Schokley Equation

$$J=J_s\left[\exp \left(\frac{qV}{nKT}\right)-1\right]$$

• $J$ is the current density. $[J]=A/m^2$
• $J_s$ is the reverse saturation current density — the leakage current under reverse bias.
• $q$ is the elementary charge.
• $V$ is the applied voltage across the junction.
• $n$ is the ideality factor — $n=1$ for pure diffusion current, $n=2$ when recombination in the depletion region dominates. Real diodes sit somewhere between.
• $k_{B}T$ is the thermal energy.

where

$$J_s=q\left(\frac{D_p{p}_{n0}}{\sqrt{D_p{\tau }_p}}+\frac{D_n{n}_{p0}}{\sqrt{D_n{\tau }_n}}\right)$$

This gives the saturation current in terms of minority carrier properties on each side of the junction:

• $D_p$, $D_n$ are the diffusion coefficients for holes and electrons respectively.
• $p_{n0}$ is the equilibrium minority hole concentration on the n-side.
• $n_{p0}$ is the equilibrium minority electron concentration on the p-side.
• ${\tau }_p$, ${\tau }_n$ are the minority carrier lifetimes.
• $\sqrt{D\tau }$ is the diffusion length $L$ — the average distance a minority carrier diffuses before recombining.

So $J_s$ simplifies to $q\left(\frac{D_p{p}_{n0}}{L_p}+\frac{D_n{n}_{p0}}{L_n}\right)$. Each term represents the minority carrier diffusion current contribution from one side of the junction. $J_s$ is small when doping is high (suppresses minority concentrations) and carrier lifetimes are long.