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In recent years, a growing number of applications demand better timing resolution from single-photon avalanche diodes (SPADs). The challenge is pursuing improved timing resolution without impairing other device characteristics such as quantum efficiency and dark count rate. This task requires a clear understanding of the statistical phenomena involved in the avalanche current growth in order to drive the device engineering process. Past studies state that in Si SPADs the avalanche injection position statistics is the main contribution to the photon-timing jitter. However, in recent re-engineered devices, this assumption has been questioned. To address this issue, we developed an experimental setup capable of characterizing the photon-timing jitter as a function of the injection position by means of a laser focused on the device active area. The results not only confirmed that the injection position statistics is not the main contribution to photon-timing jitter, but also evidenced interesting dependences of the timing performances on the injection position. Furthermore, we found a relationship between the photon-timing jitter and the specific resistance of the devices, which has been investigated by means of photoluminescence measurements.