Abrupt PN Junctions: Analytical Solutions Under Equilibrium and   Non-equilibrium
  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. 
Sina Khorasani
cond-mat.mes-hall