Dark current (I_d)
The current a reverse-biased photodetector passes with no light on it, from thermal generation, diffusion, surface leakage and tunneling. It adds an offset and a shot noise of √(2eI_d) per √Hz (18 fA/√Hz at 1 nA), roughly doubles every 6–13 K near room temperature in InGaAs, and matters most in slow, high-impedance and avalanche receivers; origins, typical values, and measurement.
Dark current is the current that flows through a reverse-biased photodetector when no light reaches it. It is the diode's reverse leakage current, carried by electron–hole pairs that are generated thermally or by defects rather than by photons, and it adds to the photocurrent without carrying any information. It matters in two ways: as a DC offset that must be subtracted from a weak signal, and as a source of shot noise that sets part of the detector's noise floor and its noise-equivalent power.
Origins
Four mechanisms contribute, and which one dominates depends on the material, the bias and the temperature. Diffusion current comes from minority carriers generated within a diffusion length of the junction in the neutral regions; it is proportional to the square of the intrinsic carrier density and so varies as
with the bandgap. Generation current comes from carriers created through defect levels inside the depletion region; it is proportional to and to the depleted volume, so it grows with bias and varies as
which is a weaker temperature dependence. Surface leakage flows along the edge of the junction where it meets a mesa sidewall or passivation layer; it scales with the perimeter rather than the area and depends on processing more than on physics, and it is often the largest term in small, fast devices and at low temperature. Band-to-band and trap-assisted tunneling become important at high field, in narrow-gap materials and in the multiplication region of an avalanche photodiode. Defects matter throughout: germanium grown on silicon has a high density of threading dislocations, and germanium-on-silicon photodetectors have much higher dark current per unit area than InGaAs devices lattice-matched to InP (Michel et al. 2010).
Temperature
Because both bulk mechanisms are activated by the bandgap, dark current falls steeply on cooling. For InGaAs ( eV) the expressions above predict that dark current doubles for every 6.5 K of warming near 300 K if it is diffusion limited, and every 13 K if it is generation limited; for silicon the intervals are 4.5 K and 9.0 K. Cooling InGaAs from 300 K to 250 K reduces the diffusion current by a factor of 570 but the generation current by only 24, and surface leakage by less than either, so cooling gives diminishing returns once the bulk terms have been suppressed. A two-stage thermoelectric cooler is the usual way to get this gain in near-infrared instruments.
Typical values
Dark current scales with the junction area and increases with reverse bias, so datasheets quote it at a stated bias and temperature, and devices of the same material span orders of magnitude. The ranges below are the typical values given by Agrawal (chapter 4) for telecom-class detectors.
| Detector | Dark current |
|---|---|
| Si PIN | 1 – 10 nA |
| Ge PIN | 50 – 500 nA |
| InGaAs PIN | 1 – 20 nA |
| Si APD | 0.1 – 1 nA |
| Ge APD | 50 – 500 nA |
| InGaAs APD | 1 – 5 nA |
As a noise source
Dark current contributes a shot-noise density of , which is 17.9 fA/√Hz at 1 nA and 566 fA/√Hz at 1 µA. Whether that matters depends on what it is compared with. A transimpedance amplifier with 3 pA/√Hz of input noise is only matched by 28 µA of dark current, so in a fast receiver even a leaky germanium detector's dark current is a small term in the noise. The thermal noise of a 1 MΩ resistor is matched by 52 nA, and that of a 1 GΩ resistor by 52 pA, so in slow, high-impedance instruments dark current can set the floor. In an APD the multiplied part of the dark current is amplified with the signal and carries the excess noise: 1 nA of multiplied dark current at a gain of 10 with an ionization ratio of 0.5 produces 437 fA/√Hz, 24 times its unmultiplied shot noise. At zero bias, in photovoltaic operation, the dark current vanishes and the noise is the thermal noise of the diode's shunt resistance instead, which is why the lowest-noise slow measurements often run the diode unbiased.
Measurement and correction
Dark current is measured with the detector shielded from light, at the operating bias and temperature, with a source-measure unit or electrometer; a sweep of bias shows the onset of tunneling or breakdown, and a sweep of temperature separates the diffusion and generation terms by their activation energies ( and ). The offset it produces is removed by subtracting a dark reading or, better, by modulating the light and detecting synchronously with a lock-in amplifier, which rejects the DC offset and its drift together; its shot noise cannot be subtracted and can only be reduced by cooling, smaller area or lower bias. The photodetector characterization article covers the measurement alongside responsivity and NEP. In photon-counting detectors such as the single-photon avalanche diode and SNSPD the same physics appears as a dark count rate.
The Photodiode Noise Calculator takes the dark current as an input and plots its shot noise against the thermal, amplifier and signal shot noise as the optical power changes.
How dark-current noise enters a measured NEP, and how to separate it from amplifier noise, is shown in How to Measure a Detector's NEP and D*.
References: G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010), chapter 4. S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed. (Wiley, 2007). J. Michel, J. Liu, and L. C. Kimerling, "High-performance Ge-on-Si photodetectors," Nature Photonics 4, 527 (2010).