The 3ω-method (3 omega method) or 3ω-technique, is a measurement method for determining the
thermal conductivities of bulk material (i.e. solid or liquid) and thin layers. The process involves a metal heater applied to the sample that is heated periodically. The temperature oscillations thus produced are then measured. The thermal conductivity and
thermal diffusivity
In thermodynamics, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It is a measure of the rate of heat transfer inside a material and has SI, SI units of m2/s. It is an intensive ...
of the sample can be determined from their frequency dependence.
The process was first published by David Cahill and
Robert Otto Pohl in 1987 in a paper titled "Thermal Conductivity of Amorphous Solids above the Plateau" in
''Physical Review''.
Theory
The 3ω-method can be accomplished by depositing a thin metal structure (generally a wire or a film) onto the sample to function as a resistive heater and a
resistance temperature detector
Resistance thermometers, also called resistance temperature detectors (RTDs), are sensors used to measure temperature. Many RTD elements consist of a length of fine wire wrapped around a heat-resistant ceramic or glass core but other construction ...
(RTD). The heater is driven with AC current at frequency ω, which induces periodic joule heating at frequency 2ω (since
) due to the oscillation of the AC signal during a single period.
There will be some delay between the heating of the sample and the temperature response which is dependent upon the thermal properties of the sensor/sample. This temperature response is measured by logging the amplitude and
phase delay
In signal processing, group delay and phase delay are functions that describe in different ways the delay times experienced by a signal’s various sinusoidal frequency components as they pass through a linear time-invariant (LTI) system (such as ...
of the AC voltage signal from the heater across a range of frequencies (generally accomplished using a
lock-in-amplifier).
Note, the
phase delay
In signal processing, group delay and phase delay are functions that describe in different ways the delay times experienced by a signal’s various sinusoidal frequency components as they pass through a linear time-invariant (LTI) system (such as ...
of the signal is the lag between the heating signal and the temperature response. The measured voltage will contain both the fundamental and third harmonic components (ω and 3ω respectively), because the Joule heating of the metal structure induces oscillations in its resistance with frequency 2ω due to the
temperature coefficient of resistance
A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature. For a property ''R'' that changes when the temperature changes by ''dT'', the temperature coefficient α is def ...
(TCR) of the metal heater/sensor as stated in the following equation:
:
,
where ''C''
0 is constant. Thermal conductivity is determined by the linear slope of Δ''T'' vs. log(''ω'') curve. The main advantages of the 3ω-method are minimization of radiation effects and easier acquisition of the temperature dependence of the thermal conductivity than in the steady-state techniques. Although some expertise in thin film patterning and microlithography is required, this technique is considered as the best pseudo-contact method available.
References
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Materials testing
Heat conduction