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 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\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 (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle cm \cdot \sqrt{Hz}/ W} ) in honor of Robert Clark Jones who originally defined it.

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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle A/Hz^{1/2}} or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle V/Hz^{1/2}} ) as ${\displaystyle NEP={\frac {S_{n}}{\mathfrak {R}}}}$, it is common to see the specific detectivity expressed as Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\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.