THERMAL MODELING OF MULTILAYER MEMBRANES FOR SENSOR APPLICATIONS

Analytical methods and the finite element method (FEM) are employed to model the temperature field in heated multilayer membranes, which are a functional part of many micromachined sensors. Analytical expressions are derived for the one-dimensional stationary temperature distribution in the membrane including an intermediate boundary dividing the membrane into two regions of different material properties. The results of the analytical and FEM calculations are compared. It is found that computer calculations based on the deduced analytical expressions, which require much less computer time and modeling effort than calculations using a FEM code, can be successfully applied in cases of highly symmetrical membrane geometries and heat loads. Otherwise FEM calculations are advantageous in yielding valuable results.