We introduce a model to account for the dielectric response of doped organic semiconductor devices. In addition to the phenomena observed for undoped devices, mobile charge carriers created by doping can alter the dielectric function of the organic material and hence the dielectric response of the devices. These extrinsic charges may be trapped and contribute to the capacitance on re-emission. We directly model the real part of the dielectric function based on this phenomenon. The imaginary part is obtained via the application of the Kramers-Kronig transformation. We use oxygen-doped poly(3-hexylthiophene):[6,6]-phenyl-C${}_{61}$-butyric acid methyl ester– (P3HT:PCBM) based organic solar cells as a model system to test our approach and hence contribute to the understanding of oxygen-induced degradation in these devices. We fit our equations to the measured dielectric data and compare it to Debye relaxation as well as two widely used equivalent circuit models. Together with the device resistance determined from the steady-state current-voltage characteristic around $0\mathrm{V}$ an excellent agreement between the experimental data and our model is achieved for both the real and the imaginary part of the dielectric function over a frequency range covering five orders of magnitude. Unlike the Debye relaxation model or the equivalent circuit approach, our model yields important device parameters such as the dopant concentration.

• Received 6 March 2011

DOI:https://doi.org/10.1103/PhysRevB.84.085208