High-speed, high-efficiency silicon photodetectors play important roles in the optical communication links that are used increasingly in data centers to handle the increasing volumes of data traffic and higher bandwidths required as use of big data and cloud computing continues to grow exponentially. Monolithic integration of the optical components with signal processing electronics on a single silicon chip is of paramount importance in the drive to reduce costs and improve performance. Here we report grating-enhanced light absorption in a silicon photodiode. The absorption efficiency is determined theoretically to be as high as 77% at 850 nm for the optimal structure, which has a thin intrinsic absorption layer with a thickness of 220 nm. The fabricated devices demonstrate a high bandwidth of 11.3 GHz and improved radio-frequency output power of more than 14 dB, thus making them suitable for use in data center optical communications.