Shockley diode equation

The Shockley ideal diode equation or diode law (which is named after transistor co-inventor William Bradford Shockley, not to be confused with tetrode Walter H. Schottky) gives I-V characteristic of the ideal diode in either forward or reverse bias. The equation can be given as:

Here

I is diode current,

I_S is reverse bias saturation current,

V_D is voltage across the diode,

V_T is thermal voltage, and

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

The thermal voltage VT is around 25.85 mV at 300 K, a temperature close to the room temperature commonly used in device simulation software. At any temperature it is a known constant can be given by:

here k is Boltzmann constant, T is the absolute temperature of PN junction, and q is magnitude of charge on the electron.

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

Under the reverse bias voltages as shown in the figure drawn the exponential in diode equation is negligible, and current is a constant (negative) reverse current value of -IS. The reverse breakdown region is not modeled by Shockley diode equation.

For even rather small forward bias voltages the exponential is quite large because the thermal voltage is very small, hence the subtracted 1'in the diode equation is negligible and the forward diode current is frequently approximated as

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

Small-signal behavior

For the circuit design, a small-signal model of diode behavior proves useful. A specific instance of diode modeling is discussed in article on small-signal circuits.

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