Saturation current

The saturation current (or scale current), more accurately, the reverse saturation current, is that 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. (Steadman 1993, 459)

I_S, the reverse bias saturation current for an ideal p–n diode, is given by (Schubert 2006, 61):

$I_\mathrm{S} = e A \left( \sqrt{\frac{D_\mathrm{p}}{\tau_\mathrm{p}}} \frac{n_\mathrm{i}^2}{N_\mathrm{D}} + \sqrt{\frac{D_\mathrm{n}}{\tau_\mathrm{n}}} \frac{n_\mathrm{i}^2}{N_\mathrm{A}} \right),\,$

where

e is elementary charge

A is the cross-sectional area

D_p,n are the diffusion coefficients of holes and electrons, respectively,

N_D,A are the donor and acceptor concentrations at the n side and p side, respectively,

n_i is the intrinsic carrier concentration in the semiconductor material,

\tau_\mathrm{p,n}

are the carrier lifetimes of holes and electrons, respectively.

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. (Bogart 1986, 40)

References

Steadman, J. W. (1993). "Electronics" in R. C. Dorf, The Electrical Engineering Handbook. Boca Raton: CRC Press.
Schubert, E. Fred. (2006). "LED basics: Electrical properties" in Light-Emitting Diodes: Cambridge Press.
Bogart, F. Theodore Jr. (1986). "Electronic Devices and Circuits": Merill Publishing Company

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