I have a PMT that requires 1000V for operation, but SiPMs, semiconductor photodiodes require only about 30V -- what fundamental feature causes this vast difference in operation bias?
There's probably no one answer to this because despite their similar names, the two kinds of devices work on substantially different principles.
But consider a couple of factors:
Multiplication process: In the PMT, the electrons colliding with each dynode must have enough energy to overcome the work function of the metal and break additional electrons out of the metallic material. In the SiPM, the "colliding" carriers only have to overcome the bandgap energy of the semiconductor, rather than the work function, in order to produce new carriers.
Size: the PMT is at least several cm long. So if the multiplication process depends on the electric field strength, it will take a larger potential difference to produce a given field strength when acting over a longer distance. The active length of the SiPM is at most a few microns.
Number of multiplication stages. PMTs typically have several dynodes, with multiplication happening as electrons strike each dynode. The applied voltage to the tube is divided between the different stages, so if you apply 1000 V to a 10-stage tube, then only 100 V acts on each stage. In a SiPM, there is effectively only one multiplication stage, with the full device voltage being applied to creating the conditions for multiplication in that stage.