Specific detectivity

This article may rely excessively on sources too closely associated with the subject, potentially preventing the article from being verifiable and neutral. Please help improve it by replacing them with more appropriate citations to reliable, independent, third-party sources. (October 2018) (Learn how and when to remove this message)

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 (reciprocal of twice the integration time).

Specific detectivity is given by ${\displaystyle D^{*}={\frac {\sqrt {A\Delta f}}{NEP}}}$, where ${\displaystyle A}$ is the area of the photosensitive region of the detector, ${\displaystyle \Delta f}$ is the bandwidth, and NEP the noise equivalent power in units [W]. It is commonly expressed in Jones units (${\displaystyle cm\cdot {\sqrt {Hz}}/W}$) in honor of Robert Clark Jones who originally defined it.^[1][2]

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

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.

${\displaystyle D^{*}={\frac {q\lambda \eta }{hc}}\left[{\frac {4kT}{R_{0}A}}+2q^{2}\eta \Phi _{b}\right]^{-1/2}}$

With q as the electronic charge, ${\displaystyle \lambda }$ is the wavelength of interest, h is the Planck constant, c is the speed of light, k is the Boltzmann constant, T is the temperature of the detector, ${\displaystyle R_{0}A}$ is the zero-bias dynamic resistance area product (often measured experimentally, but also expressible in noise level assumptions), ${\displaystyle \eta }$ is the quantum efficiency of the device, and ${\displaystyle \Phi _{b}}$ is the total flux of the source (often a blackbody) in photons/sec/cm².