Model order reduction of linear and nonlinear 3D thermal finite-element description of microwave devices for circuit analysis

Electrothermal models of power devices are necessary for the accurate analysis of their performances. For this reason, this article deals with a methodology to obtain an electrothermal model based on a reduced model of a 3D thermal finite-element (FE) description for its thermal part and on pulsed electrical measurements for its electrical part. The reduced thermal model is based on the Ritz vector approach, which ensures a steady-state solution in every case. An equivalent SPICE subcircuit implementation for circuit simulation is proposed and discussed. An extension of the method to a nonlinear reduced model based on the Kirchoff transformation is also proposed. The complete models have been successfully implemented in circuit simulators for several HBT or PHEMT device structures. Many results concerning devices and circuits are presented, including simulation of both the static and dynamic collector-current collapse in HBTs due to the thermal phenomenon. Moreover, the results in terms of the circuit for an X-band high-power amplifier are also presented. As for the nonlinear approach, results concerning an homogeneous structure is given.