# Specific detectivity

Specific detectivity, or D*, for a photodetector is a figure of merit used to characterize performance, equal to the reciprocal of noise-equivalent power (NEP), normalized per unit area.

Specific detectivity is given by $D^*=\frac{\sqrt{A}}{NEP}$, where $A$ is the area of the photosensitive region of the detector. Its common units are $cm \cdot \sqrt{Hz}/ W$, also called the Jones in honor of R. Clark Jones who defined this magnitude.[1][2]

Given that noise-equivalent power can be expressed as a function of the responsivity $\mathfrak{R}$ (in units of $A/W$ or $V/W$) and the noise spectral density $S_n$ (in units of $A/Hz^{1/2}$ or $V/Hz^{1/2}$) as $NEP=\frac{S_n}{\mathfrak{R}}$, it's common to see the specific detectivity expressed as $D^*=\frac{\mathfrak{R}\cdot\sqrt{A}}{S_n}$.

The unit Jones is now commonly used with the D* figure of merit.

It is often useful to express the specific detectivity in terms of relative noise levels present in the device. A common expression is given below.

$D^* = \frac{q\lambda \eta}{hc} \left[\frac{4kT}{R_0 A}+2q^2 \eta \Phi_b\right]^{-1/2}$

With q as the electronic charge, $\lambda$ is the wavelength of interest, h is Planck's constant, c is the speed of light, k is Boltzmann's constant, T is the temperature of the detector, $R_0A$ is the zero-bias dynamic resistance area product (often measured experimentally, but also expressible in noise level assumptions), $\eta$ is the quantum efficiency of the device, and $\Phi_b$ is the total flux of the source (often a blackbody) in photons/sec/cm².

## References

1. ^ R. C. Jones, "Quantum efficiency of photoconductors," Proc. IRIS 2, 9 (1957)
2. ^ R. C. Jones, "Proposal of the detectivity D** for detectors limited by radiation noise," J. Opt. Soc. Am. 50, 1058 (1960), doi:10.1364/JOSA.50.001058)