What are the links between semiconductor physics and quantum mechanics?

Answer 1

Quantum mechanics is actually the basis of much of solid state physics, which is the general area that includes the behavior of semiconductors. The framework of most solid-state physics theory is the Schrödinger formulation of quantum mechanics. Bloch's Theorem characterizes the wavefunctions of electrons in a periodic potential, and is an important starting point as well.

Answer 2

At the very basic level, the concept of "holes" in a semiconductor is from quantum mechanics. Electronics engineers treat the movement of holes as current but it is really a hole.

The way a transistor works, using voltage at the gate to control the larger current, is a quantum mechanical phenomenon. Engineers regard transistors and diodes as devices but the underlying physics is quantum.