DEPLETION LAYER CALCULATIONS AND MODELLING OF A SINGLE‐DIFFUSED p‐n JUNCTION WITH COMPLEMENTARY ERROR FUNCTION PROFILE

Abstract

The depletion layer of a single‐diffused with complementary error function profile has been calculated. Closed form solutions of the potential difference between the two depletion layer edges are obtained by integrating Poisson's equation and equating the positive and negative charges in the depletion layer. Using the integrability of complementary error functions, the depletion layer thickness, junction built‐in potential and junction exponential factor are computed. The customary exponential factor m in the expression for the junction capacitance, i.e. Cj ∝(1 + Valø)−m is shown to vary with the applied reverse bias. The value of ø is also found to be different from the conventional value of the junction built‐in potential. A technique for modelling the diffused p‐n junctions at various reverse biases is presented using numerical methods. These results will be useful in circuit simulation programs such as SPICE.