= Shot noise
{title2=$S_I^{(1)}=2qI$}
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Shot noise is fluctuation associated with discrete transfer events. For an <electric current>, individual <charge carriers> contribute finite amounts of <electric charge>, even when a meter displays a smooth mean. The simplest model is a stream of equal, independently arriving charges with constant rate: its <Poisson process> predicts both the mean <electric current> and the <variance> around it. Discreteness alone does not imply a <Poisson distribution>; the timing and correlations matter.
The useful surprise is that <noise> can reveal something a mean hides. Two devices can carry the same mean <electric current> yet have different fluctuations because one transfers charges independently and the other groups or regulates them. A calibrated <shot noise photocurrent measurement> can connect a macroscopic voltage <variance> to the <elementary charge>. <Thermal electrical noise> instead exists in an unbiased <resistor> at <thermal equilibrium>; a measured background can contain both mechanisms.
<Walter Schottky>'s 1918 paper \i[Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern] treated <amplifier> sensitivity limits. Part II considered independent discrete transfers, including <thermionic emission> through a <vacuum>. On p. 563 he proposed amplifying fluctuations from a separate discharge tube to determine the <elementary charge>; those experiments were prospective, not reported results.<Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern by Walter Schottky>[Schottky (1918), p. 541; Part II, pp. 547–552; p. 563, proposed experiment]{ref}
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