Reverse saturation current

The reverse saturation current $I_S$ is the tiny current that flows through a reverse-biased PN junction. Carried by minority carriers, almost independent of the reverse voltage (hence “saturation”), and the scaling constant in front of the Diode equation.

What carries it

Under reverse bias the barrier is raised and the abundant majority carriers cannot cross. But every semiconductor region still contains a small population of the other carrier type: stray electrons in the p-side, stray holes in the n-side (minority carriers). Any minority carrier generated near the junction and reaching the depletion region’s field is swept straight across. It is going downhill, so the tall barrier that blocks majority carriers does nothing to stop it. That sweep of minority carriers is the reverse saturation current.

The supply of minority carriers is limited by thermal generation, not by the applied voltage. Once the reverse voltage is large enough to collect every minority carrier that arrives, increasing it further cannot extract more: the current “saturates” at $I_S$ and stays nearly flat. Hence the name.

How small, and what it depends on

$I_S$ is extremely small for an ordinary silicon junction, typically $10^{-15}$ to $10^{-9}\text{A}$ (femtoamps to nanoamps). Its magnitude is set by device physics, not the circuit:

• Junction cross-sectional area — a bigger junction collects proportionally more minority carriers, so $I_S\propto$ area.
• Doping concentrations — fix the equilibrium minority-carrier concentrations $n_i^2/N_D$ and $n_i^2/N_A$ via the Mass-action law. Lighter doping means more minority carriers and larger $I_S$.
• Minority-carrier diffusion lengths — how far a minority carrier travels before recombining. Longer lengths mean more carriers reach the junction.
• Temperature — since $I_S\propto n_i^2$ and $n_i$ depends exponentially on temperature (see Intrinsic carrier concentration), $I_S$ climbs steeply with heat, very roughly doubling every ~5 °C near room temperature (about a $7\times$ rise per 10 °C). That’s steeper than the familiar “diode current doubles every ~10 °C” rule, which refers to the forward current at a fixed voltage, not to $I_S$ itself (the forward-voltage drift partly offsets the $I_S$ rise). Either way this sensitivity drives much of the thermal drift in diode and transistor circuits.

The diode-equation scale factor

$I_S$ isn’t only the leakage current. It’s also the constant that sets the scale of forward conduction. The Diode equation is

$i=I_S\left(e^{v/V_T}-1\right)$

where $v$ is the junction voltage and $V_T\approx 25\text{mV}$ the Thermal voltage. In strong reverse bias the exponential vanishes and $i\to -I_S$ (the small reverse leakage). In forward bias the exponential dominates and $i\approx I_S{e}^{v/V_T}$, so the same tiny $I_S$ multiplies the huge exponential to set the forward current at a given voltage. A junction with a larger $I_S$ conducts the same forward current at a lower voltage. One parameter ties together the reverse leakage and the forward turn-on of every diode and the Bipolar junction transistor.