// Blog September 13, 2023

Importance of Knowing Thin Film Thermal Expansion/Contraction

If a thin film and its substrate have a significantly different coefficient of thermal expansion (CTE), stress can be introduced when one material expands/contracts more rapidly when heated/cooled [1] [2]. Figure 1 depicts a scenario where the change in temperature causes the thin film to expand more than the substrate so when it is deposited, the thin film thermal expansion is restricted by the substrate and causes stress within the film. Often, the thin film is deposited on the substrate at a relatively high temperature, and if their CTEs are not accounted for, the thin film can be put under stress as both materials cool and contract [1]. This is why when working with thin films, knowing its CTE is important, even when the film is anticipated to remain at ambient temperature during its application. This stress can impact a thin film’s yield strength and hardness. If the stress is substantial enough, it can cause film deformation or even mechanical failure [1].

The figure is split into 3 main sections: The first shows a thin film and substrate with the same initial length.

The second shows the free expansion of the thin film and substrate. In the case shown, the film has greater thermal expansion than the substrate, so it is much longer. 

The third shows a case where the film is deposited on the substrate and is restricted from expanding. Arrows show the stress is localized to the thin film.

Figure 1. Thin Film Stress Cause by Temperature Change

Thin Film Technology

Thin films are strips of material that range from microns to nanometers in thickness. They are deposited on a bulk material, referred as the substrate, to enhance the electrical, optical, mechanical, or chemical properties of the substrate. Thin film is a rapidly growing field due to its applications in corrosion prevention, electronics, photovoltaics, optics, and biomedics [1]. One major impediment is that thin films do not share the same properties as that of a bulk material with the same chemical composition [1] [2] [3]. A thin film’s variation in properties is a result of its small thickness, large surface area to volume ratio, and unique physical structure which stems from the fabrication method [2] [3].

The term “free-standing thin film” is used when the film is not designed to attached to a substrate or any other support material. They are used independently of a substrate and are used for their own properties instead of enhancing the properties of a substrate. Although free-standing thin films are far less common, they do have uses as filters, permeable membranes, and sorbents, or in integrated circuits and micromechanical systems [4]. When designing technology that incorporates free-standing thin films, it is important to know the CTE, along with transition points and melting point, to determine the temperature limit at which can be used in.

Thin Film CTE

The CTE of a bulk material does not depend on the materials shape, or size [1] [2]. Meanwhile, the CTE of a thin film depends on the film’s thickness and fabrication method. The CTE of some thin films increase with an increasing thickness, while others have been observed to decrease. Shown in Figure 2, the CTE of an aluminium (Al) thin film increased from 18.23×10-6 to 29.97×10-6/°C when the film thickness was increased from 0.3 to 1.7 µm.[2]

A plot taken from reference 2 showing increasing CTE with thickness of an aluminum film, with an approximately linear trend from 18-30 ppm in the thickness range of 0.3 micrometers to 1.7 micrometers.

Figure 2. An Aluminum Film’s CTE Increasing with Thickness [2]

Meanwhile, as shown in Figure 3, the CTE of a titanium (Ti) film decreased from 21.21×10-6 to 9.04×10-6/°C when the film thickness increased from 0.1 to 0.3 µm. For reference, the CTE of bulk Al and Ti are 23×10-6/°C and 9.5×10-6/°C, respectively. This data was collected from 30 to 90°C, and demonstrates that depending on the thin film’s thickness, its CTE can be less than or greater than that of a bulk material with the same chemical composition [2].

A plot taken from reference 2 shows decreasing CTE with thickness of a titanium film, with a markedly non-linear trend from 21-9ppm in the thickness range of 0.1 micrometers to 0.3 micrometers.

Figure 3. A Titanium Film’s CTE Decreasing with Thickness [2]

Rigaku TMA8311 and the Tensile Loading Attachment

Rigaku is a lab instrument manufacturing company that is quickly gaining popularity in North America due to their high-quality Japanese engineering. The Rigaku TMA8311, shown in Figure 4, can be used to measure various thermomechanical properties such as thermal expansion/contraction, softening temperature, and glass transition temperature. It does so by applying a load to the sample and measuring its elongation/contraction when heated/cooled. The load can be applied by modes of compression, penetration, or tension, and can operate from -150 to 1500°C, depending on the configuration. Fibrous, metallic, ceramic, and polymeric samples can all be tested in an atmosphere of air, nitrogen, or argon.

An image showing the Rigaku 8311 thermomechanical analyzer. The instrument is pale grey and dark blue, with blue lettering spelling "Thermo plus EVO2" on the front of the device.

Figure 4. Rigaku TMA8311

Although the compression and penetration modes of the TMA8311 have their own individual strengths none of these modes can measure thin film expansion, and this is where the tensile loading attachment (TLA) outclasses the rest. There is an old saying that goes something along the lines of “you can’t push a rope” and the same goes for thin films. Due to their slenderness, it is extremely hard to measure their expansion by compression, as the slightest axial compressive load will cause a thin film to bend before it can elongate. The TLA takes advantage of an axial tensile load to measure the thin films elongation.

A translucent yellow film is suspended between two metal clamps as part of the tensile loading attachment for the Rigaku TMA 8311

Figure 5. Close Up View of a Kapton Thin Film in the TLA

The TLA can be seen below in Figure 5, and is compatible with wires, thin plates, and thin films that have a thickness of 0.01 to 0.2 mm. Equipped with the TLA, the TMA8311 can measure the change of the tensile force as the material expands/contracts from temperature change, and then convert it to an increase/decrease of length [5]. The CTE can then be calculated based on the length at a reference temperature, which is usually 20 or 25°C. Most often, a constant load is applied, however, there is also the option to constantly increase the load at a set rate (constant rate loading) or apply and relax the load at constant amplitude and intervals (cyclic sinusoidal loading) [5].

How Does the TLA Compare?

When compared to other elongation measuring methods, the TLA can hold its own. When testing a bulk Al sample (5mm width, 1 mm thickness flat dog bone shape) from 30 to 90°C, the CTE was recorded to be 22.93×10-6/°C. This aligns with value of 23×10-6/°C that was found in literature [2]. Shown in Figure 6, the CTE of Kapton HN film from -14 to 38°C was recorded to be 18.61×10-6/°C using the TLA, and the CTE reported by DuPont is 20×10-6/°C. This gives a difference of 6.7% and this is likely a result of the different testing methods. DuPont followed ASTM D-696-91, which is for the elongation of plastics in a horizontal dilatometer, while the TLA follows ASTM E1824-19, which is specifically for measuring the elongation of thin films in tension.

A plot illustrating that the recorded value of Kapton (18.6 ppm/°C) )is slightly lower than the value claimed by DuPont (20 ppm/°C) - which may be due to measurement method differences or thickness effects. The experimental data was extremely repeatable, with a recorded relative standard deviation (RSD) of 0.6% across 3 trials.

Figure 6. Kapton’s CTE as Recorded by the TLA and DuPont’s Value for Reference

A typical Elongation-Temperature plot created by the TMA8311 can be seen below in Figure 7. The specific sample used to create this plot has a thermal history effect that caused two transition points which are likely crystal polymorphism.

A TMA plot showing the tensile thermal expansion of Kapton after a preheat cycle. Two solid-state transitions are evident at 51.4°C and 66.9°C, these are likely attributable to crystal polymorphism.

Figure 7. Thermal Elongation (dL) of a Thin Film

If you have any questions on the thermomechanical analysis (TMA) of thin films, or want to inquire about testing capabilities, contact us here. Are you interested in learning more about thin film thermal properties or TMA? Check out this Trident™ application highlight on measuring thin film conductivity or these blog posts on When to Use TMA,  Measuring CTE of Polymers by TMA, or TMA in Metallurgy.

For a more detailed example test report, check out our example report here.


[1]E. Acosta, “Thin Films [Working Title],” in Thin Films/Applications, IntechOpen, 2021, pp. 1-21.
[2]W. Fang and C.-Y. Lo, “On the thermal expansion coefficient of thin films,” Sensors and Actuators, pp. 310-314, 2000.
[3]K. Chopla, “Thin Film Device Applications,” in Thin Film Technology: An Introduction, Boston, Springer, 1983, pp. 1-54.
[4]J. Saleem, M. Z. K. Baig, A. S. Luyt, R. A. Shakoor, A. Zekri and G. McKay, “Free-standing polypropylene porous thin films using energy efficient coating technique,” Energy Reports, vol. 9, pp. 31-39, 2023.
[5]S. Yamaguchi and C. Lani, “Technical know how in thermal analysis measurement -Thermomechanical analysis-,” The Rigaku Journal, vol. 26, pp. 16-20, 2010.

Keywords: Thermomechanical Analysis, Coefficient of Thermal Expansion, Thin Film, Tensile Loading, Thermal Stress, Rigaku TMA8311

About the Author

An image of a man smiling slightly at the camera. He wears a red shirt and stands in front of a white wall. Alex Mann is a laboratory technologist at the Thermal Analysis Lab division of C-Therm Technologies. He holds a Bachelor of Science in Engineering (Chemical), and a Master of Science in Engineering (Chemical) from the University of New Brunswick. His previous research area was wastewater treatment and its applications in land-based aquaculture, specifically sludge dewatering and incineration.



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