A model for static and dynamic thermal analysis of thin film MEMS structures including the thermal conductivity of the surrounding gas

In this work an analytical model for static and dynamic thermal analysis of heated thin bridges, membranes or cantilevers is presented. The analysis includes the thermal conductivity of the surrounding gas, which cannot be neglected in most MEMS devices. The model is based on Laplace transformation of the heat equations and on the Thermal Quadrupole Method. A one-dimensional approximation using these methods results in practical sets of equations that can be roughly evaluated by hand for feasibility studies of a design. Further evaluation can be done by some basic matrix operations, e.g. analytically by Mathematica or numerically using MATLAB. Plots of these functions can provide the designer with insight on the thermal behavior of the structure, without the use of finite element calculations.