| name | semiconductor-device-physics |
| description | Physical principles underlying diodes, bipolar junction transistors, and MOSFETs — carrier concentrations, drift and diffusion, the pn junction, forward and reverse bias, the Shockley diode equation, BJT operating regions, MOSFET threshold and saturation, small-signal models, and temperature effects. Use when reasoning about device-level behavior, designing bias networks, selecting transistor operating points, interpreting datasheets, or diagnosing nonlinear device failures. |
| type | skill |
| category | electronics |
| status | stable |
| origin | tibsfox |
| modified | false |
| first_seen | "2026-04-12T00:00:00.000Z" |
| first_path | examples/skills/electronics/semiconductor-device-physics/SKILL.md |
| superseded_by | null |
Semiconductor Device Physics
Before a transistor can be used, it must be biased. Before it can be biased correctly, its underlying physics must be understood well enough to predict what happens when temperature changes, when the supply sags, or when the input drives it out of its intended operating region. This skill provides the bridge between the linear, idealized circuit analysis of the previous skill and the messy, nonlinear, temperature-sensitive reality of actual silicon.
Agent affinity: shockley (junction physics and bias), bardeen (surface physics and transistor action), brattain (experimental device characterization)
Concept IDs: elec-diode-rectification, elec-transistor-amplifiers, elec-semiconductor-physics
What a Semiconductor Is
A semiconductor is a crystalline material (silicon, germanium, gallium arsenide) whose conductivity lies between that of a metal and that of an insulator, and — crucially — can be controlled by doping with impurities and by applied electric fields. At absolute zero, pure silicon has a filled valence band and an empty conduction band separated by a 1.12 eV bandgap. Above zero temperature, a small number of electrons are thermally excited into the conduction band, leaving holes behind in the valence band. Both electrons and holes act as mobile charge carriers.
Doping introduces atoms with either one extra valence electron (donors, producing n-type material) or one fewer (acceptors, producing p-type material). The equilibrium carrier concentrations satisfy the mass-action law n * p = n_i^2, where n_i is the intrinsic carrier concentration (≈ 1.5e10 cm^-3 for silicon at room temperature).
Current flows by two mechanisms: drift (carriers accelerated by an electric field, limited by mobility) and diffusion (carriers moving from regions of high to low concentration). The diffusion coefficient and mobility are related by the Einstein relation D = μ * kT / q.
The pn Junction at Thermal Equilibrium
When p-type and n-type silicon are brought into contact, holes diffuse from the p side into the n side and electrons diffuse the other way. The diffused carriers leave behind uncompensated ionized dopants, forming a depletion region with a built-in electric field that opposes further diffusion. At equilibrium, drift and diffusion exactly cancel, and a built-in potential V_bi ≈ (kT/q) * ln(N_A * N_D / n_i^2) appears across the junction (typically 0.6-0.8 V for silicon).
Key geometric facts:
- The depletion region width scales as 1/sqrt(N_dopant). Heavily doped junctions have narrow depletion regions.
- The junction capacitance C_j scales as sqrt(1/(V_bi - V_applied)). Forward bias shrinks the depletion region and increases capacitance; reverse bias widens it and decreases capacitance.
- Almost all the applied voltage drops across the depletion region because the bulk semiconductor has low resistance.
