Dark Current

Dark current is the current a photodiode or image sensor pixel produces with absolutely no light reaching it — thermally generated electron-hole pairs crossing the same depletion region that light-generated carriers would cross, indistinguishable from a real signal once they're collected, which is exactly why it shows up as the specific physical cause behind offset fixed pattern noise this series has already named without fully explaining.

The generation mechanism is thermal, not optical, which is what makes dark current fundamentally different from the signal it contaminates. A reverse-biased photodiode junction has a depletion region where thermally generated carriers — produced by the same random thermal agitation that generates thermal noise everywhere else in this series — get swept across the junction and collected as current, exactly as a photon-generated carrier would be. Because this generation process depends on thermal energy rather than incident light, it follows the same Arrhenius-type exponential temperature dependence that governs any thermally activated leakage mechanism: dark current roughly doubles for every seven to eight degrees Celsius of temperature rise, a rate of growth steep enough that a sensor's dark current at a hot ambient can be an order of magnitude higher than the same sensor cooled by only thirty or forty degrees.

This exponential temperature dependence traces back to the same thermal voltage this series has already established as the universal scale behind exponential semiconductor behavior. The generation and leakage currents driving dark current follow an exponential law in inverse temperature closely related to the Boltzmann statistics that set every other exponential I-V relationship this series has covered, which is precisely why cooling a sensor is such an effective lever — a modest temperature reduction, by this same exponential relationship, buys a disproportionately large dark current reduction, which is exactly why scientific and astronomical imaging sensors are routinely cooled to deep cryogenic temperatures specifically to suppress dark current to negligible levels.

Dark current is not one error but two, and the split maps directly onto this series' own fixed-versus-temporal distinction. The mean dark current level for a given pixel at a given temperature is a repeatable, deterministic quantity set by that specific pixel's own defect density and junction area — this is literally the source of offset fixed pattern noise already named in this series, the per-pixel additive error that correlated double sampling cancels by subtracting a reset-level reading that carries the identical dark-current contribution. Layered on top of that mean value is dark current shot noise, the random, Poisson-distributed fluctuation in exactly how many thermally generated carriers happen to be collected in any given integration period, which scales with the square root of the mean dark current rather than equaling it directly.

This shot-noise component is fundamentally untouchable by correlated double sampling, for the identical reason kT/C noise from an uncorrelated reset resists the same technique. Shot noise is a fresh, independent random draw on every single measurement — the number of thermally generated carriers collected during one integration period is uncorrelated with the number collected during a different integration period, even for the identical pixel under identical conditions, so there is no shared, repeatable component for a reset-and-signal subtraction to cancel. A pixel's mean dark current is fixable with the same tools this series has already built for fixed pattern noise; a pixel's dark current shot noise is fixable only by the same tools available against any other temporal noise source — a bigger signal to swamp it, a cooler sensor to shrink the mean it scales from, or longer averaging where the application tolerates it.

Dark current nonuniformity, the image-sensor-specific term for pixel-to-pixel variation in mean dark current across an array, is addressed by the same two tools this series has already covered for offset FPN generally. Correlated double sampling corrects it in real time during normal pixel readout, exactly as it does for any other offset-FPN source. Dark-frame subtraction, standard practice in astrophotography and other long-exposure imaging, captures a reference frame with the sensor shuttered and nothing but dark current present, then subtracts that entire frame from every subsequent light exposure — a calibration-based approach closer in spirit to the flat-field correction already described for gain FPN, useful specifically because very long integration times can accumulate enough dark current that a simple per-pixel reset-level sample from CDS no longer captures the full accumulated offset.

Dark current closes a loop this series has been building from several directions at once — it is simultaneously the physical source behind offset fixed pattern noise, another example of the thermal-voltage-driven exponential behavior this series keeps returning to, and a case study in exactly why fixed and temporal errors need entirely different correction strategies even when they originate from the identical physical mechanism. The mean and the fluctuation around that mean are not two measurements of the same problem; they are two different problems that happen to share a name, and conflating them is exactly the kind of mistake that leads to applying the wrong fix to the wrong half.