PN Junction & Diode

When P-type and N-type semiconductors join, diffusion creates a depletion region with a built-in potential barrier Vbi ≈ 0.7V for Si.

Vbi = VT ln(Na Nd / ni²)

Depletion width W ∝ sqrt(Vbi − Vapplied)

Forward bias (V > 0) reduces barrier → exponential current.

Reverse bias increases barrier → tiny leakage until breakdown.

I = Is (e^{qV/kT} − 1) (Shockley equation)

This structure is the basis of diodes, LEDs, solar cells, and BJT/MOSFET transistors.

Interactive goals: Drag doping levels and bias. See W change, bands bend, carriers flow only in forward. Measure Vbi and plot I-V.

JEE/NEET focus: Derive Vbi and W, explain forward/reverse characteristics, Zener vs avalanche breakdown, applications in rectifiers and voltage regulators.