The combination of graphene with semiconductor materials in heterostructure photodetectors, has enabled amplified detection of femtowatt light signals using micron-scale electronic devices. Presently, the speed of such detectors is limited by long-lived charge traps and impractical strategies, e.g. the use of large gate voltage pulses, have been employed to achieve bandwidths suitable for applications, such as video-frame-rate imaging. Here, we report atomically thin graphene-WS$_2$ heterostructure photodetectors encapsulated in an ionic polymer, which are uniquely able to operate at bandwidths up to 1.5 kHz, whilst maintaining internal gain as large as $10^6$. Highly mobile ions and a nanometre scale Debye length of the ionic polymer are used to screen charge traps and tune the Fermi level of graphene over an unprecedented range at the interface with WS$_2$. We observe a responsivity $R=10^6$ A W$^{-1}$ and detectivity $D^*=3.8times10^{11}$ Jones, approaching that of single photon counters. The combination of both high responsivity and fast response times makes these photodetectors suitable for video-frame-rate imaging applications.
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