The claim that semiconductor theory is fundamentally based on quantum mechanics is a matter of established scientific fact and common knowledge, as the electronic band structure, carrier transport, and behavior of semiconductors are governed entirely by quantum mechanics.
The claim is a fundamental textbook statement about the physical basis of solid-state physics and semiconductor theory, which relies on quantum mechanics (such as Bloch's theorem, energy bands, and Fermi-Dirac statistics) to explain electronic properties. Therefore, it is classified as common knowledge requiring no citation.