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.
A Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation
