Fully physical time-dependent compact thermal modelling of complex non linear 3-dimensional systems for device and circuit level electro-thermal CAD

An original, fully analytical, spectral domain decomposition approach to co mpact solution of the non linear time-dependent heat diffusion equation in complex volumes, is introduced. Its application to device and circuit level electro-thermal simulation on CAD timescales is illustrated. The first ful l treatment in coupled electrothermal CAD, of thermal non linearity due to temperature dependent diffusivity, is described. Original thermal solutions are presented in the form of analytically exact thermal impedance matrix e xpressions for thermal subsystems. These include double Fourier series solu tions for rectangular multilayers, which are an order of magnitude faster t o evaluate than existing semi-analytical Fourier solutions based on DFT-FFT . They also include double Fourier series solutions for arbitrarily distrib uted volume heat sources and sinks, constructed without the use of Green's function techniques, and for rectangular volumes with prescribed fluxes on all faces. These analytical solutions allow treatment of arbitrary device s tructures without invoking conventional numerical methods. They provide min imal boundary condition independent compact thermal models, allowing CAD ti mescale coupled electrothermal solution for complex systems, without requir ing lumped element RC network extraction or node reduction. The time-indepe ndent thermal resistance matrix description of detailed device structure is illustrated by a fully physical, coupled electro-thermal study of the inte raction of substrate thickness and surface convection in power HEMTs. The t hermal time-dependent implementation is illustrated by circuit level harmon ic balance simulation of a 3x3 MMIC amplifier array.