Abrupt PN junctions: Analytical solutions under equilibrium and non-equilibrium

• An explicit solution of abrupt PN junctions under equilibrium is presented.
• Accurate logarithmic numerical method is implemented, and results are compared to analytical expressions.
• Agreement with numerical solution and the depletion layer approximation found.
• Relations for C-V and I–V characteristics are found, and asymmetric junctions under equilibrium are discussed.

We present an explicit solution of carrier and field distributions in abrupt PN junctions under equilibrium. An accurate logarithmic numerical method is implemented and results are compared to the analytical solutions. Analysis of results shows reasonable agreement with numerical solution as well as the depletion layer approximation. We discuss extensions to the asymmetric junctions. Approximate relations for differential capacitance C-V and current-voltage I–V characteristics are also found under non-zero external bias.