New Technique Accurately Measures How 2D Materials Expand When Heated

Understand thermal expansion via the coupled effect of temperature and substrate on phonon modes. Credit: Scientists progress (2022). DOI: 10.1126/sciadv.abo3783

Two-dimensional materials, made of a single layer of atoms, can be packed together more densely than conventional materials, so they could be used to make transistors, solar cells, LEDs and other devices that work faster and perform better.

One issue holding back these next-gen electronics is the heat they generate when in use. Conventional electronics typically reach around 80 degrees Celsius, but the materials in 2D devices are so dense in such a small area that the devices can get twice as hot. This increase in temperature can damage the device.

This problem is compounded by the fact that scientists do not fully understand how 2D materials expand as temperatures increase. Because materials are so thin and optically transparent, their coefficient of thermal expansion (TEC) – the material’s tendency to expand as temperatures increase – is nearly impossible to measure using standard approaches.

“When people measure the coefficient of thermal expansion of certain bulk materials, they use a scientific ruler or a microscope because with a bulk material you have the sensitivity to measure them. The challenge with a 2D material is that we don’t can’t really see them, so we have to turn to a different type of ruler to measure TEC,” says Yang Zhong, a graduate student in mechanical engineering.

Zhong is a co-lead author of a research paper that demonstrates such a “leader.” Rather than directly measuring how the material expands, they use laser light to track the vibrations of the atoms that make up the material. Taking measurements of a 2D material on three different surfaces or substrates allows them to accurately extract its coefficient of thermal expansion.

The new study shows that this method is very accurate, obtaining results that match the theoretical calculations. The approach confirms that the TECs of 2D materials lie in a much narrower range than previously thought. This information could help engineers design next-generation electronic components.

“By confirming this tighter physical range, we give engineers great hardware flexibility to choose the bottom substrate when designing a device. They don’t need to design a new bottom substrate just to alleviate thermal stress. We believe that this has very important implications for the electronics device and packaging community,” says co-lead author and former mechanical engineering graduate student Lenan Zhang SM ’18, Ph.D. ’22, who is now a research scientist.

Co-authors include lead author Evelyn N. Wang, Ford Professor of Engineering and head of MIT’s Department of Mechanical Engineering, and others from MIT’s Department of Electrical and Computer Engineering and the Department of Mechanical Engineering and energy from the University of Southern Science and Technology in Shenzhen, China. The research is published in Scientists progress.

Vibration measurement

Because 2D materials are so small (a few microns perhaps), standard tools are not sensitive enough to directly measure their expansion. Additionally, the materials are so thin that they must be bonded to a substrate such as silicon or copper. If the 2D material and its substrate have different TECs, they will expand differently as temperatures increase, causing thermal stress.

For example, if a 2D material is bonded to a substrate with a higher TEC, when the device is heated, the substrate expands more than the 2D material, which stretches it. This makes it difficult to measure the actual TEC of a 2D material since the substrate affects its expansion.

The researchers overcame these problems by focusing on the atoms that make up the 2D material. When a material is heated, its atoms vibrate at a lower frequency and move apart, causing the material to expand. They measure these vibrations using a technique called micro-Raman spectroscopy, which involves striking the material with a laser. Vibrating atoms scatter laser light and this interaction can be used to detect their vibrational frequency.

But when the substrate expands or compresses, it impacts how the atoms in the 2D material vibrate. The researchers needed to decouple this substrate effect to focus on the intrinsic properties of the material. To do this, they measured the vibrational frequency of the same 2D material on three different substrates: copper, which has a high TEC; fused silica, which has a low TEC; and a silicon substrate dotted with tiny holes. Since the 2D material hovers above the holes in this last substrate, they can perform measurements on these tiny areas of freestanding material.

The researchers then placed each substrate on a thermal stage to precisely control the temperature, heated each sample and performed micro-Raman spectroscopy.

“By performing Raman measurements on the three samples, we can extract something called the temperature coefficient which depends on the substrate. Using these three different substrates, and knowing the TECs of fused silica and copper, we can extract the TEC intrinsic to hardware 2D,” says Zhong.

A curious result

They performed this analysis on several 2D materials and found that they all matched the theoretical calculations. But the researchers saw something they didn’t expect: 2D materials fell into a hierarchy based on the elements that make them up. For example, a 2D material that contains molybdenum always has a higher TEC than one that contains tungsten.

The researchers dug deeper and learned that this hierarchy is caused by a fundamental atomic property known as electronegativity. Electronegativity describes the tendency of atoms to pull in or pull out electrons when they bond. It is listed on the periodic table for each element.

They found that the greater the difference between the electronegativities of the elements that form a 2D material, the lower the coefficient of thermal expansion of the material will be. An engineer could use this method to quickly estimate the TEC for any 2D material, rather than relying on complex calculations that usually have to be handled by a supercomputer, Zhong says.

“An engineer can simply look up the periodic table, get the corresponding materials’ electronegativities, plug them into our correlation equation, and within a minute he can have a reasonably good estimate of the TEC. That’s very promising for quick selection of materials for engineering applications,” says Zhang.

In the future, the researchers want to apply their methodology to many other 2D materials, perhaps by creating a database of TECs. They also want to use micro-Raman spectroscopy to measure TECs of heterogeneous materials, which combine multiple 2D materials. And they hope to uncover the underlying reasons why the thermal expansion of 2D materials is different from that of bulk materials.