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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.
Later he gives a corresponding equation for current as a function of voltage under additional assumptions, which is the equation we call the Shockley ideal diode equation. [3] He calls it "a theoretical rectification formula giving the maximum rectification", with a footnote referencing a paper by Carl Wagner , Physikalische Zeitschrift 32 , pp ...
The Shockley diode equation relates the diode current of a p-n junction diode to the diode voltage .This relationship is the diode I-V characteristic: = (), where is the saturation current or scale current of the diode (the magnitude of the current that flows for negative in excess of a few , typically 10 −12 A).
From the Shockley ideal diode equation given above, it might appear that the voltage has a positive temperature coefficient (at a constant current), but usually the variation of the reverse saturation current term is more significant than the variation in the thermal voltage term.
The effect of reverse saturation current on the I-V curve of a crystalline silicon solar cell are shown in the figure to the right. Physically, reverse saturation current is a measure of the "leakage" of carriers across the p–n junction in reverse bias.
In the velocity-saturation regime, this equation takes the following form = Note the different dependence of on between the Mott–Gurney law and the equation describing the current in the velocity-saturation regime. In the ballistic case (assuming no collisions), the Mott–Gurney equation takes the form of the more familiar Child–Langmuir law.
For a surface biased strongly negative so that it draws the ion saturation current, the approximation is very good. It is customary, although not strictly necessary, to further simplify the equation by assuming that 2 χ / M 2 {\displaystyle 2\chi /{\mathfrak {M}}^{2}} is much larger than unity.
The theory is similar to that of a single probe, except that the current is limited to the ion saturation current for both positive and negative voltages. In particular, if V b i a s {\displaystyle V_{bias}} is the voltage applied between two identical electrodes, the current is given by;