Modeling of Electrostatics and Currents in a Forward-Biased p-n Junction

A general model is developed for forward-biased p-n junctions with arbitrary doping concentrations biased at any injection level. It goes beyond the commonly practiced depletion approximation, which is valid only under the low-level injection condition. It is shown that when the applied junction voltage exceeds the built-in potential, the profile of net charge density shrinks to two antisymmetric spikes, one going positive and one going negative, with the same magnitude given by the average of the n-type and p-type doping concentrations. It is also shown that under high-level injection condition, the drift current components become dominant, in some cases yielding an exp(qV/kT) dependence of the total current instead of the commonly perceived exp(qV/2kT) dependence (here, V is the intrinsic junction voltage). By equating the sum of drift and diffusion current densities on both sides of the junction, analytical expressions are derived for the electric fields and, therefore, the total currents. Finally, the decay lengths of excess carriers in the quasi-neutral regions are solved numerically from the current continuity equations coupled to Poisson’s equation with no assumptions of charge neutrality. It is shown that the decay lengths in the high-level injection regime are doping-dependent and are longer than the well-known minority-carrier diffusion lengths in the low-level injection regime.