2D Physical Modelling of Semiconductor Equations for Verification of 1D Lumped-Charge Model of Bipolar Power Devices

Abstract

The paper demonstrates a finite-element method(FEM) simulation model of semiconductor devices operation.Classical semiconductor equations employing drift, diffusionand generation-recombination transport of charge carriers areestablished and variational forms for FEM assembly are derivedin detail, including a basic voltage and current boundary conditions.Mathematically, a system of mutually coupled nonlinearequations need to be solved, which requires extensive use ofnonlinear iteration solver. The derived model was coded inPython by strict use of open source tools, mainly grouped aroundFEniCSx project. Graphic output figures and characteristics forbasic semiconductor structures are presented to demonstrate thefunctionality of model.An ultimate goal of presented effort is derivation and verificationof simplified semi-analytical model of Insulated-gate bipolartransistor (IGBT), including precise transient behavior.This kind of model should be calibrated by use ofmeasurement-obtained data, so the qualitative behavior of devicephysics at reasonable computational cost is of primary interestof presented FEM model as opposed to commercial devicedevelopment tools aiming at precise quantitative outputs; whichneed to be experimentally calibrated even so.As an additional step to simplified one-dimensional modelusability verification, results of unusual way of experimentalestimation of minority-carrier excess charge within power bipolartransistor collector and base during on-state is presented andcompared to simulation result.