Résonateurs phononiques couplés par la surface – PhoRest

The PhoRest projects combines conventional approaches of microacoutics (interdigitated transducers) and micro-electromechaical systems (micro-pillars) to achieve coherent contro of elastic waves down to the micron or even nano-scale. The works pursued rely on three main aspects:
- Finite element simulations, taking into account anisotropy, piezoelectricity and semi-infinite character of the substrate in a three-dimensional model;
- the resonator fabrication relies on focused ion-beam induced deposition (FIBID), FIBID, a unique technology providing a full control, along the three space dimensions and with nanometer accuracy, of the fabricated structures ;
- Laser scanning heterodyne interferometry allows a direct visualization of the out-of-plane component of the displacement field, giving a direct access to the elastic energy distribution.

We have experimentally demonstrated that resonator-to-surface wave coupling can be deliberately used to excite discrete micron-scale mechanical resonators and to confine elastic energy. Using focused-ion-beam-induced deposition (FIBID),a technological process that intrinsically allows a three-dimensional control of the resonator geometrical properties at an individual level, we fabricated sets of isolated cylindrical pillars of independent, arbitrary shapes and sizes to investigate the possibility of coupling surface acoustic waves propagating on the homogeneous substrate with each resonator independently. This coupling occurs through a hybridization mechanism of the supporting continuum with the resonator eigenmodes. The sample considered comprised cylindrical pillars 3 to 5 µm in diameter excited by a ten-times longer wavelength surface elastic wave. The elastic field distribution in the resonators and at the substrate surface was characterized by laser scanning interferometry, a method that allows a direct visualization of the out-of-plane component of the displacement field. A strong field enhancement as compared to the one hosted by the wave propagating on the substrate surface is reported, with an amplitude of displacement reaching 10 nm, versus 1 to 2 nm at the substrate surface. The proposed experimental configuration was used to show that the spatial distribution of the elastic energy at the substrate surface can be controlled by addressing each pillar independently as a function of drive frequency, hence opening the door for coherent, high-frequency elastic wave distribution and confinement at the micro- or nanoscale.

These results were obtained using IBID-platinum, leading to a rather limited Q-factor at room temperature (about 40 at 70 MHz, hence a Q-f factor of about 10^9). Tuning both the resonator geometry (necked resonators, for instance) and changing the material for a less dissipative one, as planned in the next steps of the project will most certainly improve this feature. Future work will obviously focus on an investigation of resonator-to-resonator coupling and their intercation with the supporting surface.

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The PhoRest project aims at the engineering of surface coupled high quality factor nanophononic resonators able to trap the elastic energy in a well-defined manner. The proposed structures will be used collectively to conceive phononic chains capable to carry the elastic energy along the most twisted paths but also individually by exploiting the dependence of the resonance frequency on their geometric properties to create complex systems of coupled micro- or nanoscale phononic resonators that can lead to phonon parametric interaction. The overall objective is to push forward a novel conceptual approach to design complex systems that could contribute to the development of disruptive Information and Communication Technologies based on advanced acoustic signal processing functionalities.

The project will first focus on the investigation of near-field coupling between elastic modes of neighboring resonators. The issue here exceeds a basic understanding of the involved mechanisms as such an experiment will provide us with unprecedented possibility to perform surface phonons guidance at the micron-scale. We will also aim at the realization of phononic circuits based on metal resonators exhibiting dimensions in the hundred of nanometer range that can open interesting prospects for interactions with surface plasmons or for charge transport.

The project will then drift towards a more ambitious perspective: we will seek to build a three-level system allowing electromechanically-driven phonon lasing. We will investigate the nonlinear mechanisms at play in the proposed phononic resonators. The expertise acquired during the first part of the
project will then allow us to design a viable resonator or set of coupled resonators fulfilling the required energy (i.e. eigenfrequency) and lifetime (i.e. quality factor) conditions to obtain enhanced parametric interactions. The added-value of the proposed solution compared to alternatives reported in the literature lies in the strong confinement of the elastic energy at the resonator vicinity that could lead to a phonon equivalent of quantum dots.

Pillar-like structures obtained either bymetal electroplating or by ion-beam induced nano-structuration will stand at the core of the experimental investigations. The resonators will be integrated on a piezoelectric substrate and designed to support frequencies in the hundreds of megahertz to a gigahertz range. The resulting dimensions will call for specific acoustic imaging techniques. A significant part of the conducted work will therefore be devoted to the development of characterization methods which, associated with existing know-how, will start building an extensive platform for a long term study of these phononic resonators and of their use in complex systems or actual devices. We will privilege optical techniques for the measurement of the mechanical energy spatial distribution and of the temporal dynamics of the resonators. We will in addition exploit the piezoelectricity of the substrate to follow the displacement of the electric charges carried by the elastic strain field using scanning electron microscopy. This unconventional method opens the exciting perspective to reach resolutions of the order of a few nanometers.

These activities will be driven and supported by theoretical and numerical studies using classical linear and nonlinear mechanics, coupled-mode theories and Hamiltonian approaches. It will indeed be critical to understand and formalize the damping and leakage mechanisms at play in our surface coupled resonator systems.

PhoRest is therefore built around two ambitious, independent though intersecting objectives. Although the second part of the project is definitely risky, the pursuit of phonon lasing will help bridging the gap between a nanomechanics and a phononics approach of local resonance effects. A successful
outcome will have a highest impact in the phononics, NEMS and optomechanics communities.