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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 square root of the sensor's area and frequency bandwidth (reciprical of its sampling rate).

Specific detectivity is given by $D^{*}=\frac{\sqrt{Af}}{NEP}$, where $A$ is the area of the photosensitive region of the detector and $f$ is the frequency bandwidth. It is commonly expressed in Jones units ($cm\cdot \sqrt{Hz}/W$)in honor of R. Clark Jones who originally defined it.

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 $A/H{z}^{1/2}$ or $V/H{z}^{1/2}$) as $NEP=\frac{S_n}{\mathfrak{R}}$, it's common to see the specific detectivity expressed as $D^{*}=\frac{\mathfrak{R}\cdot \sqrt{A}}{S_n}$.

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.

$D^{*}=\frac{q\lambda \eta }{hc}{[\frac{4kT}{R_{0}A}+2q^2\eta {\mathrm{\Phi }}_b]}^{-1/2}$

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, $R_{0}A$ 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 ${\mathrm{\Phi }}_b$ is the total flux of the source (often a blackbody) in photons/sec/cm².

References

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