Thermal Conductivity

by Dr. Patrick Hopkins

Thermal conductivity (commonly abbreviated using k, λ, or κ) is the ability of a material to transfer (or “conduct”) heat. In short, a material with high thermal conductivity will conduct heat much more efficiently than a material with a low thermal conductivity. Therefore, if you want to prevent your hand from getting too hot when holding a cup of coffee, make sure the coffee cup is made out of a material with a low thermal conductivity!

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How is Thermal Conductivity Defined?

Thermal conductivity, k, is the quantity that relates the heat flux through a material, Q, to the temperature gradient established across a material, dT/dx:

Q = -k dT/dx

This equation, known as “The Fourier Law”, predicts the temperature difference across some thickness of material in a steady state condition when the temperature is not varying in time. So, if you want to make sure your hand does not get too hot when you are holding your cup of coffee, you can either:

Make the walls of the coffee cup thicker to make sure your hand is further away from the hot coffee (maybe put a handle on the mug, spacing your hand away from the heat source).
Make the walls of the coffee cup out of a lower thermal conductivity material (maybe use a coffee sleeve which is made from porous materials with air pockets, making for very low thermal conductivity walls!).

In the International System of Units, thermal conductivity is expressed using W/m/K (Watts per meter-Kelvin).

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Validated results

SSTR-F measures the thermal conductivity of Corning Pyroceram 9606 and Corning high purity fused silica (HPFS) 7980 to within 5% of their published values.
Additional validation was provided by measuring samples from the same piece of material using the Transient Plane Source technique.
Pyroceram is no longer available from NIST but was measured on similar material to the material that was validated as a Certified Reference Material.
Corning HPFS was procured from a distributor of HPFS 7980 wafers.

	Literature Value	TPS Measurement	SSTR-F Measurement
Pyroceram 9606	4.07 +/- .26	3.95	3.95 +/- 0.2
HPFS 7980	1.38	1.39	1.39 +/- 0.09

Unparalleled reliability

Thermal conductivity measurements: Accuracy +/- 10%, Repeatability +/- 0.5%, Reproducibility +/- 1%
Accurate thermal conductivity measurements of materials in agreement with literature values
With exceptional instrumentation reliability and repeatability, SSTR-F offers unprecedented measurement stability on a daily basis for any user, exemplified by the SSTR-F data shown below. Spread in randomly sampled spots are sample related, not measurement driven.

Source

20 SSTR-F measurements at same spot

20 SSTR-F measurements at random spots

Turnkey testing

Our patented fiber-optic design enables turnkey, automated testing of thermal conductivity.
High-throughput SSTR-F testing of multiple samples facilitates, for example, screening the thermal conductivity of different thin films processed under different conditions
Defects, stresses, compositional differences, and changes in density and microstructure that occur up during film growth result in changes in thermal conductivity, easily and rapidly identified vis SSTR-F

SSTR-F data on 4 different 200 nm dielectric films on silicon with thermal conductivity ranging from ~0.35 W/m/K up to 1.8 W/m/K. SSTR-F allows for easy, rapid and automated identification of different temperature rises based on the thermal conductivity of the different films.

Nanoscale to bulk

Thermal conductivity of nanoscale thin films

SSTR is ideal for your thin film thermal conductivity testing needs.
In addition to measurements of bulk wafers and substrates (source 1, source 2), SSTR has the unprecedented spatial resolution to measure the thermal conductivity of thin films.
For example, SSTR can measure the thermal conductivity of single nanometer thick ALD grown thin films or micron thick AlN films (source).

SSTR measurements on ALD grown ultrathin film amorphous gate dielectrics (compared to TDTR) (source).

SSTR measurements of AlN crystalline thin films.2 SSTR data (temperature rise vs. power) on right for AlN film and silicon wafer control.