This thesis provides an overview of research focused on fabricating high-performance nanomechanical resonators from amorphous silicon carbide (a-SiC) and (super)conducting metallic niobium titanium nitride (NbTiN), and subsequently characterizing the superconducting NbTiN resonators using scanning tunneling microscopy (STM). The installation of on-chip nano mechanics with a minimally invasive STM detection technique enables the probing of subtle variations in the Casimir force between superconductors during their phase transition. This thesis consists of four parts.

With the aim of maximizing the coupling of the Casimir force to a large superconducting nanomembrane suspended over a sub-micron vacuum gap, we initially employed atomic layer deposition (ALD). Prior to using ALDto construct the high-aspect-ratio superconducting cavity, we investigated a novel amorphous silicon carbide (a-SiC) material in Chapter 2. Our study demonstrated that a-SiC exhibits high chemical inertness, remarkable ultimate tensile strength, and—most importantly—the capability to support nanomechanical resonators with high quality factors. Leveraging these excellent properties, we fabricated high-aspect-ratio a-SiC nanomembranes suspended over a sub-micron vacuum gap.

Subsequently, using the on-chip cavity formed by the strained a-SiC nanomembrane and the substrate with flat surface, we performed ALD to conformally coat all cavity surfaces with metallic NbTiN, thereby filling the vacuum gap atomically layer-by-layer. By optimizing the deposition conditions with the method described in Chapter 3, we achieved a high-aspect-ratio NbTiN cavity with a gap size of less than 100 nm. During this optimization, we also observed that metallic nanomechanical resonators fabricated via ALD can operate at room temperature with quality factors significantly higher than those of fully coated metallic resonators produced by other deposition techniques.

To measure the superconducting nanomembranes with minimal perturbation to their superconducting state, we installed the NbTiN nanomembrane fabricated by ALD into a scanning tunneling microscope (STM) and performed dynamic measurements in a cryogenic environment, as detailed in Chapter 4. In studying the tip–membrane interaction, we developed three measurement techniques to precisely determine the resonant frequency of the nanomembrane. One technique relies on the homodyne method, while the other two exploit the Van der Waals interaction between the STM tip and the nanomembrane.

Although the NbTiN nanomechanical resonators exhibit high performance, their superconducting properties are compromised by the absence of plasma bombardment on the inner cavity surfaces. Drawing on our experience with suspending large nanomembranes over small gap sizes in Chapter 3, we developed a new fabrication process in Chapter 5 to suspend a bare superconducting NbTiN nanomechanical membrane over another superconducting NbTiN film, with a sub-micron vacuum gap between them.

This configuration minimizes unwanted interactions that could otherwise affect the precision of measuring the variation in the Casimir force between superconductors during the phase transition. The high force sensitivity of the nanomembrane allows us to detect subtle force changes associated with the superconducting phase transition, including those arising from abrupt changes in the Casimir force.

Nonlinear dynamic simulations of mechanical resonators have been facilitated by the advent of computational techniques that generate nonlinear reduced order models (ROMs) using the finite element (FE) method. However, designing devices with specific nonlinear characteristics remains inefficient since it requires manual adjustment of the design parameters and can result in suboptimal designs. Here, we integrate an FE-based nonlinear ROM technique with a derivative-free optimization algorithm to enable the design of nonlinear mechanical resonators. The resulting methodology is used to optimize the support design of high-stress nanomechanical Si ₃N ₄ string resonators, in the presence of conflicting objectives such as simultaneous enhancement of Q-factor and nonlinear Duffing constant. To that end, we generate Pareto frontiers that highlight the trade-offs between optimization objectives and validate the results both numerically and experimentally. To further demonstrate the capability of multi-objective optimization for practical design challenges, we simultaneously optimize the design of nanoresonators for three key figure-of-merits in resonant sensing: power consumption, sensitivity and response time. The presented methodology can facilitate and accelerate designing (nano) mechanical resonators with optimized performance for a wide variety of applications. (Figure presented.)

Although strain engineering and soft-clamping techniques for attaining high Q-factors in nanoresonators have received much attention, their impact on nonlinear dynamics is not fully understood. In this study, we show that nonlinearity of high-Q Si₃N₄ nanomechanical string resonators can be substantially tuned by support design. Through careful engineering of support geometries, we control both stress and mechanical nonlinearities, effectively tuning nonlinear stiffness of two orders of magnitude. Our approach also allows control over the sign of the Duffing constant resulting in nonlinear softening of the mechanical mode that conventionally exhibits hardening behavior. We elucidate the influence of support design on the magnitude and trend of the nonlinearity using both analytical and finite element-based reduced-order models that validate our experimental findings. Our work provides evidence of the role of soft-clamping on the nonlinear dynamic response of nanoresonators, offering an alternative pathway for nullifying or enhancing nonlinearity in a reproducible and passive manner.

In recent years, the Q-factor of Si 3 N 4 nanomechanical resonators has significantly been increased by soft-clamping techniques using large and complex support structures. To date, however, obtaining similar performance with smaller supports has remained a challenge. Here, we make use of torsion beam supports to tune the Q-factor of Si 3 N 4 string resonators. By design optimization of the supports, we obtain a 50% Q-factor enhancement compared to the standard clamped-clamped string resonators. By performing experimental and numerical studies, we show that further improvement of the Q-factor is limited by a trade-off between maximizing stress and minimizing torsional support stiffness. Thus, our study also provides insight into dissipation limits of high-stress string resonators and outlines how advanced designs can be realized for reaching ultimate f 0 × Q product while maintaining a small footprint.

Resonant sensors hold great promise in measuring small masses, to enable future mass spectrometers, and small forces in applications like atomic and magnetic force microscopy. During the last decades, scaling down the size of resonators has led to huge enhancements in sensing resolution, but has also raised the question of what the ultimate limit is. Current knowledge suggests that this limit is reached when a resonator oscillates at the maximum amplitude for which its response is predominantly linear. We present experimental evidence that it is possible to obtain better resolutions by oscillation amplitudes beyond the onset of nonlinearities. An analytical model is developed that explains the observations and unravels the relation between ultimate sensing resolution and speed. In the high-speed limit, we find that the ultimate resolution of a resonator is improved when decreasing its damping. This conclusion contrasts with previous works, which proposed that lowering the damping does not affect or even harms the ultimate sensing resolution.

For decades, mechanical resonators with high sensitivity have been realized using thin-film materials under high tensile loads. Although there are remarkable strides in achieving low-dissipation mechanical sensors by utilizing high tensile stress, the performance of even the best strategy is limited by the tensile fracture strength of the resonator materials. In this study, a wafer-scale amorphous thin film is uncovered, which has the highest ultimate tensile strength ever measured for a nanostructured amorphous material. This silicon carbide (SiC) material exhibits an ultimate tensile strength of over 10 GPa, reaching the regime reserved for strong crystalline materials and approaching levels experimentally shown in graphene nanoribbons. Amorphous SiC strings with high aspect ratios are fabricated, with mechanical modes exceeding quality factors 10⁸ at room temperature, the highest value achieves among SiC resonators. These performances are demonstrated faithfully after characterizing the mechanical properties of the thin film using the resonance behaviors of free-standing resonators. This robust thin-film material has significant potential for applications in nanomechanical sensors, solar cells, biological applications, space exploration, and other areas requiring strength and stability in dynamic environments. The findings of this study open up new possibilities for the use of amorphous thin-film materials in high-performance applications.