The PN Junction

Semiconductor Devices · 11 min read

A PN junction is one continuous crystal — p-type on one side, n-type on the other. Every diode, BJT, LED and solar cell starts here.

1. Junction formation in three phases

Figure 1. Junction formation. Phase 1: carriers fill each side, no field. Phase 2: diffusion + recombination scrub a depletion band, exposing fixed ions. Phase 3: equilibrium — built-in field E balances diffusion.

Phase 1: p-side has mobile holes + fixed B⁻ ions; n-side has mobile electrons + fixed P⁺ ions. Each side neutral.
Phase 2: carriers diffuse down their concentration gradient and recombine near the boundary.
Phase 3: exposed fixed ions create an E-field opposing further diffusion — system locks at equilibrium.

2. The depletion region

Figure 2. Depletion-region cross-section. A carrier-free band of width W contains only fixed ions: B⁻ on the p-side, P⁺ on the n-side. Net charge of each strip integrates to ±qN_A·x_p and ±qN_D·x_n.

No mobile carriers in the depletion band — only fixed dopant ions.
Width $W = x_p + x_n$ ; charge balance forces $N_A x_p = N_D x_n$ .
Lighter-doped side hosts the wider depletion strip.

3. Built-in potential V₀

Figure 3. Band bending across the junction. The conduction-band edge E_C drops from p-side to n-side by qV₀. V₀ is the energy hill majority carriers must climb to cross the junction.

V_0 = \frac{k_B T}{q}\,\ln\!\left(\frac{N_A N_D}{n_i^2}\right)

Si at 300 K: $V_0 \approx 0.7\,\text{V}$ .
Ge at 300 K: $V_0 \approx 0.3\,\text{V}$ .
Cannot be measured externally — contact potentials at the wires cancel it.

4. Forward bias — barrier shrinks

Figure 4. Forward bias (V_app > 0, p-side positive). Net barrier drops to V₀ − V_app, depletion width W shrinks, majority carriers flood across. Current rises exponentially.

V_{barrier} = V_0 - V_{app}

Diode is on when $V_{app}$ approaches $V_0$ .
Width scales as $W \propto \sqrt{V_0 - V_{app}}$ .

5. Reverse bias — barrier grows

Figure 5. Reverse bias (V_app < 0, n-side positive). Barrier rises to V₀ + |V_app|, depletion widens, majority current is choked off. Only a tiny minority-driven reverse-saturation current flows.

V_{barrier} = V_0 + |V_{app}|

Reverse current ~ nA, roughly bias-independent until breakdown.
Width grows as $W \propto \sqrt{V_0 + |V_{app}|}$ .

The PN junction is the diode. Bias only modulates the depletion width and the barrier height — forward shrinks both, reverse grows both.