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photodetection

photodetection

Basics

There are three main light detection principles : external photoelectric effect, internal photoelectric effect and thermal effect.

Basically, external photoelectric effect occurs when a photon strikes a metal or semiconductor placed in vacuum. An electron is then emitted from its surface into vacuum.
Photomultipliers are based on this principle. The electron created by the incident radiation is then multiplied (hence the name) through a system
of dynodes with progressive voltage.

In the case of internal photoelectric effect, the sensitive material is a semiconductor and when struck by a photon, an electron goes from the valence to the conduction band
creating a hole - electron pair. An electrical current is then generated. These detectors are commonly called quantic photodetectors.

Temperature of a thermal detector increases when illuminated. One of its physical parameters which is sensitive to temperature ( for example its electrical resistance )
then changes and generates a detection signal.

Quantic photodetectors

Because photons make electrons move from the valence to the conduction band, they are efficient only when their energy ( and consequently their wavelength ) corresponds to the
semiconductor band gap or is at least larger than this band gap.
Photodetectors are characterized by their quantum efficiency ( nu ) representing the ratio of hole-electron pairs number by incident
photons. nu depends on
the photon wavelength ( lam ).
Photodetectors are also characterized by their sensitivity ( S ) representing the ratio of the incident optical power on the generated
electric current ( photocurrent Iph ). S depends on nu
and the photon wavelength ( lam ).

Sensitivity is constant as the power on the photodetector is less than a limit value ( the photodetector is then said linear ). It decreases when the power is greater than this limit.
It is possible to increase the limit value of power lnearity by applying a reverse voltage on the photodetector.

Different kinds of noises occur in a photodetector.
When expressed with the electric current, the rms noise dIn is the standard error on the photocurrent Iph.
dIn^{2} is
the sum of the square values of all independents RMS noises ( shot noise,
Johnson noise,…).

The signal over noise ratio ( S/N ) ( the S of S/N characterizing the "signal"
and not the "sensitivity" ) is the ratio of the current signal ( Iph ) over the noise ( dIn ).

The noise equivalent power ( NEP ) defines the minimum detectable power per square root bandwidth ( power for which
S/N = 1 : minimum input optical power generating a photocurrent equal to the rms noise in a 1 hertz bandwidth ). NEP depends at least on several parameters as the temperature ( T ),
the wavelength ( lam ), the signal frequency ( f ) and
the detector area ( A ).

The detectivity is equal to the reciprocal of the noise equivalent power NEP. The lower the NEP,
the higher the detectivity and the better the signal quality.
The specific detectivity ( D* ) is the detectivity normalized to the unit area. it's a function of
NEP and detector area ( A ).

When a reverse voltage is applied to the photodetector, a current is generated even if no light is detected. It is called the dark current ( Id ) .

Among the different kinds of noises, two can be calculated easily : the Shot noise and the Johnson noise.

The Shot noise is caused by the randomatic behaviour of quantic phenomenoms. It's a white noise limitating utltimate performances of a photodetector. Rms Shot noise
( dIs )
depends on the photocurrent ( Iph ), the detector bandwidth ( dF ), and eventually the dark current ( Id ) if a reverse voltage is applied and that Id
is not negligible.

The shot noise ( induced by the photocurrent ) can be calculated using the equivalent optical power on the photodetector. The equivalent optical Shot noise is then the rms standard error ( dPs )
on the optical power ( P ). dPs depends on P, the detector bandwidth
( dF ) and the wavelength ( lam ).

For a shot noise limited photodector, when the dark current is very small compared to the photocurrent, the ratio signal over noise ( S/N )
is a function of the detector bandwidth
( dF ) and the photocurrent ( Iph ). It can also be calculated using the optical power. It's then a
function of the wavelength ( lam ), the quantum efficiency ( nu ), the bandwidth
( dF ) and the optical power ( P ).

The thermal noise ( or Johnson noise ) is generated by the thermal agitation of electrons in the photodetector. It can be approximated by a white noise ( except for very high
frequencies ). When no reverse voltage is applied, the Rms Johnson noise ( dIj ) depends on the temperature ( T ), the shunt resistance ( Rsh )
and the frequency bandwidth ( dF ).

References

"Cours détection dans le domaine optique" - Ecole Nationale Supérieure des Télécommunications - 1988 - author : P. Gallion.

"Notes bruit dans un photodétecteur large bande" - Laboratoire Collisions, Agrégats et Réactivité, CNRS - 2008 - author : Gilles Bailly.

"Cours bruit et limite de détection" - Ecole Polytechnique Fédérale de Lausanne - 2002 - author : P.A. Besse.

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