shot noise

An electric current is not a perfectly smooth river. It is made of countless individual charges, electrons, crossing a barrier one at a time, like raindrops on a tin roof. When many fall it sounds like a steady hiss, but listen closely and it is really separate drops arriving at random moments. That graininess in a current is shot noise. It shows up wherever charges cross a junction independently, as they do in diodes, transistors, and photodiodes.

The rms shot-noise current is Inoise = sqrt(2 times q times I times B), where q is the electron charge (1.6 x 10^-19 coulombs), I is the DC current, and B is the bandwidth. Notice the surprise hidden there: the noise grows only with the square root of current, so the noise relative to the signal (noise divided by I) actually gets smaller as the current rises. Example: 1 mA through a diode over a 1 MHz bandwidth gives sqrt(2 times 1.6e-19 times 0.001 times 1e6), about 18 nanoamps rms, which is roughly 18 parts per million of the 1 mA. Like thermal noise, shot noise is white across frequency.

Shot noise matters most where the currents are tiny: a photodiode catching just a few photons, or the input bias current of a sensitive amplifier. It is fundamental, caused by the discreteness of charge itself, so you cannot wire it away. Be honest about a common confusion: an ordinary resistor carrying current does NOT show full shot noise, because the electron flow there is smoothed by countless collisions. Shot noise needs charges crossing a barrier more or less independently, as they do at a PN junction.