Random dopant fluctuation
Beginner
In a very tiny transistor, the number of added atoms changes by chance from one to the next. So transistors that should be twins act a little differently.
Novice
Variation in threshold voltage between nominally identical transistors, caused by the random number and placement of dopant atoms in the small volume under each gate.
Expert
Dopant counts follow Poisson statistics, so the relative spread scales as and grows as the depletion volume shrinks. A major reason planar transistors stopped scaling and FinFETs and nanosheets use lightly doped channels with set by the gate work function.
Explained in Bands, doping and the p-n junction (Transistors).
See also: Threshold voltage (Vt), Doping.