The poor photovoltaic performance of state‐of‐the‐art blends of poly[4,8‐bis[(2‐ethylhexyl)oxy]benzo[1,2‐b:4,5‐b′]dithiophene‐2,6‐diyl][3‐fluoro‐2‐[(2‐ethylhexyl)carbonyl]thieno[3,4‐b]thiophenediyl] (PTB7) and [6,6]‐phenyl‐C61‐butyric acid (PCBM) at large active layer thicknesses is studied using space‐charge‐limited current mobility and photovoltaic device measurements. The poor performance is found to result from relatively low electron mobility. This is attributed to the low tendency of PTB7 to aggregate, which reduces the ability of the fullerene to form a connected network. Increasing the PCBM content 60–80 wt% increases electron mobility and accordingly improves performance for thicker devices, resulting in a fill factor (FF) close to 0.6 at 300 nm. The result confirms that by improving only the connectivity of the fullerene phase, efficient electron and hole collection is possible for 300 nm‐thick PTB7:PCBM devices. Furthermore, it is shown that solvent additive 1,8‐diiodooctane (DIO), used in the highest efficiency PTB7:PCBM devices, does not improve the thickness dependence and, accordingly, does not lead to an increase in either hole or electron mobility or in the carrier lifetime. A key challenge for researchers is therefore to develop new methods to ensure connectivity in the fullerene phase in blends without relying on either a large excess of fullerene or strong aggregation of the polymer.