How “2D” materials expand | MIT News

Composed of just a single layer of atoms, two-dimensional materials can be packed more densely than traditional materials, so they could be used to make transistors, solar cells, LEDs, and other devices that run faster and perform better.

One problem holding back these next-generation electronics is the heat they generate during operation. Conventional electronics typically reach around 80 degrees Celsius, but the materials in 2D devices are so densely packed in such a small space 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 don’t know exactly how 2D materials expand with increasing temperatures. Because the materials are so thin and optically transparent, their coefficient of thermal expansion (TEC) — the material’s tendency to expand as temperatures rise — is nearly impossible to measure using standard approaches.

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

Zhong is co-lead author of a research paper demonstrating just such a “ruler”. Instead of directly measuring how the material is stretching, they use laser light to track vibrations of the atoms that make up the material. By measuring a 2D material on three different surfaces or substrates, they can accurately extract its coefficient of thermal expansion.

The new study shows that this method is very accurate and achieves results in line with theoretical calculations. The approach confirms that the TECs of 2D materials fall in a much narrower range than previously thought. This information could help engineers design next-generation electronics.

“By confirming this narrower physical range, we give engineers a lot of material flexibility in choosing the bottom substrate when designing a device. You don’t need to develop a new soil substrate just to alleviate thermal stress. We believe this has very important implications for the electronic device and packaging community,” says Lenan Zhang, SM ’18, PhD ’22, co-lead author and former mechanical engineering student-turned-research scientist.

Co-authors include senior 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 Engineering and Computer Science and the Department of Mechanical and Energy Engineering at MIT Southern University of Science and Technology in Shenzhen, China. The study is published today in scientific advances.

measure vibrations

Because 2D materials are so small – maybe just a few microns in size – standard tools are not sensitive enough to measure their expansion directly. Also, the materials are so thin that they need to be bonded to a substrate such as silicon or copper. If the 2D material and its substrate have different TECs, they will expand differently with increasing temperatures, leading to thermal stresses.

For example, if a 2D material is bonded to a substrate with a higher TEC, the substrate will expand more than the 2D material as the device heats, causing it to stretch. 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 farther apart, causing the material to expand. They measure these vibrations using a technique called micro-Raman spectroscopy, which involves hitting the material with a laser. The vibrating atoms scatter the light from the laser, and this interaction can be used to detect their vibrational frequency.

But when the substrate expands or contracts, it affects how the atoms of the 2D material vibrate. The researchers had to decouple this substrate effect in order to constrain the intrinsic properties of the material. They did this by measuring 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 riddled with tiny holes. Because the 2D material levitates over the holes on the latter substrate, they can make measurements on these tiny areas of free-standing material.

The researchers then placed each substrate on a hot 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 the so-called temperature coefficient, which is substrate-dependent. Using these three different substrates and knowing the TECs of the fused silica and the copper, we can extract the intrinsic TEC of the 2D material,” explains Zhong.

A curious result

They performed this analysis on several 2D materials and found that they all agreed with 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 containing molybdenum will always have a larger TEC than one containing tungsten.

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

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

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

In the future, the researchers want to apply their methodology to many more 2D materials and maybe build a database of TECs. They also want to use micro-Raman spectroscopy to measure TECs of heterogeneous materials that combine multiple 2D materials. And they hope to learn the underlying reasons why the thermal expansion of 2D 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 Materials Research Science and Engineering Centers, the US National Science Foundation, and the US Army Research Office.


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