Paper detail

Theory of Bulk Recombination in a Medium with Energetic Disorder under Continuous Irradiation with Excitation Light

We study bulk recombination in a medium with energetic disorder by using the multiple trapping (MT) model under continuous irradiation with excitation light. Charge densities are shown to obey power law as a function of the intensity of excitation light and the exponent is related to the dispersion parameter $α$ of the MT model. The theory is applied to analyze charge densities in bulk heterojunction photovoltaic cells measured by light-induced electron spin resonance (LESR). The values of the exponent are consistent with those obtained from the transient decay of charge densities after pulsed excitations.We show that the value of the exponent is robust against addition of Gaussian trapping energy distribution due to shallow trap states. We also show that open-circuit voltage ($V_{\rm OC}$) depends linearly on logarithm of the light intensity and the slope is equal to $k_B T/e$ when only shallow trap states are present. The same linear relation holds with a slope larger than $k_B T/e$ in the presence of an exponential trapping energy distribution due to deep trap states.