Shockley Diode Equation

I = Is × (e^(V/(n×Vt)) − 1)

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Result
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Formula

I = Is × (e^(V/(n×Vt)) − 1), Vt ≈ 25.85 mV at 25°C

Description

The Shockley diode equation describes the exponential I-V characteristic of a pn junction diode. Is is the reverse saturation current (typically pA to µA), n is the ideality factor (1 for ideal diffusion, 2 for recombination-dominated), and Vt is the thermal voltage (kT/q ≈ 25.85 mV at 25°C). At forward biases above about 100 mV, the −1 term becomes negligible and the current is purely exponential. This equation is the foundation of semiconductor device physics and is used in SPICE simulation for all diode and BJT models.

Variables

  • V — Forward voltage across the diode (V)
  • Is — Reverse saturation current (A)
  • n — Ideality factor (1-2, dimensionless)

Practical Notes

The result is the diode current in amperes. Is roughly doubles for every 10°C temperature increase. Typical Is values: small-signal silicon diode 1-10 nA, Schottky diode 1-100 µA, LED 1-100 pA. The exponential is clamped at e^500 to prevent numerical overflow. For reverse bias, the current approaches −Is (very small). Real diodes deviate from this equation at high currents (series resistance) and high reverse voltage (breakdown).

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