How do two-dimensional materials expand?


Two-dimensional materials, consisting of only one layer of atoms, can be packed together much more densely than conventional materials, so they can be used to make transistors, solar cells, LEDs and other devices that run faster and perform better.

One of the issues with these next-generation electronic devices is the heat they generate when in use. Conventional electronics typically reach about 80 degrees Celsius, but the materials in 2D devices are so densely packed into a small space that the devices can get twice as hot. This increase in temperature can damage the device.

This problem is exacerbated by the fact that scientists do not have a good understanding of how 2D materials expand when temperatures rise. Because the materials are so thin and optically transparent, their coefficient of thermal expansion (TEC)—the tendency of a material to expand when temperatures rise—is nearly impossible to measure using standard methods.

“When people measure the coefficient of thermal expansion of certain mass materials, they use a scientific ruler or a microscope because with bulk matter, you have the sensitivity to measure it. The challenge with a two-dimensional material is that we can’t really see it, so we need to resort to another type of ruler to measure TEC. says Yang Zhong, a graduate student in mechanical engineering.

Zhong is a co-author of a paper demonstrating such a “governor”. Instead of directly measuring how the material is stretched, 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 the coefficient of thermal expansion to be extracted accurately.

The new study showed that this method is highly accurate and achieves results that match theoretical calculations. The approach confirms that TECs for 2D materials lie in a much narrower range than previously thought. This information can help engineers design the next generation of electronics.

“By assuring this narrow material range, we give engineers a great deal of material flexibility to choose a substrate when designing a device. They don’t need to invent a new substrate just for thermal stress relief. We believe this has very important implications for the electronic device and packaging community.” , says co-lead author and former mechanical engineering graduate student Linan Zhang SM ’18, Ph.D. ’22, now a research scientist.

Co-authors include senior author Evelyn N. Wang, Ford Professor of Engineering and chair of MIT’s Department of Mechanical Engineering, as well as others from MIT’s Department of Electrical Engineering and Computer Science and MIT’s Department of Mechanical and Energy Engineering. Southern University of Science and Technology in Shenzhen, China. Research published in Science advances.

Measurement of vibrations

Because 2D materials are so small—perhaps only a few microns in size—standard instruments are not sensitive enough to measure their expansion directly. In addition, 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 when temperatures rise, causing thermal stress.

For example, if a 2D material is bonded to a substrate with a higher energy consumption (TEC) rate, when the device is heated, the substrate will expand more than the 2D material it is stretching. This makes it difficult to measure the actual TEC of a 2D material because the substrate affects its expansion.

The researchers got around these problems by focusing on the atoms that make up the two-dimensional matter. When a substance is heated, its atoms vibrate at a lower frequency and move away from each other, causing the material to expand. They measure these vibrations using a technique called Raman microspectroscopy, which involves hitting the material with a laser. The vibrating atoms scatter the laser light, and this interaction can be used to detect the frequency of their vibrations.

But as the substrate is stretched or compressed, it affects how the atoms of the two-dimensional material vibrate. The researchers needed to separate out this substrate effect to focus on the material’s intrinsic properties. They did this by measuring the vibrational frequency of the same 2D material on three different substrates: copper, which has a high TEC content; fused silica, which has a low electrical energy consumption ratio; A silicone substrate with small holes. Because the 2D material hovers over the holes on the latter substrate, it can perform measurements on these small regions of the freestanding material.

The researchers then placed each substrate on a thermal stage to precisely control the temperature, heat each sample, and perform microscopic Raman spectroscopy.

“By performing Raman measurements on the three samples, we can extract something called a temperature coefficient that depends on the substrate. Using these three different substrates, and knowing the TECs for fused silica and copper, we can extract the intrinsic TEC for 2D,” Chung explains.

Strange result

They performed this analysis on several 2D materials and found that they all match the theoretical calculations. But the researchers saw something they didn’t expect: the two-dimensional materials fell into a hierarchy based on the elements that made them up. For example, a 2D material containing molybdenum will always have more TEC than one containing tungsten.

The researchers dug deeper and learned that this hierarchy results from a fundamental atomic property known as electronegativity. Electronegativity describes the tendency of atoms to withdraw or withdraw electrons when they bond. It is listed on the periodic table for every element.

They found that the greater the electronegativity difference between the elements that make up a two-dimensional material, the lower the material’s coefficient of thermal expansion. An engineer can use this method to quickly estimate the typical electric consumption (TEC) rate for any two-dimensional material, rather than relying on complex calculations that normally have to be crunched by a supercomputer, Zhong says.

“An engineer can just look up the periodic table, get the electronegativity of the corresponding materials, plug it into our correlation equation, and within a minute can get a reasonably good estimate of the TEC. This is very promising for rapid material selection for engineering applications,” Zhang says.

Going forward, the researchers want to apply their methodology to many more 2D materials, possibly building a database of TECs. They also want to use Raman microspectroscopy to measure the TECs of heterogeneous materials, which combine several 2D materials. They hope to find out why the thermal expansion of two-dimensional materials differs from that of bulk materials.

This work is funded in part by the Centers for Mechanical Engineering Research and Education at MIT and Southern University of Science and Technology, the Centers for Materials Science and Engineering Research, the US National Science Foundation, and the US Army Research Office.



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