In a silicon hetero-interface photodetector, Si is used as the multiplication material to provide avalanche gain, while InGaAs is used as the absorption material. High quantum efficiency, high gain-bandwidth product, and low noise detection of wavelengths between 1.0 and 1.6 mm can be achieved in this way. We derive expressions for the frequency response for these detectors, present possible design variations, and analyze their performance. The effects of parasitics, transit time, and RC roll-off on frequency response are investigated and the 3-dB bandwidth and gain bandwidth product are calculated. Particular attention is paid to a 10 Gbit/s APD and we show that that a 3-dB bandwidth of 10 GHz and a gain-bandwidth product in excess of 400 GHz should be possible.