Semiconducting transition metal dichalcogenides (TMDs) are promising for flexible high-specific-power photovoltaics due to their ultrahigh optical absorption coefficients, desirable band gaps and self-passivated surfaces. However, challenges such as Fermi-level pinning at the metal contact-TMD interface and the inapplicability of traditional doping schemes have prevented most TMD solar cells from exceeding 2% power conversion efficiency (PCE). In addition, fabrication on flexible substrates tends to contaminate or damage TMD interfaces, further reducing performance. Here, we address these fundamental issues by employing: 1) transparent graphene contacts to mitigate Fermi-level pinning, 2) $rm{MoO}_it{x}$ capping for doping, passivation and anti-reflection, and 3) a clean, non-damaging direct transfer method to realize devices on lightweight flexible polyimide substrates. These lead to record PCE of 5.1% and record specific power of $rm{4.4 W,g^{-1}}$ for flexible TMD ($rm{WSe_2}$) solar cells, the latter on par with prevailing thin-film solar technologies cadmium telluride, copper indium gallium selenide, amorphous silicon and III-Vs. We further project that TMD solar cells could achieve specific power up to $rm{46 W,g^{-1}}$, creating unprecedented opportunities in a broad range of industries from aerospace to wearable and implantable electronics.
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