PN Junction Diode: How Doping Creates a One-Way Valve for Current

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I ≈ 0.5 mA at 0.6 V forward bias

A silicon PN junction with 10¹⁷ cm⁻³ doping at 300 K has a built-in voltage of about 0.72 V. At 0.6 V forward bias, current is approximately 0.5 mA following the Shockley diode equation.

Formula

I = I_s × (exp(V / (n × V_T)) − 1)
V_bi = V_T × ln(N_A × N_D / n_i²)
W = √(2ε(V_bi − V)(1/N_A + 1/N_D) / q)
V_T = kT / q

Where P Meets N

The PN junction is the most fundamental semiconductor device — the building block of diodes, transistors, LEDs, and solar cells. When a region doped with donor atoms (N-type, excess electrons) meets a region doped with acceptor atoms (P-type, excess holes), electrons diffuse into the P side and holes into the N side. They recombine near the junction, leaving behind a layer of fixed charges: positive donor ions on the N side and negative acceptor ions on the P side. This is the depletion region.

Built-in Potential and the Depletion Region

The fixed charges in the depletion region create an electric field that opposes further carrier diffusion. Equilibrium is reached when the drift current from the electric field exactly balances the diffusion current. The resulting built-in voltage is V_bi = V_T × ln(N_A × N_D / n_i²), typically 0.6–0.8 V for silicon. The depletion width depends on doping — heavier doping creates a thinner, more abrupt junction.

The Exponential IV Curve

Forward bias reduces the barrier, allowing an exponentially increasing current: I = I_s(exp(V/nV_T) − 1). The Shockley diode equation captures this beautifully — current doubles roughly every 18 mV increase in voltage at room temperature. In reverse bias, only a tiny saturation current I_s flows, carried by thermally generated minority carriers drifting across the junction. This asymmetry is what makes a diode a one-way valve.

Temperature Dependence

Temperature has a profound effect on PN junction behavior. The thermal voltage V_T = kT/q increases linearly with temperature, but the dominant effect comes from the intrinsic carrier concentration n_i, which rises exponentially. At 300 K, silicon has n_i ≈ 1.5 × 10¹⁰ cm⁻³; by 400 K, it reaches ~10¹² cm⁻³. This makes reverse leakage current extremely temperature-sensitive and sets the upper operating limit for silicon devices at about 150–200°C.

FAQ

How does a PN junction work?

When P-type (excess holes) and N-type (excess electrons) semiconductors are joined, carriers diffuse across the junction and recombine, leaving behind fixed ionized dopant atoms. This creates a depletion region with a built-in electric field that opposes further diffusion, establishing equilibrium and a built-in voltage of about 0.6–0.8 V for silicon.

What is the Shockley diode equation?

The Shockley equation describes the ideal diode IV characteristic: I = I_s × (exp(V/(nV_T)) − 1), where I_s is the reverse saturation current, n is the ideality factor (1–2), and V_T = kT/q is the thermal voltage (~26 mV at 300 K). Current rises exponentially with forward voltage.

What determines the width of the depletion region?

Depletion width depends on doping concentrations and applied voltage: W = √(2ε(V_bi − V)(1/N_A + 1/N_D)/q). Higher doping narrows it, forward bias shrinks it, and reverse bias widens it. This voltage-dependent width is the basis for varactor diodes.

Why does temperature affect diode behavior?

Temperature affects the thermal voltage V_T = kT/q and the intrinsic carrier concentration n_i, which doubles roughly every 11°C in silicon. Higher n_i increases the reverse saturation current I_s exponentially, so leakage current rises dramatically with temperature.

Sources

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