Effect of Energetic Disorder on the Open-Circuit Voltage in Organic Bulk Heterojunction Composites

Under open-circuit condition, the current is not extracted and the photogenerated carriers in principle disappear only by recombination. We study the open-circuit voltage $V_{\rm OC}$ and transient photovoltage under the effect of bulk recombination in a medium with energetic disorder by using the multiple trapping (MT) model. The key parameter in the MT model is the dispersion parameter $\alpha$ given by the ratio of thermal energy to the characteristic energy of trap states. We show that $V_{\rm OC}$ depends linearly on the logarithm of the light intensity and the slope depends on the $\alpha$ of the MT model. Under the continuous irradiation of light, the photovoltage response to the weak perturbation by a pulsed light obeys pseudo-first-order decay. The rate as a function of $V_{\rm OC}$ is independent of the dispersion parameter. However, it obeys the power law as a function of light intensity, and the exponent is given by $1/(1+\alpha)$, which reduces to 1/2 in the absence of energetic disorder.