Formation of Depletion Layer

The moment a p-type and n-type crystal are joined, the sharp concentration difference across the boundary drives DIFFUSION: electrons, abundant on the n-side, diffuse across into the p-side, and holes, abundant on the p-side, correspondingly diffuse into the n-side -- together constituting a diffusion current. But unlike two neutral gases mixing freely, every electron and hole that crosses leaves behind an EXPOSED, immobile charge fixed in the crystal lattice at the dopant site it vacated: the n-side is left with exposed positive ion cores near the junction, and the p-side with exposed negative ion cores. This growing double layer of fixed charge -- called the depletion region because the mobile carriers that would otherwise be there have been swept out of it -- sets up an internal electric field $\vec E$ pointing from the n-side towards the p-side. This field does two things simultaneously: it drives a DRIFT current of carriers that opposes the diffusion current (the field pulls electrons from p back to n and holes from n back to p), and it establishes a barrier potential $V_b$ across the junction. As diffusion proceeds, the depletion region and its field grow until the …