[mikewarot]

It may be that is how it started, but I'll never forget the day my Advanced Chemistry teacher at Rose-Hulman used standard chemistry (I think it was the Nerst equation, 40 years ago!) to explain how a diode works.

Then he continued and explained how a junction transistor worked with the same equations!

No QM required.

[dekhn]

The nernst equation is https://en.wikipedia.org/wiki/Nernst_equation (redox). THere's also https://en.wikipedia.org/wiki/Nernst%E2%80%93Planck_equation which also isn't exactly for diode modelling.

I'm sure you can find classical equations that model some aspects of p-n junctions but you're ultimately going to see that p-n junction physics is literally quantum physics of tunneling electrons in atomic solids.

[mikewarot]

It's not tunneling, it's conduction. There are liquid electrolytic rectifiers, they suck, but they exist.

[dekhn]

Oh, I see what you're saying now. Your teacher showed you the equations explaining a classical (pre-semiconductor) diode, then showed those equations predict some aspects of semiconductor diodes.

Yeah, that doesn't mean that diodes don't work in a fundamentally quantum way. There are a number of details about diodes (for example, the emitted frequency of light in an LED) that are very specifically due to quantum energy transitions of electrons in outer shells. It doesn't get any more quantum physics than that.

[mikewarot]

This was the equations for a doped semiconducting device, not a vacuum tube. All the equations we had previously been using to describe buffered solutions, etc. also happened to work perfectly well for semiconductors.

LEDs weren't discussed that day.