Semi conductors was my most hated and fascinating class in electrical engineering. Fucking pain because this thing is nearly witchcraft and the teacher was basically sadistic, but super fascinating concepts and scale.
EDIT :
And outside of just tools to make it happen, which is fascinating on it's own, what i always found interesting in engineering/maths is the foundation, the mathematical model that made all of this possible.
Schrödinger's wave equation, in 1925.
Schrödinger's wavefunction, simplified to a time-dependent equation in one dimension (eigenvalue equation). With quantum mechanics, unlike three basis vectors in real splace, these eigen functions span an infinite number of dimensions in an abstract space, Hilbert space. Almost impossible to solve.. unless you have a potential energy well, with infinite walls (as would be seen from an electron, ohhhh). This becomes a "particle in a box". Controlling this tunneling, is effectively the physics and probabilities of controlling the hyper complex electron waveform of the electron, consistently. A purely mathematical model of the transistor.
They solved the equations for Hydrogen first, the "easiest" part, to introduce 4 quantum numbers, dictated by quantum mechanical rules, and extrapolated these ideas/solutions to Silicon. Way beyond my own comprehension to be honest, i did not got there. But anyway, 95 years later, we have the world's library, communicate through air, take megapixel photos on a wallet size device.
Schrödinger was not human..