Thermal modeling of multilayer membranes for sensor applications

Abstract 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.

[1]  N. R. Swart,et al.  Flow-rate microsensor modelling and optimization using SPICE , 1992 .

[2]  G. R. Lahiji,et al.  A batch-fabricated silicon thermopile infrared detector , 1982, IEEE Transactions on Electron Devices.

[3]  F. Völklein,et al.  High-sensitivity radiation thermopiles made of BiSbTe films , 1991 .

[4]  Ernst Obermeier,et al.  A thin-film bolometer for radiation thermometry at ambient temperature , 1990 .

[5]  B. W. Oudheusden,et al.  The thermal modelling of a flow sensor based on differential convective heat transfer , 1991 .

[6]  A. Herwaarden,et al.  Small-size vacuum sensors based on silicon thermopiles , 1991 .

[7]  H. Baltes,et al.  Optimization tool for the performance parameters of thermoelectric microsensors , 1993 .

[8]  Pasqualina M. Sarro,et al.  Thermal sensors based on the seebeck effect , 1986 .

[9]  T. Berlicki,et al.  Thermal thin-film sensors for r.m.s. Value measurements , 1991 .

[10]  B. W. Oudheusden,et al.  Silicon thermal flow sensor with a two-dimensional direction sensitivity , 1990 .

[11]  Henry Baltes,et al.  Model of thermoelectric radiation sensors made by CMOS and micromachining , 1992 .

[12]  H. Baltes,et al.  Analytical 2D-model of CMOS micromachined gas flow sensors , 1991, TRANSDUCERS '91: 1991 International Conference on Solid-State Sensors and Actuators. Digest of Technical Papers.

[13]  S. Crary,et al.  Thermal management of integrated microsensors , 1987 .

[14]  Pasqualina M. Sarro,et al.  Integrated thermopile sensors , 1990 .

[15]  S. B. Crary,et al.  The Finite‐Element Method for Microsensors , 1987 .

[16]  A. W. van Herwaarden,et al.  Integrated true RMS converter , 1986, IEEE Transactions on Instrumentation and Measurement.