Two-dimensional (2D) materials, consisting of a single layer of atoms, are generally used in modern miniaturized devices. However, the operation of the device can lead to a significant increase in temperature and thermal load, which will cause the device to malfunction.

Such a problem arises because of a poor understanding of how 2D materials expand as the temperature rises. These materials are thin and optically transparent, so their coefficient of thermal expansion (TEC) is almost impossible to measure with standard approaches. To meet such thermal challenges, it is essential to have a good understanding of the coefficient of thermal expansion (TEC).

A new MIT study highlights a new technique for measuring exactly how atom-thin materials expand when heated. Instead of directly measuring how the material expands, they used laser light to track the vibrations of the material’s atoms. They accurately measured the coefficient of thermal expansion by measuring the same 2D material on three different surfaces or substrates.

This method is very accurate and produces results that correspond to theoretical calculations. The approach confirms that the TECs of 2D materials fall into a much narrower range than previously thought. This information can help engineers design next-generation electronics.

Co-lead author and former mechanical engineering graduate student Lenan Zhang SM ’18, Ph.D. ’22, who is now a research scientist, said: “By confirming this narrower physical range, we give engineers a lot of material flexibility for choosing the bottom substrate when they design a device. They don’t have to invent a new bottom substrate to reduce thermal stress. We believe this has important implications for the community of electronic devices and packaging.”

Scientists solved the problem by focusing on the atoms that make up the 2D material. As the temperature rises, the atoms vibrate at a lower frequency and move farther apart. This causes the material to expand.

A technique called micro-Raman spectroscopy was used to measure these vibrations. The method involves hitting the material with a laser. The vibrating atoms scatter the laser’s light, and this interaction can be used to detect their vibrational frequency.

However, the atoms of the 2D material change in vibration as the substrate stretches or contracts. To focus on the material’s intrinsic properties, the scientists must decouple this substrate impact. On three different substrates: copper, which has a high TEC, fused silica, which has a low TEC; and a silicon substrate with several microscopic holes – they measured the vibrational frequency of the same 2D material. They can measure these small areas of free-standing material because the 2D material floats above the holes on the latter substrate.

Later, scientists placed each substrate on a thermal stage to precisely control temperature, heated each sample, and performed micro-Raman spectroscopy.

The findings also showed something unexpected: 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 a material containing tungsten.

When scientists dig deeper, they discover that this hierarchy is a result of a fundamental atomic property known as electronegativity.

Yang Zhong, a mechanical engineering graduate student, said: “They found that the greater the difference between the electronegativities of elements that make up a 2D material, the lower the material’s coefficient of thermal expansion will be. An engineer could use this method to quickly estimate the TEC for any 2D material, rather than relying on complex calculations that typically need to be done by a supercomputer.

Zhang said, “An engineer can just search the periodic table, find the electronegativities of the corresponding materials, plug them into our correlation equation, and in a minute they can have a pretty good estimate of the TEC. This is promising for rapid material selection for technical applications.”

Scientists now plan to use their technique on many more 2D materials. They now want to create a database of TECs.

Magazine reference:

  1. Yang Zhong, Lenan Zhang et al. A unified approach and descriptor for the thermal expansion of two-dimensional monolayers of transition metal dichalcogenide. Scientific progress. DOI: 10.1126/sciadv.abo3783