We have found experimentally that the rise times of voltage pulses in NbN superconducting single photon detectors increase nonlinearly with increasing detector length. We fabricated superconducting single photon detectors based on NbN thin films with a meander-like sensitive region of area from 2x2um2 to 11x11um2. The effect is connected with the dependence of the detector resistance, which appears after photon absorption, on its kinetic inductance and hence on detector length. This conclusion is confirmed by our calculations in the framework of the two-temperature model.
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