We calculate operating characteristics of high-sensitivity high-speed In0.53Ga0.47As/InP avalanche photodiodes (APD's). We find that significant photocurrent gain is obtained for a total fixed-charge density of cm-2in the depleted InP and0.53Ga0.47As regions. To obtain high quantum efficiency and low tunneling currents, the fixed-charge density in the InP must be in the range cm-2 cm-2. We calculate the breakdown voltages for APD's with uniformly doped layers and find that practical detectors with avalanche breakdowns as low as 15 V can be realized. High quantum efficiency and fast response are obtained by compositional grading of the In0.53Ga0.47As heterointerface over a distance of Å, depending on the doping and amount of the In0.53Ga0.47As layer swept out at breakdown. Finally, a comparison of calculations with experimental results is presented.