shotnoise

Shot noise, also known as Schottky noise, is a type of electronic noise that arises from the discrete nature of charge carriers or photons. It is observed as random fluctuations in electric current in devices such as vacuum tubes, diodes, transistors, and photodetectors. Because the arrivals of individual electrons (or photons) follow Poisson statistics, the fluctuations are essentially white up to high frequencies and in the simplest model are independent of the average current.

Quantitatively, the single-sided power spectral density of the current fluctuations for a Poisson process is S_I(f) = 2 q I, where q is the elementary charge and I is the average DC current. This yields a root-mean-square current fluctuation over a bandwidth Δf of ΔI_rms = sqrt(2 q I Δf). In practice, devices may deviate from ideal Poisson behavior. The Fano factor F captures this, giving S_I(f) = 2 q I F, with 0 ≤ F ≤ 1; F = 1 corresponds to a pure Poisson process.

In optical detection, shot noise refers to fluctuations in the detected photon stream. Photon arrivals are Poisson distributed, so the variance of the photon count during a measurement interval equals the mean count. If detected as a current I = R P, the corresponding shot noise yields the same form S_I = 2 q I, scaled by the detector responsivity, making shot noise a fundamental limit to sensitivity in photodetection.

Shot noise is a fundamental, temperature-independent limit that contrasts with thermal (Johnson–Nyquist) noise and 1/f noise. It sets a floor for precision in metrology and communications.