Where P Meets N
The PN junction is the most fundamental semiconductor device — the building block of diodes, transistors, LEDs, and solar cells. When a region doped with donor atoms (N-type, excess electrons) meets a region doped with acceptor atoms (P-type, excess holes), electrons diffuse into the P side and holes into the N side. They recombine near the junction, leaving behind a layer of fixed charges: positive donor ions on the N side and negative acceptor ions on the P side. This is the depletion region.
Built-in Potential and the Depletion Region
The fixed charges in the depletion region create an electric field that opposes further carrier diffusion. Equilibrium is reached when the drift current from the electric field exactly balances the diffusion current. The resulting built-in voltage is V_bi = V_T × ln(N_A × N_D / n_i²), typically 0.6–0.8 V for silicon. The depletion width depends on doping — heavier doping creates a thinner, more abrupt junction.
The Exponential IV Curve
Forward bias reduces the barrier, allowing an exponentially increasing current: I = I_s(exp(V/nV_T) − 1). The Shockley diode equation captures this beautifully — current doubles roughly every 18 mV increase in voltage at room temperature. In reverse bias, only a tiny saturation current I_s flows, carried by thermally generated minority carriers drifting across the junction. This asymmetry is what makes a diode a one-way valve.
Temperature Dependence
Temperature has a profound effect on PN junction behavior. The thermal voltage V_T = kT/q increases linearly with temperature, but the dominant effect comes from the intrinsic carrier concentration n_i, which rises exponentially. At 300 K, silicon has n_i ≈ 1.5 × 10¹⁰ cm⁻³; by 400 K, it reaches ~10¹² cm⁻³. This makes reverse leakage current extremely temperature-sensitive and sets the upper operating limit for silicon devices at about 150–200°C.