Shockley Diode Equation Calculator

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.

When This Page Helps

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 the Inputs

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.

Example Calculation

Tips & Best Practices

• For large forward bias (V >> nVt), the −1 is negligible and I ≈ Iₛe^(V/nVt).
• Current doubles for every ~18 mV increase (at n=1, 25°C) — a useful rule of thumb.
• Iₛ doubles roughly every 10°C increase in temperature.
• Reverse bias: set V negative. Current plateaus at −Iₛ (before breakdown).
• Real diodes have series resistance Rs; at high currents, V_total = V_junction + I×Rs.

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.

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.