  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.
