[1]https://physics.stackexchange.com/questions/112615/why-is-it...
Yeah, somebody would probably invent them at some point. Somebody would probably even invent FETs, even if it took many decades more. MOSFETs are a completely different matter, I don't think anybody would invent them without understanding how they work.
What everybody seems to forget is modern chemistry, material engineering and medicine. The world would be a completely different place without quantum mechanics. Electronics is just a tiny part of the change.
Bipolar transistors are more complex, but they still work by controlling the bulk geometry of moving charge.
None of this requires QM, except in the very simple sense that you need to know what a bandgap is and how doping changes it. Beyond that, the "mechanical" details of the charge dynamics are just calculus - even more crudely, very very small plumbing.
QM effects are only relevant when the simple space charge models start to break down at very small geometries. Your "mechanical" space charge model becomes soft, noisy, and more complicated. Essentially the plumbing develops waves and ripples that depend on the geometry, and the edges of the pools and pipes can start to leak. And that's where QM finally starts to make a real difference.
There is a similar debate around Newtonian physics. How far might the industrial revolution have gone without a perfect understanding of how things move? You don't need newton to build complex machines. Look at any early windmill or waterwheel. You need newton to understand machines well enough to build and run them efficiently. You don't always need theory before practical, but theory always makes practical better.
Newtonian physics lets you work out loads with free body diagrams, derive Euler beam theory, and that's how they built the Eiffel tower.
