Shockley diode equation
The Shockley diode equation or the diode law, named after transistor co-inventor William Shockley of Bell Telephone Laboratories, gives the I–V (current-voltage) characteristic of an idealized diode in either forward or reverse bias (applied voltage):
where
The equation is called the Shockley ideal diode equation when n, the ideality factor, is set equal to 1. The ideality factor n typically varies from 1 to 2 (though can in some cases be higher), depending on the fabrication process and semiconductor material and is set equal to 1 for the case of an "ideal" diode (thus the n is sometimes omitted). The ideality factor was added to account for imperfect junctions as observed in real transistors. The factor mainly accounts for carrier recombination as the charge carriers cross the depletion region.
The thermal voltage VT is approximately 25.85 mV at 300 K, a temperature close to "room temperature" commonly used in device simulation software. At any temperature it is a known constant defined by:
where k is the Boltzmann constant, T is the absolute temperature of the p–n junction, and q is the magnitude of charge of an electron (the elementary charge).
The reverse saturation current, IS, is not constant for a given device, but varies with temperature; usually more significantly than VT, so that VD typically decreases as T increases.
The Shockley diode equation doesn't describe the "leveling off" of the I–V curve at high forward bias due to internal resistance. This can be taken into account by adding a resistance in series.
Under reverse bias (when the n side is put at a more positive voltage than the p side) the exponential term in the diode equation is near zero and the current is near a constant (negative) reverse current value of −IS. The reverse breakdown region is not modeled by the Shockley diode equation.
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