We report simulation results for gain and noise in avalanche photodiodes fabricated using heterojunctions of III-V compound semiconductors. We employ a recently developed nonlocal model for impact ionization. The model has been calibrated and validated on devices fabricated and measured in our labs and data from the literature. The model is then used to explore the design trade-offs related to the number of conduction band steps in staircase APDs for X-ray detection based on the GaAs/AlGaAs material system.