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We study the breakdown characteristics and timing statistics of InP and In0.52Al0.48As single-photon avalanche photodiodes (SPADs) with avalanche widths ranging from 0.2 to 1.0 mum at room temperature using a random ionization path-length model. Our results show that, for a given avalanche width, the breakdown probability of In0.52Al0.48As SPADs increases faster with over bias than InP SPADs. When we compared their timing statistics, we observed that, for a given breakdown probability, InP requires a shorter time to reach breakdown and exhibits a smaller timing jitter than In0.52Al0.48As. However, due to the lower dark count probability and faster rise in breakdown probability with over bias, In0.52Al0.48As SPADs with avalanche widths les 0.5 mum are more suitable for single-photon detection at telecommunication wavelengths than InP SPADs. Moreover, we predict that, in InP SPADs with avalanche widths les 0.3 mum and In0.52Al0.48As SPADs with avalanche widths les 0.2 mum, the dark count probability is higher than the photon count probability for all applied biases.