The saturation current IS for a p-n junction, Eq. (42.22), depends strongly on temperature. Explain why.

Given equation is

$I=I_s\left(e^{\raisebox{1ex}{$ev$}\!\left/ \!\raisebox{-1ex}{$kt$}\right.}-1\right)$

Where I = Current through a p-n junction, $I_s$=Saturation current, e = 2.71828, V = Voltage, e as power = Magnitude of electron charge, k = Boltzmann constant.

Note: Two different uses of e In $e^{\raisebox{1ex}{$ev$}\!\left/ \!\raisebox{-1ex}{$kt$}\right.}$the base of the exponent also uses the symbol e, standing for the base of the natural logarithms, 2.71828c. This e is quite different from e = 1.602 * 10-19 C in the exponent.

The saturation current $I_8$is a small flow of current when a p-n junction diode is reversed biased. This saturation current is almost independent of an applied reverse bias voltage, however, the density of this current is mainly the minority carriers whose number depends mostly on the temperature.

Hence, the saturation current $I_8$is mainly composed of minority carriers that are thermally generated. Hence $I_8$is dependent on temperature and not on the applied voltage.