Semiconductor Physics & p-n Junctions

A semiconductor device works by reshaping carrier populations and electric fields inside a crystal. The circuit-level symbols hide that internal state, but the state explains why current is nonlinear, why temperature matters, why junctions store charge, and why a device that looks open at DC can still conduct a fast transient.

Bands, carriers, and doping #

In a crystal, allowed electron energies form bands. The valence band is normally occupied; the conduction band contains states in which electrons can move through the lattice. The band gap $E_g$ separates them. Thermal energy can create an electron–hole pair: an electron enters the conduction band and leaves a mobile hole in the valence band.

Pure material is intrinsic. Deliberate impurities make it extrinsic:

• donor atoms contribute electrons, producing n-type material with electrons as majority carriers;
• acceptor atoms create holes, producing p-type material with holes as majority carriers.

Doping does not give the bulk material a net charge. Ionized dopants and mobile carriers balance in neutral regions. The important change is carrier concentration and therefore conductivity.

The junction builds its own field #

Bring p- and n-type regions together. Electrons diffuse from the high-concentration n side into the p side; holes diffuse the other way. They recombine near the boundary and expose fixed ionized dopants. Those fixed charges form a depletion region and an electric field opposing further diffusion.

flowchart TB
  P["p region<br/>holes majority"] -->|"holes diffuse"| J["depletion region<br/>fixed charge + electric field"]
  N["n region<br/>electrons majority"] -->|"electrons diffuse"| J
  J -->|"drift opposes diffusion"| EQ["thermal equilibrium<br/>net current = 0"]

At equilibrium, diffusion current and field-driven drift current cancel. There is carrier motion, but no net terminal current. The built-in potential is an internal electrostatic barrier; it is not a battery available at the terminals because contact potentials elsewhere complete the equilibrium.

Bias changes the barrier #

Forward bias lowers the barrier and narrows the depletion region. Carrier injection rises approximately exponentially:

$$I = I_S\left(e^{V_D/(nV_T)}-1\right), \qquad V_T=\frac{kT}{q}.$$

$I_S$ is the scale current, $n$ the ideality factor, and $V_T$ about 25.9 mV at 300 K. The familiar “0.7 V silicon diode” is therefore not a fixed threshold: voltage depends logarithmically on current, and shifts with temperature and device construction.

Reverse bias raises the barrier and widens the depletion region. Only a small leakage current flows until breakdown. Strongly doped narrow junctions can tunnel (Zener breakdown); more lightly doped junctions accelerate carriers into impact ionization (avalanche). Both can be nondestructive if current and power are limited. Excess temperature destroys the junction, not the mere existence of breakdown.

A junction stores energy and charge #

The depletion region is a dielectric between charged regions, giving a voltage-dependent junction capacitance. Reverse bias widens it and reduces capacitance. In forward conduction, injected minority carriers create diffusion capacitance and stored charge. When polarity reverses, that charge must be removed before blocking resumes: reverse-recovery current can dominate switching loss and EMI.

Temperature and failure reasoning #

Temperature raises intrinsic carrier concentration, increases leakage, shifts forward voltage, and changes breakdown behavior. Local power raises junction temperature; higher temperature changes current; that feedback can create thermal runaway unless ballast, feedback, current limiting, or a favourable device coefficient stabilizes it.

When diagnosing a junction circuit, ask in order: What bias exists? Which carriers dominate? Is the device in forward injection, reverse blocking, or breakdown? What capacitance or stored charge matters at this edge rate? What power is dissipated, and through what thermal path does it escape? Those questions scale from a signal diode to a transistor junction and a power rectifier.