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Recently, it has been shown that the noise characteristics of heterojunction Al0.6Ga0.4As-GaAs avalanche photodiodes (APDs) can be optimized by proper selection of the width of the Al0.6Ga0.4As layer. Similar trends have also been shown theoretically for the bandwidth characteristics. The resulting noise reduction and potential bandwidth enhancement have been attributed to the fact that the high bandgap Al0.6Ga0.4As layer serves to energize the injected electrons, thereby minimizing their first dead space in the GaAs layer. We show theoretically that the same optimized structures yield optimal breakdown-probability characteristics when the APD is operated in Geiger mode. The steep breakdown-probability characteristics, as a function of the excess bias, of thick multiplication regions (e.g., in a 1000-nm GaAs homojunction) can be mimicked in much thinner optimized Al0.6Ga0.4As-GaAs APDs (e.g., in a 40-nm Al0.6Ga0.4As and 200-nm GaAs structure) with the added advantage of having a reduced breakdown voltage (e.g., from 36.5 V to 13.7 V).