Detection jitter quantifies variance introduced by the detector in the determination of photon arrival time. It is a crucial performance parameter for systems using superconducting nanowire single photon detectors (SNSPDs). In this work, we have demonstrated that the detection timing jitter is limited in part by the spatial variation of photon detection events along the length of the wire. This distribution causes the generated electrical pulses to arrive at the readout at varied times. We define this jitter source as geometric jitter since it is related to the length and area of the SNSPD. To characterize the geometric jitter, we have constructed a novel differential cryogenic readout with less than 7 ps of electronic jitter that can amplify the pulses generated from the two ends of an SNSPD. By differencing the measured arrival times of the two electrical pulses, we were able to partially cancel out the difference of the propagation times and thus reduce the uncertainty of the photon arrival time. Our experimental data indicates that the variation of the differential propagation time was a few ps for a 3 {mu}m x 3 {mu}m device while it increased up to 50 ps for a 20 {mu}m x 20 {mu}m device. In a 20 {mu}m x 20 {mu}m large SNSPD, we achieved a 20% reduction in the overall detection timing jitter for detecting telecom-wavelength photons by using the differential cryogenic readout. The geometric jitter hypothesis was further confirmed by studying jitter in devices that consisted of long wires with 1-{mu}m-long narrowed regions used for sensing photons.
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