Heat Transfer Macromodels for MEMS Devices with 3D Geometries
Che-Chia Yu and Yao-Joe Yang
Department of Mechanical Engineering, National Taiwan University, TW
Keywords: Model Order Reduction, MOR, Heat Transfer, FEM, FDM, System-level simulation, Macromodel
There are numerous heat transfer applications in MEMS, such as thermal actuating, uncooled infrared sensing, chip cooling, temperature sensing, PCR, and so on. Most of the applications need feedback loops for precise control or actuation, and thus require compact but accurate heat transfer models for system-level modeling and simulation. The typical approach for creating heat-transfer compact models (macromodels) is to use lumped-element methods . For example, a lumped constant heat capacity can be used to represent an average heat capacity for a complex geometry; lumped heat resistors can be used to account for each energy leakage mechanism, including conduction, convection, and radiation. Although this approach significantly simplifies complex heat transfer systems, it required many costly FEM (or FDM) simulations to extract lumped heat capacity and lumped heat resistors, and the accuracy of lumped-element models is detrimentally affected by the complexity of original geometries.
In this work, we implemented a 3-D FDM heat transfer solver, and demonstrated that the numerical models created by FDM/FEM heat transfer solvers can be transformed into macromodels using an Arnoldi-based model order reduction technique. Because the macromodels are generated from the FEM/FDM approximation of complex geometries, they preserve the original geometric characteristics. Also, since the order of macromodels is much less than original FEM/FDM models, the total computational time is significantly reduced by about 2-3 order-of-magnitude. This performance improvement thus makes the macromodels compatible for system-level or circuit simulations, which is essential for overall performance prediction.
NSTI Nanotech 2003 Conference Technical Program Abstract