Analytical analysis of the CELIV theory

Charge extraction by linearly increasing voltage (CELIV) has attracted much interest in organic semiconductor research, due to its feature of measuring charge carrier mobility and density directly and simultaneously. Up to now the theoretical description of this method has been solved for a low mobility approximation only, because the general solution was impeded by a Ricatti type first order differential equation. In this contribution we present the analytical solution for this Ricatti equation, thus completing the analytical framework of the CELIV method. We compare it with the approximated theory and show that especially for standard organic solar cell materials the low mobility approach is hardly valid. The evaluation of photo-CELIV measurements on poly(3-hexyl thiophene-2,5-diyl):[6,6]-phenyl-C{sub 61} butyric acid methyl ester solar cells can then be done by fitting the current transients. Surprisingly the fit results are only in a good agreement with the experimental currents, if two extraction currents are taken into account - the origin of which we will discuss. Furthermore we present a new equation for mobility evaluation from numerical analysis within our framework, which can be applied over the entire experimental range.