What is Shot Noise?

Shot noise or Poisson noise is a type of noise that arises due to the discrete nature of electric charge or other particles. The concept of shot noise was first introduced in 1918  by Walter Schottky who studied the fluctuations of current in vacuum tubes. This noise is significant in situations where the detection of particles occurs in a quantized manner, such as in electronics or photonics. In electrical systems, it is caused by the random arrival times of discrete charge carriers. The carriers (electrons) flow through a conductor not in a smooth, continuous manner but rather as individual packets. Each packet corresponds to a single charge (electron), and their random arrival leads to fluctuations in current, whereas in an optical system, it results from the random emission and detection of individual photons. 

Shot noise simulation. As the number of photons increase with time, the picture gets clear. 

Characteristics of Shot Noise

Poisson Distribution: Shot noise follows a Poisson statistical distribution which reflects the random and independent nature of particle arrivals.  This means that the variance (σ2) in the number of particles arriving in a given time interval is equal to the mean (μ). For example, if N particles arrive on average, the standard deviation of the fluctuations is SQRT(N).

Number of photons collected by a given detector varies, and follows the Poisson distribution. 

White Noise Spectrum: Shot noise has a flat or “white” power spectral density implying its intensity is constant across all the frequencies up to a certain cutoff. This flat spectrum is a direct result of the random and uncorrelated nature of particle arrivals. The white spectrum serves as a reference for comparing other types of noises (e.g., thermal or flicker noise) which often have frequency-dependent behavior. 

Temperature and Frequency independence: Unlike thermal noise which depends on temperature, shot noise is independent of temperature. And, unlike the flicker noise which is directly proportional to the frequency, shot noise is independent of frequency. It arises purely from the stochastic nature of particle transport and not from the thermal agitation. Mathematically, the PSD for shot noise is given by: 

where, 

SI is the power spectral density, 

e is the elementary charge (1.6 x 10-19 C) 

I is the average current 

Impact of Shot Noise 
Shot noise is found across electronics, optics, quantum physics, communication systems, and image processing. In high-frequency circuits, such as microwave systems, shot noise dominates over most other forms of noise. This makes it an important factor when designing low noise amplifiers (LNAs). In communication systems, shot noise limits the signal-to-noise ratio (SNR) thereby impacting receiver performance. In optical systems, the shot noise limits the sensitivity of photon detectors used in low-light conditions, such as in astronomy, microscopy, and night vision cameras.