Modern electronics begins with band structure. In intrinsic semiconductors, carriers arise thermally, with electron and hole concentrations governed by the density of states and the Fermi-Dirac distribution. The equilibrium carrier product satisfies $np = n_i^2$, where $n_i$ is the intrinsic concentration. Doping shifts the Fermi level and changes conductivity by altering majority-carrier density.

Carrier transport is driven by drift and diffusion. The current density for electrons can be written as $J_n = q n \mu_n E + q D_n \nabla n$, combining mobility-driven drift with concentration-driven diffusion. Similar expressions apply for holes. At small dimensions and high fields, velocity saturation, hot-carrier effects, and nonlocal transport become important and invalidate simple low-field models.

Recombination mechanisms include radiative, Shockley-Read-Hall, and Auger processes. The effective carrier lifetime depends on defect density, injection level, and temperature. In strongly scaled devices and optoelectronic structures, recombination engineering is central to efficiency and speed.