Shockley Diode Calculator
Enter the saturation current, forward voltage, temperature, and ideality factor to instantly calculate the diode current from the Shockley ideal diode equation. Switch to reverse-solve mode to find the forward voltage from a known current. The calculator also derives the thermal voltage from temperature, shows a live I-V curve from 0 V to 1 V, and walks through each step of the computation.
Formula
Worked example
A 1N4148 silicon diode (Is = 2.52 nA, n = 1) at 25 degC: Vt = 25.85 mV. At Vd = 0.6 V: exponent = 0.6 / (1 x 0.02585) = 23.21, I = 2.52e-9 x (e^23.21 - 1) = 2.52e-9 x 1.20e10 = 30.2 mA. Dynamic resistance rd = 25.85 mV / 30.2 mA = 0.86 ohm.
The Shockley ideal diode equation
The Shockley ideal diode equation, named after Nobel laureate William Shockley, describes the current-voltage (I-V) relationship across a p-n semiconductor junction. The equation is I = Is x (exp(Vd / nVt) - 1), where I is the diode current, Is is the reverse saturation current, Vd is the forward voltage across the junction, n is the ideality factor (also called the emission coefficient), and Vt is the thermal voltage. This single equation captures both forward bias (exponential current growth) and reverse bias (leakage current approaching -Is) behaviour.
Thermal voltage and temperature dependence
The thermal voltage Vt = kT/q arises from the physics of carrier diffusion across the junction, where k is the Boltzmann constant (1.38 x 10^-23 J/K), T is the absolute temperature in Kelvin, and q is the elementary charge (1.60 x 10^-19 C). At room temperature (25 degC = 298.15 K), Vt is approximately 25.85 mV. Because Vt appears in the exponent, temperature has a strong effect on diode current: every 10 degC rise roughly doubles the saturation current Is (and therefore the forward current at a fixed voltage). This calculator recomputes Vt from your entered temperature automatically.
Ideality factor and real diode behaviour
An ideal diode has an ideality factor n of exactly 1. Real devices deviate for two reasons: recombination currents in the depletion region add a component that follows exp(Vd / 2Vt) (n = 2 dominated), and surface recombination or ohmic resistance shift the curve further. Silicon signal diodes typically have n between 1.0 and 1.2 in the mid-current range, Schottky diodes stay close to 1, and LEDs span 1.5 to 2. For a precise model of a specific device, extract n from the slope of the measured ln(I) versus Vd curve.
Dynamic resistance and circuit design
The dynamic resistance rd = nVt / I is the small-signal resistance of the diode at its DC operating point. It represents how much the voltage changes for a small change in current. At 10 mA and n = 1, rd = 25.85 mV / 10 mA = 2.59 ohm. This resistance determines the diode's contribution to AC gain in amplifier bias networks and the impedance it presents to high-frequency signals. In a full large-signal model, the ohmic resistance of the bulk semiconductor (typically 0.1 to 2 ohm for signal diodes) adds in series with rd.
Typical diode parameters by type
| Diode type | Is (typical) | Ideality factor n | Forward voltage (approx.) |
|---|---|---|---|
| Silicon signal (1N4148) | 2.52 nA | 1.0 - 1.1 | 0.6 - 0.7 V |
| Silicon rectifier (1N4007) | 10 nA | 1.1 - 1.2 | 0.7 - 1.0 V |
| Schottky (1N5817) | 10 uA | 1.0 - 1.05 | 0.2 - 0.4 V |
| Germanium (1N34A) | 1 - 10 uA | 1.0 | 0.2 - 0.3 V |
| LED (red, typical) | 10 pA | 1.5 - 2.0 | 1.8 - 2.2 V |
| LED (blue/white, typical) | 10 pA | 1.5 - 2.0 | 2.8 - 3.5 V |
| Zener (reverse model) | 1 - 100 nA | 1.0 - 2.0 | Breakdown voltage |
Representative saturation currents and ideality factors. Actual values vary by manufacturer and operating conditions.
Frequently asked questions
What is the Shockley diode equation used for?
The Shockley equation models the current-voltage relationship of any p-n junction diode - from signal diodes and rectifiers to LEDs and photodiodes. It is used to predict the current for a given forward voltage, to reverse-solve for the voltage required to drive a target current, to compute power dissipation, and to derive the small-signal dynamic resistance at an operating point. Circuit simulators like SPICE use extensions of this equation as the core diode model.
What is the thermal voltage (Vt) and why does it matter?
Thermal voltage Vt = kT/q is a fundamental quantity derived from temperature. At 25 degC it is about 25.85 mV. It appears in the exponent of the Shockley equation, so even small temperature changes significantly affect diode current. Increasing temperature from 25 degC to 50 degC raises Vt from 25.85 mV to 27.99 mV, but also roughly doubles the saturation current Is, producing a net increase in forward current at the same voltage. This is why power diodes heat up and draw more current in a destructive thermal runaway if not current-limited.
What is the ideality factor (n) and how do I choose it?
The ideality factor n (also called the emission coefficient) accounts for the deviation of a real diode from ideal behaviour. n = 1 corresponds to diffusion-dominated current (ideal), n = 2 to recombination-dominated current in the depletion region. Silicon signal diodes are typically n = 1.0 to 1.2 in the forward-conduction range, Schottky diodes are close to 1, LEDs range from 1.5 to 2. For the most accurate result, use the value from the device datasheet or extract it experimentally from the slope of a log(I) vs. Vd plot.
How do I find the saturation current (Is) for my diode?
Datasheets rarely list Is directly. You can estimate it from the datasheet's forward current and voltage values by rearranging the Shockley equation: Is = I / (exp(Vd / nVt) - 1). For silicon signal diodes, Is at room temperature typically ranges from about 1 pA to 10 nA. The reference table in this calculator gives representative values for common diode types as a starting point.
What is the dynamic resistance of a diode?
Dynamic resistance rd = nVt / I is the AC resistance of the diode at its DC operating point. It falls as current increases: at 1 mA and n = 1 it is about 25.85 ohm; at 10 mA it drops to about 2.6 ohm. This matters for small-signal circuit analysis - for example, in emitter followers, the diode's rd adds to the output impedance. At high currents the bulk ohmic resistance of the diode dominates and rd becomes negligible.
Can this calculator handle reverse bias?
Yes. Enter a negative forward voltage (for example, -300 mV) in current-solve mode. The Shockley equation gives a current of approximately -Is, the reverse saturation current. At 25 degC with Is = 1 pA, the leakage current in full reverse bias approaches -1 pA. Note that this ideal model does not include avalanche or Zener breakdown, which occur at much larger reverse voltages and are not described by the basic Shockley equation.