 Diode minority-carrier diffusion current

For a long, nondegenerate, ideal p-n junction under low injection, the diode saturation current is set by minority carriers supplied from the neutral regions. Their equilibrium densities are $n_{p0}=n_i^2/N_A$ and $p_{n0}=n_i^2/N_D$. Solving the steady diffusion and recombination equations gives $I_S=e\mathcal{A}(D_n{n}_{p0}/L_n+D_p{p}_{n0}/L_p)$, where $\mathcal{A}$ is junction area, $D_n,D_p$ are diffusion coefficients, and $L_n,L_p$ are diffusion lengths. Reverse bias suppresses opposite majority-carrier injection exponentially while collecting this minority supply. Thus $I_S$ is approximately bias independent before breakdown, but depends strongly on temperature through $n_i^2$ and on transport, doping, and geometry.