An array of black-phosphorus photodetectors with channel lengths down to 100 nm is fabricated, and temperature-dependent photodetection measurements from 300 K down to 20 K are carried out. The devices show high photoresponse in a broadband spectral range with a record-high photoresponsivity of 4.3 x 10(6) A W-1 at 300 K for the 100 nm device.