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.

Optimal drift region for diamond power devices

“…All these models were implemented in the approach of avalanche breakdown calculation described in details in Rouger work [24]. This method was chosen for its accuracy (more than an analytical method which needs approximations) and its shorter CPU time compared to a finite element numerical method.…”

“…Using the realistic model proposed by Hiraiwa et al [12], the optimal drift layer parameters were considered as a function of the targeted breakdown voltage. For the breakdown voltage analysis, avalanche breakdown has been considered, using a one dimensional discrete approach [24]. Similar analysis based on other methods have been reported on diamond [20,23,25].…”

“…To investigate such a phenomenon, 2D cylindrical structures have been considered as depicted on Figure 6. The calculation method is derived from 1D one and is also described in details in ref [24]. Using this method it is possible to compare the breakdown voltage of a 1D structure with the same structure (i.e.…”

Design of Diamond Power Devices: Application to Schottky Barrier Diodes

“…The cathode with Schottky boundary conditions is defined on top of the drift layer and the anode with ohmic boundary conditions at the bottom of the structure. The expected BV of this 1D drift layer design is BV1D = 1070 V as estimated by 1D analytical modelling [49]. Cross-sectional view of the simulated diodes for a breakdown voltage design of 1.07 kV.…”

“…Thus, the termination efficiency depicted in Figure 10a reaches 93% of the 1D BV at 300 K when using a single FMR with parameters W s = 0.15 µm and W FMR = 2 µm. This termination efficiency drops to 79% at 500 K. However, this observation needs to be mitigated by the fact that the BV is normalized by the 1D analytical BV at 300 K. In fact, the analytical model does not take into account the temperature dependence of the impact ionization coefficients [49]. Figure 10b shows the BV improvement as a function of the ring spacing W s normalized to the BV of the device without edge termination for 300 K and 500 K. One can notice that the optimum spacing between the first floating ring and the cathode, which is W s = 0.15 µm, induces a high stress on the fabrication process and lithography.…”