Nonlinear Thermal Reduced Model for Power Semiconductor Devices

The challenge in terms of accurate prediction of electrical behavior, reliability and thermal management of semiconductor power devices goes through the coupling of multi physics analysis and especially through the coupling of nonlinear thermal models with nonlinear electrical models. In order to obtain a precise nonlinear thermal model which can be implemented as an equivalent SPICE (simulation program integrated circuits especially) subcircuit in circuit simulators, we present a methodology based on a model order reduction technique applied to a three dimensional finite element thermal description. This reduction method is based on the Ritz vector approach. In order to take into account the nonlinear thermal properties of materials, an extension of the method based on the Kirchoff transformation and an interpolation formula is proposed. This method, theoretically suitable only for homogeneous structures, exhibits in practice a very good accuracy for heterogeneous structures. Another improvement in the nonlinear transient response relies on the self consistent calculation of a coefficient related to the thermal conductivity approximation law. Thus, obtaining directly in time domain a nonlinear thermal reduced model for inhomogeneous structure is possible. The complete model has been successfully implemented in circuit simulator for several power devices and for various nonlinear materials such as GaAs, GaN or silicon. The nonlinear behavior has been validated on a wide range of input power and baseplate temperature. The influence of the interpolation formula is discussed for strongly nonlinear materials. Thermal infrared and electrical measurements have been performed to validate the simulation results