Definition and Experiment

A phononic nanostructure is made of a base material in which a regular array of phonon scatterers is embedded. Here, the base material is silicon as thin membrane and the scatterers are nanoholes which positions are drawn by electron beam lithography.

The silicon phononic membrane is suspended and placed in a high-vacuum variable-temperature cryostat with an optical window to make time-dependent thermoreflectance measurements from 4K to 300K. A short pulsed laser heats the center of the nanostructure while a continuous laser records the variations in reflectance at the same spot. The obtained cuve is a decayed reflectance over time that depicts the dynamics of the phonons. This curve is characterized by a decay time that can be related to the thermal conductivity.

Schematic of phononic crystal and thermoreflectance signal

Impact of holes alignement

We studied two types of periodic holes lattices: (i) square lattice and (ii) staggered lattice where every two raws the holes are shifted of half a period. For the same period and hole diameter, we compare the decay times of the two lattices.

As the diameter-to-period ratio increases, the decay time of the staggered lattice becomes longer than the square lattice. This difference becomes more significant as the period is small and the temeprature is low.

By coupling these lattices with nanowires, we demonstrated that the difference in decay times is due to ballistic phonons directionality in the phononic nanostructure.

Aligned and staggered lattices

The aligned and staggered lattices experiments showed that ballistic phonons acquire specific directions following the path between the holes. It opens the possibility to control the direction of heat propagation by judiciously arranging the holes in the phononic nanostrucuture.

We created a radial array of holes with a focal point where all the direct passages beween the holes converge. Monte Carlo simulations predict that a hotspot will appear at the focal point, the radial array of holes acting like a lens focusing the heat.

The heat focusing is measured with thermoreflectance by placing a slit around the focal point as only way for the phonons to exit to the cold bath. When the slit is in front of the focal point, most phonons directly reach the cold bath resulting in a rapid decay time. The slit is progressively shifted aside of the focal point so that more and more phonons are backscattered as measured by a longer decay time.

Heat focusing. a: Fabricated nanostructure. b: Monte Carlo simulations.

A single row of holes are perforated in a narrow beam of 300 nm width to create a 1D phononic crystal. We observe a reduction of the thermal conductivity as the dimater of the holes increases. This reduction reaches 90% when the diameter is 180 nm as compared to a beam without holes. However, no significant impact is observed when the period of the holes is changed which comes from the directionality effect mentioned above as confirmed by Monte Carlo simulations.

1D phononic crystal

Inspired by the directionality effect, I proposed a new model for the phonon transport in phononic crystal based on the straight paths between the holes. It is called the Direct Passage Model.

The idea is that ballistic phonons travel in straight lines over long distances, bigger than a few periods in a phononic crystal. Therefore, heat will propagate more easily in the direct passages between the holes. The larger the direct passage, the easier phonons can travel through the structure and, consequently, the higher the thermal conductivity.

Direct passages in aligned and staggered lattices