Relationship between Fill Factor and Light Intensity in Solar Cells Based on Organic Disordered Semiconductors: The Role of Tail States

The origin of the relationship between fill factor (FF) and light intensity (I) in organic disordered-semiconductor-based solar cells is studied. An analytical model describing the balance between transport and recombination of charge carriers, parameterized with a factor, ${\mathrm{\ensuremath{\Gamma}}}_{m}$, is introduced to understand the FF-I relation, where higher values of ${\mathrm{\ensuremath{\Gamma}}}_{m}$ correlate to larger FFs. Comparing the effects of direct and tail-state-mediated recombination on the FF-I plot, we find that, for low-mobility systems, direct recombination with constant transport mobility can deliver only a negative dependence of ${\mathrm{\ensuremath{\Gamma}}}_{m,\mathrm{dir}}$ on light intensity. By contrast, tail-state-mediated recombination with trapping and detrapping processes can produce a positive ${\mathrm{\ensuremath{\Gamma}}}_{m,t}$ versus sun dependency. The analytical model is validated by numerical drift-diffusion simulations. To further validate our model, two material systems that show opposite FF-I behavior are studied: poly{4,8-bis[5-(2-ethylhexyl)thiophen-2-yl]benzo[1,2-b;4,5-b\ensuremath{'}]dithiophene-2,6-diyl-alt-[4-(2-ethylhexyl)-3-fluorothieno[3,4-b]thiophene)-2-carboxylate-2-6-diyl]} (PTB7-Th):[6,6]-phenyl-${\mathrm{C}}_{71}$-butyric acid methyl ester (${\mathrm{PC}}_{71}$BM) devices show a negative FF-I relation, while PTB7-Th:(5Z,5\ensuremath{'}Z)-5,5\ensuremath{'}-{[7,7\ensuremath{'} -(4,4,9,9-tetraoctyl-4,9-dihydro-s-indaceno[1,2-b:5,6-b\ensuremath{'}]dithiophene-2,7-diyl)bis(benzo[c][1,2,5]thiadiazole-7,4-diyl)]bis(methanylylidene)}bis(3-ethyl-2-thioxothiazolidin-4-one) (O-IDTBR) devices show a positive correlation. Optoelectronic measurements show that the O-IDTBR device presents a higher ideality factor, stronger trapping and detrapping behavior, and a higher density of trap states, relative to the ${\mathrm{PC}}_{71}$BM device, supporting the theoretical model. This work provides a comprehensive understanding of the correlation between FF and light intensity for disordered-semiconductor-based solar cells.