Dark count rate (DCR)

The dark count rate (DCR) of a single-photon detector is the rate of output pulses it produces with no light falling on it, in counts per second (often written Hz). Each dark count is indistinguishable from a photon detection, so the DCR is the noise floor of photon counting, the counterpart of dark current in a linear photodiode. Typical values span several orders of magnitude: below 1 count/s for a superconducting nanowire detector (SNSPD) with good stray-light control, a few to thousands per second for a photomultiplier tube depending on cathode and temperature, tens to thousands per second for a cooled silicon single-photon avalanche diode (SPAD), and hundreds of counts per second to tens of kilohertz for InGaAs/InP SPADs at telecom wavelengths, where the figure depends strongly on temperature, excess bias and gating.

Sources of dark counts

In avalanche detectors any carrier generated in the high-field region without a photon can start an avalanche and a count. Thermal generation through defect levels (Shockley-Read-Hall) dominates at room temperature; trap-assisted and band-to-band tunneling dominate at high field and low temperature, and grow with excess bias. Afterpulsing, the release of carriers trapped during an earlier avalanche, adds counts correlated with real detections; it is specified separately but inflates a DCR measurement that does not exclude it. In photomultipliers the main source is thermionic emission from the photocathode. In SNSPDs the intrinsic rate is very low; the measured value is usually set by blackbody radiation and stray light reaching the nanowire through the input fiber, and rises steeply as the bias approaches the critical current.

Because generation scales with the active volume, DCR scales roughly with detector area: a 500 µm diameter SPAD has 100 times the area of a 50 µm device and, other things equal, about 100 times the dark count rate. Array detectors such as the silicon photomultiplier therefore quote DCR per unit area, typically tens to hundreds of kilohertz per mm² at room temperature.

Measurement and temperature dependence

DCR is measured by blocking the input completely, counting pulses over a long integration time at the operating bias, threshold and temperature, and dividing by the time. A histogram of inter-arrival times separates the Poisson dark counts from afterpulses. Thermal generation follows an Arrhenius dependence, so cooling is the main remedy. For silicon SPADs the DCR is often found to fall by roughly a factor of two for every 8–10 K of cooling, so cooling by 40 K reduces it by a factor of roughly 16–32; the factor depends on which mechanism dominates, and tunneling-limited devices improve less.

Key relations

Dark counts arrive as a Poisson process, so the probability of a false count in a gate or time window $\tau$ is $1 - e^{-\text{DCR}\,\tau} \approx \text{DCR}\,\tau$. A detector with 100 counts/s has a false-count probability of $1.0 \times 10^{-7}$ in a 1 ns gate, which is why gated and coincidence measurements tolerate relatively high DCRs.

In photon counting with signal rate $r_s$, dark rate $r_d$ and integration time $T$, the signal-to-noise ratio is

$$\text{SNR} = \frac{r_s^2\, T}{r_s + r_d}.$$

With $r_s$ = 1000 counts/s, $r_d$ = 100 counts/s and $T$ = 1 s, SNR = 909 (29.6 dB); with $r_s$ = 10 counts/s and the same dark rate, SNR = 0.91.

A photon counter can also be assigned a noise-equivalent power, the optical power whose count rate equals the dark-count fluctuation in a 1 Hz bandwidth:

$$\text{NEP} = \frac{h\nu}{\eta}\sqrt{2\,\text{DCR}}.$$

At 1550 nm ($h\nu = 1.28 \times 10^{-19}$ J), with DCR = 100 counts/s and detection efficiency $\eta = 0.8$ (typical of a fiber-coupled SNSPD; for a SPAD, η is the absorber's quantum efficiency times the triggering probability), NEP = $2.3 \times 10^{-18}$ W/√Hz. Conventions differ by the factor $\sqrt{2}$, so the definition should be stated with the number.

Where it matters

In quantum key distribution a dark count in a detection window yields a random bit, which is wrong half the time. As fiber loss brings the signal detection probability toward the dark-count probability per gate, the error rate climbs toward 50% and the key rate falls to zero; low DCR lets SNSPD systems reach the longest distances. In lidar and time-correlated single-photon counting, dark counts form a flat background under the timing histogram that limits the weakest return that can be resolved.

Pitfalls

A DCR quoted without temperature, bias and threshold cannot be compared with another. Light leaking through connectors and fiber jackets often dominates a measured value; checking whether the rate changes when the room lights are switched off is a quick test.

Common questions

Is dark count rate the same as dark current?

They share the same generation processes. Dark current is the average current of a linear detector; DCR is the rate of discrete pulses in counting mode, where each carrier that triggers an avalanche becomes a full-size pulse.

Why is the dark count rate of InGaAs SPADs so much higher than silicon?

The narrower bandgap of InGaAs, needed to absorb at 1550 nm, raises thermal generation and tunneling, and the InP multiplication layer has more traps, which also raises afterpulsing. These detectors are therefore cooled and gated.

References: R. H. Hadfield, "Single-photon detectors for optical quantum information applications," Nature Photonics 3, 696 (2009); M. D. Eisaman, J. Fan, A. Migdall and S. V. Polyakov, "Invited review article: Single-photon sources and detectors," Review of Scientific Instruments 82, 071101 (2011); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019).