The electrons "boiled off" a hot filament, or indirectly "boiled off" the cathode in a heater tyoe of a vacuum tube do not
contribute noise anywhere near the level as created by the migration of electrons (and the "holes" migrating in the opposite direction) within semiconductors. Electron mobility is SO much higher in a tube that such noise within
vacuum tube circuits is primarily from carbon resitors.
It is not all bad, in fact, if this random noise did NOT exist, oscillators would not start up without some knd of
triggering pulse.
Sometimes this is called "shot noise".
Good old fashioned bipolar NPN PNP transistors are chock full of this noise,
which is why downconverter LNA heads on satellite antenna have special low noise semiconductors
and amplifiers right at the dish.
In the pictorial below, holes ( nothing where something might have been ) are seen migrating in an orderly fashion
from left to right.
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See? If this were not occuring, there would be no ability for the electrons (primary carriers) to flow
within the silicon lattice structure of the semiconductor.