Enlarge /. Tiny wires can promote heat flow.
Heat dissipation is one of the central challenges of modern technology. It doesn't matter whether the technology is a high-end server CPU or a pathetically anemic processor in a unbranded set-top box, someone had to think about heat management. One of the central issues in heat management is heat resistance, the tendency of a material to limit heat flow. The thicker a material, the greater the temperature gradient required to achieve the same amount of cooling, since the thermal resistance increases with the thickness.
Unless it isn't. If the heat is carried by ballistic phonons, the thermal resistance remains constant.
Energy in motion
Basically, heat is energy. In a solid material, energy is stored in two places: the movement of the electrons and the movement of the nuclei. The movement of electrons can set nuclei in motion, while nuclei also throw electrons around, causing energy to move back and forth between the two.
The way energy is stored also implies that energy is moving. When a nucleus moves, it moves its neighbors in a natural way so that the energy goes outside from wherever it was originally injected. If they are in an electrically conductive material, electrons are always in motion, so that they also transport energy from place to place. Electrons are not important for today's history.
The energy transport via the movement of nuclei takes place in the form of vibrations with fixed energy packets, so-called phonons – analogous to light waves and photons. Phonons are very sensitive: they can be easily dispersed by imperfections in the structure of the material. An atom that is not quite in the right place, or an impurity like the wrong atom in the material leads to the scattering of the phonon.
A phonon scatters many times over a distance of a few micrometers. The result is that the flow of energy from hot to cold is slow. The heat diffuses like the stain on the wall of a teenager's bedroom.
When phonons travel long distances with minimal scatter – perhaps just reflections from the surfaces of a material – we call this ballistic transport. This is exactly what the researchers observed with gallium phosphide wires. In fact, the researchers show that the material enables ballistic transport over distances of up to 15 µm, which is a surprisingly long way for phonons. I am assuming that longer wires are possible, but the data end at 15µm.
However, the length over which ballistic transport is possible depends on the wire diameter. There is a sharp transition between 40 nm and 50 nm. Below 40 nm, ballistic transport of up to 15 µm appears to be possible. No ballistic transport is observed above 50 nm.
Why is that? The wires act as waveguides for the phonons, just like fiber optic cables as waveguides for light. The phonons move along the wire by being reflected from its walls. When the wall is perfectly smooth, the reflections are like light reflected from a mirror, and the phonon moves on as if it were walking straight along the wire at a slightly reduced speed.
If the wall is rough, the phonon reflection can be at any angle – they can even return in the direction they came from. Each phonon takes a different time to traverse the wire. This is a typical heat diffusion.
But smooth and rough are a question of perspective. A mirror-like reflection from a rougher surface can be obtained for low-energy phonons than for a high-energy phonon. Think of it this way: your bathroom mirror is much smoother than a satellite dish, but the satellite dish works like a mirror for radio waves. Radio waves are low in energy (and therefore long-wave) so that the surface of the bowl appears smooth, while the surface of the bowl looks like the Himalayas in visible light.
Since it is quieter for long-wave phonons with low energy, these can move ballistically in the wires, while high-energy short-wave phonons diffuse. The roughness of the walls captures the high-energy phonons within the confines of a narrow wire; They are scattered at the same frequency towards the cold end as the hot wire end, so that on average they never go anywhere.
As the wire diameter increases, the number of ways in which a phonon can be trapped (or more precisely, the number of ways in which a phonon can move along the wire) decreases, so that the high-energy phonons begin to flow. The diffusing phonons carry more energy than the ballistic phonons, so that heat transfer is dominated by diffusion instead of faster ballistic phonons.
This is bad news for those of you who are looking for great new heat absorbing material. Under ballistic transport conditions, both the thermal conductivity and the thermal resistance are high. The difference (compared to diffuse transport) is that the thermal resistance does not increase with increasing wire length. This means that at the moment you are probably better off with short, fat wires with slow transport than with long, thin wires with fast transport.
Nano Letters, 2020, DOI: 10.1021 / acs.nanolett.0c00320 (About DOIs)