Single-Photon Detector: Dead Time & Dark Counts

Incident Light

Photon rate λ 2.0 MHz

Detection efficiency η 30%

Detector

Dead time τ_d 50 ns

Dark count rate 50 kHz

Afterpulse prob. p_ap 3%

Live Readout

Click rate

0 kHz

Total clicks

True photon clicks

Dark + afterpulse

Live busy fraction

Signal-to-noise

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How it works

A single-photon avalanche diode (SPAD) is a p-n junction biased above breakdown (Geiger mode). One absorbed photon can trigger a self-sustaining avalanche of ~10⁶ carriers, giving a macroscopic electrical pulse from a single quantum of light. Incident photons arrive as a Poisson process with rate λ:

P(k photons in Δt) = (λΔt)^k e^(−λΔt) / k!

Each arriving photon triggers a click only with probability η (detection efficiency — includes absorption probability and avalanche-triggering probability). After every click the diode is quenched and held below breakdown for a non-paralyzable dead time τ_d, during which it is blind:

true click rate  R = η·λ / (1 + λ·τ_d)   (non-paralyzable dead-time model)

Two noise mechanisms add spurious clicks with no photon involved:

Dark counts — thermally- or field-generated carriers trigger an avalanche exactly like a photon would, at a rate independent of illumination.
Afterpulsing — carriers trapped during the previous avalanche release later and re-trigger it, with probability p_ap per prior click, clustered shortly after each real event.

The timeline shows every click as it happens (blue = true photon detection, amber = dark count, red = afterpulse) and a red bar under the detector marks the dead-time window after each click, during which further arrivals are silently dropped — this is exactly what limits the maximum count rate of real SPADs used in LIDAR, quantum key distribution and fluorescence-lifetime imaging.

Photon click Dark count Afterpulse

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