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.

literature

Rudolf Müller: Rauschen (= semiconductor electronics. Vol. 15). 2nd, revised and expanded edition. Springer, Berlin et al. 1990, ISBN 3-540-51145-8 .
Walter Schottky : About spontaneous current fluctuations in different electricity conductors . In: Annals of Physics . tape 362 , no. 23 , 1918, pp. 541-567 , doi : 10.1002 / andp.19183622304 .
Walter Schottky: Small-Shot Effect and Flicker Effect . In: Physical Review . tape 28 , no. 1 , 1926, pp. 74-103 , doi : 10.1103 / PhysRev.28.74 .
Reinhard Lerch: Electrical measurement technology: analog, digital and computer-aided processes. Springer, 2012, ISBN 978-364222-609-0 , p. 207.

Web links

What is noise (pdf, 1.15 MB)