Microscopic Heat Transport

In the world of nanophysics and nanomaterials, heat flow is a confusing phenomenon. According to postdoctoral scientist Dr. Joshua Knobloch from the group of JILA Fellows Margaret Murnane and Henry Kapteyn: “What we found is that when you have heat flowing on very small scales, it starts to behave differently. Large-scale hot spots cool by spreading the heat out in all directions.... However, when you start to bring arrays of hot nano structures close together, you start to see that heat transport that is radically different from the macro scale. The past understanding of nanoscale heat transport was that it was not as efficient—the heat is kind of bottlenecked and cooling slowed down a lot." But two new papers from the Murnane and Kapteyn group are changing the way heat transport is viewed on a nanoscale, and explain the group’s surprising finding that nanoscale heat transport can be far more efficient than originally thought. One of these papers, published in the Proceedings of the National Academy of Sciences (PNAS), explains heat transport for the tiniest of hotspots, with sizes <100 nm. The other, published in American Chemical Society Nano (ACS Nano), presents a theory that is applicable to larger arrays of hotspots. Both papers postulate theories that can fully explain the surprising data collected by the team of researchers, showing that heat transport on scale lengths relevant to a wide range of nanotechnologies is more efficient than originally thought.

Silicon Structures

"Experimentally we found something very counterintuitive —when you start packing small hotspots very close together, heat actually starts to transport more efficiently," Knobloch explained about the increased efficiency. "Although not quite as efficient as on large scales, we found that it was more than what you would expect for a nanoscale structure. The reason it is counterintuitive is because we are essentially saying that if you have really small nanoscale heaters, and you want them to cool down quickly, you need to pack them closer together rather than spreading them farther apart." The team had been looking at these nanoscale heat transports for approximately six years. Knobloch added: "Our previous experimental work demonstrated that this behavior is possible. Our new theoretical papers tell us why this happens."

In order to see heat transport in the smallest of systems, the team created metal nanolines and nanodots on a silicon substrate. They then heated these nanostructures, which cool as lattice vibrations in the silicon substrate, called phonons, carry the heat away from the hotspots. As reported in one paper (ASC Nano), the group, looked at these structures from a larger, "mesoscopic" (intermediate between microscopic and macroscopic) scale, in collaboration with theory groups from the Universitat Autonoma de Barcelona. In the other work (PNAS)  the group, in collaboration with Mahmoud Hussain’s group in Aerospace Engineering at CU Boulder, focused in on the deep nanoscale behavior . This way, the team could see if the  ‘counterintuitive’ materials behavior applied to multiple length scales. Knobloch and the group found that their theories agreed very well with their data. "It is really exciting, and important, that we now have a predictive model that can now be used to explore various geometries for better heat transport," Knobloch stated.

Computer Chips and Predictions

When it comes to these predictive models, Knobloch believes that they can be used for smart thermal management in nanodevices. As one example, one of the limiting factors for faster computing is the heat processing system. If the computer gets too hot, it overheats and can no longer function effectively. Having a predictive model when designing and building the nanostructures for computer parts can help to regulate heat flow and  reduceoverheating.

While this model can be applied to computers, it also has broader implications. The two scales shown in the two papers give two different aspects of the predictive model. For the nanoscale paper, Knobloch explained that "we observed the phonons from the neighboring heat sources, when you start to pack them together, they start scattering off each other and this drives the heat downward, into the cooler regions of the substrate." This model provides the researchers with a fundamental explanation for the unexpectedly efficient cooling of nanoscale structures.

In contrast, the model in the more 'mesoscopic" ASC Nano paper can be used to predict the time involved in the heat transfer process. "We were able to use our more mesooscopic model to be able to predict the time scales of this heat," Knobloch clarified. "So, if I have a very small heat source, we can tell you, ‘This is exactly how long it is going to take to cool down.’” While this relates to how many computations can be done in any time interval, without heating up the computer, this model provides a practical tool to help engineers design more general applications nano-sized systems which effectively manage heat and is not just limited to computers.

Finding Connections

While the team found that this more efficient heat transfer occurred on both a nanoscale and a slightly larger mesoscopic scale, there are still connections between the two papers that need to be made. "The next step is to see if we can come up with what I would say is a more formal way of deciding how these two theoretical thrusts are connected," said Knobloch. "We can look at the plots and just say intuitively, 'Oh they seem similar.' So how we try to connect these together, that exact theory is not yet developed." As the research continues, Knobloch and the team are hopeful to create a more general model to be used on even more intricate nanosystems.

Written by Kenna Castleberry, JILA Science Communicator