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Perovskite solar cells have recently seen rapid improvements in performance with certified efficiencies of above 23%. Fullerene compounds are a very popular electron-transfer material in these devices. In a previous report, it has been shown that while an ultrathin fullerene layer of just 1 nm is sufficient to achieve good device performance, removal of this layer causes a drastic decrease in performance. We provide an explanation to these observed effects by use of a numerical device model. This work provides theoretical support to the experimental understanding of the dominant role of fullerenes in perovskite solar cells. [ABSTRACT FROM AUTHOR]