PN Junction and Diodes

When P-type semiconductor (doped with acceptors — has holes) is joined to N-type semiconductor (doped with donors — has free electrons), a PN junction forms at the interface.

At the junction, electrons from N-side diffuse into P-side (and holes do the opposite):

• They recombine and annihilate each other
• This leaves behind a region of ionised atoms with no free carriers
• This region is the depletion layer (or space charge region)

The depletion region creates a built-in electric field pointing from N to P that opposes further diffusion.

Built-in potential (Vbi): For silicon ≈ 0.6–0.7 V

V_bi = V_T × ln(N_a × N_d / n_i²)

where V_T = kT/q ≈ 26 mV at room temperature

Battery positive terminal → P-side, negative → N-side:

• External field opposes the built-in field
• Depletion layer narrows
• When applied voltage > Vbi (~0.7V for Si), current flows exponentially

Diode equation: I = I₀(e^(V/V_T) − 1)

• At V = 0.7V (Si), diode conducts strongly
• Silicon diode: Vf ≈ 0.7V | Germanium: Vf ≈ 0.3V

Battery negative terminal → P-side, positive → N-side:

• External field adds to the built-in field
• Depletion layer widens
• Only tiny reverse saturation current I₀ flows (due to minority carriers)
• The diode effectively acts as an open switch

At very high reverse voltage, the diode breaks down:

• Zener breakdown: narrow depletion layer, quantum tunnelling of electrons (~5V, used in Zener diodes)
• Avalanche breakdown: high-energy carriers knock out more carriers in a chain reaction (>6V)

Zener diodes are specially designed to operate in breakdown — used as voltage regulators.

Diodes allow current in only one direction → used to convert AC → DC:

Ripple factor measures how "smooth" the DC output is. Lower = better.

• Depletion width W ∝ √(Vbi − V_applied) — widens in reverse, narrows in forward
• Threshold voltage Si = 0.7V, Ge = 0.3V — below this, no significant current
• Diode I-V characteristic graph: flat near 0, exponential rise at Vf, tiny reverse current until breakdown
• Zener breakdown vs avalanche breakdown — know both mechanisms
• Half-wave vs full-wave rectifier: efficiency, ripple factor formulae
• LED: energy emitted = hν = E_g (band gap), longer wavelength = smaller band gap