CAD MODELING OF DIFFUSED p‐n JUNCTIONS

Abstract

Closed form solutions of the potential difference between the two depletion layer edges of a single‐diffused Gaussian p‐n junction are obtained by integrating Poisson's equation and equating the positive and negative charges in the depletion layer. Using the closed form solution of the Poisson's equation, the depletion layer width, junction capacitance and junction built‐in potential are calculated. The customary exponential factor m in the expression for the junction capacitance, i.e., Cj α(1 + Va/φ)−m is shown to vary with the applied reverse bias. The value of φ is found to be different from the conventional value of the junction built‐in potential especially at high voltages. A technique for modeling diffused p‐n junctions at various reverse biases is presented. These results will be useful in circuit simulation programs such as SPICE, particularly for applications involving digital integrated circuits.