Shockley Diode Equation Calculator

Calculate diode current from voltage using the Shockley equation. Includes ideality factor, thermal voltage, dynamic resistance, and I-V sweep mode.

About the Shockley Diode Equation Calculator

The Shockley diode equation I = Iₛ(e^(V/nVt) − 1) is the fundamental relationship describing current flow through a p-n junction. It captures the exponential dependence of current on voltage, the temperature sensitivity through the thermal voltage Vt = kT/q, and the material properties through the saturation current Iₛ and ideality factor n.

This equation is foundational in semiconductor physics and circuit design. At room temperature (25 °C), Vt ≈ 25.85 mV, and the exponential increases by a factor of ~e ≈ 2.718 for every 26 mV increase in forward bias. This steep curve is why diodes have a sharp "turn-on" characteristic around 0.6-0.7 V for silicon.

The ideality factor n ranges from 1 (pure diffusion current, ideal diode) to 2 (recombination current dominates, as in LEDs). Real diodes fall between these limits. This calculator lets you explore the Shockley equation for different diode types, compute dynamic resistance, and generate I-V sweep tables.

Why Use This Shockley Diode Equation Calculator?

Use this when you want to estimate diode current from a bias voltage, compare devices with different saturation currents, or check the small-signal resistance around an operating point. It is useful in rectifier design, sensor interfaces, and basic semiconductor coursework.

How to Use This Calculator

  1. Select a diode preset or enter custom parameters.
  2. Enter the saturation current Iₛ (use scientific notation like 1e-12).
  3. Set the ideality factor n (1 for silicon, ~2 for LEDs).
  4. Enter the junction temperature in °C.
  5. Choose single-point mode for one voltage, or sweep mode for an I-V table.
  6. Review current, dynamic resistance, power, and thermal voltage.

Formula

Shockley Equation: I = Iₛ(e^(V/nVt) − 1), where Vt = kT/q (thermal voltage), k = 1.381×10⁻²³ J/K (Boltzmann), q = 1.602×10⁻¹⁹ C (electron charge), T = temperature in Kelvin. Dynamic resistance: rd = nVt/(I + Iₛ).

Example Calculation

Result: 7.17 mA

At 25 °C, Vt = 25.85 mV. With Iₛ = 10⁻¹² A, n = 1, and V = 0.65 V: I = 10⁻¹² × (e^(650/25.85) − 1) ≈ 7.17 mA. The dynamic resistance is about 3.6 Ω.

Tips & Best Practices

Interpreting the Curve

The equation is most accurate for idealized junction behavior. At very low current it helps explain the turn-on knee, and at higher current it shows why current rises rapidly with only a small voltage increase.

Temperature Effects

The thermal voltage increases with temperature, and the saturation current also rises strongly with temperature. That is why the forward voltage at a fixed current drops as the diode warms up.

Limits of the Model

This calculator does not model avalanche breakdown, series resistance, or package heating in detail. Use it for first-order diode behavior and then switch to a richer device model if the circuit operates near the limits of the junction.

Sources & Methodology

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Frequently Asked Questions

What is the ideality factor?

The ideality factor n (emission coefficient) is 1 for ideal diffusion-dominated junctions and up to 2 for recombination-dominated. Silicon diodes are ~1.0-1.2; LEDs are ~1.5-2.0.

What is thermal voltage?

Vt = kT/q ≈ 25.85 mV at 25°C. It represents the voltage equivalent of thermal energy and sets the scale for the exponential turn-on. It increases linearly with temperature.

Why is saturation current so small?

Iₛ represents thermally generated minority carriers crossing the junction. In silicon, this is picoamps. In germanium (smaller bandgap), it is microamps.

Does this model breakdown voltage?

No. The Shockley equation does not model avalanche or Zener breakdown. Reverse bias beyond the breakdown voltage requires modified models.

How does temperature affect the curve?

Increasing temperature increases both Vt (shifting the curve right) and Iₛ (shifting it left). Net effect: forward voltage drops ~2 mV/°C at constant current.

What is dynamic resistance used for?

Dynamic resistance shows how much the diode current changes for a small voltage change around the bias point. It is the value you use when linearizing the diode for AC or small-signal circuit analysis.

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