a more detailed understanding of recombination losses, we determined the SE parameters, i.e. the ideality factor and the dark saturation current, from temperature dependent static j/V-measurements on poly(3-hexylthiophene-2,5-diyl)(P3HT):[6,6]-phenyl-C$_{61}$ butyric acid methyl ester (PCBM) bulk heterojunction solar cells. As we show here, these parameters are directly related to charge carrier recombination and become also accessible by transient photovoltage and photocurrent methods in the case of field-independent charge carrier generation. Although determined in very different ways, both SE parameters were found to be identical. The good agreement of static and transient approaches over a wide temperature range demonstrates the validity of the Shockley model for OSC based on material systems satisfying the requirement of field-independent polaron-pair dissociation. In particular, we were able to reproduce the photocurrent at various light intensities and temperatures from the respective nongeminate recombination rates. Furthermore, the temperature dependence of the dark saturation current $j_0$ allowed determining the effective band gap of the photoactive blend perfectly agreeing with the literature values of the energy onset of the photocurrent due to charge transfer absorption. We also present a consistent model directly relating the ideality factor to recombination of free with trapped charge carriers in an exponential density of tail states. We verify this finding by data from thermally stimulated current measurements.