Calculate diode current from voltage using the Shockley equation. Includes ideality factor, thermal voltage, dynamic resistance, and I-V sweep mode.
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.
Understanding the Shockley equation is essential for circuit designers working with rectifiers, voltage regulators, solar cells, and LEDs. This calculator provides instant I-V analysis, dynamic resistance for small-signal models, and comparison across diode technologies. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain. Use this clarification to avoid ambiguous interpretation.
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).
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.
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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.
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.
Iₛ represents thermally generated minority carriers crossing the junction. In silicon, this is picoamps. In germanium (smaller bandgap), it is microamps.
No. The Shockley equation does not model avalanche or Zener breakdown. Reverse bias beyond the breakdown voltage requires modified models.
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.
Dynamic resistance rd = nVt/I is the small-signal resistance of the diode at the operating point. It is essential for AC analysis and impedance matching in rectifier and detector circuits.