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# Responsivity

Definition: photocurrent per unit optical power incident on a photodetector

German: Empfindlichkeit

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The responsivity (or radiant sensitivity) of a photodiode or some other kind of photodetector is the ratio of generated photocurrent and incident (or sometimes absorbed) optical power (neglecting noise influences), determined in the linear region of response. In the case of photodiodes, the responsivity is typically highest in a wavelength region where the photon energy is somewhat above the band gap energy, and declining sharply in the region of the bandgap, where the absorption decreases. It can be calculated according to

where h ν is the photon energy, η is the quantum efficiency, and e the elementary charge.

For example, a silicon photodiode with 90% quantum efficiency at a wavelength of 800 nm, the responsivity would be ≈ 0.58 A/W. Values for other types of photodiode are basically always of that order of magnitude.

## Calculator for the Responsivity

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For avalanche photodiodes and photomultipliers, there is an additional factor for the internal current multiplication, so that values far above 1 A/W are possible. Note that the current multiplication is usually not subsumed in the quantum efficiency.

Note that the term responsivity cannot be directly applied to photoconductive detectors (photoresistors), where the response to incident light is not a photocurrent proportional to the incident intensity but rather an increase of conductivity – often with a quite nonlinear behavior.

The responsivity is usually defined for the steady state. The photodiode response typically falls off for signal frequencies above some detection bandwidth.

The term sensitivity is often used instead of responsivity, but that is not recommended, since the term can also have other meanings. It should be avoided particularly when a clear quantitative meaning is intended.

The responsivity is usually meant to be a wavelength-dependent quantity and thus considered for monochromatic light. However, one may consider an effective responsivity for non-monochromatic light with a certain spectral bandwidth.

A photodetector should ideally be operated in a spectral region where its responsivity is not far below the highest possible value, because this leads to the lowest possible detection noise and thus to a high signal-to-noise ratio and high sensitivity.

If some detector has a voltage rather than a current output, one can define its responsivity as the ratio of output voltage and optical power. This leads to units of V/W (volts per watt). If a photodiode is combined with some detector electronics generating a voltage output, the output voltage is the photocurrent times the so-called transimpedance of the electronics. In the simplest case, one uses a shunt resistor, and the transimpedance is then its resistance.

Thermal detectors usually have a responsivity with a weak wavelength dependence in a broad spectral range – in contrast to photodetectors like photodiodes, where the responsivity typically drops sharply for photon energies around the band gap energy.

## Questions and Comments from Users

2020-12-06

Consider, for example, the responsivity of a PIN photodiode at 1.3 μm and 1.55 μm, in both cases with a quantum efficiency of 80%. Why is the photodiode more responsive at 1.55 μm?

This is because in light with the longer wavelength you have a larger number of photons per joule of optical energy.

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