# Saturation current

The saturation current (or scale current), more accurately the reverse saturation current, is the part of the reverse current in a semiconductor diode caused by diffusion of minority carriers from the neutral regions to the depletion region. This current is almost independent of the reverse voltage.[1]

The reverse bias saturation current ${\displaystyle I_{\text{S}}}$ for an ideal p–n diode is:

${\displaystyle I_{\text{S}}=qAn_{\text{i}}^{2}\left({\frac {1}{N_{\text{D}}}}{\sqrt {\frac {D_{\text{p}}}{\tau _{\text{p}}}}}+{\frac {1}{N_{\text{A}}}}{\sqrt {\frac {D_{\text{n}}}{\tau _{\text{n}}}}}\right),\,}$

where

${\displaystyle q}$ is elementary charge
${\displaystyle A}$ is the cross-sectional area
${\displaystyle D_{\text{p}},D_{\text{n}}}$ are the diffusion coefficients of holes and electrons, respectively,
${\displaystyle N_{\text{D}},N_{\text{A}}}$ are the donor and acceptor concentrations at the n side and p side, respectively,
${\displaystyle n_{\text{i}}}$ is the intrinsic carrier concentration in the semiconductor material,
${\displaystyle \tau _{\text{p}},\tau _{\text{n}}}$ are the carrier lifetimes of holes and electrons, respectively.[2]

Increase in reverse bias does not allow the majority charge carriers to diffuse across the junction. However, this potential helps some minority charge carriers in crossing the junction. Since the minority charge carriers in the n-region and p-region are produced by thermally generated electron-hole pairs, these minority charge carriers are extremely temperature dependent and independent of the applied bias voltage. The applied bias voltage acts as a forward bias voltage for these minority charge carriers and a current of small magnitude flows in the external circuit in the direction opposite to that of the conventional current due to the moment of majority charge carriers.

Note that the saturation current is not a constant for a given device; it varies with temperature; this variance is the dominant term in the temperature coefficient for a diode. A common rule of thumb is that it doubles for every 10 °C rise in temperature.[3]

## References

1. ^ Steadman, J. W. (1993). "Electronics". In R. C. Dorf (ed.). The Electrical Engineering Handbook. Boca Raton: CRC Press. p. 459. ISBN 0849301858.
2. ^ Schubert, E. Fred (2006). "LED basics: Electrical properties". Light-Emitting Diodes. Cambridge University Press. p. 61.
3. ^ Bogart, F. Theodore Jr. (1986). Electronic Devices and Circuits. Merill Publishing Company. p. 40.