This work presents a combination of analytical and numerical approaches to gain an insight of the dynamics of marine risers and micro machined resonators. Despite their scale difference, we show that both systems share similarities in terms of initial static deformation, quadratic and cubic nonlinearities, and internal resonances. First, we utilize the state space method to study the eigenvalue problem of vertical riser. An orthonormalization step is introduced to recover the numerical scheme during numerical integration and we investigate the effect of applied tension, apparent weight, and higher-order modes on the accuracy of the scheme. We show that the method is advantageous to find eigenvalues and mode shapes of vertical risers in comparison to other methods. The work is extended to study the eigenvalue problem of inclined risers considering the influence of static deflection, self-weight and mid-plane stretching. The linear dynamics is solved using Galerkin method. The results demonstrate that under the influence of tension and configuration angle, the frequencies exhibit commensurate ratio with respect to the first natural frequency leading to the possible activation of internal resonances. Next, we study the nonlinear interactions of inclined risers considering two-to-one and three-to-one internal resonances under single and multifrequency excitations. The multiple times scale method is applied to study the nonlinear interaction and results are compared to those from a Galerkin solution showing good agreement. Time histories and perturbation’s response curves, in addition to the dynamical solution obtained by Galerkin and stability analysis using Floquet theory are utilized to examine the system. These results feature nonlinear energy exchange, saddle node jumps, and Hopf bifurcations leading to complex dynamic motion that can endanger the riser structure. Finally, the analysis using pertubation is extended to investigate the two-to-one internal resonance in micromachined arch beams between its first two symmetric modes. The response is analyzed using the perturbation method considering the nonlinear interaction and two simultaneous excitations at higher AC voltages. Good agreement is found among the results of pertubations, Galerkin and experimental data from fabricated Silicon arch beam. Different types of bifurcations are observed which can lead to quasi-periodic and potentially chaotic motions.

The interest in implementing energy-efficient digital circuits using micro and nanoelectromechanical resonator technology has increased significantly over the last decade given their lower energy consumption in comparison to complementary metal oxide-semiconductor circuits. In this thesis, multiple circuit designs based on micro and nanoelectromechanical beam resonators are presented. These circuits include a nano resonator-based flash style analog-to-digital converter, a 4-bit digital-to-analog converter, and a micro-resonator-based 7:3 counter, all among the key building blocks of a microcomputing system. Simulations and experimental results were obtained for all circuits. In general, the proposed circuits based on nanoelectromechanical resonators show up to 90% reduction in energy consumption compared to their complementary metal-oxide-semiconductor counterparts in MHz operation speeds, fulfilling requirements for many applications such as Internet of Things and biomedical devices.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第16400号 / 工博第3481号 / 新制||工||1526(附属図書館) / 29031 / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 引原 隆士, 教授 田畑 修, 准教授 山田 啓文 / 学位規則第4条第1項該当

In line with the rising demand for smarter solutions and embedded systems, Microelectromechanical systems (MEMS) have gained increasing importance for digital computing devices and Internet-of-Things (IoT) applications, most notably for mobile wearable devices. This achievement is driven by MEMS resonators' inherent properties such as simplicity, sensitivity, reliability, and low power consumption. Hence, they are being explored for ultra-low-power computing machines. Several fundamental digital logic gates, switching, and memory devices have been demonstrated based on MEMS microstructures' static and dynamic behavior. The interest of researchers in using MEMS resonators is due to seeking an alternative approach to circumvent the notable current leakage and power density problems of complementary metal-oxide-semiconductor (CMOS) technology. The continuous miniaturization of CMOS has increased the operating speed and reduces the size of the device. However, this has led to a relative increase in the leakage energy. This drawback in CMOS has renewed the interest of researchers in mechanical digital computations, which can be traced back to the work of Charles Babbage in 1822 on calculating engines. This dissertation presents axially-loaded and coupled-MEMS resonators investigations to demonstrate memory elements and different logic functions. The studies in this dissertation can be categorized majorly into three parts based on the implementation of logic functions using three techniques: electrothermal frequency tunability, electrostatic frequency modulations, and activation/deactivation of the resonant frequency. Firstly, the influence of the competing effects of initial curvature and axial loads on the mechanical behavior of MEMS resonator arches are investigated theoretically to predict the tunability of arches under axial loads. Then, the concept of electrothermal frequency tunability is used to demonstrate fundamental 2-bit logic gates. However, this concept consumes a considerable amount of energy due to the electrothermal technique. Next, the dynamic memory element and combinational logic functions are demonstrated using the concept of electrostatic frequency modulation. Though this approach is energy efficient compared to the electrothermal technique, it does not support the cascadability of MEMS resonator-based logic devices. Lastly, complex multifunctional logic gates are implemented based on selective modes activation and deactivation, resulting in significant improvement in energy efficiency and enabling cascadability of MEMS resonator-based logic devices.

The notion of mechanical computation has been revived in the past few years, with the advances of nanofabrication techniques. Although electromechanical devices are inherently slow, they offer zero or very low off-state current, which reduces the overall power consumption compared to the fast complementary-metal-oxide-semiconductor (CMOS) counterparts. This energy efficiency feature is the most crucial requirement for most of the stand-alone battery-operated gadgets, biomedical devices, and the internet of things (IoT) applications, which do not require the fast processing speeds offered by the mainstream CMOS technology. In particular, using Micro-Electro-Mechanical (MEM) resonators in mechanical computing has drawn the attention of the research community and the industry in the last decade as this technology offers low power consumption, reduced circuit complexity compared to conventional CMOS designs, run-time re- programmability and high reliability due to the contactless mode of operation compared to other MEM switches such as micro-relays. In this thesis, we introduce digital circuit design techniques tailored for clamped-clamped beam MEM resonators. The main operation mechanism of these circuit blocks is based on fine-tuning of the resonance frequency of the micro-resonator beam, and the logic function performed by the devices is mainly determined by factors such as input/output terminal arrangement, signal type, resonator operation regime (linear/non-linear), and the operation frequency. These proposed circuits include the major building blocks of any microprocessor such as logic gates, a full adder which is a key block in any arithmetic and logic operation units (ALU), and I/O interface units, including digital to analog (DAC) and analog to digital (ADC) data converters. All proposed designs were first simulated using a finite element software and then the results were experimentally verified. Important aspects such as energy per operation, speed, and circuit complexity are evaluated and compared to CMOS counterparts. In all applications, we show that by proper scaling of the resonator’s dimensions, MHz operation speeds and energy consumption in the range of femto-joules per logic operation are attainable. Finally, we discuss some of the challenges in using MEM resonators in digital circuit design at the device level and circuit level and propose solutions to tackle some of them.

This dissertation investigates dissipation in microelectromechanical (MEMS) resonators via detailed analysis and modeling of the energy loss mechanisms and provides a framework toward creating resonant devices with ultra-low dissipation. Fundamental mechanisms underlying acoustic energy loss are explored, the results of which are applied to understanding the losses in resonant MEMS devices. Losses in the materials, which set the ultimate limits of the achievable quality factor of the devices, are examined. Other sources of loss, which are determined by the design of the resonator, are investigated and applied to example resonant MEMS structures. The most critical of these designable loss mechanisms are thermoelastic dissipation (TED) and support (or anchor) loss of acoustic energy through the attachment of the MEMS device to its external environment. The dissipation estimation framework enables prediction of the quality factor of a MEMS resonator, which were accurate within a factor of close to 2 for high-frequency bulk acoustic wave MEMS resonators, and represents a signficant step forward by closing one of the largest outstanding problems in MEMS devices: how to predict the quality factor for a given device. Dissipation mitigation approaches developed herein address the most critical dominant loss mechanisms identified using the framework outlined above. These approaches include design of 1D phononic crystals (PCs) and novel 3D MEMS structures to trap and isolate vibration energy away from the resonator anchors, optimization of resonator geometry to suppress thermoelastic dissipation, and analysis of required levels of surface polish to reduce surface dissipation. Phononic crystals can be used to manipulate the properties of materials. In the case of the 1D PC linear acoustic bandgap (LAB) structures developed here, this manipulation arises from the formation of frequency stop bands, or bandgapwhich convert silicon from a material capable of supporting acoustic waves to a material which rejects acoustic propagation at frequencies in the bandgap. The careful design of these LAB structures is demonstrated to be able to enhance the quality factor and insertion loss of MEMS resonators without significant detrimental effects on the overall device performance.

The growing demand for wireless communication systems is driving the integration of radio frequency (RF) front-ends on the same chip with multi-band functionality and higher spectral efficiency. Microelectromechanical systems (MEMS) have an overarching applicability to RF communications and are critical components in facilitating this integration process. Among a variety of RF MEMS devices, piezoelectric MEMS resonators have sparked significant research and commercial interest for use in oscillators, filters, and duplexers. Compared to their bulky quartz crystal and surface acoustic wave (SAW) counterparts, MEMS resonators exhibit impressive advantages of compact size, lower production cost, lower power consumption, and higher level of integration with CMOS fabrication processes. One of the promising piezoelectric MEMS resonator technologies is the aluminum nitride (AlN) contour mode resonator (CMR). On one hand, AlN is chemically stable and offers superior acoustic properties such as large stiffness and low loss. Furthermore, CMRs offer low motional resistance over a broad range of frequencies (few MHZ to GHz), which are lithographically-definable on the same silicon substrates. To date, RF MEMS resonators (include CMRs) have been extensively studied; however, one aspect that was not thoroughly investigated is how to modulate/tune their equivalent parameters to enhance their performance in oscillators and duplexers. The goal of this thesis is to investigate various modulation methods to improve the thermal stability of the resonator, its “effective” quality factor when used in an oscillator, and build completely novel non-reciprocal components. Broadly defined, modulation refers to the exertion of a modifying or controlling influence on something, herein specifically, the resonator admittance. In this thesis, three categories of modulation methods are investigated: thermal modulation, force modulation, and external electronic modulation. Firstly, the AlN CMR’s center frequency can be tunned by the applied thermal power to the resonator body. The resonator temperature is kept constant (for example, 90 °C) via a temperature sensor and feedback control such that the center frequency is stable over the whole operation temperature range of interest (e.g. –35 to 85 °C). The maximum power consumption to sustain the maximum temperature difference (120 ºC in this thesis) between resonator and ambient is reduced to a value as low as 353 μW – the lowest ever reported for any MEMS device. These results were attained while simultaneously maintaining a high quality factor (up to 4450 at 220 MHz device). The feedback control was implemented by either analog circuits or via a microprocessor. The analog feedback control, which innovatively utilized a dummy resistor to compensate for temperature gradients, resulted in a total power consumption of 3.8 mW and a frequency stability of 100 ppm over 120 ºC. As for the digital compensation, artificial neural network algorithm was employed to facilitate faster calibration of look-up tables for multiple frequencies. This method attained a frequency stability of 14 ppm over 120 ºC. The second modulation method explored in this thesis is based on the use of an effective external force to enhance the 3-dB quality factor of AlN CMRs and improve the phase noise performance of resonator-based oscillators. The force modulation method was embodied in a two-port device, where one of the two ports is used as a one-port resonator and the other is driven by an external signal to effectively apply an external force to the first port. Through this technique, the quality factor of the resonator was boosted by 140 times (up to 150,000) and the phase noise of the corresponding oscillator realized using the resonator was reduced by 10 dBc/Hz. Lastly, a novel magnetic-free electrical circulator topology that facilitates the development of in-band full duplexers (IBFD) for simultaneous transmit and receive (STAR) is proposed and modeled. Fundamentally, a linear time-invariant (LTI) filter network parametrically modulated via a switching matrix is used to break the reciprocity of the filter. The developed model accurately predicts the circulator behavior and shows very good agreement with the experimental results for a 21.4 MHz circulators built with MiniCircuit filter and switch components. Furthermore, a high frequency (1.1 GHz) circulator was synthesized based on AlN MEMS bandpass filters and CMOS RF switches, hence showing a compact approach that can be used in handheld devices. The modulation frequency and duty cycle are optimized so that the circulator can provide up to 15 dB of isolation over the filter bandwidth while good power transfer between the other two ports is maintained. The demonstrated device is expected to intrinsically offer low noise and high linearity. The combination of the first two modulation methods facilitates the implementation of monolithic, temperature-stable, ultra-low noise, multi-frequency oscillator banks. The third modulation technique that was investigated sets the path for the development of CMOS-compatible in-band full duplexers for simultaneous transmit and receive and thus facilitates the efficient utilization of the electromagnetic spectrum. With the aid of all these three modulation approaches, the author believes that a fully integrated, multi-frequency, spectrum-efficient transceiver is enabled for next-generation wireless communications.

Microelectromechanical resonators have found widespread applications in timing, sensing and spectral processing. One of the important performance metrics of MEMS resonators is the temperature sensitivity of their frequency. The main objective of this dissertation is the compensation and control of the temperature sensitivity of silicon resonators through engineering of device geometry and structural composition. This has been accomplished through formation of composite platforms or novel geometries based on dispersion characteristics of guided acoustic waves in single crystalline silicon (SCS) microstructures. Furthermore, another objective of this dissertation is to develop efficient longitudinal piezoelectric transduction for in-plane resonance modes of SCS resonators that have lithographically-defined frequencies, to reduce their motional resistance (Rm). A uniformly distributed matrix of silicon dioxide pillars is embedded inside the silicon substrate to form a homogenous composite silicon-oxide platform (SilOx) with nearly perfect temperature-compensated stiffness moduli. Temperature-stable micro-resonators implemented in SilOx platform operating in any desired in- and out-of-plane resonance modes show full compensation of linear temperature coefficient of frequency (TCF). Overall frequency drifts as small as 80 ppm has been achieved over the industrial temperature range (-40°C to 80°C) showing a 40x improvement compared to uncompensated native silicon resonators. A 27 MHz temperature-compensated MEMS oscillator implemented using SilOx resonator demonstrated sub-ppm instability over the industrial temperature range. Besides this, a new formulation of different resonance modes of SCS resonators based on their constituent acoustic waves is presented in this dissertation. This enables engineering of the acoustic resonator to provide several resonance modes with mechanical energy trapped in central part of the resonator, thus obviating narrow tethers traditionally used for anchoring the cavity to the substrate. This facilitates simultaneous piezoelectric-transduction of multiple modes with different TCFs through independent electrical ports, which can realize highly accurate self-temperature sensing of the device using a beat frequency (fb) generated from linear combination of different modes. Piezoelectrically-transduced multi-port silicon resonators implemented using this technique provide highly temperature-sensitive fb with a large TCF of ~8500 ppm/°C showing 100x improvement compared to other Quartz/MEMS counterparts, suggesting these devices as highly sensitive temperature sensors for environmental sensing and temperature-compensated/oven-controlled crystal oscillator (TCXO/OCXO) applications. Another part of this dissertation introduces a novel longitudinal piezoelectric transduction technique developed for implementation of low Rm silicon resonators operating in lithographically defined in-plane modes. Aluminum nitride films deposited on the sidewalls of thick silicon microstructures provides efficient electromechanical transduction required to achieve low Rm. 100 MHz SCS bulk acoustic resonators implemented using this transduction technique demonstrates Rm of 33Ω showing a 100x improvement compared to electrostatically transduced counterparts. Low-loss narrow-band filters with tunable bandwidth and frequency have been implemented by electrical coupling of these devices, showing their potential for realization of truly reconfigurable and programmable filter arrays required for software-defined radios.

With the advent of micro and nano electromechanical systems (MEMS/NEMS), there has been rapid development in the design and fabrication of sensitive resonant sensors. Sensitivity of such devices depends on the resonant frequency and the quality factor (Q). The Q of these devices are dependent on process induced prestress in the structural geometry, interaction with the external environment, and the encapsulation method. For high frequency sensors operating in air and under encapsulation condition, the Q is dominated by structural and fluid-structure interaction losses. In this thesis, we set out to study the dominant energy dissipative mechanisms that are constituent of the experimentally observed loss (Q-factor) in two specific test geometries—uncapped and capped circular MEMS drumhead resonators. Considering the importance of various factors, we consider four important problems pertaining to the uncapped as well as capped resonators. In the first problem, the most important factors perhaps are the acoustic radiation losses emanating from the annular plate, and the effect of added mass effect on the natural frequencies of the annular plate. The second problem is to investigate the dominant contribution of squeeze film losses and acoustic radiation losses with respect to various natural frequencies of the annular plate. The third problem is to consider the effect of prestress on the natural frequencies of the annular plate and its associated fluid-structure interaction losses (quality factors due to squeeze film damping and acoustic radiation losses). The fourth problem is to study the dominant fluid-structure interaction losses and structural losses that are constituent of experimentally measured Q-factors of the encapsulated annular plate (conceptual representation of MEMS device under packaged conditions). In the first problem, we study the mode dependent acoustic radiation losses in an uncapped drumhead microresonator which is represented by a annular circular plate fixed at its outer edge, suspended over a fixed substrate. There are two main effects which are associated with such systems due to the fluid-structure interaction. First is the “added mass effect,” which reduces the effective resonance frequency of the structure. The second is the acoustic radiation loss from the top side of the resonator, that affects the quality factor of the vibrating structure. In deriving the analytical solution, we first obtain the exact mode shapes of the structure ignoring any effect of the surrounding fluid (air) on the mode shape. Subsequently, we use these mode shapes to study the effect of the surrounding fluid on the associated natural frequencies and the Q-factor. The effect of “added mass” on the frequencies of the structure is found to be negligible. However, the acoustic radiation losses found to be significant. Additionally, we found that the variation in Qac over the first few modes (< 40 MHz) is marked with a local maximum and a minimum. Beyond this range, Qac increases monotonically over the higher frequency modes. It is also found that such kind of variation can be described using different acoustics parameters. Finally, comparing the acoustics radiation loss based quality factor with the experimental results for the uncapped drumhead resonator, the acoustic damping dominates only at higher modes. Therefore, our second problem forms the basis of finding other fluid-related damping. In the second problem, we explore the fluid losses due to squeeze film damping in the uncapped drumhead micro resonator. In this case, the squeeze film loss is due to the flow of the fluid film between the bottom surface of the annular plate and the fixed substrate. Based on the literature survey, it is found that the squeeze film damping reduces with increase in the air-gap thickness and the operating frequencies respectively. However, the squeeze film effect can not be ignored at lower frequencies. In order to investigate the contribution of squeeze film damping in uncapped resonator, we determine squeeze-film damping based quality factor Qsq corresponding to different modes of the resonators using FEM based software, ANSYS. On comparing Qsq with the experiments, we found that Qsq matches well with the experiments corresponding to the lower modes. Therefore, it is found that Qsq dominates at low frequencies (< 20 MHz) and Qac plays significant role at high frequencies (> 40 MHz). Both types of damping should be considered while modeling the fluid damping in uncapped resonator. In the next study, we discuss the effects of prestress on the resonant frequencies and quality factor. In the third study, we discuss the applicability of thin-plate theory with prestress and membrane theory in computing the frequencies and quality factor due to acoustic and squeeze film losses in the uncapped drumhead resonator. In the first two studies, although the quality factor due to acoustic losses and the squeeze film captures the correct trend of the experimental results, there is a mismatch between the experimental and theoretical frequencies computed with added mass effect. In order to improve the computation of frequencies corresponding to measured modes, we first used membrane theory to predict the frequencies, and finally we quantify that there exists discrepancy between computed and the corresponding experimental frequencies with error of about 8–55%. Since, both the membrane as well as thin plate theory without prestress do not correctly model the frequencies, we used the thin plate theory with prestress. For a prestress level of 96 MPa, we found the match between the computed frequencies and the corresponding quality factors with the measured values. However, we also found that there exists strong dependence of prestress on the acoustic radiation loss, with decrease in the acoustic loss based quality factors with increase in the prestress level. In the subsequent problem, we focus on the computation of losses in capped drumhead resonator which leads to a design possibility of improving the quality factor by containing the acoustic radiation losses. In the fourth problem, we study the structural and fluid-structure interaction losses which are dominant constituent of net Q-factor observed in experiments due to encapsulation of uncapped drumhead resonator. Essentially, the geometry of the capped resonator constitutes upper and lower cavities subjected to fluid-structure interaction losses on both sides of the annular plate. The dominant fluid-structure interaction loss is found to be due to squeezing action acting simultaneously in the upper and lower cavities. However, as we go to the higher modes, squeeze film damping become very small and the damping due to structure related losses such as clamping and thermoelastic losses becomes significant. We found the thermoelastic damping to be the dominant source of structural damping at higher resonant modes, whereas, the clamping losses are found to be relatively smaller. Finally, on comparing the net quality factor with the experimental results, we observed that the squeeze film losses are dominant at lower frequencies, and thermoelastic losses dominate at the higher frequencies. However, there remains some discrepancy between theoretical and experimental Q-factors particularly over higher frequency range. Such discrepancy may be due to some unaccounted factors which may be explored to improve the modeling of damping in capped resonators. The emphasis of this work has been towards developing a comprehensive understanding of different dominant dissipative mechanisms, classified into the fluid-structure interaction and the structural losses, that are constituent of the Q-factor at various resonant modes of uncapped and capped drumhead resonators.