# Shot noise

Shot noise (also Poisson shot noise or Schottky noise ) is a form of white noise in optics and electronics that can be modeled using a Poisson process .

## With electricity

Electrical shot noise always occurs when an electrical current has to overcome a potential barrier. The shot noise stems from the fact that the total current flow is composed of the movement of individual charge carriers ( electrons or holes ), and each charge carrier crosses this barrier by itself. This does not happen evenly, but is a stochastic process. In sum, certain fluctuations in the current flow can also be observed on a macroscopic level.

The mean square of the noise current can be expressed by the equation ${\ displaystyle i}$

${\ displaystyle {\ overline {i _ {\ text {Rausch}} ^ {2}}} = 2eI \ Delta f}$

express, where

• ${\ displaystyle e}$the elementary charge ,
• ${\ displaystyle I}$ the current flowing in the conductor and
• ${\ displaystyle \ Delta f}$is the bandwidth of the measurement.

The dimension of the mean noise current square is [  A 2 ].

The size of the shot noise depends on the size of the flowing current and does not show any direct temperature dependence. This distinguishes it from noise in thermal equilibrium , the Johnson-Nyquist noise .

For technical frequencies , the noise current square is proportional to the width of the frequency band, but independent of the frequency. Only at frequencies with a period as short as the transit time does the shot effect decrease . ${\ displaystyle \ Delta f}$${\ displaystyle 1 / f ^ {2}}$

Shot noise is important in electronics , communications, and basic physics because it can be used to measure the noise ( noise figure and noise temperature ) of electronic components . For this purpose, semiconductor diodes with avalanche breakdown are matched to a specified wave impedance as normal noise and are supplied with a calibration table which indicates the noise power density as a function of the diode current . This noise source is connected upstream of the quadrupole to be measured . ${\ displaystyle Z}$

## In optics

Due to the quantization into individual photons , the output of an ideal, monochromatic radiation source is not completely constant, but rather shows small deviations from the mean output . The mean square of the power deviations can be expressed by the equation ${\ displaystyle \ Delta p}$${\ displaystyle P}$

${\ displaystyle {\ overline {\ Delta p ^ {2}}} = 2h \ nu P \ Delta f \,}$

express, where

• ${\ displaystyle h}$the Planck constant ,
• ${\ displaystyle \ nu}$the frequency of the radiation (order of magnitude 10 14  Hz) and
• ${\ displaystyle \ Delta f}$is the bandwidth of the measurement.

Since this noise cannot be suppressed by technical measures, the term shot noise limit is also used.

## Raindrops

Raindrops create shot noise because they fall independently of each other. They are similar to quantized particles, as their size hardly fluctuates with a diameter of 2–3 mm.