Shot noise is a type of electronic noise

Electronic noise

Electronic noise is a random fluctuation in an electrical signal, a characteristic of all electronic circuits. Noise generated by electronic devices varies greatly, as it can be produced by several different effects...

 that may be dominant when the finite number of particles that carry energy (such as electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s in an electronic circuit or photon

Photon

In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s in an optical device) is sufficiently small so that uncertainties due to the Poisson distribution

Poisson distribution

In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since...

, which describes the occurrence of independent random events, are of significance. It is important in electronics

Electronics

Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

, telecommunications, optical detection, and fundamental physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

.

The term can also be used to describe any noise source, even if solely mathematical, of similar origin. For instance, particle simulations may produce a certain amount of "noise", where due to the small number of particles simulated, the simulation exhibits undue statistical fluctuations which don't reflect the real-world system. The magnitude of shot noise increases according to the square root of the expected number of events, such as the electrical current or intensity of light. But since the strength of the signal itself increases more rapidly, the relative proportion of shot noise decreases and the signal to noise ratio (considering only shot noise) increases anyway. Thus shot noise is more frequently observed with small currents or light intensities following sufficient amplification.
For large numbers the Poisson distribution approaches a normal distribution, typically making shot noise in actual observations indistinguishable from true Gaussian noise

Gaussian noise

Gaussian noise is statistical noise that has its probability density function equal to that of the normal distribution, which is also known as the Gaussian distribution. In other words, the values that the noise can take on are Gaussian-distributed. A special case is white Gaussian noise, in which...

 except when the elementary events (photons, electrons, etc.) are so few that they are individually observed. Since the standard deviation

Standard deviation

Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...

 of shot noise is equal to the square root of the average number of events N, the signal-to-noise ratio

Signal-to-noise ratio

Signal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...

 is given by:
.

Thus when N is very large, the signal-to-noise ratio is very large as well, and any relative fluctuations in N due to other sources are more likely to dominate over shot noise. However when the other noise source is at a fixed level, such as thermal noise, increasing N (the DC current or light level, etc.) can sometimes lead to dominance of shot noise nonetheless.

Intuitive explanation

It is known that in a statistical experiment such as tossing a fair coin and counting the occurrences of heads and tails, the numbers of heads and tails after a great many throws will differ by only a tiny percentage, while after only a few throws outcomes with a significant excess of heads over tails or vice versa are common; if an experiment with a few throws is repeated over and over, the outcomes will fluctuate a lot. (It can be proven that the relative fluctuations reduce as the square root of the number of throws, a result valid for all statistical fluctuations, including shot noise.)

Shot noise exists because phenomena such as light and electric current consist of the movement of discrete, quantized

Quantization (physics)

In physics, quantization is the process of explaining a classical understanding of physical phenomena in terms of a newer understanding known as "quantum mechanics". It is a procedure for constructing a quantum field theory starting from a classical field theory. This is a generalization of the...

 'packets'. Consider light—a stream of discrete photons—coming out of a laser pointer and hitting a wall to create a visible spot. The fundamental physical processes that govern light emission are such that these photons are emitted from the laser at random times; but the many billions of photons needed to create a spot are so many that the brightness, the number of photons per unit time, varies only infinitesimally with time. However, if the laser brightness is reduced until only a handful of photons hit the wall every second, the relative fluctuations in number of photons, i.e., brightness, will be significant, just as when tossing a coin a few times. These fluctuations are shot noise.

In electronic devices

Shot noise in electronic circuits is due to the quantized nature of the electric charge. It consists of random fluctuations of the electric current

Electric current

Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

 in a DC

Direct current

Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...

 current due to that current actually consisting of a flow of discrete charges (electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s). Because the electron has such a tiny charge, however, shot noise is of relative insignificance in many (but not all) cases of electrical conduction. For instance 1 ampere

Ampere

The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...

 of current consists of about electrons per second; even though this number will randomly vary by several billion in any given second, such a fluctuation is minuscule compared to the current itself.

But with very small currents and considering shorter time scales (thus wider bandwidths) one may find otherwise. For instance, a microwave circuit operates on time scales of less than a nanosecond

Nanosecond

A nanosecond is one billionth of a second . One nanosecond is to one second as one second is to 31.7 years.The word nanosecond is formed by the prefix nano and the unit second. Its symbol is ns....

 and if we were to have a current of 16 nanoamperes that would amount to only 100 electrons passing every nanosecond. According to Poisson statistics the actual number of electrons in any nanosecond would vary by 10 electrons rms

Root mean square

In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids...

, so that one sixth of the time less than 90 electrons would pass a point and one sixth of the time more than 110 electrons would be counted in a nanosecond. Now with this small current viewed on this time scale, the shot noise amounts to 1/10 of the DC current itself.

While this is the result when the electrons contributing to the current occur completely randomly, unaffected by each other, there are important cases in which these natural fluctuations are largely suppressed due to a charge build up. Take the previous example in which an average of 100 electrons go from point A to point B every nanosecond. During the first half of a nanosecond we would expect 50 electrons to arrive at point B on the average, but in a particular half nanosecond there might well be 60 electrons which arrive there. This will create a more negative electric charge at point B than average, and that extra charge will tend to repel the further flow of electrons from leaving point A during the remaining half nanosecond. Thus the net current integrated over a nanosecond will tend more to stay near its average value of 100 electrons rather than exhibiting the expected fluctuations (10 electrons rms) we calculated. This is the case in ordinary metallic wires and in metal film resistors, where shot noise is almost completely cancelled due to this anti-correlation between the motion of individual electrons, acting on each other through the coulomb force.

However this reduction in shot noise does not apply when the current results from random events at a potential barrier which all the electrons must overcome due to a random excitation, such as by thermal activation. This is the situation in p-n junction

P-n junction

A p–n junction is formed at the boundary between a P-type and N-type semiconductor created in a single crystal of semiconductor by doping, for example by ion implantation, diffusion of dopants, or by epitaxy .If two separate pieces of material were used, this would...

s, for instance. A semiconductor diode

Diode

In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

 is thus commonly used as a noise source by passing a particular DC current through it.

Shot noise is distinct from voltage and current fluctuations expected in thermal equilibrium; this occurs without any applied DC voltage or current flowing. These fluctuations are known as Johnson-Nyquist noise or thermal noise and increase in proportion to the Kelvin

Kelvin

The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

 temperature of any resistive component. However both are instances of white noise

White noise

White noise is a random signal with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency...

 and thus cannot be distinguished simply by observing them even though their origins are quite dissimilar.

Since shot noise is a Poisson process

Poisson process

A Poisson process, named after the French mathematician Siméon-Denis Poisson , is a stochastic process in which events occur continuously and independently of one another...

 due to the finite charge of an electron, one can compute the root mean square

Root mean square

In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids...

 current fluctuations as being of a magnitude


where q is the elementary charge

Elementary charge

The elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called...

 of an electron, Δf is the bandwidth in hertz

Hertz

The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....

 over which the noise is considered, and I is the DC current flowing.

For a current of 100 mA, measuring the current noise over a bandwidth of 1 Hz, we obtain

If this noise current is fed through a resistor a noise voltage of
would be generated. Coupling this noise through a capacitor, one could supply a noise power of
to a matched load.

In optics

In optics

Optics

Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

, shot noise describes the fluctuations of the number of photons detected (or simply counted in the abstract) due to their occurrence independent of each other. This is therefore another consequence of discretization, in this case of the energy in the electromagnetic field in terms of photons. In the case of photon detection, the relevant process is the random conversion of photons into photo-electrons for instance, thus leading to a larger effective shot noise level when using a detector with a quantum efficiency

Quantum efficiency

Quantum efficiency is a quantity defined for a photosensitive device such as photographic film or a charge-coupled device as the percentage of photons hitting the photoreactive surface that will produce an electron–hole pair. It is an accurate measurement of the device's electrical sensitivity to...

 below unity. Only in an exotic squeezed coherent state can the number of photons measured per unit time have fluctuations smaller than the square root of the expected number of photons counted in that period of time. Of course there are other mechanisms of noise in optical signals which often dwarf the contribution of shot noise. When these are absent, however, optical detection is said to be "photon noise limited" as only the shot noise (also known as "quantum noise" or "photon noise" in this context) remains.

Shot noise is easily observable in the case of photomultiplier

Photomultiplier

Photomultiplier tubes , members of the class of vacuum tubes, and more specifically phototubes, are extremely sensitive detectors of light in the ultraviolet, visible, and near-infrared ranges of the electromagnetic spectrum...

s and avalanche photodiodes used in the Geiger mode, where individual photon detections are observed. However the same noise source is present with higher light intensities measured by any photodetector

Photodetector

Photosensors or photodetectors are sensors of light or other electromagnetic energy. There are several varieties:*Active pixel sensors are image sensors consisting of an integrated circuit that contains an array of pixel sensors, each pixel containing a both a light sensor and an active amplifier...

, and is directly measurable when it dominates the noise of the subsequent electronic amplifier. Just as with other forms of shot noise, the fluctuations in a photo-current due to shot noise scale as the square-root of the average intensity:


The shot noise of a coherent optical beam (having no other noise sources) is a fundamental physical phenomenon, reflecting quantum fluctuations in the electromagnetic field (due to the so-called zero-point energy

Zero-point energy

Zero-point energy is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have an associated zero-point energy, a consequence of their wave-like nature...

. This sets a lower bound on the noise introduced by quantum amplifier

Quantum amplifier

A quantum amplifer is an amplifier that uses quantum mechanical methods to amplify a quantum signal; examples include the active elements of optical lasers and optical re-transmitters....

s which preserve the phase of an optical signal.

External links

• Shot noise on arxiv.org