Electric field distribution and voltage breakdown modeling for any PN junction

Abstract

Purpose

Scientists and engineers have been solving Poisson’s equation in PN junctions following two approaches: analytical solving or numerical methods. Although several efforts have been accomplished to offer accurate and fast analyses of the electric field distribution as a function of voltage bias and doping profiles, so far none achieved an analytic or semi-analytic solution to describe neither a double diffused PN junction nor a general case for any doping profile. The paper aims to discuss these issues.

Design/methodology/approach

In this work, a double Gaussian doping distribution is first considered. However, such a doping profile leads to an implicit problem where Poisson’s equation cannot be solved analytically. A method is introduced and successfully applied, and compared to a finite element analysis. The approach is then generalized, where any doping profile can be considered. 2D and 3D extensions are also presented, when symmetries occur for the doping profile.

Findings

These results and the approach here presented offer an efficient and accurate alternative to numerical methods for the modeling and simulation of mathematical equations arising in physics of semiconductor devices.

Research limitations/implications

A general 3D extension in the case where no symmetry exists can be considered for further developments.

Practical implications

The paper strongly simplify and ease the optimization and design of any PN junction.

Originality/value

This paper provides a novel method for electric field distribution analysis.

Citation

Rouger, N. (2016), "Electric field distribution and voltage breakdown modeling for any PN junction", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 35 No. 1, pp. 137-156. https://doi.org/10.1108/COMPEL-12-2014-0330