Signal-to-noise ratio of Geiger-mode avalanche photodiode single-photon counting detectors

Geiger-mode avalanche photodiodes (GM-APDs) use the avalanche mechanism of semiconductors to amplify signals in individual pixels. With proper thresholding, a pixel will be either “on” (avalanching) or “off.” This discrete detection scheme eliminates read noise, which makes these devices capable of counting single photons. Using these detectors for imaging applications requires a well-developed and comprehensive expression for the expected signal-to-noise ratio (SNR). This paper derives the expected SNR of a GM-APD detector in gated operation based on gate length, number of samples, signal flux, dark count rate, photon detection efficiency, and afterpulsing probability. To verify the theoretical results, carrier-level Monte Carlo simulation results are compared to the derived equations and found to be in good agreement.