Shockley Diode Calculator

The Shockley diode equation describes the current-voltage (I-V) relationship of a semiconductor diode: I = IS × (e^(VD / (n × VT)) − 1), where IS is the saturation current, VD is the diode voltage, n is the ideality factor, and VT is the thermal voltage. It was derived by William Shockley and is the foundational model for understanding diode behavior in both forward and reverse bias.

Thermal voltage (VT) is a temperature-dependent quantity defined as VT = kT/q, where k is Boltzmann's constant (1.380649 × 10⁻²³ J/K), T is the absolute temperature in Kelvin, and q is the electron charge (1.602176634 × 10⁻¹⁹ C). At room temperature (300 K), VT ≈ 25.85 mV. It sets the scale of the exponential I-V curve.

An ideal diode perfectly conducts current in one direction and blocks it completely in the other, modeled with an ideality factor n = 1. Real diodes deviate due to recombination currents and other effects, giving ideality factors between 1 and 2. The Shockley equation models both: set n = 1 for an ideal diode or n = 1–2 for a real silicon or germanium diode.

The ideality factor (also called the emission coefficient) accounts for non-ideal recombination mechanisms in the diode junction. For an ideal diode, n = 1. For real diodes, it typically ranges from 1 to 2. Silicon signal diodes often have n ≈ 1.1–1.4, while diodes dominated by recombination current approach n = 2. The value affects how steeply the current rises with voltage.

The saturation current IS, also called the reverse saturation or leakage current, is the tiny current that flows through the diode when it is reverse biased. It is typically in the range of 10⁻¹² A (1 pA) to 10⁻⁹ A (1 nA) for silicon diodes at room temperature. IS increases strongly with temperature, roughly doubling every 10 °C.

Temperature affects the diode current in two ways: it increases the thermal voltage VT (reducing the steepness of the I-V curve) and significantly increases the saturation current IS. The net effect in forward bias is that for a fixed current, the required forward voltage decreases by approximately 2 mV/°C as temperature rises. In this calculator, changing the temperature in Kelvin updates VT automatically.

The Shockley equation is used in rectifier design, voltage regulator circuits, solar cell modeling (single-diode model for photovoltaic cells), RF detectors, temperature sensors, and SPICE circuit simulation. Understanding the I-V relationship helps engineers select diodes and predict circuit behavior across operating temperatures and bias conditions.

Yes. In reverse bias (negative VD), the exponential term e^(VD/(n×VT)) approaches zero, so the current approaches −IS — a very small negative current equal to the saturation current. The simple Shockley model does not account for avalanche or Zener breakdown, so it is only accurate up to the breakdown voltage of the diode.