banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
A generalized 3ω method for extraction of thermal conductivity in thin films
Rent this article for


Image of FIG. 1.
FIG. 1.

(Color online) (a) Schematic illustration of an experimental test structure used for the 3ω method. A metallic strip with four contact pads serves as the heater and the thermometer. (b) Cross-section in the x-y plane of the temperature profile in the test structure. The silicon substrate is considered semi-infinite, and the heat is assumed to spread out radially forming cylindrical coaxial isotherms in the substrate with the bottom center of the metal strip as the coordinate origin.

Image of FIG. 2.
FIG. 2.

Frequency dependence of the difference in temperature rise between the heater strip and the Si surface for sample b according to Cahill’s model.

Image of FIG. 3.
FIG. 3.

(Color online) Thermal conductivity of SiO2 extracted using Cahill’s vs our model with two different pad structures shown as inset. The theoretical thermal conductivity of SiO2 is ∼1.4 Wm−1K−1 and α TCR is 3.83×10−3 K−1 for Al. The lines connecting the data points are used to guide the eyes.

Image of FIG. 4.
FIG. 4.

Temperature rise extracted from 3ω Cahill model in four-pad configuration (solid, rectangular) and two-pad configuration (solid, triangular), in comparison with the simulated temperature rises of the middle point of the metal strip by numerical software for four-pad heater (open, rectangular) and two-pad heater (open, triangular), respectively

Image of FIG. 5.
FIG. 5.

Comparison between the measured third harmonic voltage signal V 3 ω and the third harmonic component Vz -3 ω corresponding to lateral heat diffusion in the heater strip over wide range of frequencies.

Image of FIG. 6.
FIG. 6.

Comparison of extracted thermal conductivity for the different heater configurations in Table I, using Cahill’s (solid, continuous) vs our model (open, broken).

Image of FIG. 7.
FIG. 7.

Dependence of the heat flow ratio m(ω) on frequency for the different heater configurations in Table I.

Image of FIG. 8.
FIG. 8.

(Color online) Temperature oscillation amplitude along the length of the heater strip at different frequencies. Inset shows a typical temperature development history in one time-cycle at 1 Hz. T = 1/(2f), with T as the heater temperature oscillation period which is half of that for the ac current.


Generic image for table
Table I.

Structure parameters for the experiment


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A generalized 3ω method for extraction of thermal conductivity in thin films