Test Service for Measuring the Thermal Conductivity of Thin Films
By Ethan Garnier, Electrical Engineer-In-Training
Jan 6, 2025
Thermal Conductivity Measurement
The measurement of thermal conductivity is accomplished through both steady-state and transient measurement techniques. Transient techniques measure the thermal conductivity by observing the temperature gradient in a material as a function of time or frequency. This traditionally allows for much faster testing times, proving them to be more favorable when compared to their steady-state counterparts. Examples of transient techniques include transient hot wire (THW), transient plane source (TPS), and modified transient plane source (MTPS). Each of the previously mentioned measurement techniques are time-domain methods, where the heating of the sample is measured as a function of time. In contrast, the 3-Omega Method is a frequency-domain technique that leverages a relationship between temperature and frequency to determine the thermal conductivity of a sample.
How Does the 3-Omega Method Work?
The 3-Omega Method uses a small, electrically conductive film in intimate contact with a sample as both a heater and a thermometer, which will be referred to as the heater element throughout this text. Figure 1 shows a 2D cross-section of a heater element with width 2b deposited on a sample with thickness t.
An alternating current (AC) of known angular frequency ω is applied across the heater element to induce joule heating at frequency 2ω. This joule heating causes thermal oscillations at the same frequency to heat the sample in contact with the element. The effect of these thermal oscillations on heating the sample can then be measured by observing the change in resistance of the heater element, as the resistance of an electric conductor is a function of its temperature. These resistance oscillations, also at frequency 2ω, multiplied by the original AC signal at frequency ω cause a voltage response at 3ω to develop across the heater element. This voltage response at frequency 3ω demonstrates a relationship to the thermal properties of the sample when modeled as a function of the excitation frequency ω. As such, it is the measurement of this 3ω signal across multiple frequencies which allows the 3-Omega Method to determine the thermal conductivity of the sample.
Thin Film Measurement with the 3-Omega Method
A major selling point of the 3-Omega method is its usefulness in measuring the thermal conductivity of thin film materials. Thin films present challenges in thermal conductivity testing due to their small sizes, different properties when compared to their bulk counterparts [1], and the various processes required for fabrication. Traditional methods of thermal conductivity testing have difficulty with thin films primarily due to the size of the samples. Their small size makes it difficult to mechanically test without damaging the sample, in addition to making the presence of error caused by thermal boundary resistance (TBR) much greater when using contact measurement techniques. Furthermore, when a thin film exhibits anisotropic properties, testing must be performed in multiple directions, and for a material that is already difficult to test this becomes very challenging. The 3-Omega Method avoids these obstacles through the design of the heater element used for contact measurement and its frequency-domain approach. Examples of two commonly used heater configurations to be deposited onto a thin film sample, the 2-wire and 4-wire configuration, can be seen in Figure 2 where I+/- and V+/- indicate electrical connections to the system.
When designing this heater element, its total area can be made smaller than or equal in size to the sample being measured. Additionally, the line width, 2b, of the heater can be made thin to provide two-dimensional heat flow to measure anisotropic properties. Finally, the heater can be deposited directly onto the sample to mitigate the impact of TBR on results. As a result, the 3-Omega Method solves many of the problems faced by other techniques in the measurement of thin films through the clever design of its heater element. In addition to the problems solved through heater design, the 3-Omega Method also allows for the penetration depth of thermal oscillations, λ, to be tightly controlled. The penetration depth λ is a function of the AC signal frequency applied across the heater [2]. As such, samples of arbitrarily small thicknesses, as well as multi-layered samples, may be tested given that an appropriate test frequency is used. However, care must be taken to ensure thermal oscillations do not penetrate past the sample of interest as to ensure only the sample’s thermal properties are being measured. The diagram in Figure 3 visualizes this with two examples, one where λ stays within the sample, and another where λ penetrates the underlying substrate.
Advantages of the 3-Omega Method
- Rapid testing times.
- Versatile testing method.
- Can be used to measure thin films and bulk materials.
- Solves many of the issues other transient techniques encounter when testing thin films.
- Design of heater element tailored to test specific samples.
- Ability to modulate penetration depth of thermal oscillations into sample.
- Enables testing of thin films and multilayered structures.
- Reduced radiative losses at high temperatures.
- A small sample area under heater element minimizes the area contributing to radiation heat loss.
- Radiation error found to be a function of thermal penetration depth [1]; thus, larger surface areas can still be tested via the 3-Omega Method by adjusting AC signal frequency ω accordingly.
Challenges of the 3-Omega Method
- Construction and deposition of heater elements on sample.
- Requires special fabrication techniques, photolithography traditionally used.
- Heater must be deposited such that it is in intimate contact with sample.
- Heater line width and thickness must be sufficiently small compared to thickness of sample and penetration depth of thermal wave for mathematical model assumptions [2].
Conclusion
The 3-Omega Method is recommended by C-Therm as an alternative method for measuring the thermal conductivity of thin films. The method’s ability to circumvent traditional pain points of thin film testing through clever contact heater design and AC frequency relationship make it a viable option for those in need of thin film thermal conductivity testing.
Testing Services
Thermal Analysis Labs (TAL) offers the 3-Omega Method as a contract testing service. If interested, you can contact the lab by email at info@thermalanalysislabs.com, by phone at +1 (506) 457-1515, or by filling out the form on this page.
References
[1] R. G. Bhardwaj and N. Khare, “Review: 3-w Technique for Thermal Conductivity Measurement—Contemporary and Advancement in Its Methodology,” Int J Thermophys, vol. 43, no. 9, p. 139, Jul. 2022, doi: 10.1007/s10765-022-03056-3.
[2] D. G. Cahill, “Thermal conductivity measurement from 30 to 750 K: the 3ω method,” Review of Scientific Instruments, vol. 61, no. 2, pp. 802–808, Feb. 1990, doi: 10.1063/1.1141498.
About the Author
Ethan Garnier is an Electrical Engineer-in-Training at C-Therm Technologies. He recently graduated from the University of New Brunswick with a Bachelor of Science in Software Engineering and is currently pursuing a Masters of Science in Electrical and Computer Engineering at the University of New Brunswick. He has held previous roles in software development and his current focus at C-Therm is on the 3-Omega Method of measuring thermal conductivity.