Optical Transduction for Vertical Nanowire Resonators

Abstract

We describe an optical transduction mechanism to measure the flexural mode vibrations of vertically aligned nanowires on a flat substrate with high sensitivity, linearity, and ease of implementation. We demonstrate that the light reflected from the substrate when a laser beam strikes it parallel to the nanowires is modulated proportionally to their vibration, so that measuring such modulation provides a highly efficient resonance readout. This mechanism is applicable to single nanowires or arrays without specific requirements regarding their geometry or array pattern, and no fabrication process besides the nanowire generation is required. We show how to optimize the performance of this mechanism by characterizing the split flexural modes of vertical silicon nanowires in their full dynamic range and up to the fifth mode order. The presented transduction approach is relevant for any application of nanowire resonators, particularly for integrating nanomechanical sensing in functional substrates based on vertical nanowires for biological applications. N anomechanical sensing with resonant devices based on semiconductor nanowires (SCNWs) is currently consolidated as one of the most fruitful research lines involving this kind of nanostructure. SCNWs are highly useful as resonators for high-performance applications because of their unique structural and dynamic properties. The former imply an exceptional combination of very low mass, single-crystal quality, and controllable dimensions and geometry. 1 Regarding dynamic properties, the characteristic high aspect ratio of SCNWs results in flexural modes which are extremely sensitive to external perturbations of a different nature. 2 On one hand, this facilitates detecting their thermomechanical vibrations, as the effect of temperature alone results in relatively large vibration amplitudes; on the other hand, it also simplifies external driving schemes, as external forces of a different nature can be used to drive flexural vibrations even beyond the fundamental mode. These properties provide SCNW resonators with singular sensing capacities which are otherwise impossible to achieve with other structures. Some of the most significant ones are based on the splitting of each flexural mode in a doublet of nearly degenerate orthogonal oscillations, which occurs for both single-clamp 3,4 and double-clamp nanowires. 5 This effect has indeed already been explored for innovative applications such as simultaneous mass and elasticity sensing of adsorbates, 4,6 vectorial force sensing/imaging, 7−9 and the exploration of complex dynamics 10−13 or optomechanical back-action effects. 14,15 Exploiting the unique properties of SCNW resonators for developing an equally high performance and practical functionalities requires an efficient conversion of the nanowire vibrations into readable signals with high sensitivity, linearity, and minimum constraints regarding the nanowires' arrangement. Different transduction schemes have been demonstrated so far to that end, but arguably all of them have ...

Modeling the Electrostatic Actuation of Nanomechanical Pillar Dimers

“…If the pillars are 5 µm long, the deflection lies in the order of 10 pm. Considering the displacement amplification by the quality factor, with typical values up 10,000 (Molina et al, 2020), vibrational amplitudes in the nanometer regime can be expected.…”

“…This means quasistatic deflections in the order of smaller than one fm for the shortest pillars and in the order of 0.1 pm for the 5 µm ones. Considering a quality factor of the order of 10,000 (Molina et al, 2020), this results in vibrational amplitudes of the order of 1 nm.…”

“…Optical detection of mechanical motion is the most sensitive technique available. Recently it was shown that the vibration of vertical nanowires can be readily detected optically (Molina et al, 2020). When the vertical nanowires are situated at the slope maximum of the Gaussian light beam, the displacement of the light-scattering nanowires cause a modulation of the reflected light.…”

Observing polarization patterns in the collective motion of nanomechanical arrays

“…On the other hand, nanopillar resonators [2,3,[24][25][26]] offer large flexural motion in two orthogonal directions, and have thus been proposed [27] as a natural candidate for rapid spatially resolved optical whole-array imaging of polarization patterns.…”

“…Due to the large vibration amplitudes of the pillar heads even in the linear response regime, the envelope of their trajectories can be captured by optical imaging from the top (for details see Appendix A). The optical imaging allows for the simultaneous detection of up to several thousands of nanopillars and their spatial trajec- tories as a function of frequency, whereas typical measurement techniques for resonator arrays rely on sequential measurements of every single resonator [26] or compromise by giving up spatial resolution [7].…”