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The recurrence theory for the breakdown probability in avalanche photodiodes (APDs) is generalized to heterostructure APDs that may have multiple multiplication layers. The generalization addresses layer-boundary effects such as the initial energy of injected carriers as well as the layer-dependent profile of the dead space in the multiplication region. Reducing the width of the multiplication layer serves to both downshift and sharpen the breakdown probability curve as a function of the applied reverse-bias voltage. In structures where the injected carriers have an initial energy that is comparable to the ionization threshold energy, the transition from linear mode to Geiger-mode is more abrupt than in structures in which such initial energy is negligible. The theory is applied to two recently fabricated Al0.6Ga0.4As-GaAs heterostructure APDs and to other homostructure thin GaAs APDs and the predictions of the breakdown-voltage thresholds are verified.