Table of Contents
The Shockley Diode Equation
The Shockley diode equation, developed by Nobel laureate William Shockley, describes the current-voltage (I-V) characteristic of a semiconductor diode. It models the exponential relationship between forward voltage and current that defines diode behavior. This equation is fundamental to all semiconductor device physics and circuit analysis.
The equation predicts that below the threshold voltage (approximately 0.6-0.7V for silicon), very little current flows. Above this threshold, current increases exponentially with voltage. The equation also accounts for temperature effects through the thermal voltage term, explaining why diode characteristics shift with temperature.
Formula and Parameters
Where Is is the reverse saturation current, VD is the voltage across the diode, n is the ideality factor (1 for ideal, 1-2 for real diodes), VT is the thermal voltage, k is Boltzmann's constant (1.381 × 10-23 J/K), T is absolute temperature in Kelvin, and q is the electron charge (1.602 × 10-19 C).
Typical Diode Parameters
| Diode Type | Is (typical) | n (ideality) | VF (forward) |
|---|---|---|---|
| Silicon (1N4148) | 2.5 nA | 1.0-1.1 | 0.65 V |
| Silicon Power (1N4001) | 14 nA | 1.0-1.2 | 0.7 V |
| Germanium | 1-100 μA | 1.0-1.1 | 0.3 V |
| Schottky | 1-100 nA | 1.0-1.2 | 0.2-0.4 V |
| LED (red) | 0.01-1 nA | 1.5-2.0 | 1.8-2.2 V |
Temperature Effects
- The thermal voltage VT increases linearly with temperature: approximately 0.087 mV per degree Celsius.
- The saturation current Is roughly doubles for every 10 degrees Celsius increase in temperature.
- The forward voltage drops by approximately 2 mV per degree Celsius at constant current.
- Reverse leakage current increases dramatically with temperature, which can cause thermal runaway in power circuits.
Frequently Asked Questions
What is the ideality factor?
The ideality factor (n) accounts for non-ideal behavior in real diodes. For an ideal diode, n = 1. For real diodes, n ranges from 1 to 2. A value of 1 indicates diffusion-dominated current (ideal), while higher values indicate recombination in the depletion region or other non-ideal effects. LEDs typically have n between 1.5 and 2.0.
What is the saturation current?
The saturation current (Is) is the tiny reverse leakage current that flows when the diode is reverse-biased. It depends on the semiconductor material, doping levels, junction area, and temperature. Silicon diodes have Is in the range of nanoamperes, while germanium diodes have Is in microamperes due to their smaller bandgap.
How accurate is the Shockley equation?
The Shockley equation is accurate for moderate forward bias conditions (a few hundred millivolts above the threshold). At very high currents, series resistance effects cause the actual voltage to exceed the prediction. At very low currents, generation-recombination currents dominate. For most practical circuits, however, the equation provides excellent accuracy with appropriate parameter values.