intermediate Semiconductor Physics

PN Junction Physics

Explore the abrupt PN junction — built-in potential, depletion region, electric field, and the Shockley I-V relationship.

Na (p-side)10^16.0 cm⁻³

Nd (n-side)10^16.0 cm⁻³

Vbias0.00 V

Vbi = 0.612 VW = 397.9 µmEmax = 0.00 MV/cmJ = 0.00e+0 A/m²

Charge density ρ(x)

Electric field E(x)

Potential ψ(x)

I-V characteristic (●)

Abrupt junction model at T=300 K. Forward bias (V>0) narrows depletion width; reverse bias widens it. I-V follows Shockley equation: J = J_s(e^V/Vt − 1).

A PN junction forms where p-type silicon (doped with acceptors, Na) meets n-type silicon (doped with donors, Nd). At equilibrium, electrons diffuse from n→p and holes from p→n, leaving behind ionised dopants.

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The ionised donors (positive) on the n-side and ionised acceptors (negative) on the p-side form the space charge — this is the depletion region.
The built-in potential Vbi appears in the display. At Na = Nd = 10^16 cm⁻³, Vbi ≈ 0.72 V for silicon. Increase Na or Nd — notice Vbi increases logarithmically.

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Vbi = (kT/q) ln(Na·Nd / ni²). Higher doping → stronger chemical potential → larger built-in field.
Apply forward bias (increase Vbias toward +0.6 V). Watch the depletion width W decrease. The E-field panel shows the peak field Emax dropping.

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Forward bias opposes the built-in field, narrowing the depletion region. At V ≈ Vbi, the junction is fully 'flooded' with carriers.
Apply reverse bias (Vbias → -1 V). W increases significantly. This is the operating principle of varactor diodes (voltage-controlled capacitors).

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Cj = ε·A/W. A wider depletion region = smaller junction capacitance. Varactors are used in VCOs and tunable RF filters.
Look at the I-V curve panel. The current is negligible under reverse bias (≈ -Js) but grows exponentially with forward bias. This is the Shockley diode equation: J = Js(e^(V/Vt) - 1).

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The 'knee' of the diode I-V curve occurs around 0.6–0.7 V for silicon. Below this, only leakage current flows.