Abrupt PN Junctions: Analytical Solutions Under Equilibrium and Non-equilibrium

TL;DR

This paper provides explicit analytical solutions for carrier and field distributions in abrupt PN junctions under equilibrium and non-equilibrium conditions, validated by numerical methods and extended to asymmetric junctions.

Contribution

It introduces an explicit analytical solution for abrupt PN junctions and extends analysis to asymmetric cases with approximate relations under bias.

Findings

Analytical solutions agree well with numerical results.

Depletion layer approximation is validated.

Derived relations for capacitance and I-V characteristics under bias.

Abstract

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 and I-V characteristics are also found under non-zero external bias.