Nonlinear heat-transfer macromodeling for MEMS thermal devices

In this paper, we present a nonlinear heat-transfer macromodeling technique using the trajectory piecewise-linear model-order-reduction (TPWLMOR) method. A 3D nonlinear heat-transfer model, which is capable of accounting for the temperature-dependent material properties as well as the radiation effect, is implemented using the finite-difference method (FDM). The numerical models generated by the FDM are reduced into compact models using the TPWLMOR technique, which is based on the concept of a piecewise-linear approximation and an Arnoldi-based model-order-reduction (MOR) algorithm. Nonlinear macromodeling case studies of different MEMS thermal devices are demonstrated using the TPWLMOR technique. The calculated steady and transient characteristics of the thermal devices are discussed. In terms of computational cost, the TPWLMOR models are at least 2 orders of magnitude faster than the original nonlinear full-meshed models with a negligible compromise in accuracy. The simulated results by the TPWLMOR models are also verified with the experimentally measured results.