I have a very poor understanding of how an electron "actually exists" in a crystal -- how it can be visualized. So conduction band electrons are supposed to be plane waves modulated by a periodic wavefunction (my understanding of Bloch theorem). This means they're basically everywhere in the crystal simultaneously. And yet we often talk about the real space location of electrons and holes. For example: 1. How electron-hole pairs are pulled apart by the electric field in the depletion region of a solar cell, which gives rise to photocurrent (or else they find each other and recombine). 2. Electrons/holes scattering from ionized dopants, which have specific real space locations. 3. Electrons/holes diffusing here and there because of concentration gradients from varied doping. 4. Boltzmann Transport equation or Monte Carlo simulations which treat them as particles. Etc. What gives? Is an individual electron everywhere or is it localized? I just don't see how to reconcile what I've seen in EE device courses with the "electron as a plane wave" notion from solid state physics. Just how physically extensive is an electron's wavefunction in, say, silicon?