Parameter extraction from three omega measurements

C. Raudzis, F. Schatz and D. Wharam
Corporate Research, Robert Bosch GmbH, DE

Keywords: MEMS, thermal conductivity, testing, parameter extraction

Abstract:
Automated wafer level testing of MEMS requires methods to measure geometry and material related parameters by purely electrical means. The three omega method to measure the thermal conductivity seems to be appropriate for this task. It is purely electrical, non-destructive and compatible to typical MEMS processes. Furthermore, it permits the determination of multiple parameters: while the original three omega method as presented by Cahill et al. is capable to measure the thermal conductivity and thermal capacity of bulk material, a modification of this method can be used to measure also the thermal conductivity of a thin film on a substrate. However, these methods make high demands on the device under test, that are generally not fulfilled at typical MEMS. Recently, Kim et al. and Borca-Tasciuc et al. have proposed generalized mathematical models for the three omega method on multilayer systems, considering finite substrate thickness, anisotropic thermal conductivity, thermal boundary resistances and finite heater capacitance. We have adapted these models to the requirements in MEMS testing, considering additional effects such as covering layers on top of the heater or thermal conduction through the air. We test our model by extracting physical properties of a well-known multilayer system by means of least square fitting. By using an extended frequency range for the measurement we are able to extract a wide range of physical properties simultaneously. The results are in good agreement with literature values and with the results of other measurements. The calculated temperature oscillations are in excellent agreement with the measured data, justifying the model assumptions and making the method best suited for MEMS testing.

NSTI Nanotech 2003 Conference Technical Program Abstract