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

An fully analytical spectral domain decomposition approach to solution of the nonlinear time-dependent heat diffusion equation in complex volumes is introduced. Its application to device/circuit level electro-thermal simulation on CAD timescales is illustrated. The full treatment in coupled electro-thermal CAD of thermal nonlinearity due to temperature dependent diffusivity is described. Thermal solutions are presented in the form of thermal impedance matrix expressions for thermal subsystems. These include double Fourier series solutions for rectangular multilayers, which are an order of magnitude faster to evaluate than existing semi-analytical Fourier solutions based on DFT-FFT. They also include double Fourier series solutions for arbitrarily distributed volume heat sources and sinks, constructed without use of Green´s function techniques, and for rectangular volumes with prescribed fluxes on all faces. These analytical solutions allow treatment of arbitrary device structures without invoking conventional numerical methods. They provide minimal boundary condition independent compact thermal models, allowing CAD timescale coupled electro-thermal solution for complex systems, without requiring lumped element RC network extraction or node reduction. The time-independent thermal resistance matrix description of device structure is illustrated by a fully physical, coupled electro-thermal study of the interaction of substrate thickness and surface convection in power HEMTs. The thermal time-dependent implementation is illustrated by circuit level harmonic balance simulation of a 3×3 MMIC amplifier array