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Practical superconducting nanowire single photon detectors (SNSPDs) demonstrate a strong trade-off between detection sensitivity and the reset time. Often, there are wide variations in sensitivity and response times from SNSPDs of the same superconducting material. Here, using detailed physical models, we show that the dirtiness in a superconductor enforces a sensitivity and bandwidth trade-off in all practical devices. More importantly, a certain degree of dirtiness is a necessary requirement for achieving single photon detection. Under typical bias conditions close to the transition setpoints, the minimum number of photons required to register a voltage pulse decreases by the dirtiness parameter (Ioffe-Regel parameter) and the reset time of SNSPD increases by the same dirtiness parameter, thereby giving a constant value for the sensitivity-bandwidth product. The constant is weakly modified by biasing current and the temperature. Since dirtiness in the superconducting nanowire is a physically controllable parameter with an important bearing on the final response of an SNSPD, this work opens new opportunities to develop SNSPD devices with engineered sensitivity-bandwidth setpoint as dictated by an application., Comment: 12 Pages, 05 Figures

Superconducting Nanowire Single Photon Detector (SNSPD) emerges as a potential candidate in the multiple fields requiring sensitive and fast photodetection. While nanowires of low temperature superconducting detectors are mature with commercial solutions, other material options with higher transition temperature and faster responses are currently being explored. Towards this goal, we develop a generalized numerical model that incorporates the thermodynamic properties of the superconducting material and identifies the minimum resolvable photon count for a given bias and device parameters. A phase diagram of detection and latching phases with the minimum number of photons as a function of biasing current and biasing temperature for each material system is presented. We show using the developed model that while low temperature superconducting (LTS) nanowires are more sensitive to the incident photon at different wavelengths, the ultimate limit of a single photon can be achieved using high temperature superconducting (HTS) material such as YBa2Cu3O7-{\delta}, albeit at stringent biasing conditions. On the contrary, ultrafast response time with three orders of magnitude smaller response times can be achieved in select HTS materials making it an appealing for several practical applications.