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 and bandwidth.

Specific detectivity is given by $D^*=\frac{\sqrt{A}\sqrt{B}}{NEP}$ , where $A$ is the area of the photosensitive region of the detector and $B$ is the bandwidth in Hz. 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.

$D^* = \frac{q\lambda \eta}{hc} [\frac{4kT}{R_0 A}%2B2q^2 \eta \Phi_b]^{-1/2}$

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, R0A is the Zero-Bias dynamic resistance area product (often measured experimentally, but also expressable 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 and footnotes

^ R. C. Jones, "Quantum efficiency of photoconductors," Proc. IRIS 2, 9 (1957)
^ 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)

This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".