Semiconductor Diode Calculator

Use the Shockley equation to find the current through a diode, the voltage it needs, and its small signal resistance.

What it does

A diode passes current one way and blocks it the other, and the reason is a junction where electrons and holes meet. The behaviour of that junction is described by one equation, the Shockley diode equation, and every current, voltage drop and resistance figure on a diode data sheet comes out of it.

The equation says the current is the saturation current times an exponential of the voltage across the junction divided by the thermal voltage, and the thermal voltage is the Boltzmann constant times the temperature over the charge on the electron. The NIST page on single diode models for solar cells writes it out in exactly that form and adds that the ideality factor, which is usually between 1 and 2 for a single junction, accounts for recombination in the depletion region.

The exponent is what makes the device interesting. At room temperature the thermal voltage is about 26 mV, so a change of 60 mV in the forward bias multiplies the current by roughly ten. That is why a diode is described by a voltage drop rather than by a resistance, and why a series resistor has to be calculated rather than guessed.

This page solves the equation in both directions. Give it the saturation current, the ideality factor, the junction temperature and a voltage, and it returns the current, the thermal voltage, the voltage needed to reach a target current, and the small signal resistance at that current. The last of those is the slope of the curve, and it is what sets the impedance a diode presents to a small signal.

The model is the ideal one. A real diode has a series resistance that takes over at high current, a leakage current that rises faster than the saturation current as the junction warms, and a reverse breakdown that the equation knows nothing about. It also says nothing about the forward voltage at very low currents, where the exponential term is no longer larger than one.

How to use

1. Choose the scale for the junction temperature, Celsius or Fahrenheit.
2. Enter the reverse saturation current from the data sheet. A common value for a small silicon signal diode is 1e-13 A.
3. Enter the ideality factor, which is 1 for a diffusion limited diode and closer to 2 when recombination matters.
4. Enter the junction temperature, which is usually well above the ambient temperature in a power circuit.
5. Read the current at the voltage you entered, and the thermal voltage that sets the steepness of the curve.
6. Set the target current you care about to get the voltage it needs and the small signal resistance there.

Formula

I

Current through the diode in amperes.

Is

Reverse saturation current in amperes.

V

Voltage across the junction in volts.

Vt

Thermal voltage, k T over q, in volts.

n

Ideality factor, usually between 1 and 2.

The logarithm in the reverse calculation is the natural one, and the plus one in the bracket matters only at very small currents where the current is close to the saturation current. The thermal voltage is 25.852 mV at 300 K, so the current multiplies by about ten for every 60 mV of extra forward bias. The equation is a steady state relation and says nothing about switching speed or reverse recovery time.

Worked example

Reference table

Limits

• The equation covers the forward and reverse bias behaviour but not reverse breakdown, where the current runs away and the diode is destroyed.
• Series resistance is ignored, so the prediction is wrong at high current, which is exactly where a real diode needs a current limit.
• The saturation current is treated as fixed, while in a real device it roughly doubles for every 10 degrees C of temperature rise.
• There is no leakage, capacitance or switching time in the model, so it cannot predict anything about a circuit in a transient.

Common mistakes

• Using the ambient temperature instead of the junction temperature. A diode that has warmed up conducts noticeably more.
• Forgetting the ideality factor, which shifts the curve by a factor of n in the exponent and is the difference between 0.6 V and 0.7 V of drop.
• Treating a diode like a resistor with a fixed drop. The drop is a consequence of the exponential, and it moves with current and temperature.
• Leaving out the minus one inside the bracket. It is what makes the current zero at zero volts.
• Expecting the small signal resistance to stay constant. It falls as the current rises, because the curve gets steeper.

Try it yourself

Quick checks. Answers sit tucked under each question.

Questions

Sources

• NIST PV Performance Modeling Collaborative: single diode equivalent circuit models
• IIT Bombay lecture notes: diode circuits and the Shockley equation
• Caltech physics laboratory: the solid state diode and the ideal diode equation

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