When $p$- and $n$-type regions are joined, diffusion causes charge separation and a depletion region forms. The built-in potential is approximately $V_{bi} = \frac{kT}{q} \ln\!\left(\frac{N_A N_D}{n_i^2}\right)$ for an abrupt junction under equilibrium and nondegenerate doping.

The ideal diode law is $I = I_S \left(e^{qV/(nkT)} - 1\right)$, where $n$ is the ideality factor. Real devices deviate because of series resistance, recombination in the depletion region, high-level injection, and self-heating. Reverse bias introduces leakage, avalanche breakdown, and tunneling in heavily doped junctions.

A Schottky contact forms a rectifying barrier at a metal-semiconductor interface. Its barrier height depends on work function, interface states, and Fermi-level pinning rather than just ideal work-function differences. These contacts are crucial in power rectifiers, RF switches, and high-speed logic.