Hong Life CalculatorsUnderstanding the Shockley diode equation calculator — concept and principle
This calculator applies the Shockley ideal-diode equation to find the current through a p–n junction for a given voltage, or the voltage for a given current. It also gives the thermal voltage, the small-signal resistance, the power dissipated and the extra voltage needed per tenfold increase in current. It is used in electronics and semiconductor courses.
How it is calculated
I = I_S (e^(V ÷ (n V_T)) − 1)
V = n V_T ln(1 + I ÷ I_S)
V_T = k T ÷ q
Small-signal resistance r_d = n V_T ÷ (I + I_S)
Voltage per decade = n V_T ln 10
- I_S is the saturation current, n the ideality factor (1 to about 2), T the junction temperature.
The principle
In a forward-biased junction, the applied voltage lowers the energy barrier that carriers must climb. The number of carriers with enough thermal energy to cross rises exponentially as the barrier falls, so the current grows exponentially with voltage. The thermal voltage kT/q sets the scale: about 26 mV at room temperature. The ideality factor accounts for recombination in real diodes, stretching the exponential.
Worked example
Default inputs: current from voltage, I_S = 10⁻¹² A, n = 1.5, 25 °C, V = 0.6 V.
- V_T = 1.380649 × 10⁻²³ × 298.15 ÷ 1.602 × 10⁻¹⁹ = 25.693 mV.
- V ÷ (n V_T) = 0.6 ÷ 0.03854 = 15.57.
- I = 10⁻¹² × (e^15.57 − 1) = 0.005773 mA (5.77 µA).
- r_d = 0.03854 ÷ 5.773 × 10⁻⁶ = 6,675.74 Ω; power = 0.6 × 5.773 µA = 0.003464 mW.
- Voltage per decade = 1.5 × 25.693 × 2.3026 = 88.7 mV.
| Forward voltage V (V) | Diode current (mA) |
|---|---|
| 0.15 | 4.802e-8 |
| 0.3 | 0.000002402 |
| 0.45 | 0.0001178 |
| 0.6 | 0.005773 |
| 0.75 | 0.283 |
| 0.9 | 13.87 |
| 1.2 | 33,330 |
How to read the result
Because of the exponential, small voltage changes cause large current changes: here every 88.7 mV multiplies the current by ten. The dynamic resistance falls as current rises. I_S depends strongly on temperature and on the device, so use a value for your part.
Common mistakes
- Using a fixed 0.7 V drop for all currents.
- Ignoring the ideality factor.
- Forgetting series resistance at high currents.
- Using I_S from a different temperature.
Frequently asked questions
What is the thermal voltage at room temperature?
About 25.7 mV at 25 °C.
What does the ideality factor mean?
How far the diode departs from the ideal exponential; 1 is ideal, up to about 2 with recombination.
Why is the forward voltage roughly constant?
The current is so sensitive to voltage that a wide range of currents corresponds to a narrow range of voltages.
Does temperature change the forward voltage?
Yes; at constant current it decreases as temperature rises.
Sources: Shockley ideal-diode equation (standard semiconductor result); BIPM SI Brochure (2019) for k and q