Metamaterial Directs Vibrations Along Set Paths

Metamaterials - the term may sound esoteric to the layman. In science and engineering, however, this is an interesting field of research that has developed at a highly dynamic pace, particularly since the 1990s.

To the naked eye, a metamaterial looks like an ordinary material. On smaller scales, however, it features an unusual, carefully engineered structure, endowing it with special mechanical or physical properties that the original basic material does not possess.

Such artificially designed materials are, for example, very light, stiff, highly deformable, or they mitigate impact and attenuate vibrations. Applications range from shoe soles ( as reported by ETH News ) and helmets all the way to microelectronics.

Special properties thanks to a special microstructure

Dennis Kochmann, Professor of Mechanics and Materials Research at ETH Zurich has extensively worked on metamaterials in his research. "It is fascinating how, through a special microstructure, you can endow a material with special properties that it does not possess without this structure," he explains.

Kochmann and his collaborators recently presented a novel so-called phononic metamaterial in two scientific publications - a material capable of precisely controlling mechanical waves, such as vibrations or acoustic signals.

Such a metamaterial could, for example, be deployed to harvest energy from vibrations or to process signals purely mechanically, which is of interest for sensors and mechanical computers that operate without electricity.

Wafer-thin silicon membrane as a wave guide

If a metal plate is excited to vibrate - for example, by hitting it with a hammer - these vibrations usually spread in a circular fashion, similar to surface waves in water. If this plate has a carefully designed structure, however, it can redirect waves along specific paths - and it is precisely this effect that the ETH researchers have exploited.

Instead of a metal plate, they used an extremely thin silicon membrane into which the researchers etched countless holes by way of photolithography and etching techniques, thereby forming a specific pattern.

A pattern comprising millions of elements

The pattern consists of millions of repeating square elements - minute squares, each further divided diagonally into four squares. At the centre of the main square is a four-pointed star.

Unlike in many other metamaterials, these unit cells are not identical across the entire pattern but change incrementally, as the lengths of the star's arms vary.

The ETH researchers used custom-built computer models to generate these patterns and simulated how a wave striking the pattern propagates in rays.

"If one were to simulate the entire wave field in a conventional manner, it would be extremely computationally expensive, because the design space is huge with millions upon millions of degrees of freedom," explains Kochmann's former team member Charles Dorn, now an assistant professor at the University of Washington, who was in charge of the simulations.

Playing puzzle with metamaterials

"The design of our metamaterial is modular, just like a jigsaw puzzle," as Kochmann explains. In this way, different puzzle pieces perform specific functions, such as deflecting rays at right angles or splitting waves into different directions based on their frequency. When the researchers skilfully assemble the appropriate puzzle pieces, they can generate complex wave paths, such as a figure-eight path.

Manufactured in the cleanroom on silicon substrates

In a further step, the researchers fabricated the computationally designed structures with high precision in the cleanroom at the Binnig and Rohrer Nanotechnology Centre at ETH Zurich and IBM. To this end, they used a conventional silicon wafer as the starting point and, in several steps, turned it into a silicon membrane that is structured exactly like the simulated pattern, with hundreds of thousands of unit cells - each measuring just a few micrometres in size and hence barely visible to the naked eye.

As a final step, the researchers tested the metamaterial membranes they had produced in an experiment. Using laser pulses, they caused the silicon membrane to vibrate. Deploying an optical measurement technique, they tracked the propagation of the vibrations in real time.

This enabled Kochmann and his colleagues to confirm that the waves did indeed follow the specified paths - and in some cases over long periods of time.

The structures not only function at a single vibration frequency: although the researchers designed the system for 750 kilohertz (750,000 vibrations per second), it operates effectively at frequencies ranging from around 250 to 800 kilohertz. "We hadn't planned for this broad frequency range, so it came as a pleasant surprise," comments Vignesh Kannan, co-author of the study published in the journal external page Nature Communications .

As silicon, the base material, has naturally low damping characteristics, waves can propagate for a long time. This is a major advantage over polymer-based 3D-printed structures, whose damping quickly suppresses any vibrations, explains Kannan, who is now an assistant professor at the École Polytechnique in Paris.

Harvesting energy from vibrations

The novel silicon membrane could find use in micro- and nanoelectronics, for example to better control vibrations on chips. The phononic metamaterial is also of interest for mechanical signal processing without a power supply, such as in sensors for monitoring infrastructure in remote areas. In the long term, they could also be deployed for novel computer architectures.

Kochmann, however, is also considering energy harvesters - devices that specifically direct vibration energy to piezoelectric energy converters, which generate usable electricity from vibrations.

In the next stages, he and his collaborators hope to push miniaturisation even further - right up to the limits of what is feasible, where manufacturing defects in the micro- or even nanostructure begin to have a significant impact.

"We also want to gain a better understanding of the physics behind the phenomena at play. It is not yet entirely clear why the design works so robustly across such a wide range of frequencies," states Kochmann.

For him, basic research is the top priority, as some of the underlying phenomena still remain a mystery. Applications often arise naturally, as the researcher comments. "That's the beauty of being here at ETH: we can try things out and explore the fundamentals without commercial pressure."