Semiconductor Physics (Doping and p-n Junctions)

Core Idea

Intrinsic semiconductors have equal concentrations of thermally excited electrons and holes (n = p = n_i). Doping — substituting impurity atoms with more or fewer valence electrons — creates extrinsic semiconductors: n-type (donor impurities, excess electrons) or p-type (acceptor impurities, excess holes). The Fermi level shifts toward the conduction band in n-type and toward the valence band in p-type material. A p-n junction forms a depletion region with a built-in electric field that permits current flow in one direction (forward bias) but blocks it in the other (reverse bias), creating a diode — the fundamental building block of all semiconductor electronics.

Explainer

Pure semiconductors like silicon at room temperature have roughly equal numbers of electrons in the conduction band and holes in the valence band, with carrier concentrations around 10¹⁰ cm^-3 — far too few for practical electronics. The breakthrough that enabled the semiconductor industry is doping: intentionally introducing impurity atoms to control the carrier concentration. Substituting a silicon atom with phosphorus (Group V, one extra valence electron) creates an n-type semiconductor with a donor level just below the conduction band. At room temperature, virtually all donors are ionized, adding their extra electrons to the conduction band. Similarly, boron (Group III) creates an acceptor level just above the valence band, producing p-type material with excess holes.

The Fermi level acts as the thermodynamic "dial" that tracks the carrier balance. In n-type material, E_F shifts upward toward E_c; in p-type, it shifts downward toward E_v. At equilibrium, the carrier concentrations are constrained by the law of mass action: np = n_i², regardless of doping. This means doping cannot increase both carrier types — adding electrons necessarily suppresses holes, and vice versa. The constraint arises from the mathematical structure of Fermi-Dirac statistics and is one of the most powerful relationships in semiconductor physics.

The p-n junction — the interface between p-type and n-type regions — is the fundamental device structure. When the two regions are brought into contact, electrons diffuse from n to p and holes from p to n, leaving behind fixed ionized dopants. This creates a depletion region devoid of mobile carriers, with a built-in electric field pointing from n to p. In equilibrium, the drift and diffusion currents balance exactly (as required by thermodynamics), and no net current flows. The Fermi level is constant across the entire junction.

Applying a forward bias (positive voltage on the p-side) reduces the built-in potential barrier, exponentially increasing the current as carriers flood across the junction: I = I_0(e^V/V_T - 1), where V_T = k_BT/e ~ 26 mV at room temperature. Reverse bias increases the barrier, leaving only a tiny saturation current I_0 from thermally generated minority carriers. This asymmetric current-voltage characteristic is the diode — the building block from which transistors, solar cells, LEDs, and laser diodes are all constructed. The physics of the p-n junction is band theory made tangible: the interplay of Fermi statistics, electrostatics, and diffusion in a system with controlled band filling.