Look at it this way: The physical limits of materials are based on the strength of the electrical fields that they're exposed to. (Air arcs over about about 20,000V per cm, for instance.) Electrical field strength is measured in "Volts per Meter." You get stronger electric field strength by increasing the voltage or by making your distances smaller. The reason that modern electronics are so cheap is that the size of individual transistors keeps getting smaller; to keep the electric field strength similar, the operating voltage has to go down.
A vacuum tube operates at hundred of volts and has distances of a few mm; about 20000V/m field strength. The transistors in a modern CPU have layers than are about 5 nano-meters thick (that's "not very many" atoms thick, BTW.) Even at 1V operating voltage, that's something like 200000000V/m field strength!