SPAD Detector Calculator

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

A fixed non-paralyzable dead time acts on photon and dark avalanches, afterpulses are first order, and the SNR is that of the dead-time corrected photon rate over the stated gate. DCR(T) is Arrhenius at a fixed excess bias. 0.25 eV is an effective value that matches the lower bound of the drop of more than 100× that Korzh et al. saw from −50 to −110 °C; they report the step is not constant, and tunnelling flattens it at lower T. Afterpulses are counted but start no dead time of their own. Defaults: their InGaAs/InP NFAD at −110 °C with a 20 µs hold-off: the counts saturate at 1/τ = 50 kcps, and 10 % are already lost at about −112 dBm.

1. Korzh B., Walenta N., Lunghi T., Gisin N., Zbinden H. (2014). Free-running InGaAs single photon detector with 1 dark count per second at 10% efficiency. Appl. Phys. Lett. 104, 081108. At −110 °C: 11.5 % efficiency, 1.19 cps, 2.2 % afterpulsing with 20 µs dead time; DCR falls over two orders of magnitude from −50 to −110 °C. doi:10.1063/1.4866582
2. Webster E. A. G., Henderson R. K. (2013). A TCAD and spectroscopy study of dark count mechanisms in single-photon avalanche diodes. IEEE Trans. Electron Devices 60, 4014–4019. Arrhenius activation energies of dark counts. doi:10.1109/TED.2013.2285163
3. Müller J. W. (1973). Dead-time problems. Nucl. Instrum. Methods 112, 47–57. Dead-time models and the statistics of the recorded counts. doi:10.1016/0029-554X(73)90773-8