 One-sided depletion voltage

For a uniformly doped p-n junction whose depleted thickness $d$ lies almost entirely on the donor side, Poisson's equation gives $dE/dx=e{N}_D/ϵ$. The minimum field obeys $E(d)=0$. Integrating the triangular electric field profile gives $V_{\mathrm{dep}}=e{N}_D{d}^2/(2ϵ)$. The external reverse bias is this total voltage minus the built-in junction potential.