The PN Junction

Pure silicon has four valence electrons and conducts poorly. Doping adds impurity atoms: a pentavalent donor such as phosphorus contributes a spare electron (N-type), and a trivalent acceptor such as boron leaves a vacancy that behaves as a positive carrier (P-type).

Both blocks start electrically neutral. Every mobile carrier is balanced by the fixed impurity ion that supplied it. This is the fact the whole rest of the argument turns on.

Majority carriers

Electrons in N-type, holes in P-type. Their number is set by the doping and barely changes with temperature.

Minority carriers

Holes in N-type, electrons in P-type. Thermally generated, so their number roughly doubles every 10 °C — which is where every temperature-dependent term in this subject comes from.

1. 1Contact. A huge concentration gradient exists at the boundary.
2. 2Diffusion. Electrons cross into P and holes into N, purely from the gradient — the same statistics that spreads ink in water. Near the junction they recombine.
3. 3Exposed ions. Each departed carrier leaves behind a *fixed* ion: positive donors on the N side, negative acceptors on the P side. These are locked into the lattice and cannot follow.
4. 4A field appears. The exposed charge creates an electric field pointing from N to P, which pushes electrons back toward N and holes back toward P — against the diffusion.
5. 5Equilibrium. Each carrier that crosses strengthens the field opposing the next. The process is self-limiting and settles where diffusion current exactly cancels drift current.

The stripped region is the depletion region — depleted of *mobile* carriers, though full of fixed charge. The potential across it is the built-in potential V₀, about 0.7 V in silicon and 0.3 V in germanium.

You cannot measure V₀ with a voltmeter. Attaching probes creates two more junctions whose potentials exactly cancel it — which is fortunate, because a battery you could make out of a diode would violate the second law of thermodynamics.

Connect the positive terminal to N and the negative to P. The applied voltage adds to the built-in field. Majority carriers are pulled away from the junction, the depletion region widens, and the barrier gets taller. Almost nothing crosses.

What remains is the reverse saturation current I₀ — nanoamps, produced by thermally generated minority carriers that the field is happy to sweep across. It is nearly independent of the applied voltage and roughly doubles per 10 °C, which is why it matters far more in a hot circuit than a cold one.

Increase the reverse voltage enough and the junction breaks down, by tunnelling (Zener, below ~5 V) or by impact ionisation (avalanche, above it). Breakdown is not destruction — a Zener diode is built to live there — provided the power dissipated is limited.

Connect positive to P and negative to N. Now the applied voltage opposes the built-in field. The depletion region narrows, the barrier drops, and the fraction of carriers with enough energy to cross rises — as a Boltzmann factor, so exponentially.

That exponential is why the diode appears to have a threshold. At 0.5 V the current is microamps, at 0.7 V it is milliamps, at 0.8 V amps. Nothing switches on at 0.7 V; that is simply where an exponential becomes visible on a linear axis. Every extra ~60 mV multiplies the current by ten.

• Rectification — one-way conduction turns AC into pulsating DC. The first module after this one.
• Voltage reference — reverse breakdown occurs at a sharply defined voltage, which is a Zener regulator.
• Amplification — two junctions back to back is a BJT, and the base-emitter junction's exponential is where its transconductance comes from.
• Light — recombination across the junction can emit a photon (LED); absorbed photons can create carriers (photodiode, solar cell).
• Variable capacitance — the depletion region is an insulator between two conductors, and reverse bias changes its width. That is a varactor, and it tunes radios.