Electron current density and electrostatic potential in a p--n-abrupt-junction diode as obtained by exact computer solution of the differential equations

A computer solution for the current, continuity and Poisson´s differential equations has been obtained for the forward steady-state behaviour of a one-dimensional abrupt p⁺--njunction germanium diode at zero and at low to high injection levels at 300°K. The numerical integration has been performed in and outside the space-charge layer of the p-njunction by using the Hall-Shockley-Read and the Auger recombination processes, and by eliminating the Boltzmann equilibrium approximation in the space-charge layer and the space-charge neutrality approximation in the quasineutral p and nregion. The numerical results for the electron-current density and the electrostatic potential distributions are given. The computed characteristic of the p-njunction is compared with experiment.