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The dependence of the performance of separate-absorption-multiplication (SAM) single-photon avalanche diodes (SPADs) on the width of the multiplication region is theoretically investigated. The theory is applied to SAM SPADs with InP homojunction multiplication regions and InAlAs-InP heterojunction multiplication regions. In both cases the absorber layer is InGaAs. Two scenarios for the dark counts are considered: (i) low-temperature operation, when the number of dark carriers is dominated by field-assisted mechanisms of band-to-band tunneling and tunneling through defects; and (ii) room-temperature operation, when the number of dark carriers in the multiplication region is dominated by the generation/recombination mechanism. The analysis utilizes a generalized theory for breakdown probability, which takes into account the random locations where dark and photogenerated carriers are produced in each layer. Depending upon the detector temperature, as the width of the multiplication region is increased the effects from the reduction in the number of dark carriers due to field-assisted generation mechanisms are counteracted by the effects from the elevation in the number of generation/recombination dark carriers. Thus, there exists an optimal width of the multiplication region that achieves the best performance of the SPAD.