Diode - Semiconductor Diodes - Shockley Diode Equation

Shockley Diode Equation

The Shockley ideal diode equation or the diode law (named after transistor co-inventor William Bradford Shockley) gives the I–V characteristic of an ideal diode in either forward or reverse bias (or no bias). The equation is:

where

I is the diode current,

I_S is the reverse bias saturation current (or scale current),

V_D is the voltage across the diode,

V_T is the thermal voltage, and

n is the ideality factor, also known as the quality factor or sometimes emission coefficient. The ideality factor n varies from 1 to 2 depending on the fabrication process and semiconductor material and in many cases is assumed to be approximately equal to 1 (thus the notation n is omitted).

The thermal voltage V_T 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 on an electron (the elementary charge).

The reverse saturation current, I_S, is not constant for a given device, but varies with temperature; usually more significantly than V_T, so that V_D typically decreases as T increases.

The Shockley ideal diode equation or the diode law is derived with the assumption that the only processes giving rise to the current in the diode are drift (due to electrical field), diffusion, and thermal recombination–generation (R–G). It also assumes that the R–G current in the depletion region is insignificant. This means that the Shockley equation doesn’t account for the processes involved in reverse breakdown and photon-assisted R–G. Additionally, it doesn’t describe the "leveling off" of the I–V curve at high forward bias due to internal resistance.

Under reverse bias voltages (see Figure 5) the exponential in the diode equation is negligible, and the current is a constant (negative) reverse current value of −I_S. The reverse breakdown region is not modeled by the Shockley diode equation.

For even rather small forward bias voltages (see Figure 5) the exponential is very large because the thermal voltage is very small, so the subtracted ‘1’ in the diode equation is negligible and the forward diode current is often approximated as

The use of the diode equation in circuit problems is illustrated in the article on diode modeling.