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
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
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