– 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.
– 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.
– 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.
– A general 3D extension in the case where no symmetry exists can be considered for further developments.
– The paper strongly simplify and ease the optimization and design of any PN junction.
– This paper provides a novel method for electric field distribution analysis.
