Study of High-Q Nanomechanical Silicon Nitride Resonators

Abstract

The growing interest in the field of nanomechanical resonators stems from their potentialuse as high performance sensors of a variety of physical quantities by means of detecting the resonance frequency shift. With the recent advancements in nanofabrication techniques as well as an abundance of new materials, sensors optimized for the detection of mass, force, and temperature with unprecedented responsivities are within reach. Central to many reported nanomechanical sensor investigations has been to maximize the mechanical quality factor Q, which directly results in an enhanced force sensitivity. Concurrently, high-Q resonators present an opportunity to unite the quantum regime with real-world applications by allowing quantum phenomena to be observed at room temperature, which is a topic of the so-called cavity optomechanics research field. As such, methods employed to reliable enhance the Q are in high demand in several fields employing nanomechanical resonators. In order to properly use high-Q resonators, both as sensors as well as building blocks in optomechanics, an in-depth analysis of their properties needs to be made. The most important questions to answer would be, what are the fundamental limits to the dissipation of mechanical resonators, and what sources of fluctuations determine the maximum sensitivities? This thesis aims to partly answer the above questions using high-stress silicon nitride nanomechanical resonators. Such resonators present a nanomechanical system capable of room temperature Qs approaching 1 billion due to the dissipation dilution effect. The presented results follow a linear pattern, first focusing on methods used to enhance the mechanical Q, then discussing fundamental limits to the frequency stability, and finally presenting a possible application of high-Q resonators as thermal sensors. Two approaches to Q-enhancement are presented, one focusing on the optimization of the dissipation dilution effect and the other on reducing intrinsic losses. The former works by widening the clamping of nanomechanical string resonators, which is numerically shown to reduce the curvature at the string clamping, thus potentially circumventing one of the limiting mechanisms of stressed resonators. Through a systematic investigation of strings with different orientations relative to the surrounding substrate, only marginal Q-enhancements result from the method, attributed to the increased material bending resulting from the clamp-widening. Finite element method simulations corroborate all the presented measurements, thus offering a path to further optimization of the resonator design. For nanomechanical resonators, with increasingly large surface-to-volume ratios, surfacefriction becomes the dominant intrinsic loss mechanism. In the second Q-enhancement approach, an effort is made to reduce the surface friction by means of high-temperature annealing of resonators in an ultrahigh vacuum environment. This procedure is performed on a variety of stressed resonator geometries, resulting in a clear Q-enhancement regardless of the geometry. Increases in the intrinsic Q approaching an order of magnitude are observed, which is shown to be directly related to reduced surface losses. The annealing treatment is shown to be reproducible and nondestructive, only marginally influencing the mechanical properties of the resonator. Given that this approach can be applied to current state-of-the-art high-Q resonators in literature, these results present an important step forward in the pursuit of room-temperature quantum experiments. Moving on to the second part of the thesis concerning applying high-Q resonators as sensors, a detailed investigation into the frequency fluctuations of such resonators is presented. Nanomechanical string resonators are employed as the system under consideration and the frequency stability is characterized using the Allan deviation, both in open-loop and closed-loop tracking configurations. For open-loop tracking, it is shown how the Allan deviation is divided into a regime limited by thermomechanical noise and another limited by the back-ground noise of the detection. Despite the latter noise source potentially lower in level than the thermomechanical noise, the frequency stability is shown to always be limited fundamentally by thermomechanical noise with a response time defined by intrinsic properties of the resonator. Closed-loop tracking is shown to offer a response faster than the intrinsic limit at the expense of increased noise. Additionally, when employing optical detection schemes, the laser power fluctuations are shown to be a potentially limiting factor in the frequency stability. Measurements are supported by theory-based calculations of the Allan deviation, showing great agreement, allowing the design of future sensors with optimized frequency stability.The final part of the thesis demonstrates how localized defect modes of low-stress phononiccrystal (PnC) membranes can be utilized as thermal sensors. Here, the thermal response is quantified through laser heating of the membrane center, which shifts the frequency through the photothermal effect. Owing to the perforation of the membranes and the increased over-lap between the defect modes and the temperature field resulting from the laser heat source, the thermal responsivity of PnC membranes is shown to be potentially an order of magnitude greater than that of uniform membranes of equal size. Even larger thermal response is reported through geometrical stress reduction, achieved by fabricating a PnC membrane inside a nanomechanical trampoline. Lastly, defect mode and bandgap tuning through laser heating are presented, demonstrating how the defect mode can be thermally detuned enough to completely exit the phononic bandgap. These results serve as a basis upon which further optimization of resonator design can be made, paving the way for a new class of thermal sensors with unparalleled thermal response.