  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.
