AVANT-GARDE MATERIALS FOR ENERGY HARVESTER TECHNOLOGIES AND TUNABLE MICRO-ELECTRO-MECHANICAL (MEMS) RESONATORS By Juan Jos´e Pastrana-Gonz´alez A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Electrical Engineering – Doctor of Philosophy 2023 ABSTRACT In the context of multifunctional materials, this dissertation presents the utilization of carbon nanotube fibers (CNTF) and vanadium dioxide (V O2) in an effort to improve energy harvesting and micromechanical systems research areas, respectively. First, a characteriza- tion study of the electrode interface in polypropylene ferroelectret nanogenerators, focusing on a comparison between carbon nanotube fiber electrodes with traditional metallic thin film electrodes is introduced. The study also included the effects of acetone treatment on CNTF- based electrodes and PPFE. Results showed a higher VOC values for the thin film metal electrodes regardless of the applied pressure. Factors such as conductivity and thickness of the electrodes were considered. Although the analysis points out these are the dominant factors on the VOC for metallic electrodes, volume and roughness of the CNTF-based elec- trodes might play additional roles in the open-circuit voltage outputs. On the other hand, the difference in ISC values between metal and CNTF-based electrodes were not as signifi- cant. Ultimately, a study on generation and leakage of induced charge in the electrodes was done. It was found, in contrast to dipole relaxation, that current leakage through parasitic elements is a faster process for discharge. Moreover, this work presents -for the first time- a tunable V O2 comb drive resonator. A theoretical model was proposed to incorporate V O2 phase transition material on comb drive resonators. A change in the Young’s modulus of the material was first considered. The- oretically, an active tuning capability of 5% was feasible when the material was deposited over the beams. On the other hand, V O2 deposition on the shuttle showed a 1.5% tuning capability when the thermal expansion coefficient of the material changed between the mon- oclinic and rutile phases. To better predict the resonant frequencies and electrical output of the resonators, an FEM model was also proposed. From the results, it was determined an increase on the number of combs would allow a larger displacement current. From the afore- mentioned analysis, deposition of V O2 over the beams or shuttle would result in a shifting of resonance frequencies to lower values. To validate the theory, comb drive resonators were fabricated and electrically characterized. It was shown the V O2 deposited over the shuttle resulted in a ∼2% active tuning. Finally, in the attempt to improve the effects of V O2 as an active tuning method, a second generation of comb drive resonators was fabricated. By utilizing static beam theory, the mode shape equation describing the beam’s shape is derived. Combined with the Rayleigh’s method of energy conservation, the presented work extends on the vibration analysis of comb drive resonator beams towards the derivation of an analytical equation able to estimate residual stress from measured lateral resonances. In addition, for a heating cycle, it was found the V O2 can increase the lateral frequencies up to 10% when transitioning from monoclinic to rutile. More importantly, a clear hysteretic behavior was measured on a heating-cooling cycle, demonstrating the feasibility of the comb drive resonator’s design to incorporate active tuning due to V O2 phase transition material. To my family... Thank you for the sacrifices done in order for me to achieve my dreams. To my friends... Thank you for being understanding and supportive all these years. iv ACKNOWLEDGMENTS I would like to thank the current and past members of the Applied Materials Group for their friendship and the fun memories. To Henry, Jos´e, and Ian, thank you for your support, advice, and all the good times we had at MI. I am very thankful to Dr. John Albrecht, Dr. Wen Li, and Dr. Nizar Lajnef for being part of my graduate committee, the support and feeback. I would also like to thank the family from Wright Patterson Air Force Research Laboratory for all their help. To Mr. Will Gouty, Dr. Erick Kreit, Dr. Jos´e Figueroa, Mr. Thomas Taylor, Dr. Harris Hall, Dr. LaVern Starman, Mr. Andrew Browning, Mr. Adam Geiger, Mr. John O’mara, and Mr. Aaron Adams. Thank you for providing immediate assistance on the times I needed help. Very special thanks to Dr. Matthew Cherry for granting me the opportunity to be under his wing for three months and for teaching me the ”dark arts” of lasers and vibrations. Thank you! From the same family, and more importantly, a big thank you to my mentor and friend Dr. David Torres-Reyes. Since day one, Dr. Torres-Reyes was involved in my struggles and successes for my second research topic. His encouragement, great insight and feedback highly contributed to the main reasons for the completion of this work. Thank you for providing me with opportunities to keep growing intellectually and professionally, and thank you for always touching base and making sure I had everything at hand to achieve my goals. Last, but not least, I am and will be forever grateful to my advisor, mentor, and friend Dr. Nelson Sep´ulveda for taking a chance on me and giving me the opportunity to work with him. Dr. Sep´ulveda’s guidance, encouragement, tenacity, vision, careness, and humility have been of great motivation towards my personal, academic, and professional growth. Having him as an advisor is a blessing, an honor, and a privilege. He is an inspiration and example to follow. Like family, I would not be where I am now if it was not for his unconditional support. Thank you. v TABLE OF CONTENTS CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Problem Description and Motivation . . . . . . . . . . . . . . . . . . . . . . 1.2 Thesis Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER 2 BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Flexible Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 MEMS Resonators CHAPTER 3 ELECTRODE EFFECTS ON FLEXIBLE AND ROBUST POLYPROPYLENE FERROELECTRET DEVICES FOR FULLY INTEGRATED ENERGY HARVESTERS . . . . . . . . . . . . . . . 3.1 Experimental Setup for Measuring Open Circuit Voltage and Short Circuit Current for Different Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Compression of Films with Different Thickness due to Uniform Load . . . . . 3.3 Fabrication of FENG Devices . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Scanning Electron Microscopy (SEM) Characterization . . . . . . . . . . . . 3.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER 4 DESIGN, SIMULATION, FABRICATION, AND TESTING OF FIRST GENERATION TUNABLE VO2 COMB DRIVE RESONATORS. . . 4.1 Design Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Experimental Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER 5 CHARACTERIZATION OF SECOND GENERATION OF TUNABLE VO2 COMB DRIVE RESONATORS . . . . . . . . . . . 5.1 Theoretical Approach to Estimate Residual Stress of Lateral Resonant Struc- tures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Experimental Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 4 5 6 6 16 34 34 35 37 40 40 50 51 51 69 73 78 80 80 87 89 99 CHAPTER 6 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 vi CHAPTER 1 INTRODUCTION Traditional electronics are based on using integrated circuits that are mostly manufac- tured over printed circuit boards (PCB), and planar semiconductor wafers. These electronics represent the dilemma of not fitting in irregular, soft and moving objects such as clothes and human skin [1, 2]. However, the aforementioned predicament has also resulted in the birth of flexible electronic technologies directly. The attempt of satisfying the increasing demands generated by the vast amount of consumers of wearable electronics has inspired growing research interests on developing and improving self-powered flexible systems. Wear- able electronic devices can be defined as ”electronic devices constantly worn by a person as unobstructively as clothing to provide intelligent assistance that augments memory, in- tellect, creativity, communication, and physical senses” [2]. The dramatic progress in this research field currently provides a wide-variety of applications such as prosthetics [3], flex- ible pressure sensors [4], biosensors [5], biomedical instruments [6], and health monitoring [7]. A self-powered system requires supplying energy from renewable energy sources. Energy harvesting technologies address this call, and consist of gathering energy from the human activity or the surrounding environment, and transforming it into electrical energy. Among the materials that can be combined with energy harvesting technologies are called smart textiles and are defined as textile products such as fibers, filaments, yarns, and woven structures that can interact with the environment or user [8]. By exploiting their electrical and mechanical properties, fabric-based sensors have been a large field of research in the medicine area. Sensors can be used as electroencephalography (EEG) [9], electrocardiogram (ECG) [10], temperature monitoring [11], and biophotonics [12]. At the component level, a smart textile can be used as an input or output element. As such, combining the electrical and mechanical properties of both technologies -energy harvesters and smart textiles- results in a converging point of research interest. Hence, in the first part of this work, a characterization study is presented where the 1 polypropylene ferroelectret nanogenerator (FENG) energy harvesting material is combined with carbon nanotube fiber (CNTF) smart textile [13]. Piezoelectric patches can now be attached to automotive [14], submerged systems [15], and aerospace applications [16] that enable energy harvesting [17]. These applications require robust yet flexible materials ca- pable of sustaining large deformations like twisting, folding, bending, and stretching, all while maintaining their electrical properties. Carbon-based materials have received plenty of attention due to their ability to offer robustness whilst being flexible, and retaining accept- able conductivity for their use as electrodes. Moreover, polymers like the FENG exhibiting ferroelectric-like behavior -together with its flexibility- have shown great promise in energy harvesting applications [18]. A comparative study was done on open-circuit voltage (VOC) and short-circuit current (ISC) output values between silver metal electrodes and CNTF electrodes. It was found that metal electrodes showed higher VOC peak values regardless of the applied force. Interestingly, the difference in ISC values between metal and carbon nanotube-based fiber electrodes was not as significant. The CNTF electrodes were further in- vestigated by post-treating the fiber with acetone, and comparing the results with untreated CNTF and metal electrodes. Still, traditional electronics built on planar semiconductor wafers like microelectrome- chanical systems (MEMS) are a disruptive technology that have an overarching applicability and impact on wearable electronics. Specifically, MEMS resonators are generating significant research and commercial interest, and are poised to capture a significant piece of the MEMS market. High impact applications of these devices can be divided in two classes: sensing and radio frequency (RF). In the sensing applications a change in the resonance frequency of the resonant element is used to monitor a specific quantity [19] whereas RF applications require reconfigurable flexibility of the resonance element [20, 21]. Both classes have a need of a design that can cope with the high demand of reshaping functionalities and mitigate energy dissipation while maintain high quality factors. Advancements have addressed these issues by incorporating smart materials, like vanadium dioxide (V O2), to the resonator’s design. 2 It has been demonstrated repeatable behavior with reconfigurable states that offers ease of fabrication, low power consumption, and low transition temperature [22]. Therefore, the second part of this work focuses on the design, simulation, fabrication and characterization of a passive tunable V O2 MEMS comb drive resonator. Possessing a monoclinic structure at room temperature, V O2 undergoes a phase transition above 68◦C to a tetragonal structure. This insulator-to-metal transition (IMT) is reversible, and is ac- companied with changes in the mechanical [23], optical [24], and electrical properties [25]. An hysteretic behavior is anticipated during the phase transition, and has been exploited to demonstrate MEMS devices with programmable capabilities [26]. By combining such poten- tial of the V O2 smart material with a MEMS resonator we further contribute to solutions in achieving high reliability, high quality factor, and tunability. 1.1 Problem Description and Motivation The improvement of current technologies, together with the birth of new but immature, presents a quest opportunity to find reliable and multifunctional materials capable of exe- cuting particular roles. For example, a shared element between all energy harvesters is the need for a conductive electrode that can collect and/or transfer charges from one device to another. In the context of multifunctional devices, efforts have attempted to find new materials and develop new gadgets complying with important requirements on performance such as high electrical conductivity, surface area, chemical stability, all while simultaneously being light and mechanically durable [27]. Although previous work has addressed the in- tegration of such devices [28], there exists a current need for fundamental research on the characterization of robust, reliable electrodes for electric component in flexible, wearable, monolithically integrated systems. Furthermore, in the attempt to extend and contribute to solutions that achieve reliability and tunability of MEMS resonators, a proof-of-concept for a passive tunable comb drive resonator is proposed for the first time by utilizing V O2. On both strategic ends, a characterization is presented together with discussions on device performances. The problems addressed in this work are: 3 • Integration of carbon nanotube fibers (CNTF) as tough electrodes on polypropylene ferroelectret nanogenerators (FENG). • Evaluating and understanding of induced charge movement, particularly at the elec- trode interface. • Comparison of electrical and mechanical performance between metal electrodes and CNTF electrodes. • Understanding the dynamic discharging behavior of the FENG in combination with CNTF electrodes. • Evaluating and comparing chemically post-treated CNT fiber performance. • Integration of V O2 thin films on comb drive resonators. • Development of a tunable V O2 resonator able to be electrostatically actuated and electrically measured. • Characterization of comb drive resonators across the V O2 transition. • Implementation of phase transition materials to standard fabrication processes such as PolyMUMPs. 1.2 Thesis Statement The main contribution of this work is to study and characterize the combination of multifunctional materials with current and new technologies. More specifically, the focus resides in carbon nanotube fiber and V O2 materials. The first contribution is the combination of carbon nanotube fiber material with a ferroelectret nanogenerator. This was done in the attempt to develop new devices that can withstand severe environmental stimuli. A complete electrical characterization of the device is presented, together with its fabrication process. The second contribution is the proposition, for the first time, of a tunable comb 4 drive resonator due to V O2 phase transition. Moreover, the fabrication process is adapted such that any MEMS prototype technology can be realized by global company services such as PolyMUMPs. Thesis Statemen: The present work demonstrates a step forward towards the devel- opment and understanding of monolithically integrated, flexible, robust ferroelectret energy- harvesting systems in terms of voltage and current outputs and, together with the fabrication and electromechanical characterization of the first passive tunable V O2 comb drive resonator, further enable new approaches for design considerations in applications on new materials to wearable electronics and MEMS resonators. 1.3 Outline The remaining chapters are organized as follows: Chapter 2 presents a thorough back- ground on carbon nanotube fibers (CNTF), energy harvesters with focus on polypropelene ferroelectret nanogenerators (FENG), and vanadium dioxide (V O2) material; each with their fundamental physics that enables their diverse applications. An exhaustive background is given on resonant elements with emphasis on comb drive structures. It further expands on previous works and technologies. Chapter Chapter 3 involves details on the fabrication of the FENG, the fabrication of the CNTF, and the combination of both technologies. It provides a characterization of the electrical output compared to typical metal electrodes. Chapter 4 provides the design and modeling of a comb drive resonator, focusing on the rubric needed to incorporate a phase transition material such as V O2. To validate the the- ory, a detailed fabrication process is introduced and carried out for first generation devices; Initial electrical measurements are presented showing the first tuning capabilities of a comb drive resonator using the phase transition material. Finally, Chapter 5 shows a second ge- neration of devices together with a comprehensive electrical and mechanical characterization of passive tunable V O2 comb drive resonators. 5 CHAPTER 2 BACKGROUND 2.1 Flexible Electronics The concept of flexible electronics has been around for several decades. In general, any material that is thin and lengthy can become flexible. The prime examples of flexibility are cables and wires, although it was not until the space race that silicon wafers were used as flexible solar cells in satellites. These were thinned to increase their power per weight ratio, and this allowed certain degree of deformation. Such event gave birth to the first flexible solar cell [29]. The following decades were sounding with drumming rolls signaling a huge stride toward flexibility and processability due to developments in conductive polymers [30] and amorphous silicon [31]. These materials became the base for applications that required electronic devices to bend, roll, fold, stretch, among other properties that conventional elec- tronics cannot fulfill. Figure 2.1 Research publication trend on flexible electronics from years 2000 to 2019. Taken from [32]. For the past two decades, there exist an increasing trend on the flexible electronics re- 6 search as shown in Figure 2.1. It has become beneficial to many applications since they have the potential to be thin [33], have increase corrosion resistance [34], can be manufacture to cover large or small areas [35] and, more importantly, flexible. While there is clear progress and many important innovations achieved, this field still face some challenges before it can become part of our life. These challenges present great opportunities for scientific research and development. The following sections are focused on discussing some of the materials of interest, and applications where the need for tough materials able to withstand large mechanical deformations during operation exists. Ferroelectret Materials Polymers that are nonpolar and exhibit ferroelectric-like behavior when a high electric field is applied are classified as ferroelectret materials [36]. Ferroelectrets are a class of piezoelectric-active polymers where many macro-size pore spaces (generally less than 1 µm) within the material are filled with gas. The material is then subjected to electrical breakdown during the application of a high electric field by a corona poling process [37]. Due to the gas breakdown, microplasma discharges are formed inside the pore spaces and micrometer-scaled dipoles are created inside the polymer; this is shown in Figure 2.2. Like ferroelectrics, ferro- electrets materials exhibit dipole switching and polarity reversal depending on the direction of the applied field. Although polyvinylidene difluoride (PVDF) is the most conventional polymer that gen- erates electricity due to the ferroelectric orientation of its dipolar crystals [38, 39], cellular ferroeletret polymers have expanded applications of nonpolar polymers as high performance piezoelectric materials. Polyurethanes (PU) [40], polyolefins (PO) [41], polyvinyl chloride (PVC) [42], polyethylene terephthalate (PET) [43], and polyethylene napthalate (PEN) [44] materials have been used to create ferroelectrets. One thing to point out is that the polymers ideally should have acceptable electrical insulating properties as to maintain highly charged pores. In addition to the aformentioned ferroelectret materials, cellular polypropylene (PP) is 7 Figure 2.2 Polypropylene ferroelectret. Inset shows zoom-in of internal voids with trapped charges. the most researched material as a result of its outstanding properties, flexibility, lightweight- ness and low cost [45, 46, 47]. After the electrical breakdown step, the charges are highly retained inside the popypropylene cell walls due to its great dielectric nature. Furthermore, it has good fatigue resistance and large d33 coefficient. It is for these reasons the research and development of cellular polymers with piezoelectric properties started with PP [48]. Ta- ble 2.1 shows a brief comparison of different polymers with their respective piezoelectric d33 coefficients to that of PP. In general, polypropylene films that are 50 µm to 100 µm are highly considered for piezoelectric applications. Piezoelectric coefficient values for single layered PP films can go up to 1200 pC N at low frequencies [49]. It has also been shown the d33 coefficient to have higher values for multilayered hybrid films [45]. Both -single and multilayered films- exhibit a linear relationship between an applied pressure and electrical output. That is, the conversion of mechanical energy into electrical energy and vice versa. For all this, PP material has been extensively investigated in applications like microphones [50], ultrasonic transducers [51], and energy harvesting [52]. 8 Table 2.1 Piezoelectric d33 Coefficient for Polymer-Based Ferroelectrets. Material Piezoelectric Coefficient Reference ( pC N ) 34 15 10 to 80 80 to 150 0.5 to 1.3 24 to 2100 [53] [43] [44] [41] [54] [49, 55] PVDF PET PEN PO PVC PP Piezoelectric Effect of Ferroelectrets As previously mentioned, ferroelectrets are a class of piezoelectric materials. In fact, ferroelectrets have been referred to as piezoelectrets in prior work [56]. The word piezo is of Greek origin meaning ”pressure”. This effect was discovered by Pierre and Jacques Curie in 1880 while investigating the well-known phenomena of generating a spark by striking certain materials such as quartz [57]. Throughout years, the concept has been refined to address materials that have an electric polarization as a result of an applied mechanical strain. The polarization is directly proportional to the strain, and two effects can be defined. The direct piezoelectric effect refers to the generation of electrical charges from a mechanical stress, whereas the inverse piezoelectric effect refers to the generation of a mechanical motion due to an applied electric field. This reversible effect can be measured via the so-called d33 coefficient [58]. Literature shows this coefficient has been associated with other names such as piezoelectric d33 coefficient [59] or electromechanical d33 coefficient [60]. Classic piezoelectric systems consist of organic, ceramic, or single crystals. Examples are quarts [57], lead zirconate titanate (PZT), and lithium niobate (LiNbO3) to mention a few. To describe these materials, a set of linear equations known as constitutive equations are used, S = sT + dE D = dT + ϵE 9 (2.1) (2.2) where E is the electric field, ϵ is the permittivity, d is the piezoelectric coefficient, T is the stress, s is the elastic compliance, S is the strain, and D is the electric displacement. Following Neumann’s principle [61], 20 groups out of the 32 crystal point groups can exhibit piezoelectric effects, which generally are the result of noncentrosymmetry. The polypropylene ferroelectret (PPFE) does not has a crystalline arrangement. In- stead, its piezoelectric behavior is attributed to the opposite charges accumulated at the top and lower bounds of the internal artificial voids which become highly oriented dipoles after the breakdown process. When the material experiences a compression or expansion in the thickness direction, a reshaping of the dipoles occurs, leading to charge accumulation at the electrodes which can be measured as an electrical output (e.g., voltage or current). The inverse effect is also observed; by applying a potential difference between the electrodes also reshapes the internal dipoles, causing the PPFE to mechanically contract of expand. As mentioned in section 2.1, the piezoelectric coefficient d33 is of interest when considering polymer materials. The reason for this matter is that, due to the anisotropy of the lens shaped voids and low symmetry of charge distribution, the highest piezoelectric sensitivity is in the 3rd axis, or better known as the thickness direction; this is also where the electrodes are placed. This value is typically larger than in-plane piezoelectric coefficients (e.g., d31 and d32). For this reason –and together with additional exploitable properties– the PPFE and other ferroelectret materials have been the heart of extensive research in many scientific areas. Energy Harvesters Energy scavenging is defined as transforming natural environmental energy into electrical energy by different transduction mechanisms to supply low-powered electronics [62]. One common example is photovoltaic technology which involves converting solar radiation into electricity using solar cells. It has been shown output powers of 100 mW cm2 can be generated during day time with a 30% conversion efficiency [63]. After the first flexible solar cell [29] the photovoltaic technology has been well developed by improving physical and electrical 10 properties. However, two main drawbacks still remain: 1) the output power is proportional to the size of solar panels, and 2) it becomes somewhat inefficient on cloudy days and nights. Anton et al. performed an electrical characterization on cellular PP [64]. Input frequen- cies ranged from 10 Hz to 1 kHz, representing typical ambient vibrations [65]. They found the d33 coefficient to be 175 pC N and fairly constant at the given frequency range. To further investigate the material’s potential to harvest energy, a pre-tensioned 15.2 x 15.2 cm2 sam- ple was harmonically actuated by a electromagnetic shaker at 60, 80, and 100 Hz. Results showed average powers of 6 µW that were delivered to a 1 mF storage capacitor, charging the capacitor to 5 V in 30 minutes. This proves the ability of ferroelectrets to supply power to small electronic components. Multilayered stacks of ferroelectrets have also been investigated for energy harvesting applications. Luo et al. developed an insole that could harvest the energy from footsteps [66]. The insoles varied in number of staked layers from 20 to 80. It was found that increasing the number of stacked layers reduce the time a 2.2 µC was completely charged from 7 seconds to 1 second. Furthermore, the authors used the insole harvesting mechanism to power a commercial ZigBee wireless transmitter. A LED on the receiver was used as an indicator when the 8-bit data was received. Every 3 to 4 steps the LED would turn off, signaling the data transfer. One drawback -the authors point out- is the loss of 50% of the harvested energy. 400 µJ of energy were generated from the insole for 3 to 4 steps, but only 150 µJ were consumed by the transmitter. Still, the study showed the potential of ferroelectrets have for harvesting energy from wearable applications. More recently, a ferroelectret nanogenerator (FENG) was developed to harvest energy out of two elements that has become very important to our everyday lives: displays and com- puters. Li et al. shows the proof-of-concept of powering an LCD touch screen by scavenging energy from finger touch [52]. In addition, they show the proof-of-concept of developing a FENG-based flexible/foldable self-powered keyboard. An electrical characterization is also presented where open circuit voltages (VOC) up to 10 V are possible with the FENG; short 11 circuit current (ISC) values were up to 1 µA. A more rigurous characterization of the FENG was followed by Cao et al. [67]. It was shown the dependency of the current as a function of the rate the force was applied, in addition to a dependency in the output of the FENG due to instrumental loads. Carbon-based Materials While documented observations on hollow carbon nanofibers were done as early as 1950s, the widespread of carbon nanotube (CNT) research began in early 1990s [68]. A single walled carbon nanotube (SWCNT) can be thought as a single sheet of graphene wrapped as a tube. Likewise, a multi-walled carbon nanotube (MWCNT) is made of multiples layers of graphene wrapped together; These can be either open or close ended. Perfect CNTs have an hexagonal lattice structure. However, carbon-based materials can be fabricated by at least four different methods [69] and, depending on the application, they can be tailored to posses unique properties. Figure 2.3 shows an increasing trend on CNT and graphene research, together with a prognostic and confirmation of production capacity from 2004 to 2011. Down the line, CNT production has relied on bulk composites and thin films. Their CNT lattice architecture is usually unarranged resulting in limited properties. More organized ar- chitectures are being studied where yarns, vertically aligned forests, and fibers show promise in new functionalities such as shape recovery [70], large stroke actuation [71], and structural electronics [27]. Even with their organized construction, CNT macrostructures present me- chanical and electrical properties that are beneath those of individual CNTs. Still, it opens a scientific opportunity to carry on the quest to find carbon-based materials that can perform their electrical functionality while simultaneously having mechanical robustness. CNT-Fiber Synthesis and Properties As mentioned in Section 2.1, properties of carbon-base materials depend on their fab- rication process, and at least four different processes are used to create fiber-like CNTs. Coagulation spinning is a technique used to fabricate polyacrylonitrile (PAN) fibers. In 2000, Vigolo et al. first showed the application of the technique to assemble CNTs into long 12 Figure 2.3 CNT and graphene research from 2014 to 2011. A) shows trend and number of publications per year, in addition to prognostic and confirmed commercialization. B) CNT- composite bicycle frame. C) CNT coating as fouling protection. D) CNT transistors over polymer films. E) CNT material used as electrostatic discharge shield. Taken from [68]. Reprinted with permission from AAAS. ribbons and fibers [72]. SWCNTs are dispersed in a sodium dodecyl sulfate (SDS) solution and injected -through a syringe- into a co-flowing stram of polymer solution having 5 wt% of polyvinylalcohol (PVA). The PVA is absorbed by the nanotubes while displacing SDS molecules, resulting in a nanotube ribbon. By varying parameters such as injection rate and flow conditions, the authors were able to vary the fiber’s diameter from a few microns up to 100 µm. Even though the authors don’t show an electrical characterization of the fiber, it was found the Young’s modulus varied between 9 and 15 GPa by tensile loading measurements. Just like thread from a silk cocoon, CNT fibers can also be produced by spinning vertically aligned array forests. In general, an array of CNT parallel to each other must first be done [73], followed by picking of the yarn; the yarn’s diameter was controlled by the tip size of 13 the picking tool. Jiang et al. demonstrated this process [74], although it was found later on that not all CNT arrays could be spun into fibers [75]. Since the fiber was loosely packed, it greatly reduced the load transfer, limiting the fiber’s strength. To improve the fiber using the aforenamed method, Zhang et al. proposed to twist the yarn during the picking step, making MWCNTs from a nanotube array [76]. The MWCTNs array was grown on an iron catalyst-coated substrate using chemical vapor deposition method (CVD). The authors recorded CNT fiber diameters as small as 1 µm while having a tensile strength between 150 and 300 MPa. Moreover, the electrical conductivity of the fiber was 300 S/cm at room temperature, and showing an inverse dependency with temperature. Moving forward, the CNT fibers can also be assembled directly from a furnace chamber where CNTs are synthesized using aerogels. One advantage is that is does not require post- processing, in contrast with the previously mentioned synthesis methods. First reported by Zhu et al., long strands of ordered SWCNT were fabricated using a floating catalyst CVD method in a vertical furnace [77]. The furnace is heated to the pyrolysis temperature of n-hexane while hydrogen is introduced as a carrier gas for ferrocene and thiophene. The SWCNT strands had strength and stiffness values of 1 and 100 GPa, respectively. The electrical conductivity for strands with diameter ranging from 50 µm to 0.5 mm were about 1.5 x 103 S cm. Finally, fibers can also be produced by twisting CNT films. First, the film is prepared using the floating catalyst method. A strip is then sliced from the film, followed by twisting it into a CNT fiber. The feasibility of this method was first demonstrated by Ma et al. [78]. Tensile test showed the fiber had a Youngs modulus that varied from 9 to 15 GPa. One main remark is that this method is limited to the size of the film. Twisting the film may not be suitable for continuous production of CNT fibers. Structural Electronics Due to a growing interest on electronic devices able to withstand larger mechanical de- formations during operation, extensive research has been dedicated to structural electronics. 14 The vision embraces the development of flexible, stretchable, strong electronics that results in the generation of new energy storage devices, sensors, and actuators. In the quest of tough electronic materials, carbon nanotube fibers (CNTF) have shown great promise. Following the previous section, fibers have shown moduli values ranging from 150 MPa to 100 GPa, in addition to electrical conductivity values ranging from 300 S cm to 1.5 x 103 S cm . Although elec- trical conductivity of individual CNTs are still superior to that of fibers (e.g., 106 S cm ) [79], recent advances in fabrication of high performance fiber has resulted in depth exploration of new tough electronic components. A very important component utilized on the majority of electronic devices are wires. From passive to active elements, connections between elements must be physically resilient to severe environmental conditions, able to sustain long periods of use, and present chemical stability during use, all while providing constant flow of charges. Table 2.2 shows a brief comparison between CNTF wires and copper wires. Zhao et al. demonstrated the application of a CNTF wire as the standard electrical wire by replacing metal wires in a household light bulb circuit [80]. The authors found conductivity variations as a function of temperature to be five times smaller than that of copper. Electrical resistivity was in the order of 10-7 Ω m. Due to their low density, specific conductivity was found to be higher than copper and aluminum. Table 2.2 Comparison between CNT wires and copper wires. Taken from [81]. Properties Density ( g cm−3 ) Electrical conductivity ( S Specific electrical conductivity ( S m−1 g cm−3 ) Current carrying capacity ( S cm−2 ) cm−1 ) Strength (GPa) Working life Corrosion resistance Temperature stability (Oxygen atm) Temperature stability (Inert atm) Copper wires 0.28 - 2 10 - 67k 7 x 102 - 19.6 x 106 104 - 107 0.013 - 1.91 Long High Low High CNT wires 8.29 580k 6.5 x 106 3 x 104 0.22 Long Low Medium Medium Maintenance In applications for energy storage, electrodes are the centerpiece. Senokos et al. presented 15 a scalable method to produce robust double-layered capacitors [82]. The fiber electrodes were fabricated in-house and consisted of long networks of CNTs in bundles but imperfectly packed, giving rise to large porosity. By placing an ionic liquid-based polymer between two CNT fibers, free standing device robust capacitors operating at 3.5 V and exhibiting 28 F g−1 were shown. Because of the flexibility of the materials, the capacitor showed no deterioration of the electromechanical properties after several bending cycles. Galvanic charge-discharge curves showed a slight decrease in the ohmic drop (ESR), but kept the appropiate coulombic efficiency. More importantly, after the device was unfolded to its original state, all properties were recovered. 2.2 MEMS Resonators The term MEMS stands for microelectromechanical system. The system consist of com- ponents of sizes ranging from 1 mm to 1 µm. MEMS are designed to target a specific application using electromechanical or electrochemical means. Core elements in MEMS technologies consist of two components: 1) a sensing and/or actuating component, and 2) a transduction component. A resonator can be defined as any device with a vibratory nature. More specifically, it oscillates such that at certain frequencies -called resonant frequencies- their amplitude is maximized or minimized, depending on the interest. This effect is often taken advantage of to measure physical variables of interest. The performance of MEMS resonators is often evaluated by their stability and accuracy of internal clocks and referencing frequency circuits. The global positioning system (GPS) is an example where precision and navigation speeds are highly dependent on their internal clocks [83]. Moreover, RF communication systems using vibrating mechanical tank compo- nents require devices with high stability and high frequencies [20]. Conventional vibrating mechanisms use quartz crystals which is well known and understood [84]. Although quartz- based resonators possess a high point of reliability, high resonant frequencies and Q-factors, there are two main drawbacks. Quartz technology requires off-chip components due to fabri- cation incompatibilities with traditional integrated circuit processes such as complementary 16 metal-oxide-semiconductor (CMOS). Additionally, the footprint and energy consumption are significant. MEMS resonators address these drawbacks because of their small size, low power consumption, and fabrication feasibility. As it was previously mentioned in Chapter 1, MEMS resonators can be divided into sensing and RF applications. Sensing applications include mass sensing [85], temperature sensing [86], vapor/gas sensing [87], flow sensing [88], and so on. The principle of operation relies on measuring a shift of the resonant frequency of the device that is proportional to changes induced from the sensed parameter. This can be accomplished by altering the effective mass of the resonant structure (e.g., deposition of molecules) or changes in the drag force (e.g., fluid velocity, damping effects). The RF class is driven by the wireless communication industry [20, 83]. In this case, the interest is to create resonant devices able to go -according to Nguyen [20]- from 800 MHz to 2.4 GHz. Table 2.3 shows the frequency bands designated by the International Telecommunications Union. Comb drives [89], micro- bridges and micro-cantilevers [22], surface acoustic wave (SAW) [90], bulk acoustic wave (BAW) [91], thermal-piezoresistive [92], piezoelectric [93], and optical rings [94] are few of many resonators. Although each design possess their own trade-offs to consider, most of the frequency bands and specific applications are covered by their unique capabilities. Table 2.3 Frequency values for different frequency bands. Band name Extremely Low Frequency Super Low Frequency Ultra Low Frequency Very Low Frequency Low Frequency Medium Frequency High Frequency Very High Frequency Ultra High Frequency Super High Frequency Extremely High Frequency Tremendously High Frequency Abbreviation ELF SLF ULF VLF LF MF HF VHF UHF SHF EHF THF Frequency 3 - 30 Hz 30 - 300 Hz 300 Hz - 3 kHz 3 - 30 kHz 30 - 300 kHz 300 kHz - 3 MHz 3 - 30 MHz 30 - 300 MHz 300 MHz - 3 GHz 3 - 30 GHz 30 - 300 GHz 300 GHz - 3 THz 17 Modeling and Properties Equivalent Mechanical Model In a vibrating mechanical system, kinetic and potential energies are continuously trans- ferred back and forth. Optimum transfer of energy happens when losses are minimum, and is achieved when the mechanical system is in resonance. Resonant frequencies of a me- chanical system depend on many factors. For example the geometry (e.g., anchor points), dimensions, and materials selected for their fabrication highly impact where the resonance frequency is located (e.g., frequency band). In addition, each resonant frequency is mapped to a particular pattern of motion known as mode shapes. The classic resonator structure is a mass-spring system. In physical systems there is also energy loss mechanisms, and these can be represented with a dampener. The combination of a mass-spring-dampener (MSD) system represents the most simplest model for a MEMS resonator, and is shown in Figure 2.4. Figure 2.4 An equivalent mechanical model for resonators. A mass M is connected to a massless spring and massless dampener, both anchored to a fixed surface. The dampening coefficient, b, is proportional to the velocity of the mass. Moreover, k is the stiffness constant of the spring and x the position of the mass at a given time. By applying Newton’s second law, the relationship that describes the behavior of the MSD system is given by, 18 M x′′(t) + bx′(t) + kx(t) = F (t) (2.3) where F (t) represents the input force to the system. For most mechanical resonating devices, the solution under a sinusoidal or harmonic excitation F (t) = F0Sin(ωt) is of great interest and represents the case of forced harmonic oscillation. As it will be explained later on, in typical MEMS resonator applications the micromechanical structure is forced into vibrations by converting an input electrical signal into a force and applying it to the device. The case of unforced and undampened system can also be described by equation 2.3. By considering the conditions b = 0 and F (t) = 0 and assuming a solution of the form, results in, x(t) = A0Sin(ω0t) ω0 = (cid:114) k M (2.4) (2.5) where ω0 is defined as the undamped natural frequency of the system. Although it is rather simplistic, MEMS resonator can be designed using equation 2.5 to target a band or particular frequency (ω0 = 2πf0) by considering k and/or M of the device. Table 2.4 shows some theoretical resonance frequency expressions for various types of resonator devices similar to equation 2.5. Equations are expressed in terms of structural parameters. Equivalent Electrical Model Although MEMS resonators can be explained using the MSD model, an electrical equiv- alent circuit can also be used due to the analogy that exists between electrical and mechan- ical systems [97]. Table 2.5 shows a summary of the quantities equivalence between models. MEMS resonators are commonly applied as electronic devices, and it has become common to portray them in an electrical manner. A point of clarification must be done to the reader. Table 2.5 shows what are called direct analogies. However, when translating from one net- work topology to another (e.g., mechanical to electrical and vice versa), these are not the 19 Table 2.4 Resonance frequency expressions of micromechanical resonators. Resonator Design Microcantilever and Microbridge SAW; BAW Folded-Beam Comb Drive Disk Resonance Frequency (f0) Reference (cid:113) E ρ [95] f0 = n 2π f0 = ν (cid:113) h L2 λ; f0 = ν f0 = 1 (Ms+ 1 2π f0 = n 2Rπ 2h 24EI 4 Mt+ 12 (cid:113) E ρ 35 Mb)L3 [90]; [91] [89] [96] h = thickness; L = Length; E = Young’s modulus; ρ = density; ν = wave velocity; λ = wavelength; I = Moment of inertia; Ms = Shuttle mass; Mt = Trusses mass; Mb = Beams mass; R = Radius; n = Factor corresponding to a particular mode. same. This comes from the fact that the physical meaning of the variables are different. For example, the force is a through variable, and is analogous to voltage which is an across variable; Current (a through variable) is analogous to velocity (an across variable). Hence, a parallel connection in the mechanical model becomes a series arrangement in the electrical model, and vice versa. Table 2.5 Direct equivalence analogies between mechanical and electrical systems. Mechanical Quantity Electrical Quantity Force (F ) Velocity (v) Displacement (x) Mass (M ) Compliance ( 1 Damper (b) k∗ ) Voltage (V ) Current (i) Charge (q) Inductance (L) Capacitance (C) Resistance (R) *k represents the spring constant. The electrical modeling of resonant devices depend on their design. However, Figure 2.5 shows a series Resistance-Inductance-Capacitance (RLC) circuit, which is both the electrical equivalence of the mechanical system in Figure 2.4 and what most resonant devices are modeled with. Other elements, especially parasitic and feedthrough capacitors are added to the model to reproduce results close in agreement with experimental measurements. To highlight the fact that the electrical elements for mechanical resonators are representative of a physical moving structure (and not actual electronic elements), they are preceded by the 20 term motional, better know as motional parameters of the system. Figure 2.5 An equivalent electrical model for resonators. Quality Factor For many sensor applications, the energy loss and sharpness of the resonant frequency are important. The quality factor (Q) relates to both phenomena. In physics it is defined as the ratio between the total energy stored of the system and the average energy loss in one radiant at resonance [95]. More explicitly, Q = 2π T otal energy stored Energy dissipated per cycle = 2π Es ∆E (2.6) As the damping ratio that determines the Q factor is usually very small and difficult to estimate theoretically, it is mostly found through experimental measurements. The total stored energy of a system is given by, Assuming a solution in the form of equation 2.4, the total energy is, Es = 1 2 M ˙x2 + 1 2 kx2 Es = 1 2 M A2ω0 2 21 (2.7) (2.8) The energy dissipation in one cycle is calculated as, ∆E = (cid:90) 2π 0 F d ˙xdt (2.9) where Fd = −b ˙x is the damping force. Substituting equation 2.4 into the integration result of equation 2.9 generates, Replacing equations 2.8 and 2.10 into equation 2.6 results in, ∆E = πbA2ω0 Due to the direct analogies between mechanical and electrical domains, Q = 2π Es ∆E = M ω0 b Q = Lω0 R = ω0 ∆ω = f 0 ∆f (2.10) (2.11) (2.12) where it is known that ∆ω = R L . It must be recognized, by replacing ω0 with equation 2.5 and utilizing the corresponding electrical equivalence it becomes clear Q also depends on the capacitance of the system (e.g., mechanical compliance). From the previous analysis, when the electrostatic actuation and detection technique is used to measure the resonance of a MEMS resonator, the quality factor can be extracted by using the full width half maximum (FWHM) from the resonance data. Figure 2.6 shows a measurement example of a MEMS resonator. When a resonator is vibrating and resonance occurs, large output currents are produced by the structure. This output is transmitted and/or reflected to the device’s measuring port(s). Typically, scattering parameters are used in RF circuits to measure the ratio between output and input signals. In most cases, the transmission coefficient magnitudes (e.g, S21 or S12) are plotted as a function of frequency. The half power points (e.g., AM ax − 3dB in Figure 2.6) are then found to the right and left of the resonant peak f0; These values are found −3dB below the maximum amplitude (AM ax). 22 Figure 2.6 Example of a resonance measurement using electrostatic actuation and detection technique. Quality factor can be obtained directly from the measured data. A final comment must be made regarding the quality factor parameter. Following equa- tion 2.6, a portion of energy stored in the system is inevitably lost. Viscous losses (e.g., liquid or gaseous mediums), anchor losses (e.g., boundary conditions), and material losses are some the most recognized means of dampening a system [98]. To this end, the overall quality factor Q of MEMS devices can be described as, QTotal = ( (cid:88) 1 Qi )−1 (2.13) where Qi represents the damping effect from each of the potential loss mechanism. Transduction Mechanisms Nearly all MEMS resonator applications (see section 2.2) are interfaced with electronic circuits. To that end, the mechanical vibration of the structure should be excited and sensed by electrical means. Traditionally, the transduction methods are classified into two groups: capacitive (electrostatic) and piezoelectric. Nevertheless, actuation methods like electrical or piezoelectric, in combination with optical sensing, are also utilized to measure resonance frequencies. Both are non-destructive techniques, which is their great advantage. One familiar instrument to measure mechanical resonance is a vibrometers. The res- onator is placed on top of a thick piezoelectric substrate to induce mechanical vibrations in the structure. The device itself –either by electrostatic forces or thin film piezoelectric 23 means– can also be resonated through direct electrical inputs. An infrared laser is aimed at the surface of the structure and reflects back to the instrument. Most vibrometers have a specialized Michelson interferometer that allows the extraction of vibration amplitude and frequency. A variation of this technique consists on using a photodetector to engulf the reflected laser spot from the resonator’s surface. Any movement of the mechanical structure (hence, the reflected laser) is picked up as an electric signal. To sense electrically, the capacitive technique is widely used due to its easy implementa- tion. The design of the resonator considers two conducting plates separated by a dielectric. A voltage is applied in which a force displaces one of the plates, given one is free to move. Changes in capacitance results in induced currents, and output signals are measured. This method is further explained in detail in the following section. Electrostatic The theory governing of electrostatic actuation is well-established. The essential compo- nents of an electrostatically actuated resonator are depicted in Figure 2.7. A capacitor is formed between the well-known microbridge (i.e., moving plate) and the sensing port (i.e., fixed plate). The static capacitance is given by, C Static = Aϵϵ0 d (2.14) where A is the overlapping area of the plates, d is the distance between the two plates, ϵ0 is the permittivity in vacuum (ϵ0 = 8.85x10−12 F m ), and ϵ is the relative permittivity of the dielectric medium between the plates (approximated as unity for air). Equation 2.15 shows the static capacitance is dependent upon the geometry of the electrodes. To achieve an electrical measurement from the structure, a DC voltage (VDC ) is applied to the structure, and an AC voltage (VAC) is applied to drive the structure. In this case the capacitance is give by, Q = CV 24 (2.15) Figure 2.7 Schematic representation of a two-port MEMS resonator. Taking the time derivative, dQ dt = i(t) = V ∂C ∂t + C ∂V ∂t (2.16) The microbridge is biased with a DC voltage, while it’s actuated with an AC voltage. The applied voltage to the structure is composed of, where, V = V DC + V AC V AC = V 0Sin(ωt) (2.17) (2.18) Considering only a DC voltage (e.g., VAC = 0) is applied to the microresonator, and assuming the right hand electrode is only present (e.g., actuation port), an electrostatic force is created such that the moving plate will bend towards the actuation electrode. Since both the capacitance and voltage of the system are constant with respect to time ( ∂C ∂t = ∂VDC ∂t = 0), there is no output current. On the other hand, if VAC is only applied to the microstructure (e.g., VDC = 0), the structure will not vibrate unless ω = ω0. In this case, the output current will be given by i(t) = C ∂VAC ∂t . If equation 2.17 is now considered as the electrical input, expression 2.16 becomes, i(t) = (V DC + V AV) ∂C ∂t 25 + C ∂(V DC + V AC) ∂t (2.19) In practice, the magnitude of VAC is much smaller than VDC. If large values of driving voltage are used, nonlinearities in the structure are present [99]. Also, VDC does not change with time. Applying both conditions to equation 2.19 results in, i(t) = V DC ∂C ∂t + C ∂V AC ∂t For a moving plate, the expression for capacitance can be described as, C = Aϵϵ0 d − x (2.20) (2.21) where A is the overlapping area of the plates, d is the distance between the two plates, ϵ0 is the permittivity in vacuum (ϵ0 = 8.85x10−12 F m ), ϵ is the relative permittivity of the dielectric medium between the plates (approximated as unity for air), and x is the plate displacement. Using the product rule, the derivative of capacitance with respect to time can be expressed as, which gives, ∂C ∂t = ∂C ∂x ∂x ∂t ∂C ∂t = Aϵϵ0 (d − x)2 ∂x ∂t (2.22) (2.23) As will be shown later, the driving force is proportional to the driving voltage (e.g., VAC). Since the magnitude of this voltage is small, the displacement of the moving plate is also small compared to the gap between plates (e.g., x << d). By applying this condition to equation 2.23 and further substituting its result into equation 2.20 gives, i(t) = η ∂x ∂t + C ∂V AC ∂t (2.24) 26 where η = VDC Aϵϵ0 d2 is defined as the electromechanical transduction factor. The first term in the left hand side of equation 2.24 describes the motional current that comes from the varying capacitance while the second term describes the AC-current through the capacitor. Previously it was mentioned the driving force is proportional to the voltage applied to the structure. In the attempt to describe this fact, the energy stored in a parallel plate capacitor is considered and is given by, From equation 2.25, the force is calculated as, Ecapacitor = 1 2 CV 2 F = ∂Ecapacitor ∂x = 1 2 V 2 ∂C ∂x Substituting equations 2.17 and 2.18 results in, F = 1 2 [VDC 2 + 2VDCV0Sin(ωt) + V0 2Sin2(ωt)] ∂C ∂x (2.25) (2.26) (2.27) From equation 2.27, three forces can be utilized to actuate a resonator. First, a standard drive technique can be used where only the VAC is applied, and corresponds to the third term in equation 2.27. However, the Sin2(ωt) results in an applied signal at twice the drive frequency. This results in nonlinearities between the force and applied bias. In addition, the magnitude of VAC must be large to drive the resonator, which results in a cross-talk between the input and output ports. The first term corresponds to the case where a DC bias is applied to the structure. As previously mentioned, a purely DC-force bends the beam but does not have a dynamical impact on the structure. Finally, the second term represents the case where a DC and AC voltage are applied to the structure. In this instance, the magnitude of the force can then be controlled by the DC voltage, limiting AC signal feedthrough, which has the same frequency as the overall driving force. For this reason, the force can be approximated as, 27 F = VDCV0Sin(ωt) ∂C ∂t = ηVAC (2.28) where η is the electromecanical transduction defined in equation 2.24. It represents the connection between the mechanical and electrical domains of the system. Piezoelectric The piezoelectric effect was briefly described in section 2.1. Piezoelectric materials are anisotropic in nature. This means their electrical, mechanical, and electromechanical prop- erties differ for the electrical/mechanical excitations along different directions. Depending on the application, standarized reference axes are used by crystallographers to identify them, e.g., 1 corresponds to x axis; 2 corresponds to y axis, and 3 corresponds to z axis. These axes are defined during the poling process that induces the corresponding piezoelectric properties in the piezoelectric material. In MEMS technology, most piezoelectric thin films are polycrystalline which manifests in an averaged piezoelectric effect over all the grains. Materials such as aluminum nitride (AlN) and zinc oxide (ZnO) are of interest and commonly sputter deposited [93, 100]. Al- though both thin films materials exhibit quite similar piezoelectric properties, the transverse piezoelectric coefficient is larger in ZnO. On the other hand, AlN is mostly prefeared over ZnO due for two main advantages. First, it is perfectly compatible with CMOS technology, whereas zinc (Zn) is problematic due to its fast ion diffusion. Second, AlN is a large band gap material (e.g., 6 eV) while ZnO is a semiconductor (e.g., 3 eV) that is prone to increased conductivity due to its off-stoichiometric doping susceptibility. Thin films and bulk piezoelectric devices differ on how the elastic properties are dom- inated by the structure material, in combination with their geometry. Figure 2.8 shows a silicon cantilever (e.g., substrate) where a piezoelectric thin film has been sandwiched be- tween electrodes. Interactions with the substrate is anisotropic [101]. The thin film and the substrate have identical strains along the in-plane direction (e.g., 1- and 2- axis). In the 3rd direction, the structure is free to move. As a consequence of this fact -and ap- 28 Figure 2.8 Example of a piezoelectric resonating cantilever structure in actuator and sensor applications. plying a potential difference between the electrodes- the cantilever moves perpendicular to the film/substrate planes (e.g., vertical mode) [102]. On the other hand, if a thin film is deposited on a microbridge of bulk substrate, in-plain strain can be dominant and excite lateral and extensional modes [93]. Tuning Techniques Tuning techniques applied to MEMS resonators can be classified in two major groups. One group corresponds to the passive tuning of the resonance frequency. This type of tuning results in one-time permanent changes on the device. The other group corresponds to actively tuning the resonance frequency. In contrast to the passive group, active tuning is reversible and is the most used tuning technique. Passive Frequency Tuning A common approach to passively tune a resonator is the use of post-fabrication steps. Courcimault et al. passively tuned single-crystal silicon resonators by depositing gold at the surface of the device [103]. Resonance frequency shifts over 11% were recorded, with a tuning resolution of 90 Hz nm. Although the quality factor decreased from 25,000 to 5,000, the authors were able to restore it by post-annealing the device. Enderling et al. provided a novel frequency tuning method by depositing platinum on top of silicon carbide and polysilicon microcantilevers using the focused ion beam (FIB) method [104]. A 15.5% in shift of the 29 resonant frequency was observed, together with a decrease in the quality factor. Passively tuning a resonator is suitable to compensate any frequency shift as a result of inadequate manufacturing. However, the devices treated with this technique will not be able to perform real-time tuning. In applications where significant tuning is desired, the use of this technique is not recommended; After the reshaping process, the frequency tuning is limited to a few Hertz. More importantly, post-fabrication process can result in complications towards the end result, increasing the cost of the manufacturing process. Active Frequency Tuning Transduction mechanisms, such as the ones mentioned in section 2.2, can also be used to implement active tuning on resonators. Table 2.6 shows a comparison between some actua- tion mechanisms that are used to actively tune resonant structures. Tuning configurations can be either on-chip schemes including eletrothermal, capacitive, and magnetomotive; or they can be done off-chip such as photo-thermal tuning. Table 2.6 Active tuning methods for MEMS resonators. Taken from [105]. Tuning Method Fabrication Process Power Consumption Applied Voltage Current Electrothermal Electrostatic Magnetomotive Photothermal Simple Simple Simple Complex High Low Medium Medium High Low Medium - Low High Low - Electrothermal tuning consist on applying localized heating to induce thermal stress and strain. The expansion or contraction of the material changes the spring constant of the structure, effectively changing the resonant frequency. Remtema et al. implemented the electrothermal tuning capability to a comb drive resonator [106]. By forming a localized Joule heating on one of the structure’s suspension, a shift in resonance frequency up to 6.5% was measured with a central frequency at around 31 kHz. Electrothermal tuning can also be induced by heating the device externally, resulting in the heating of both the resonator and the substrate. In contrast with localized heating, this layout resulted in the tuning of 30 resonant frequency only of 1%. The authors attribute this to the expansion of both the resonator and substrate, keeping the thermal stresses to a minimum. Electrostatic tuning is one of the most attractive methods for active tuning capabilities. The stiffness of the system can be adjusted by mechanically changing the length of the suspension. Zine-El-Abidine et al. were successfully able to implement this capability [107]. The design consisted on a curved electrode close to the beams. Isolated stoppers were incorporated into the curved electrode to prevent shorting. When a DC bias was applied to the curved electrode, an electrostatic force resulted in the pulling of the beams and effectively reducing their length. As a result, the resonant frequency of the structure was tune from its original value of 10.8 kHz to 17.6 kHz and 21.4 kHz. Although not mentioned in Table 2.6, stress tuning is also an active tuning technique. In general, the resonant frequency of a MEMS resonator is dependent upon tensile or compres- sive stresses. Cao et al. were able to implement this technique by exploiting the mechanical properties of a solid-to-solid phase transition material [22]. Microbridges were coated with vanadium dioxide (V O2), followed by placing the sample above a piezoelectric. A heater was incorporated inside the structure, and this was used to induce the phase transition of V O2, which occurs above 68◦C. Authors recorded frequency shifts up to 8%. Vanadium Dioxide Oxide materials that undergo reversible transitions between metallic and insulating states have been of great interest for both theoretical and practical reasons. Their unique phys- ical properties, along with their phase transitions at different temperatures, offer a wide range of applications in the fields of high speed electronics, memory devices, electro-chromic and thermo-chromic applications, field emission displays, cathode material in batteries, etc. Among these strongly correlated materials, vanadium oxides can adopt a wide range of V:O ratios that result in different structural motifs which determine their physical properties. The most studied of these materials is vanadium dioxide (VO2), but several other vanadium oxides have been studied to varying degrees. The main advantage of this polymorph is its 31 phase transition close to room temperature. V O2 Crystal Structure V O2 presents a reversible solid-to-solid phase transition at 68◦C. Figure 2.9 shows the crystalline structure for each phase. The most stable structure is V O2(R). It is stable from 68◦C to 1540◦C with tetragonal cell parameters aR = bR = 4.55 ˚A, cR = 2.88 ˚A; The structure is rutile type, and the space group is P42/mmm(S.G. #136) [108]. When the temperature is lower than 68◦C, the V O2(R) structure changes to a monoclinic (M1) phase with spacegroup P21/c(14) . In this case, the lattice parameters are aM1 = 5.75 ˚A, bM1 = 4.53 ˚A, cM1 = 5.38 ˚A, and βM1 = 122.64◦ [108]. When a V O2 film is deposited over amorphous silicon oxide (SiO2) or single crystal silicon (SCS), the material orients itself such that the plane (011) of the M1 phase and (110) of the R phase are parallel to the substrate [109]. From the previous lattice parameters it can bee seen the area of the plane for the tetragonal phase is smaller than that of the monoclinic phase. Substantial strains up to -0.30% on heating through the solid-to-solid phase can be achieved. This deformation is then exploited to develop actuators [110] and tunable resonators [22]. 32 Figure 2.9 Crystalline structures for high-temperature tetragonal rutile phase (R) and low- temperature monoclinic phase (M1). Blue atoms denote Vanadium (V) and red atoms oxygen (O). Take from [111]. 33 CHAPTER 3 ELECTRODE EFFECTS ON FLEXIBLE AND ROBUST POLYPROPYLENE FERROELECTRET DEVICES FOR FULLY INTEGRATED ENERGY HARVESTERS This work is focused on the integration of CNTFs as electrodes in flexible polypropylene ferroelectret films (PPFEs) that have an electric response to a mechanical stimulus. The purpose is to shed light on the understanding of the movement of induced charge, particu- larly at the electrode/supercapacitor interface, which is necessary to control ripple currents from the device to energy storage components and enable fully integrated thin film-based energy harvesting system development. The study includes a characterization and com- parison between metallic and CNT fiber electrodes that requires robustness and flexibility. Although cracks are used in electrodes to improve detection in sensors or to enhance mass transport, this work emphasises on crack-free electrodes which are important on assisting FENG devices in their integration to tough electrodes applications. 3.1 Experimental Setup for Measuring Open Circuit Voltage and Short Circuit Current for Different Electrodes Figure 3.1a shows the schematic for the experimental setup. The stepper motor was computer-controlled using a DAQ NI cRIO9075. To measure the applied force, a flexible force sensor (A502, Tekscan, Inc.) was placed between the samples and the holding scaffold. By using a voltage divider -where the force sensor was the variable resistor- the force amplitude and velocity resulted in an output signal measured by a Digital Storage Oscilloscope (TDS 2004C). The open-circuit voltage (VOC) and short-circuit current (ISC) of the samples were measured using a Keithley 2450 Source Meter. Both instruments were connected to a second computer in order to extract the data. Figure 3.1b shows a picture of the set-up. 34 Figure 3.1 a) Schematic illustration of the experimental configuration and b) close-up picture of the motor-piston configuration. 3.2 Compression of Films with Different Thickness due to Uni- form Load A uniform load is considered to be applied on two samples with different thicknesses L1 and L2, where L1 > L2. From the setup described in Section 3.1, the piston generates the uniform load and travels a fixed distance. This is represented by the red dashed line in Figure 3.2. The thickness reduction is represented by ∆L1 and ∆L2 on samples 1 and 2, 35 Figure 3.2 Uniform load distributed over two samples with different thickness. respectively. Assuming L1 = 2L2, Re-writing ∆L1 as, ∆L1 L1 = ∆L1 2L2 ∆L1 = L1 − L2 + ∆L2 and substituting into equation 3.1 results in, ∆L1 L1 = L1 − L2 + ∆L2 2L2 = 2L2 − L2 + ∆L2 2L2 = L2 + ∆L2 2∆L2 which can be simplified to, ∆L1 L1 = 1 2 [1 + ∆L2 L2 ] (3.1) (3.2) (3.3) (3.4) The previous expression can be extended to a more general case where L1 = αL2, where α > 1. This brings the following general expression, ∆L1 L1 = 1 α [(α − 1) + ∆L2 L2 ] (3.5) 36 3.3 Fabrication of FENG Devices In order to study and compare the effects of different electrodes (and their processing) on the electrical output of the FENG, three devices with distinct electrodes were prepared: silver electrodes (S-FENG), CNT fiber with no treatment (CNTF-NT), and CNT fiber treated with acetone (CNTF-A). Figure 3.3 Frabrication process for a) S-FENG, b) CNTF-NT, and c) CNTF-A and S-FENG- A samples. S-FENG Fabrication Figure 3.3a shows the fabrication process. A thin film of silver (∼ 500 nm) was deposited over both sides of the polypropylene (20 mm x 40 mm) with a sputter coater (Hummer X, Anatech Inc.) (Figure 3.3a2). This was followed by manually attaching electrical wires to 37 each electrode using copper tape (Figure 3.3a3). Finally, Kapton tape was used to encapsu- late the sample (Figure 3.3a4). CNTF-NT Fabrication Figure 3.3b shows the fabrication process for this device. Fabrication and characteri- zation of the CNTF are discussed in detail elsewhere [82]. Briefly described, CNT fiber samples consisted of unidirectional fabrics of multiple overlaid carbon nanotube (CNT) fiber filaments. These are produced by spinning directly from the gas phase during CNT growth by chemical vapor deposition. The volumetric fraction for the CNTF-NT sample was around 0.512. Electrical wires were connected similarly to the S-FENG sample (Figure 3.3b3). The process was followed by placing Kapton tape over the fiber, trying to avoid electrical dis- continuity or additional mechanical wrinkling of the fiber by carefully placing the tape and placing it over the fiber. The tape was lifted with the fiber, and then placed over the surface of the polypropylene foam (Figure 3.3b4). The CNT fiber is made up of multiwalled CNTs (MWCNTs) with an average outer diam- eter of 5 nm and three layers, as reported previously [112], making it a complex hierarchical structure. Microscopically, the fiber is made up of few-layer MWCNTs. They are coupled into bundles, somewhat analogous to elongated graphitic crystals, where the CNTs are in close proximity under turbostratic stacking. At the macroscopic level, the CNT fibers consist of networks formed by continuous bundles. The axial elastic modulus of the constitutent MWCNT is in the range of 1 TPa. In the CNT fiber, the MWCNTs are predominantly aligned in the layer direction, but randomly oriented in the plane. The longitudinal modulus of the densified CNT fiber layer is around 10 GPa. CNTF-A Fabrication The CNT fiber and the PPFE foam were submerged in a Petri dish with acetone (Figure 3.3c). To attach the second electrode, a visually transparent substrate was used to cover the side; the first electrode was already placed in order to monitor the electrode while removing the substrate. This process fixed the electrode, preventing it from detaching or moving from 38 its intended position. The sample was left drying for 3 minutes. Finally, electrical wires were attached to the electrodes, and the sample was encapsulated in Kapton tape. The volumetric fraction for the CNTF-A sample was around 0.272. Dimensions for the silver and CNTF-NT electrode devices were 20 mm x 40 mm. The CNTF-A sample was cut with these dimensions but, upon acetone exposure, the fiber wrin- kled in both lateral and longitudinal directions. Stretching of the fiber was done immediately after it was placed over the foam, taking advantage the fiber was still wet and allowed easier manipulation. Despite this effort, the final size of the CNTF-A sample was slightly smaller. Figure 3.4 SEM pictures of CNT fiber a) with no treatment (CNTF-NT) and b) with acetone treatement (CNTF-A). A higher density and packing fraction of the CNTF-A film can be noticed. Cross-sectional view for c) CNTF-NT and d) CNTF-A. 39 3.4 Scanning Electron Microscopy (SEM) Characterization SEM pictures were obtained using a JEOL 7500F field emission emitter scanning electron microscope (JEOL Ltd., Tokyo, Japan) operated at 5 kV. Figure 3.4a and 3.4c show a top view and cross section of the carbon nanotube fiber without acetone treatment, respectively. From the top view it is clear the fiber density is lower for the sample with not acetone treatment; the thickness is 98 µm. In contrast, Figure 3.4b and 3.4d shows how the acetone treatment decreased the air voids, increasing the fiber density; the fiber’s thickness decreased by a factor of 10. From the SEM image it can also be observed non-uniform thickness. Finally, acetone treatment on the polypropylene also had the same shrinking effect. In this case, the thickness was reduced by 30 µm when treated with acetone. 3.5 Results and Discussion VOC Output The mechanical load for these results consisted of a cyclic pressure applied through a computer-controlled piston that resulted in a triangular profile. The applied pressure was calculated by using a force sensor and the dimensions of the device. It has been shown the open-circuit voltage (VOC) of the FENG device depends linearly on the magnitude of the applied force (or pressure) [113]. For this reason, each sample was expected to show a profile in which VOC peak value (Vp) would increase with pressure. Profiles of the outputs are shown in Figure 3.5. The experiment was repeated three times for each sample and pressure, and the same behavior was measured. Results show that, for any given pressure, the S-FENG shows larger Vp values, and the difference in this value between the two CNT fiber-based FENGs is smaller in contrast with the difference between the Vp for the S-FENG and CNTF samples. This observation indicates that the difference in conductivity between samples may be playing a dominant role in determining VOC following that the difference in conductivity between silver and CNTF is about 3 orders of magnitude (σ (Silver) ≈1 x 107 S m , σ (CNTF-NT) ≈1 x 104 S m ), while the difference in conductivity of CNTF after acetone treatment is by a 40 factor of 2 [114, 115]. These results provide the first demonstration that the CNTF layer can be used as a current collector to transfer charge from piezoelectric energy-harvesting processes. The interest then is to compare CNT fiber-based electrical performance to that of conventional metallic conductors. It is worth mentioning that, although silver-based devices show higher Vp values, their peak widths and integrals values were consistently smaller than those obtained for CNTF-based samples. Recalling that the electrical energy produced by each pulse if proportional to the integral of the voltage-current product, this suggests that higher energies can be obtained from the CTNF-based samples. Figure 3.5 VOC for 20 mm x 40 mm S-FENG, CNTF-NT, and CNTF-A samples. From left to right, peaks corresponds to pressure of 20, 50, 75, and 100 kPa for each sample. The Vp values for each corresponding pressure are summarized on the tables. In addition to conductivity, another difference between electrodes is the process in which 41 the force of the mechanical input is transferred to the PPFE film. As described in Section 3.1, the applied force by the step motor was computer-controlled through the total displacement of the piston. In this case, the force applied on the electrode is a uniform distributed load which is transferred through the electrode to the surface of the PPFE film. This in turn generates compression of the microscaled dipoles across the film’s thickness (see section 2.1). The force acting on the PPFE surfaces (for any of the different electrodes) can be expressed as F = EA∆t t (3.6) where E represents the Young’s modulus of the electrode, A is the cross-sectional area, t is the initial thickness of the electrode, and ∆t represents the change in thickness of the electrode during compression. Since the surface area of the piston was invariable throught the measurements, it leaves E and ∆t t as the two parameters that influence the force across the different electrodes. Following the step motor uses a change in the piston’s displacement to control the applied force, an electrode with a larger thickness will show a larger thickness compression. It can be shown that (see Section 3.2), ∆t1 t1 = 1 α [(α − 1) + ∆t2 t2 ] (3.7) In this case, the thickness of the silver electrodes (∼ 500 nm) is more than 2 orders of magnitude smaller than the thickness of the CNTF-NT. It would not be accurate to give an exact thickness of the CNTF based-electrodes since the film is very rough and non-uniform, with thicknesses up to ∼ 100 νm for CNTF-NT and ∼ 10 νm for CNTF-A (see Section 3.4). Nontheless, the thickness variation does not affect the following analysis. The value of ∆t t for the samples with CNTF-based electrodes will be larger than from the silver-based counterpart. However, if this parameter dominated, the force (and hence Vp) would be larger for CNTF-based samples, which is exactly the opposite of the results. 42 This implies the higher conductivity value and larger Young’s modulus of silver electrodes must be the dominant factor in determining the force applied on the PPFE surface. A significant difference exists between the Young’s modulus of CNT fibers (∼ 0.21 GPa) for transverse direction [116]) and silver (∼ 69 GPa). Although this ratio (e.g., ESilver ECN T F ≈ 310) is not as large as the largest possible difference in the ∆t t ration between S-FENG and CNTF- NT samples, there exist other physical conditions that nee to be considered. It should be noted that the volume occupied by a CNTF-NT electrode holds a large amount of air-filled spaces, in constrast to a continuous solid film such as the silver electrodes. This reduces the strain resistance of CNT fiber electrodes. In fact, compression through a thicker, less dense electrode increases compression time, which reflects on the widest measured VOC pulse for the CNTF-NT sample, followed by the CNTF-A sample, which has an electrode thickness and density values between the CNTF-NT and silver electrodes. In addition, the roughness of the CNTF electrodes causes a force distribution on the PPFE surface to be less uniform, causing dipoles across the film thickness to be compressed at different times and rates. Given that ESilver ECN T F is much lower than the difference in electrode conductivity, the result suggests a higher charge accumulation at the electrodes when using metal electrodes with a higher conductivity compared to CNTF-based electrodes. Comparing Vp between the two CNTF-based FENG devices, the difference is not dom- inated by a difference in conductivity since the relative small increase in conductivity of CNTF after acetone treatment would be expected to generate an increase in Vp; this is op- posite to the obseved behavior. Vp measurements between the two CNT fiber-base electrodes can be analyzed in terms of the same two parameters: E and ∆t t . However, such analysis would not provide insight on the behaviour of the output. Acetone treatment results in a reduction of the fiber by 50x [115], but makes the film denser by reducing the air voids. These two effects induce opposite consequences of similar magnitude on the force transferred to the PPFE surface. Hence, analyzing these two parameters will not reveal the mechanisms for the in Vp between the CNT fiber-based electrodes. 43 The dominant mechanism for the decrease in Vp in CNTF-based sample after acetone treatment was found after taking a closer look at the cross section of the CNTF-A sample under the SEM. From Figure 3.4d, the PPFE film thickness was ∼ 30% smaller compared with the CNTF-NT and S-FENG samples. This thickness reduction also reduces the average size of the dipoles within the PPFE. Given that Vp in FENG devices is porportional to the dipole size [113], it stands to reason observing smaller values of Vp for the sample exposed to acetone. To further validate this, PPFE samples were treated with acetone and then coated with silver electrodes (hereinafter referred as S-FENG-A), and the testing of such samples indeed revealed lower Vp values than their counterparts without acetone treatment. Table 3.1 shows the contrast between the S-FENG and S-FENG-A values of Vp. Table 3.1 Average Vp values for S-FENG and S-FENG-A samples. Pressure S-FENG Average Peak Voltage S-FENG-A Average Peak Voltage (V ) 13.16 30.88 44.51 69.49 (V ) 13.74 29.2 39.55 55.02 (kP a) 20 50 75 100 ISC Output Unlike VOC, short circuit current (ISC) curves show a bipolar peak-to-peak response as shown in Figure 3.6. Briefly explained, in contrast with VOC which is dependent on the compression load and internal impedance of the instrument, ISC is only dependent upon the magnitude and the rate of change of the load [67, 113]. Hence, loading and unloading of the FENG results in an undulating behavior of the current output. The average of the first ISC peak value (Ip−ave) resulting from the pushing cycle was used. It should be pointed out to the reader that both Ip−ave values (e.g., positive and negative) were very similar, and using either does not change the following analysis. As previously mentioned, ISC of the FENG depends on the magnitude and rate of change of the applied force (or pressure). From Figure 3.6, for the same sample, Ip−ave increased as 44 Figure 3.6 Short circuit current for 20 mm x 40 mm S-FENG, CNTF-NT, and CNTF-A samples at a) 20, b) 50, c) 75, and d) 100 kPa. the applied pressure magnitude increased from 20 to 100 kPa while keeping the actuation speed as a constant. A closer look shows there is a smaller percentage increase on the output, in contrast with the results of VOC for the same sample and change in pressure. Given the rate of change was constant, this suggests there are additional mechanisms impacting ISC. In the previous section it was explained how electrode conductivity played a significant role in the charge accumulation (e.g., VOC). It would be expected to play a more significant role in charge flow (e.g., ISC). The smaller Ip−ave output for the CNTF-based electrodes is most likely due to smaller conductivity in contrast with the S-FENG. However, this is not the dominant factor when considering the CNTF-A sample since the CNTF conductivity is not significantly changed after acetone treatment. The difference in thickness between 45 the two CTNF-based electrodes is not the dominant factor either since ISC measurements for S-FENG-A and S-FENG did not show a significant or consistent difference. Hence, the difference in the ISC output could be attributed to the densification process due to accetone treatment; the interfacial area between CNT fiber and PPFE is reduced, relative to the CNTF-NT sample. Still, it happens at the cost of reducing the total contact with the polymer phase. Induced Charge: Generation and Leakage FENG devices have traditionally been the focus study for mechanical energy-harvesting applications, which involves the use of a train of mechanical puch-pull cycles [67, 113]. The studies have also provided insight for deriving electromechanical lumped models to obtain the system’s response to typical cyclic pressure found in real applications [117]. Cyclic mechanical input was also used in previous sections to describe VOC and ISC outputs for metallic and CNTF-based electrodes. From Figure 3.7, the change in dipole moment during compression (i.e., Stage 1) induces a polarization field across the PPFE dielectric. In the attempt to balance the field, the system reacts by accumulating induced free charges at each electrode with opposite polarity to the polarization field. If the electrodes are forced to be at the same potential -by connecting them through a short circuit- during the compression process, the induced charges flow, giving rise to ISC. During decompression (Figure 3.7, Stage 2), the change in the dipole moment flips sign, the flow charge also changes direction crossing ISC = 0 at the point where the mechanical input changes direction. In terms of the electric potential, charge accumulation during the compression cycle generates an electric field that is largest at the end of the compression, and returns to zero at the end of the release cycle. Hence, the ”push-pull” mechanical cycle results in a ”positive-negative” ISC profile, and a ”increasing-decreasing” VOC profile as shown in Figures 3.5 and 3.6. If FENG devices are to be integrated with supercapacitors in order to have both, energy generation and storage, it is necessary to understand the dynamics of the leakage of the induced charge. The charge accumulated at the electrode interface will remain until the 46 Figure 3.7 During compression (Stage 1), free charge accumulates at each surface to balance the electric potential generated by the displacement field due to dipole moment changes across the PPFE. After the mechanical input is applied with a pressure P 0, surface charge slowly flows in the opposite direction (Stage 2). Orange dashed lines represent the regions that correspond to each stage. polarization field in the PPFE decays, or until a discharge path is created. The mechanical input in this study was a step signal, where a pressure is applied and held on the device while VOC is monitored. Almost identical to the cyclic mechanical input, a single mechanical step also induces charge in the electrodes and generates an electric field during the compression cycle (Figure 3.7, Stage 1). In this case, however, the generated electric potential VOC is held until the generated displacement field decays due to dipole relaxation, or the charge is leaked through parasitic elements (Figure 3.7, Stage 2). This could be done through a resistive load, the internal resistance of the voltmeter used to measure VOC, or through the 47 input impedance of a power management circuit connected between the FENG and an energy storage unit. In both discharging processes, charge flows in the same direction, but they do not necessarily have to flow at the same rate. It is important to note, before analyzing the results, that VOC measurements are influ- enced by the internal resistance of the instrument used [67]. Measurements get closer the correct VOC profile as the internal impedance of the instrument used increases. This implies that the lumped parameters obtained for each device in the work described next may vary from the ideal scenario where an ideal voltmeter (e.g., Rinst = 0) is used, but the qualitative comparison still holds. In the present study, an impedance of Rinst = 10 GΩ (Keithley 2450 Source Measure Unit) was used for all experiments. Figure 3.8 Transient response for a) S-FENG, b) S-FENG-A, c) CNTF-NT, and d) CNTF-A samples for a 100 kPa. 48 Figure 3.9 Discharge time for the four samples as a function of applied pressure. The total time represents the combination of dipole relaxation and leakage current process. Figure 3.8 shows example results for the mechanical step input experiment, while Figure 3.9 show the discharge times for each sample. The experiment was repeated three times for each sample at each pressure, and the results consistently show a longer discharging time for the silver-based electrodes, and the shortest time for the CNTF-A sample. Faster discharging times were found when using lower Rinst. It was found that dipole relaxation is not the faster mechanisms for the discharging of the dipole-generated charge at each surface after the mechanical input. This was confirmed by connecting a switch between one of the measuring terminals and a device electrode. In a sequence of separate experiments, the switch was closed at increasing times after applying the mechanical input, until no electric potential was measured. Having an open switch between 49 the electrode and measuring instrument results in the induced charge to be pathless, halting an electrical discharge and leaving the relaxation of the dipoles as the only charge leak mechanism. It was found that the voltage reading after closing the switch was different than zero for up to 180 seconds, which is more than 7 times higher than the total discharge time measured for any sample at any pressure. Thus, if the dipole-induced charge generated by FENG devices is to be stored, discharge by leakage through parasitic elements or input impedance of the energy storage device need to be considered. The leakage current was found to be the slowest for the two silver-based electrodes, and fastest for the CNTF-A sample. This indicates that the reduction of the thickness of the PPFE due to acetone treatment does not dominate the leakage discharging time for any of the tested pressures. This comes from the fact that the S-FENG-A sample aslo has a reduced thickness of the PPFE but shows larger current discharge times. The faster responses for the two CNTF-based electrodes suggest that discharge times decrease with electrode resistivity. 3.6 Summary A characterization study of the electrode interface in polypropylene ferroelectret nanogen- erators was presented, focusing on a comparison between carbon nanotube fiber electrodes with traditional metallic thin film electrodes. The study also included the effects of acetone treatment on CNTF-based electrodes and PPFE. Results showed a higher VOC values for the thin film metal electrodes regardless of the applied pressure. Factors such as conduc- tivity and thickness of the electrodes were considered. Although the analysis points out these are the dominant factors on the VOC for metallic electrodes, volume and roughness of the CNTF-based electrodes might play additional roles in the open-circuit voltage outputs. On the other hand, the difference in ISC values between metal and CNTF-based electrodes were not as significant. Finally, a study on generation and leakage of induced charge in the electrodes was done. It was found, in contrast to dipole relaxation, that current leakage through parasitic elements is a faster process for discharge. 50 CHAPTER 4 DESIGN, SIMULATION, FABRICATION, AND TESTING OF FIRST GENERATION TUNABLE VO2 COMB DRIVE RESONATORS. This work starts by outlining the details that must be contemplated to incorporate VO2 phase transition material tuning capability into MEMS comb drive resonators. Devel- oped and prototyped three decades ago [118], extensive work has been done on comb drive structural applications, and active tuning capabilities have been successfully incorporated [106, 107]. However, this work proposes -for the first time- the use of V O2 smart material to achieve active tuning on a comb drive resonator. From a simple theoretical perspective, and by taking into account the resonator’s structural design and effects of V O2 transition, frequency tuning of 5% could potentially be achieved. Moreover, the PolyMUMPs process is used for prototyping several comb drive resonator designs to further understand fabrication limitations and allow suggested solutions to extend the incorporation of a phase transition material to MEMS resonators. 4.1 Design Principles As it was previously explained (see Section 2.2), V O2 undergoes a solid-to-solid transition. In turn, the electrical, optical, and mechanical properties changes go along. The latter has been demonstrated to produce large stress levels able to shift the resonant frequency of micro-mechanical structures [110, 119]. To exploit this effect on a comb drive resonator, an initial discussion on the typical comb drive design is considered, followed by the evaluation of the structural parameters on which the resonant frequency is dependent upon. The standard comb drive resonator design is shown in Figure 4.1. It consists of a shuttle (also known as the proof mass), anchors, beam design, ground plane, and sense/drive ports. The ground plane is essential for successful electrostatic actuation as there is a need to shield the structure from relatively large vertical electric field lines. The drive/sense port allow for the electrical measurement of the resonator. Applying a small AC signal in the drive port results in a displacement current output at the sense port (see section 2.2). 51 Figure 4.1 Standard design for a linear comb drive resonator. In contrast with a moving plate case where the gap between electrodes varies, the gap between combs is constant while the overlapping area of the face of each comb varies due to the resonator’s displacement. For a comb drive resonator, equation 2.21 can be written as, C = N hlϵϵ0 d (4.1) where N is the number of gaps between comb-drive fingers, h and l are the height and length of the overlapping area, respectively. Considering the resonator moves in the l directions (e.g., y direction) then the displacement current for a comb drive resonator is given by, is(t) = V DC ∂C ∂y ∂y ∂t = V DCN hϵϵ0 d ∂y ∂t (4.2) One convenience of the comb drive structure over electrostatic actuation method is the independence between the change in capacitance and displacement. In other words, by tailoring C the sensitivity of the comb drive can be increased to detect any effect the V O2 can have over the resonance frequency of the structure. As it will be explained in the 52 following sections, applications could be limited to those on the low frequency spectrum (LF band and lower) due to resonant frequency trade-off. Along with the aforementioned consideration, the beam design is of utmost importance. The combination of beams and truss results in a folded-beam suspension, and has several advantages. First, a high x-axis to y-axis stiffness ratio averts any unwanted vibration in the x-direction. Second, large in-plane displacement amplitudes in the order of 10 to 20 µm can be achieved by such design, and this makes them attractive for actuator applications. Lastly is the inherent stress relief. Since the folding truss is free to move in the x-direction, beams can expand and contract more readily to relieve stress. Although this is beneficial during the V O2 thin film deposition, perhaps could be a disadvantage during the material’s transition. Theoretical Analysis on Frequency Impact due to VO2 Transition In contrast with the standard design, Figure 4.2a shows a pictorial representation of a comb drive resonator that takes into account beam and comb design to incorporate the V O2. Increasing the number of combs results in an increase of sensitivity, allowing the detection of any changes on the resonant frequency due to V O2 transition. In addition, the folded- beam design has been substituted by simple beams that directly connect the shuttle and anchors. To some extend,the analytical resonant frequency of the presented resonator can be approximated to [89], f0 = (cid:115) 1 2π k (Ms + 12 35Mb) (4.3) where k is the spring constant of the system, Ms and Mb are the mass of the shuttle and beams, respectively. From equation 4.3, the resonant frequency is dependent upon the spring constant and mass of the system. When the V O2 thin film is deposited over the structure, the overall mass of the resonator increases, shifting the natural resonance frequency to lower values. This effect can be considered a passive tuning capability since, after deposition and during 53 Figure 4.2 a) Pictorial representation of a bridge-shape comb drive resonator. b) Fixed-fixed beam and c) fixed-translation beam examples. the V O2 phase transition, the mass of the system will remain constant. On the other hand, the spring constant of the system can be expressed in terms of structural parameters such that, k ∝ E L (4.4) where E and L are the Young’s modulus of the material and length of the beam, respectively. As the transition of V O2 occurs, the Young’s modulus is different for each phase. In addition, the expansion/contraction of the crystalline structures between rutile and monoclinic phases could potentially change the length of the beam, inducing the necessary stress for tuning. It must be pointed out no specific frequency is targeted in the following analyses; it rather explores the variables the V O2 transition can exploit to achieve active frequency tunability. Spring Constant To better analyse the equivalent spring constant of a comb drive resonator system, one can make use of known relationships between force and displacement. Figure 4.2b shows 54 a fixed-fixed beam which is a well known elastic structure in mechanics. Considering a static loading F is applied at a particular location on the bridge, it can be shown the spring constant is given by [120], kF-F = 3EI(a + b)3 a3b3 (4.5) where E is the Young’s modulus of the material, I is the moment of inertia, a and b are the distances from each anchor to the point where the force is being applied. If the force is applied at the center of the bridge (e.g., a = b = L), equation 4.5 transforms in a more recognizable manner, kF-F = 24EI L3 (4.6) It must be realized the beam design on Figure 4.2a does not represent a fixed-fixed case since the beams are ”free” to move on one end. Hence, a fixed-translation beam is a better representation, and is shown in Figure 4.2c. Recognizing kF −F is equal to the total equivalent stiffness of a parallel spring combination of two end-loaded beams, the spring constant for a fixed-translation beam is given by, kF-T = kF-F 2 = 12EI L3 (4.7) However, the previous expression describes the spring constant of one beam. From Figure 4.2a, a total of 4 beams are connected to the shuttle. Applying a force F in the y-direction results in a simultaneous bending of the beams. This means the springs are connected in a parallel configuration, and the equivalent spring constant of the system is, ksystem = 4 ∗ kF-T = 48EI L3 (4.8) 55 Moment of Inertia The moment of inertia (I) in equation 4.8 needs to be expressed in terms of physical dimensions. Considering an ideal beam with rectangular cross section having width w and thickness h, the moments of inertia are [121], Izy = hw3 12 and Izx = wh3 12 (4.9) Izy comes from the lateral displacement. Although the structure is designed to execute forced lateral vibrations, vertical vibrations could also be induced, and the effects of Izx must be examined. Therefore, the ratio of spring constant in the y-direction to that in the z-direction is, ky kz = w2 h2 (4.10) Equation 4.10 shows the lateral vibration will dominate as long as thickness of the beams is larger than their width. By depositing V O2 over the resonator, the thickness of the structure is increased (i.e., ignoring residual stress). However, a thin film (≈ 150 nm) is considered for this work, making the thickness of the resonator the dominant element. V O2 Young’s Modulus Effect on Resonant Frequency The case where the geometric dimensions of the beams are unvaried is first considered. This implies the spring constant of the system can only be modified by changing the Young’s modulus of the system as shown by equation 4.8. In addition, it assumes the V O2 is deposited on the beams. Considering the substrate material for V O2 is polysilicon, the weighed average of the Young’s modulus (also known as the effective Young’s modulus) is given by, Eeffective = (cid:80)i n=1 hiEi (cid:80)i n=1 hi (4.11) 56 where Ei is the Young’s modulus of an individual layer, and hi is the thickness of that particular layer. It is assumed the Young’s modulus of polysilicon (Epoly) remains constant (e.g., 150 GPa) in the temperature range of 30◦C to 100◦C. On the other hand, literature shows a change in the Young’s modulus between the monoclinic (EM = 140 GP a)) and rutile (ER = 155 GP a) phase of V O2 [122]. Table 4.1 shows geometric and material property values used to determine the frequency tuning due to the change in the elastic modulus of vanadium dioxide. From the results, a 5% active tuning capability due to V O2 seems to be feasible. Table 4.1 Summary of geometric dimensions, material properties, and calculated resonance frequencies. Parameter Beam Length Beam Width Beam Thickness Beam Mass (x4) Shuttle Mass Young’s Modulus Polysilicon (Epoly) Young’s Modulus VO2 (M) (EM) Young’s Modulus VO2 (R) (ER) Value 50 µm 2 µm 3.5 µm 6.5 x 10-12 kg 4.4 x 10-10 kg 150 GPa 140 GPa 155 GPa Calculated Resonant Frequency Resonant Frequency [VO2 (M)] 124.11 kHz Resonant Frequency [VO2 (R)] 130.37 kHz V O2 Structural Change Effect on Resonant Frequency In contrast with the previous section, this scenario considers the Young’s modulus of the system to remain constant while the length of the beam is varied due to the structural change of the V O2. Furthermore, it also considers the V O2 thin film is deposited on the shuttle. Figure 4.3a and 4.3b shows a top and side view, respectively, after VO2 deposition. In view of the fact that the contraction of the V O2 pertains to a stress tuning technique, a residual strain analysis is proposed. In the attempt to provide a clear qualitative and quantitative description of the analysis, a prelude to the fabrication process on section 4.2 is introduced. Similar to the Young’s modu- 57 lus, the thermal expansion coefficient of vanadium dioxide varies between phases. Therefore, the assumption is done where the structural expansion/contraction of the V O2 expresses itself through the effects of the thermal expansion coefficient of V O2. Most material depositions require heating. Materials will then expand or contract due to a change in temperature, and this is dictated by the thermal expansion coefficient. For surface micromachined structures, polysilicon is commonly deposited by low-pressure chem- ical vapor deposition (LPCVD), and temperatures for this technique range from 550◦C to 900◦C [123]. In general, as-deposited polysilicon has compressive residual stress, although reports of polysilicon with tensile stress can also be found in the literature [124]. To reduce these inherently stresses that affect device performance, annealing can be used. For polysili- con doped with phosphorous by diffusion, a decrease in the magnitude of compressive stress occurs [125]. Figure 4.3 Pictorial representation of a bridge-shape comb drive resonator after V O2 depo- sition. a) Shows a top view while b) shows a side view of the resonator. Following the fabrication process considered for this work -where a P-doped polysilicon 58 material acts as the structural material- it is assume the initial stress on a the resonator’s beam is compressive, yet the beams and shuttle do not exceed Euler’s buckling criterion [121]. For a given material, the expansion/contraction is described by, Lchange = Loriginal(1 − α∆T ) (4.12) where Loriginal is the original length of the material, Lchange is the material’s length after heating, α is the thermal expansion coefficient of the material, and ∆T is the difference between the material’s deposition temperature and room temperature. Table 4.2 shows thermal expansion coefficient values for polysilicon, V O2(M ), and V O2(R). Table 4.2 Summary of thermal expansion coefficient values for materials used in this work, length change calculations, and theoretical resonance frequencies. Material V O2(M ) V O2(R) P olysilicon Thermal Expansion Coefficient α (K −1) 5.7 x 10−6 13.6 x 10−6 4.4 x 10−6 Reference [126] [126] [127] Calculated Length Change due to Thermal Effects LP oly 49.895 µm LV O2(M ) 49.864 µm LV O2(R) 49.675 µm Calculated Resonant Frequency Resonant Frequency [VO2 (M)] 124.11 kHz Resonant Frequency [VO2 (R)] 122.27 kHz Deposition of V O2 is done at ∼ 500◦C, and the rutile phase is most stable at this temperature. Noticing αV O2(R) > αP oly, the polysilicon will contract and expand less per degree temperature in contrast with the V O2(R) phase. Hence, after returning to room temperature and assuming there is no phase transition of V O2, the V O2(R) film will be in tensile stress and the polysilicon in compressive stress. This is validated by using equation 4.12, and the calculated changes in length are shown in Table 4.2, where LV O2(R) < LP oly. On the other hand, the monoclinic phase is stable at temperatures lower than 68◦C. Still, for the purpose of consistency and analysis, it is assume the monoclinic phase is stable at 59 the required deposition temperature and no phase change of V O2 occurs after reaching room temperature. The calculated changes in length between polysilicon and the V O2(M ) also show the film will be in tensile stress. When the V O2 transitions from monoclinic to rutile, there is a contraction on the c-axis, which is parallel to the substrate. The shrinkage, in the case where the V O2 only resides on top of the shuttle, results in the elongation of the beams, reducing the spring constant, and lowering the resonant frequency of the structure. Between LV O2(R) and LV O2(M ) values, a difference of 0.189 µm is observed. Considering the beams are elongate from 50 µm to 50.189 µm, and substituting the arising spring constant into equation 4.3 results in a tuning capability of ∼ 1.5%. FEM Modelling of Tunable VO2 Comb Drive Design Accurate estimation of the electrostatic configuration, together with the evaluation of mechanical resonances is crucial for comb drive resonator design. To provide more insight regarding the blueprint, in addition to further validate the theoretical analysis presented in Section 4.1, electrostatic and mechanical simulations were done using the finite element analysis software COMSOL. In this section, the dependency of capacitance relative to the number of combs and displacement is first explored. This is followed by estimating the me- chanical resonances of the comb drive resonator. Finally, an analytical equation is considered in the modeling to further study the effects of V O2 transition on the tunability of the comb drive resonator. Capacitance Typical resonant microstructures are driven in a vertical manner, i.e., perpendicular to the substrate. One main drawback is the inherent nonlinearity that comes from such configuration. In this sense, the amplitude of vibration is limited to a small fraction of the capacitor gap to prevent: 1) structural collapse (i.e., shorting) and 2) frequency-jump phenomena [128]. Considering equation 2.23, ∂C ∂z is nonlinear, thus the vibration amplitude is limited. Comb drive resonators address these issues. 60 Figure 4.4 a) Pictorial representation of the simulated section of interest for the comb drive design. b) Shows the variation of capacitance as a function of number of combs and dis- placement. c) Shows the variation of capacitance as a function of comb width and structural thickness. From Figure 4.4b, a linear increase in capacitance is observed as the number of combs increase when the voltage, structural thickness, comb gap and width are 40 V, 2 µm, 3 µm, and 3 µm, respectively (i.e., kept constant throughout the study). The red dashed line represents the initial area overlap of 20 µm, and a capacitance increase of 1.32 f F follows every three added combs. A parametric sweep was done to vary the displacement of the movable combs towards the fixed combs. For each case study -where the number of combs is fixed- a linear increase in capacitance is observed as the shuttle’s comb fingers are displaced into the slot between the adjacent electrodes (i.e., fixed combs). Additionally, the dependency of capacitance as a function of the comb’s width and thick- ness was also studied; the results are shown in Figure 4.4c. The thickness of the combs was increased from 2 µm to 5 µm, and a significant increase in capacitance follows. This is explained by the fact that the overlapping area of the combs is larger as the thickness of the structure (h) is directly proportional to the capacitance as shown in equation 4.1. In 61 contrast, varying the finger’s width while the gap value is constant (i.e., 3 µm) has little effect on the capacitance value. From the results shown in Figure 4.4, it is encouraged to increase the number of combs and their thickness. This will increase the resonator’s sensitivity to any induced stress due to V O2. However, an increase on the resonator’s mass will follow, lowering the resonant frequency. The number of combs is dependent on the design, while the thickness will be limited by the selected fabrication process. Another factor to consider is the gap between the combs. A decrease in the gap (d) will result in a additional and significant increase in the capacitance following equation 4.1. Nevertheless, a smaller gap rises the risk of having a short between combs. Mechanical Resonant Frequencies: Baseline Table 4.3 summarizes the geometric dimensions, simulation parameters, and material properties used as initial inputs for the model. An Eigenfrequency study was first done to estimate the natural frequencies and modes of vibration of the proposed comb drive resonator. It must be pointed out the estimated resonances in this particular study come without any electrical input to the model, any temperature dependency nor energy loss. The results are interpreted as a free existing vibrations without any external excitation. The boundary conditions applied simply included free movement of the beams and shuttle, while a fix boundary is enforced on everything else. Figure 4.5 shows a summary of several different modes available and their frequency for the polysilicon baseline geometry resulting from the analysis. The lateral mode results in a frequency of 272.2 kHz, which is an overestimation when compared with the result of 124 kHz using equation 4.3. An Eigenfrequency analysis can only provide resonant frequency and shape for a given frequency, not the amplitude of the vibration. This can only be determined by adding an excitation input together with damping properties. To this end, a Small Signal Perturbation analysis was done in the attempt to provide a clear picture on the dependency between resonant frequency and resonator’s properties such as geometry, quality factor, and elec- 62 Table 4.3 Summary of input parameters used for initial calculations on Eigenfrequency and Small Signal Perturbation study. Device Geometry and Simulation Parameters Material Parameters (PolySi) Property Density Young’s Modulus Poisson’s ratio Relative Permittivity Value 2320 kg m3 150 GP a 0.22 4.5 Parameter Beam Length Beam Width Structural Thickness # Combs Comb Length Comb Width Shuttle Length Shuttle Width DC Voltage AC Voltage Quality Factor Value 50 µm 3 µm 3 µm 24 (each side) 40 µm 3 µm 279 µm 50 µm 20 V 112 mV 50,000 Figure 4.5 Estimated mechanical resonant frequencies and shape modes for the comb drive geometry of this work. trical input. Following equation 2.3, the dampening coefficient b can be incorporated into the structural model. To provide a source of energy dissipation in analyses of structures responding to dynamic loads, Rayleigh damping is commonly used and is given by, 63 b = αdKM + βdKk (4.13) where M and k are defined as the mass and stiffness matrix, respectively; α and β are constants. For most micromechanical resonator applications it is safe to assume αdk = 0. Applying this condition, in addition to substituting equations 2.5 and 2.11 into equation 4.13 results in, βdK = b k = b√ mk (cid:113) k m = 1 4πQf 0 (4.14) An experimental Q value can be fed accordingly to properly set this parameter after preliminary measurements. For initial calculations, a value of 50, 000 was used as quality factor, and this value represents a drive frequency measured in vacuum [89]. The purpose of this value is two-fold. First, utilizing a high quality factor increase sharpness and smoothness of the output results while allowing a step size large enough to reduce computation time. In addition, experimental measurements should be done in an isolated environment to prevent any external noise on the measurement, and allow a uniform movement (i.e., displacement current output) of the resonator. Figure 4.6 shows the results for the mechanical amplitude as a function of resonance frequency for different geometric parameters. Width and thickness parameters were swept to study the effects of geometric variations on the lateral resonance mode. For any given thickness, increasing the beam’s width increases the resonant frequency. This is explained by the fact that the spring constant increases in the lateral direction as the width of the beam increases. Although frequencies in the medium spectrum seem to be feasable (i.e., ∼ 550 kHz), the mechanical amplitude decreases with increasing frequency. Smaller me- chanical displacement will translate to smaller values of sensing current. To compensate, a transimpendance amplifier (TIA), a sensitive instrument (e.g., VNA) or a combination of both could potentially be implemented into the experimental setup. 64 A final remark is done on the location of the resonance frequencies. For a typical comb drive resonator, an electrostatic force is created by biasing the shuttle with a DC voltage and applying a small AC signal at one of the ports, driving the structure to move in a lateral manner. Following equation 4.10, as long as the thickness of the beam is larger than its width, the lateral mode will dominate. The results in Figure 4.6 show that, for any given width, thicknesses below 5 µm will allow the lateral mode to be separated from any other mechanical resonance mode. Figure 4.6 a) Lateral resonance mode for comb drive resonator. b) Shows the shifting of the lateral resonance frequency as the beam thickness is varied while maintaining the beam width constant at 1 µm. c) and d) show variation on resonances for 3 µm and 5 µm beam width, respectively. 65 VO2 Transition Effect on Resonant Frequency The simulation of the structural changes of V O2 crystal could potentially be addressed by modeling the lattice changes during the transition (see Section 2.2). However, for the case of polycrystalline V O2 is more complicated. In general, it consists of multiple layers of V O2 crystals and orientations. As a consequence, a synchronized structural change is not experienced and the induced strain during the phase change is not uniaxial. Cabrera et al. previously studied the integration of V O2 thin films on MEMS actuators [129]. From their experimental data, the authors were able to reach an empirical equation that described the behavior of their actuator’s deflection. To incorporate the V O2 into the model presented in this section, a modified expression is used such that the induced stress due to V O2 is described by, σ(T ) = −2.5 x 108 1 + e−0.4(T −68) (4.15) where T is the temperature of the V O2 at any given moment. Figure 4.7 shows the simulated V O2 stress variation as a function of temperature following equation 4.15. In general, the numerator limits the stress the V O2 induces on the structure once it completes the transition from monoclinic to rutile. From the graph, a value of -250 MPa is utilized; it has been shown the V O2 can induce stresses up to -500 MPa [110]. There are two major assumptions regarding equation 4.15. First, it contains all the information concerning V O2 such as changes in the Young’s modulus, thermal expansion coefficient, and structural change. In addition, it accounts for the polycrystallinity and orientation. If the V O2 is deposited on top of the beams, stresses due to the transition will displace the resonator in the vertical direction (i.e., z-axis). To investigate the effects, a Stationary study is first introduced. The study was done over one beam with one end fixed while the other is free to moved (i.e., simple cantilever); this is shown in Figure 4.8a. The thickness and width remain constant (i.e., 3 µm) while the length of the beam is varied from 50 µm to 150 µm. The displacement reference (i.e., edge point) was selected to map the beam’s 66 Figure 4.7 Simulated induced stress due to V O2 transition. trajectory in the z-axis as a function of V O2 temperature, and Figure 4.8b shows the results. As the length of the beam is increased, so does its downward displacement. This factor needs to be taken into account during the fabrication process. A maximum gap of 2 µm exists between the bottom of the shuttle and the top of the bottom electrode. Hence, it is encouraged to design tunable V O2 comb drive resonators with beam lengths up to 100 µm, since only half of the maximum V O2 induced stress value was used as input. One possible drawback of this effect is combs misalignment. However, the same electric potential will exist between the shuttle and bottom electrode, perhaps resulting in a corrective repulsive force. The Eigenfrequency analysis is repeated with V O2 selectively deposited on the beams 67 Figure 4.8 Simulated induced stress due to V O2 transition. 68 and the shuttle. From Figure 4.9, depositing vanadium dioxide on any location results in a decrease of the initial resonant frequency when compared to the 272.2 kHz baseline. This behavior agrees with the expected performance of resonators utilize on sensing applications [130]. If a passive tuning capability is of interest, the deposition of a 150 nm thin film of V O2 on the beams or shuttle could result in shifts of 2% and 4.6% from the baseline, respectively. On the other hand, active tuning capabilities result in shifts of 0.6% and 1.11% for the beams and shuttle, respectively. Figure 4.9 Effects of V O2 transition on the resonant frequency of the proposed comb drive resonator. a) V O2 deposited on the beams and b) V O2 on shuttle. 4.2 Experimental Procedures Fabrication Flow Process of Comb Drive Resonators The Multi-User MEMS Processes (MUMPs) foundry fabrication was selected for this work [131]. The foundry brings forth a cost-effective process compared to other foundries (e.g., SUMMIT) to fabricate proof-of-concept MEMS. In addition, it has a fast and pre- dictable turn-around time, allowing the user to verify the design and re-submit any neces- sary modification for the next run. From the three offered standard processes, the three-layer 69 polysilicon surface micromachining process PolyMUMPs was selected for the comb drive res- onator fabrication. Figure 4.10 a) Fabricated comb drive resonator following b) PolyMUMPs fabrication process flow. Figure 4.10a shows a pictorial representation of the fabricated comb drive resonator. The red-dashed line corresponds to the cross-section shown in Figure 4.10b, and illustrates the step-by-step microfabrication process flow following the PolyMUMPs process. The starting 70 substrate is a 150 mm n-type (100) silicon wafer of 1-2 Ω − cm. Prior to any material deposition, the surface of the wafer is heavily doped with phosphorus using a phosphosilicate glass (PSG) in a standard diffusion furnace. This helps in the reduction of charge feedthrough to the substrate from electrostatic devices on the surface. After the removal of the PSG, a 600 nm of silicon nitride (Si3N4) is deposited by low pressure chemical vapor deposition (LPCVD), and serves as an electrical insulation layer. Following the silicon nitride deposition, a 500 nm of LPCVD polysilicon film (Poly0 ) is deposited and patterned using standard photolithography techniques and reactive ion etching (RIE). The Poly0 layer is primarily used for wiring; in this work is used to fabricate the bottom electrodes of the resonators. Over the patterned Poly0 layer, a 2.0 µm of PSG (Oxide1 ) is deposited by LPCVD and annealed at 1050 ◦C for 1 hour in an argon atmosphere. This layer serves as the sacrifical layer and is removed at the end of the fabrication process. Two different photolithographic processes happen to the Oxide1 layer. First, the Dimples step is used to define and etch 0.75 µm holes in the oxide. These holes are then filled during the deposition of the first structural layer. The Dimples serve as means to help prevent stiction effects between the two layers by reducing the surface contact area. This is followed by the etch of the anchors (Anchor1 ) which go completely through the Oxide1 layer for attaching the first structural layer. After the patterning and RIE of the anchors, 2 µm of structural layer, Poly1, is deposited by LPCVD over the entire wafer surface. This is followed by the deposition of 200 nm of PSG over the Poly1 layer, and the wafer is annealed at 1050 ◦C for 1 hour. The anneal dopes the polysilicon with phosphorus from the top and bottom PSG layers. In addition, it helps reduce the intrinsic stress in the Poly1 layer; The Poly1 layer is then patterned and etched, defining the resonator’s body. Afterwards, the wafer is blanketed with a 0.75 µm of PSG (Oxide2 ) and annealed. Two distinct photolithographic processes are applied. A Poly1-Poly2-via step (not shown in Figure 4.10b) provides etch holes between the two structural layers (i.e., Poly1 and Poly2 ). 71 This allows for a mechanical and/or electrical connection between both structural layers. This step is important when considering mechanical structures with different thicknesses, and to further include the deposition of V O2 over specific locations of the resonator. The anchoring for the second structural layer, Poly2, to the Si3N4 or Poly0 layers is accomplished by using Anchor2 step. Poly2, which is the second structural layer of 1.5 µm, is deposited and patterned in the same manner as the Poly1 layer. This is followed by the deposition of 200 nm of PSG, and the wafer is again annealed for 1 hour at 1050 ◦C in argon atmosphere. The PSG is removed, and a deposition of approximately 150 nm of V O2 by pulsed laser deposition (PLD) is done using a KrF laser operated at 10 Hz. A fluence of 2 J cm2 was used during the 25 minutes deposition under an oxygen atmosphere with a 20 sccm flow. During the deposition, the substrate was heated to 495 ◦C by a ceramic heater located behind the sample holder, and a 30-minute post annealing step was done at the same deposition conditions. After the patterning and etching of V O2, a 150 nm-thick Si3N4 layer was deposited over the V O2. This layer serves as a protective layer for the V O2 during the subsequent structural release. The typical release etch is performed by immersing the die in a bath of room temperature 49% hydrofluoric acid (HF) for 2-3 minutes. Finally, the samples are submitted to supercritical CO2 drying process. Experimental Setup for 1st Generation of VO2 Comb Drive Resonators The resonators of this work use capacitive transduction, and the measurement setup is shown in Figure 4.11. A vacuum chamber (Lakeshore TT-Prober System) with electrical feedthroughs and heating chuck was used to characterize the resonators. For vacuum mea- surements, a rough pump was used to evacuate the chamber to pressures on the order of less than 10 mTorr before device testing to remove viscous gas dampening mechanisms. To excite the resonators in their two-port configuration, a direct current (DC) bias voltage was applied to the structure, and an alternating current (AC) signal (v i) was applied to the drive port; the displacement current is measured at the sense port. The application of the 72 DC-bias (VDC) only charge the capacitance between the movable and fixed combs, and does not experiences power consumption. Power input and DC bias were varied over range of frequencies to study the behavior of the resonators provided different inputs. Figure 4.11 a) Schematic illustrating the comb-drive resonator identifying key features on a two-port configuration scheme. 4.3 Results and Discussion Comb drive resonators without V O2 are first studied. The resonant frequencies were first found by visual observation under 20x magnification on a probe station with a waveform generator at ambient conditions. A sinusoidal signal and DC bias voltages were applied to the resonators via probes contacting the bottom and drive electrodes (see Figure 4.11). To provide large-amplitude lateral motion in air for visual observation, DC biases and driving voltages up to 160 V were supplied. The resonant frequencies were determined by maximizing 73 the amplitude of vibration, and results are shown in Table 4.4. It is observed the resonant frequencies decrease as the beam length increases for every given case. Considering Poly1 (P1) and Poly2 (P2) designs, lower frequency values were observed on the latter structures. Following equation 4.3, it might be expected an increase on the resonant frequency since there is an decrease on the overall mass of the structure. However, in this case the resonant frequency is dominated by the beams, more specifically, the moment of inertia Izy given by equation 4.9; A reduction of the thickness decreases the spring constant. In contrast, Poly1-Poly2 (P1P2) and Poly1-Oxide-Poly2 (P1OXP2) designs have the same beam thickness, but the latter showed lower frequency values. An additional oxide layer of 750 nm is interposed between the poly layers. Since the moment of inertia of the beams is the same for both designs, an increase in the shuttle mass would explain the lower frequency values in this case. Table 4.4 Measured Resonant Frequency Values of Linear Resonant Structures. Design Beam Length Beam Thickness Shuttle Thickness Measured Frequency P1 P2 P1P2 P1OXP2 (µm) 50 100 150 50 100 150 50 100 150 50 100 150 (µm) 2 2 2 1.5 1.5 1.5 3.5 3.5 3.5 3.5 3.5 3.5 (µm) 2 2 2 1.5 1.5 1.5 3.5 3.5 3.5 4.25 4.25 4.25 (kHz) 204 80 50 188 75 38 262 116 96 242 97 69 Electrical measurements of the resonators were initially pursued at atmospheric condi- tions. Following the experimental setup shown in previous section (see Section 4.2), DC bias up to 50 V and power values ranging from -40 dBm to 10 dBm were supplied, both limited by the triaxial-BNC adapters and VNA, respectively. For any given input, no electrical 74 output was measured from the resonators at the 30-300 kHz frequency range. In air, these structures require large driving voltages to provide sufficient vibrational amplitudes. How- ever, supplying large AC signals resulted in signal feed-through between the drive and sense ports, and this was verified by a spectrum analyzer. During the measurements, a peak would appear at the given frequency signal even when the probe was not touching the sensing pad. Nevertheless, electrical measurements were successful at low pressures (i.e., less than 10 mTorr). A DC bias of 30 V and power of -10 dBm were supplied to each design in Figure 4.12a. For the purpose of clarity, only results of resonators with 50 µm beam length are shown. Resonance peaks are observed for each design except for P2 where a subtle resonance-antiresonance behavior appears. Moreover, quality factors (Q) for each design are measured using a Lorentzian fit [132]. Low Q-values were measured, portraying losses on the system. Since the measurements are done under vacuum, viscous gas losses should be less significant than any other possible factors such as anchor and material losses. Figure 4.12 a) Measured electrical resonant frequencies for designs with 50 µm beam length. b) DC tuning effect for uncoated P1OXP2 resonator design. 75 Figure 4.12b shows the active tuning capability of an uncoated P1OXP2 design resonator by varying the DC bias. It has been widely reported that the resonant frequency of MEMS devices vary with applied DC voltages. The general tendency results in a softening effect with increasing DC bias, translating to a decrease in resonance frequencies [132]. In contrast, the resonators in this work show a stiffening effect since increasing DC bias results in an increase of the resonance frequency. Deposition of VO2 was done over all the chip using PLD technique. Once deposited, RIE etch of vanadium dioxide was done, leaving the material on the shuttle of the resonators. This was followed by deposition and etching of a 300 nm Si3N4 material which purpose was to protect the VO2 from the subsequent release step, which consisted on submerging the samples in a bath of room temperature 49% hydrofluoric acid (HF) for 3 minutes fol- lowed by supercritical CO2 drying process. The following discussion focuses on Si3N4-coated P1OXP2, and Si3N4/VO2-coated P1OXP2 resonators. Since these underwent the Si3N4 de- position simultaneously, it allows a fair comparison in terms of intrinsic effects from the post-fabrication processes while utilizing the Si3N4-coated resonator as our baseline. The effects of temperature over the resonance frequency, f0, are studied. To this end, electrical measurements were documented in a temperature range from 60 ◦C to 72 ◦C in steps of 1 ◦C. This temperature range is within the temperature window of the phase transition of VO2. At each temperature point, a Lorentzian fit was applied to the observed resonance peak as shown in Figure 4.13a, and Figure 4.14b shows the measured f0 at each temperature for the Si3N4-coated resonator. It is observed that as temperature increases, f0 decreases (∼ 0.3%). This behavior can be explained by considering the beam structure. As the structure is heated, the beams would want to increase its length due to thermal expansion. However, since the beams are fixed at both ends, this length increase transforms to a compressive stress, which is known to cause a decrease in frequency [134]. In addition –and following equation 4.3– the resonance frequency is directly proportional to the stiffness constant, which is dependent on E. An 76 Figure 4.13 a) Measured resonance frequency for the Si3N4/VO2-coated P1OXP2 resonator at 60 ◦C with Lorentzian fit. b) and c) show frequency as a function of frequency for Si3N4- coated and Si3N4/VO2-coated resonators, respectively. Taken from [133]. 77 increase in temperature increases atomic vibrations inside the material, increasing atomic distances which translates to a decrease in the atomic forces. This results in a ”softening effect” of the material. Figure 4.13b shows the results for the Si3N4/VO2-coated resonator. From 60 - 63 ◦C a decrease in frequency is observed. This can be attributed to the added compressive stress and softening effect previously explained. On the other hand, after 63 ◦C (i.e., approaching the IMT) the measured frequency increases from 133.53 kHz to 136.27 kHz. This increase is perhaps the most noticeable observation in the two compared resonators. As temperature approaches ∼ 68 ◦C the transformation of polycrystalline VO2 from monoclinic to rutile is accompanied by a reduction in the area of the crystal planes (011) to (110), respectively. Such contraction adds tension to the structure, thus increasing the resonant frequency. Conversely, when the structure is cooled to room temperature, the crystal planes of VO2 parallel to the substrate increase in area, adding compressive stress to the structure and reducing the resonant frequency. The beams in the comb-drive reported here can be treated as being fixed-fixed structures where a force trying to reduce the length of the beams (i.e., VO2 IMT) translates to added tensile stress. Such behavior has been observed before on unbuckled bridges [134]. 4.4 Summary A theoretical model has been proposed to incorporate V O2 phase transition material on comb drive resonators. A change in the Young’s modulus of the material was first considered. A conceptual active tuning capability of 5% was estimated when the material was deposited over the beams. On the other hand, V O2 deposition on the shuttle showed a 1.5% tuning capability when the thermal expansion coefficient of the material changed between the mon- oclinic and rutile phases. To better predict the resonant frequencies and electrical output of the resonators, an FEM model was also proposed. From the results, it was determined an increase on the number of combs would allow a larger displacement current. In addition, a modified analytical expression was used to model the phase transition of the V O2. From the 78 results, deposition of V O2 over the beams or shuttle would result in lowering the frequency of the resonators, the latter resulting on a 1.11% active tuning capability. Finally, the first passive tunable VO2 comb drive resonators were fabricated and initial electrical characteri- zation was done. It was shown the V O2 deposited over the shuttle resulted in a 2% active tuning, increasing the resonance. The low active tuning was attributed to a dampening of the V O2 stress release due to a Si3N4 layer that served as a protective layer for the release step of the resonators. 79 CHAPTER 5 CHARACTERIZATION OF SECOND GENERATION OF TUNABLE VO2 COMB DRIVE RESONATORS In the attempt to further improve and implement the effects of VO2 as an active tuning method, this work builds on a second generation of VO2 comb drive resonators. By utilizing beam theory, the mode shape equation for the comb drive beam displacement is calculated. While it has been shown the resultant analytical equation allows the estimation of the lateral resonant frequency to a certain degree, the equation does not acknowledges the residual stresses of the structure. To this end, this work extends on the vibration analysis to calculate residual stress base on measured lateral frequencies. Although the fabrication process is the same as in the previous chapter, this work expands on the metallization and release steps. In addition, a complete modification of the experimental setup was done that allowed the implementation of a transimpedance amplifier and a peltier heater. The former allows better detection of the measured resonances while the latter allows for better temperature control over the VO2 phase transition. Hence, the setup is used to study an uncoated, Si3N4-coated, and Si3N4/VO2-coated resonators with higher reliability. 5.1 Theoretical Approach to Estimate Residual Stress of Lateral Resonant Structures We consider a beam clamped in one end, and simply supported in the other. Taking into account the effects of axial forces, and free undamped vibrations in the transverse direction (i.e., y-direction), the equation of motion is given by [135], ∂2 ∂x2 (EI ∂2w(x, t) ∂x2 ) + ρA ∂2w(x, t) ∂t2 + σA ∂2w(x, t) ∂x2 = 0 (5.1) where E is the Young’s modulus, I is the moment of inertia of the beam, ρ is the density of the material, A is the cross sectional area, σ represents stress, and w(x,t) is the mode shape equation. Following equation 5.1, the first term describes the beams curvature, the second term describes the oscillation, and the third term the axial strain on the beam. A solution 80 can be assumed in the form of w(x, t) = eax. Nevertheless, this results in an additional differential equation which solution is not straight forward [136]. To circumvent the issue, Rayleigh’s method is used. Rayleigh’s energy method (also known as Rayleigh’s quotient) allows for the estimation of natural frequencies of vibrating bodies by using conservation of energy [118, 135, 137, 136]. In general, T otal P otential Energy (P.E.max) = T otal Kinetic Energy (K.E.max) (5.2) where [135], P.E.max = 1 2 (cid:90) L 0 EI( ∂2w(x, t) ∂x2 )2dx K.E.max = 1 2 (cid:90) L 0 ρA( ∂w(x, t) ∂x )2dx (5.3) (5.4) E is the Young’s modulus of the material, I is the moment of inertia of the beam, ρ is the density of the material, A is the cross sectional area of the beam, and w(x,t) is the mode shape equation of the beam. It must be pointed out that E, I, and ρ can be a function of x which represent the case for non-homogeneous materials. However, we consider our PolySi layers (i.e., Poly1 and Poly2) to be homogeneous. Hence, the approximation considers the aforementioned variables to be constants. Considering a solution in the form, w(x, t) = w(x)Sin(ωt) and substituting in equations 5.3 and 5.4 yields the frequency formula, ω2 = P.E.max K.E.max (5.5) (5.6) By taking the displacement of the vibrating mode as equation 5.5, the time coordinate is taken care of and the mode shape equation only needs to describe the maximum displacement 81 of the beam. Potential energy can be stored in the beam in the form of strain energy as it undergoes flexure. From equation 5.1, the first and third term represent the strains on the beam, while the second term represents the movement. Since the frequency is the ratio of total potential energy to the total kinetic energy of the system, equation 5.6 becomes [136], ω2 = EI (cid:82) L 0 ( ∂2w(x) ∂x2 )2dx + σA (cid:82) L 0 w(x)2dx ρA (cid:82) L 0 ( ∂w(x) ∂x )2dx (5.7) One last remark is done regarding Rayleigh’s method and the shape mode equation. The resonant frequency of a specific mode can be found as long as the mode shape function for the particular mode of interest is known. This task is not trivial, and presents certain difficulty. On the other hand, for the fundamental mode (i.e., lowest frequency of vibration), the estimation is accurate when a static displacement function w(x) is used as an approximation for the mode shape function. In the following section, the mode shape function is derived and, by adding corrections to the resulting analytical equations, an estimation of the natural resonant frequency is done; an expression to estimate the residual stress is also shown. Mode Shape Functionals On Chapter 4 it was shown the beams of the presented comb drive resonator in this work are fixed-guided beams. Figure 5.1a shows the fixed-guided boundary that represents one beam of the system, while Figure 5.1b shows the model of one from two cantilevers connected in series that represents the same beam. For a cantilever with an end-load, the spring constant is given by, Since we consider the cantilevers to be connected in series, the equivalent spring constant is, kC = 3EI 3 LC (5.8) 1 kEquivalent = 1 kC + 1 kC (5.9) 82 Figure 5.1 a) Pictorial representation of a fixed-guided beam. b) Shows one of two cantilevers in series that represents a fixed-guided beam. c) Shows a typical cantilever beam and d) shows its corresponding free body diagram. 83 1 kEquivalent = 3 LC 3EI + 3 LC 3EI = 3 2LC 3EI kEquivalent = 3EI 3 2LC From Figure 5.1a-b we observe that 2LC = L. The spring constant results in, kEquivalent = 12EI L3 (5.10) (5.11) (5.12) Considering the system has 4 beams in parallel arrangement, the stiffness of the system for lateral movement is, kx = 48EI L3 (5.13) The equivalent spring constant of two cantilevers connected in series results in the spring constant for a fixed-guided beam. This confirms the potential of approximating our mode shape equation to that of a cantilever that bends as a fix-guided beam (see Figure 5.1a. To find its maximum displacement, a load is applied to the free end as shown in Figure 5.1c. Figure 5.1d shows the free body diagram for the following force analysis. Our interest resides on the bending moment at any point on the cantilever, which is described by LC − x. The cantilever beam is split such that each separated section needs to be balanced. The equilibrium of bending moments (i.e., (cid:80)∞ n=1 Mi = 0) results in, Using the bending-moment equation [121], M = F (L − x) EIw′′(x) = F (L − x) (5.14) (5.15) Boundary conditions need to be placed in order to determine the integration constants. Since only one side is fixed, the boundary conditions are, 84 w(0) = 0; w′(0) = 0 Integrating equation 5.15 and applying boundary conditions, w′(x) = F EI (LCx − x2 2 ) w(x) = F EI ( LCx2 2 − x3 6 ) Recalling that 2LC = L (see Figure 5.1a-b) we get, (5.16) (5.17) (5.18) w(x)1 = F 12EI (3Lx2 − 2x3) f or 0 ≤ x ≤ L (5.19) Figure 5.2 Assumed beam mode shape for frequency estimation using Rayleight’s method. Figure 5.2 shows the plot of the shape mode functional of equation 5.19. Such shape resem- bles that of the fixed-guided beam (see Figure 5.1). 85 Analytical Equation for Frequency Estimation of Lateral Resonances Taking the respective derivatives from equation 5.19, substituting into equation 5.7 and integrating results in the following expression, ω2 = 12EI L3 13ρAL 35 + (1.2)σA L 13ρAL 35 (5.20) Three corrections must be implemented to the equation in order to capture the resonance and stress of the entire comb drive system. First, the system contains 4 beams in parallel arrangement. This means a factor of 4 is at play at the numerator and denominator to capture both the parallel arrangement and the total mass of the beams add to the system. The mass of the plate must also be added to each term. Equation 5.20 turns to be, ω2 = 48EI L3 mEff + (4.8)σA L mEff where we defined the effective mass as, mEff = 52ρAL 35 + mplate (5.21) (5.22) When σ → 0, we are left with the corresponding analytical resonant frequency equation where the numerator corresponds to the spring constant of a fixed-guided beam, and the denominator corresponds to the effective mass of the system. Analytical Equation for Axial Stress Evaluation on Lateral Resonances The case is considered where the lateral frequency of ”identical” resonators is measured, yet the only geometric difference is the beam length. For a particular beam length, the resonance frequency is given by equation 5.20 as, ω1 2 = 48EI 3 L1 mEff1 + (4.8)σA L1 mEff1 (5.23) 86 ω2 2 = 48EI 3 L2 mEff2 + (4.8)σA L2 mEff2 (5.24) where the subscripts 1 and 2 represent resonators of different beam length. Bearing in mind the Young’s modulus of the materials is the same, equation 5.24 is solved for 48EI. By substituting into equation 5.23 and solving for σ results in, σ = 4π2 (4.8)A L1 3mEff1f 1 L1 2 − L2 2 − L2 2 3mEff2f 2 2 (5.25) where σ can be considered as a representation of the residual stress. This equation is used in the following section to estimate the residual stress of uncoated resonators. 5.2 Experimental Procedures Fabrication Flow Process of V O2 Comb Drive Resonators The resonators were fabricated using Polysilicon Multi-User MEMS Processes (Poly- MUMPS) from MEMSCAP. We followed the same terminology used in the PolyMUMPS handbook [131], and is explained in detail in section 4.2. Briefly explained, the starting substrate is a heavily P-doped silicon wafer using phosphosilicate glass (PSG) in a standard diffusion chamber. Following the removal of the PSG, a 600 nm layer of silicon nitride (Si3N4) is deposited by low pressure chemical vapor deposition (LPCVD) that serves as an electrical isolation layer. The following steps consisted on the deposition and patterning of PolySi and Oxide layers (i.e., Poly0, Oxide1, Poly1, Oxide2, Poly2) defining the comb drive resonators. The first post-processing step involved depositing ∼250 nm of V O2 by pulsed laser de- position (PLD) using KrF laser operated at 10 Hz. A fluence of ∼2 J cm2 was used for a 45-minute deposition under oxygen atmosphere at a 15 mTorr pressure. During the deposi- tion, the substrate was heated to 550◦C by a ceramic heater located at the back of the sample holder. A 10-minute post annealing step was done at the same deposition conditions. After patterning and etching of the V O2 [138], a 600 nm-thick Si3N4 layer was deposited at 300◦C 87 using physical enhanced chemical vapor deposition (PECVD), and patterned over the V O2. The purpose of this layer is to protect the V O2 during the subsequent structural release. The metal layer of gold(Au)/chrome(Cr) (200/20 nm) for the electrical pads was patterned using standard lift-off processes. However, before the metal evaporation, the samples were submerged in buffered oxide etch (BOE) for 10 seconds to remove any native oxide layer and V O2 residue over the pads. The structural release was performed by immersing the chip in a bath of room temperature 49% hydrofluoric acid (HF) for 4 minutes. Finally, samples were supercritical CO2 dried. Experimental Setup for 2nd Generation of V O2 Comb Drive Resonators To test the resonators, a printed circuit board (PCB) was designed and fabricated (Figure 5.3). The resonator chip was placed at the center of the PCB using thermally conductive double-sided tape, followed by wire bonding of the device in a 2-port configuration. A Peltier heater was placed at the back center of the PCB while a resistance temperature detector (TH100TP) was place at the side of the resonator chip; Both pieces were connected to a temperature controller (Thorlabs TED4015). To render a heat sink to the system, the back side of the heater was placed on top of a copper plate (3 x 8 x 0.5 in3). The Proportional- Integral-Derivative (PID) parameters of the controller were manually adjusted. As means to represent the measuring conditions of the devices, the PID calibration was carried out under vacuum that resulted on a ±0.2◦C temperature overshoot. The measurement setup is shown in Figure 5.4. The input port of a transimpedance amplifier (ADA4530-1R-EBZ-TIA) was connected to the output port of the resonators. The amplifier was chosen to ensure that the input bias current (±20f A) was significantly smaller than expected current levels for detecting the motion of the devices. The resonator was excited in a two-port configuration where a direct current (DC) bias voltage (VDC−Bias) was applied to the structure, and an alternate current (AC) bias voltage (vi) was applied to the driving port of the resonator. The displacement current (ix) from the resonator was measured at the output of the amplifier (v0). A pair of bias tees protected the Vector Network Analyzer 88 Figure 5.3 Printed circuit board designed and fabricated for electrical measurements. The resonator’s chip was placed at the center of the front face while the Peltier heater was placed at the center of the back face. (VNA) from any shorting of the devices. All electrical measurements were carried out under vacuum pressures in the order of 30 µTorr. Full heating-cooling cycles were done from 26◦C to 80◦C in steps of 2◦C to study the effects of temperature on the lateral frequencies of the devices. The selected temperature range was well within the transition window of V O2. 5.3 Results and Discussion For baseline purposes, an uncoated resonator with beam length of 100 µm is first dis- cussed. The resonance frequency for the lateral vibrating mode on atmospheric conditions was first found by visual observation under 20X magnification, and results are shown in Ta- ble 5.1. For structures with beam length of 100 µm, the corresponding resonance frequency for the lateral mode was found at ∼15 kHz taking an average from 4 resonators. At this point, one resonator was then wirebonded and placed inside the vacuum chamber for electrical testing. To asses whether the observed electrical resonant peak was in fact from the resonator, the first measurements were carried with bias voltages of 0 V and 50 V with 89 Figure 5.4 Schematic illustration of the experimental setup. For clarity, the PCB is omitted. Table 5.1 Measured Resonant Frequency Values of Linear Uncoated Resonant Structures at Atmospheric Conditions. Design Beam Length Beam Thickness Shuttle Thickness Measured Frequency (µm) (µm) (µm) P1P2Unc-A P1P2Unc-B P1P2Unc-C P1P2Unc-D 100 100 100 100 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 @ 50 VDC (kHz) ∼14 ∼19 ∼16 ∼14 input power of -55 dBm. Figure 5.5a shows the distinction between noise and the device’s output while Figure 5.5b shows the characteristic lateral frequency measured at room tem- perature. For each temperature point, a Lorentzian fit was applied to extract the observed resonance values. The maximum and minimum points are known as resonance and antires- 90 onance –more commonly– series and parallel resonances, respectively. This behavior can be explained by considering the electrical circuit on Figure 5.6. The Butterworth Van-Dyke (BVD) model is commonly used for resonance analysis since it simplifies the transcendental functions that characterize filter elements. The resonator is modeled as a motional resistor (Rm), motional capacitor (Cm), and motional inductor (Lm) connected in series. The branch is then connected in parallel with a capacitor (Cp) representing electrical feed-through and parasitic effects in the circuit. The reactances of each element are, X Rm = Rm X Lm = ωLm X Cm = 1 ωC m (5.26) (5.27) (5.28) where the inductor and capacitor are dependent on the signal’s input frequency ω = 2πf . Figure 5.5 a) Shows distintion between noise and device’s resonance having a b) resonance/anti-resonance behavior. At the first resonance point (i.e., series resonance) the reactance of both Lm and Cm cancel out and the impedance of the circuit drops sharply to a minimum value given by 91 Rm. Consequently, the comb drive moves with maximum amplitude resulting in a maximum current displacement output (i.e., measured output). At some higher frequency (i.e., away from series resonance), XLm dominates over XCm. At an instant, the circuit becomes a parallel RCL circuit. At the second resonant point (i.e., parallel resonance) the reactance of the circuit becomes maximum (i.e., Lm and Cp impedances become maximum) and most of the current will travel around the loop instead of past it. Consequently, the comb drive moves at its minimum amplitude resulting in a minimum current output. In the attempt to provide a clear discussion and analysis, only the series resonant frequency will be examined and –hereinafter– will be addressed as resonant frequency. Figure 5.6 The Butterworth Van-Dyke model often used for MEMS devices. Once the first resonant frequency was found, frequency measurements were done as a function of temperature and Figure 5.7a shows the results. An increasing linear behavior is observed on the resonance in the range of 26◦C - 80◦C. It is well known the overall residual stress from PolyMUMPs fabrication process is compressive. Since the beam structures in this 92 work can be treated as being fixed-fixed structures, and no sign of buckling was observed, increasing temperature would result in stress relaxation that translates to an increase in frequency. This behavior has been observed on unbuckled microbridge [134]. To confirm the claim of the compressive stress, a second ”identical” uncoated resonator with beam length of 50 µm was measured and, using equation 5.25, an stress of -5 MPa was estimated. To quantify the frequency change, the temperature coefficient of frequency (TCF) is used as figure of merit. As such, it is determined by, αfrequency = ∆f ∆T 1 f 0 (5.29) where f0 is the resonance frequency at room temperature, ∆f is the change in frequency, and ∆T is the change in temperature. From Figure 5.7b, the extracted TCFs are 480.76 ppm ◦C and 503.36 ppm ◦C for heating and cooling, respectively, showing the small impact of temperature over the measured frequency. Figure 5.7 Linear dependency between frequency and temperature for the uncoated comb drive resonator of 100µm beam length. Table 5.3 shows the measured values for 4 different Si3N4-coated resonators measured at atmospheric conditions, and Figure 5.8 shows the results of frequency as a function of temperature for the Si3N4-coated resonator. Compared to the 21.14 kHz of the uncoated 93 Table 5.2 Measured Resonant Frequency Values of Linear Si3N4-coated Resonant Structures at Atmospheric Conditions. Design Beam Length Beam Thickness Shuttle Thickness Measured Frequency (µm) (µm) (µm) P1P2Nit-A P1P2Nit-B P1P2Nit-C P1P2Nit-D 100 100 100 100 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 @ 50 VDC (kHz) ∼14 ∼14 ∼14 ∼14 resonator, a value of 19.97 kHz was measured at room temperature. The frequency of the devices is inversely proportional to the effective mass of the system. Hence, by depositing a thin layer of Si3N4 over the resonator, frequencies are shifted to lower values. Figure 5.8 also shows a linear behavior of frequency as a function of temperature. In this case, the two distinct materials can introduce strain to the system given by the difference in their thermal expansion coefficients (TEC). The linear thermal expansion is described by, ∆L = ∆T α (5.30) Figure 5.8 Linear dependency between frequency and temperature for the Si3N4-coated comb drive resonator of 100µm beam length. 94 where ∆L represents the change in length, ∆T is the change in temperature, and α is the TEC for each material. The thermal expansion coefficient of Si3N4 is 3.27 x 10−6 1 K [139], and 2.65 x 10−6 1 K for PolySi [127]. Since αSi3N4 > αP olySi, the polysilicon will expand less per degree temperature. Following the fabrication process, at room temperature the Si3N4 layer would induce a tensile stress over the resonator, which would work up the beams. However, since the structure was not buckled, adding a tensile stress would have been followed by higher resonant frequency at room temperature when compared with the uncoated resonator. Considering the results, the residual stress from the change in TEC on this scenario might not be as impactful as intrinsic stresses of the film (i.e., etching, release, etc). Nevertheless, it stands to reason the overall outcome is a net compressive stress that, in the presence of increasing and decreasing temperature, resonant frequency shifts accordingly. Table 5.3 Measured Resonant Frequency Value of a Linear Si3N4/V O2-coated Resonant Structure at Atmospheric Conditions. Design Beam Length Beam Thickness Shuttle Thickness Measured Frequency (µm) P1P2V O2-A 100 (µm) 3.5 (µm) 3.5 @ 50 VDC (kHz) ∼13 Figure 5.9 shows the frequency results for the Si3N4/V O2-coated resonator as a function of temperature. In contrast with the Si3N4-coated resonator case, the measured frequency at room temperature was 17.52 kHz. The two mechanisms responsible for this effect are the thermal expansion of the materials and the phase transition of the V O2. At its dif- ferent phases, the V O2 TEC values are 5.7 x 10−6 1 K for the monoclinic phase (M1) and 13.35 x 10−6 1 K for the rutile phase (R). It holds firm that at any point in temperature αV O2 > αSi3N4 > αP olySi. The deposition of V O2 occurred at 550◦C while the Si3N4 pro- tective layer deposition was at 300◦C. At high temperatures, rutile phase is the most stable. Following equation 5.30, the V O2 will contract at a faster rate when temperature decreases. Still, the Si3N4 and PolySi materials will damp the contraction as they both have smaller 95 Figure 5.9 Frequency tuning of Si3N4/V O2-coated comb drive resonator of 100µm beam length. TEC values. If the phase transition effects of V O2 during cooling to room temperature are now included, the crystal planes parallel to the substrate increase in area, adding compression to the structure and lowering the frequency. It is important to note that the TEC of V O2 film outside the phase transition relates to the traditional linear process of expansion and contraction due to temperature changes. For example, at the 26◦C - 54◦C and 74◦C - 80◦C range the frequency behavior is fairly linear. On the other hand, the mechanism of expansion and contraction for V O2 during the transition is different, having an opposite effect as seen at the 56◦C - 72◦C temperature range. As the transformation of polycrystalline V O2 from monoclinic to rutile is accompanied by a reduction in the area of the crystal planes (011) to (110), respectively, it induces a tensile 96 stress over the structure resulting in an increase in resonant frequency of 10%. It can be extrapolated from these observations that the magnitude of the induced stress of each mechanism are remarkably different given the frequency changes at each region. Effects of V O2 Transition on Electrical Motional Parameters Figure 5.6 shows the equivalent electrical circuit for a two-port comb drive resonator. The motional resistance (Rm), motional capacitance (Cm), and motional inductance (Lm) are related to the losses, inverse spring constant, and the system’s effective mass, respectively. The expressions that relate the motional parameters to the measured frequencies are well- defined in literature as [140, 141, 142, 143]: Rm = Ramp 10− −S21 20 Lm = ωsRm p − ω2 ω2 s Cm = 1 Lmω2 s Cp = Cmω2 s p − ω2 ω2 s (5.31) (5.32) (5.33) (5.34) where ωs and ωp are the series and parallel resonances in radians, and can be extracted from the measurements. The S21 parameter is extracted from the data at the series resonance point, while Ramp is given by the transimpedance amplifier (10 GΩ). Figure 5.10a-b shows the extracted values of Cm and Lm as a function of temperature for the uncoated and V O2–coated resonators. It is observed a fairly linear behavior as the temperature increased. The purpose of the deposition of V O2 was to mechanically modify the spring constant of the beams, shifting the frequency as previously shown. In this sense, it was expected to observer a change in Cm at temperatures higher than 68◦C given the fact Cm relates to the inverse spring constant of the system. This was not the case, and the 97 Figure 5.10 Graphical plot of a) motional capacitance, b) motional inductance, c) motional resistance, and d) parasitic capacitance as a function of temperature for uncoated and V O2– coated comb drive resonators. reason becomes clear when the forces acting at resonance are considered. Note that, as the frequency of the driving force is increased, the acceleration (i.e., inertial force) of the shuttle increases more rapidly than its displacement (i.e., spring force). At the point of resonance, the two forces are equal but opposite in direction, compensating but cancelling each other at each temperature point. In terms of Rm –and as shown in Figure 5.10c– the uncoated resonator shows no losses as the temperature was increased. The same linear trend is observed on the V O2–coated resonator from room temperature up to 62◦C where, at higher temperatures, a subtle but clear increase in Rm happens. Figure 5.10c inset shows the frequency as a function of 98 temperature, where Rm closely agrees with the characteristic transition of V O2. The result validates that the losses are, in fact, coming from the V O2 transition. The energy dissipation can be caused by grain sliding of the film [144]. Nevertheless, it must be pointed out that other factors such as thermal damping [145], anchor losses [146], and material losses due to the relaxation of defects [147] also contribute to the dissipation mechanisms that affect the resonator. In contrast with the motional resistance, the parameter Cp exhibits a decreasing tendency after 62◦C as shown in Figure 5.10d. The parasitic capacitance is mostly attributed to capacitive coupling through the substrate via the bond pads, interconnects, and the electrical packaging [148]. Since the V O2 is nonexistent at the preceding constituents, an additional mechanism must be at play. A more intuitive scenario considers the parasitic capacitance in parallel with the comb-drive static capacitance (Cs) and is given by [149], Cp = Cs + Ctp = C(x) + C0 + Ctp (5.35) where C(x) = εN hx g is the change in capacitance when the shuttle moves a distance x from its initial position, ε is the dielectric constant in vacuum, N the number of gaps between moving and static fingers, h is the thickness of the combs, g is the gap between combs, C0 describes the capacitance due to the initial overlap of the fingers (i.e., at x = 0), and Ctp defines a true parasitic capacitance. The V O2 transitions from monoclinic to rutile gives rise to a stiffening effect over the resonant beams. The increase in spring constant renders a larger restorative force able to pull the shuttle away from the static combs. Hence, the decrease of Cp is interpreted as a reduction of the overlapping area between the combs. 5.4 Summary By using Rayleigh’s method and the very well known beam theory, a simple equation was derived to estimate the axial stress over the resonator beams. Moreover, the fabrication of the 2nd generation of tunable V O2 comb drive resonators was done. The devices were electrically tested using a PCB board. To increase the reliability of the measurements, a 99 transimpedance amplifier and a Peltier heater were adapted to the experimental setup. It was shown the resonance frequency had a resonance-antiresonance behavior. The effect was explained using a Butterworth Van-Dyke circuit which is used to design crystal resonators. From the measurements it was shown the uncoated and Si3N4-coated resonators increased frequency as a function of temperature. The effect was attributed to the relaxation of com- pressive stressed on the device. On the other hand, the Si3N4/V O2-coated resonator showed an increased in frequency on the 60-70◦C temperature range. As the V O2 transitions from its monoclinic to rutile phase, the crystal planes parallel to the substrate contract, produc- ing tensile stress over the beams and increasing the frequency of the device. The calculated change in frequency was 10%. The tunability of the resonator were also accompanied by the characteristic hysteresis behavior of the material. Moreover, the electrical motional pa- rameters were extracted from the measured resonances. The results showed an increase in losses due to the V O2 transition, attributed to a grain sliding effect. In contrast, the par- asitic capacitance showed a decrease in value. The trend was attributed to a decrease in the overlapping area between combs due to stiffening of the beams as a result of the V O2 transition. 100 CHAPTER 6 SUMMARY 6.1 Summary of Contributions In the context of multifunctional materials, this dissertation presents the utilization of carbon nanotube fibers (CNTF) and vanadium dioxide V O2 in an effort to improve energy harvesting and micromechanical systems research areas, respectively. The energy harvesting capability and reliability of flexible polypropelene ferroelectret films was proposed. First, the integration of CNTF electrodes on a ferroelectret nanogenerator (FENG) was done by replacing the traditional metal electrodes. A characterization study was done focusing on the current need for fundamental research on mechanical robustness and flexibility while maintaining reliable electrical outputs. The results showed higher voltage output values for the metal electrodes regardless of the applied pressure to that of the CNFT electrodes. How- ever, the current output from the CNTF-base electrodes were not as significant compared to its counterpart. In terms of charge leackage, it was found, in contrast with dipole relaxation, that current leackage through parasitic elements was faster as faster process for discharge. Finally, it was shown the metal electrodes were susceptible to degradation by folding. In contrast, the CNTF-based electrodes showed same electrical output. The fabrication of microelectromechanical systems (MEMS) is well developed and un- derstood along the lines of silicon and other common CMOS standard compatible materials. However, when exotic materials are incorporated into the process, it presents certain lim- itations by the underlying physical capabilities of said material. In this sense, a design model was proposed to incorporate the V O2 phase transition material as an active tuning capability on comb drive resonators. Modeling of the device was done, showing the incre- ment on the number of combs and structural thickness played a significant role in the total capacitance that translates to the electrical output of the device. The fabrication of the devices was done using PolyMUMPs process, which is a reliable operation for prototyping. As such, the protection of V O2 during the release step was achieved by utilizing a 600 nm- 101 thick Si3N4 layer. This allowed the fabrication of the first passive tunable V O2 comb drive resonator. The electrical characterization was carried out under vacuum. As temperature was increased, the resonant frequency for the uncoated and Si3N4-coated devices increased linearly. Since the beams of the resonator were treated as fix-fix beams, the frequency be- havior was attributed to the relaxing of the residual compressive stress on the structures. The V O2-coated resonator, at the transition temperature, showed a increased of 10% on the resonant frequency. Problems Solved in this Thesis This work addressed the following: • The successful integration of carbon nanotube fibers (CNTF) as tough electrodes on polypropylene ferroelectret nanogenerators (FENG). • Evaluation and understanding of induced charge movement, particularly at the elec- trode interface. • Comparison of electrical and mechanical performance between metal electrodes and CNTF electrodes. • Understanding the dynamic discharging behavior of the FENG in combination with CNTF electrodes. • Evaluating and comparing chemically post-treated CNT fiber performance. • Successful integration of V O2 thin films on comb drive resonators. • Development of a tunable V O2 resonator able to be electrostatically actuated and electrically measured. • Characterization of comb drive resonators across the V O2 transition. • Successful implementation of phase transition materials to standard fabrication Poly- MUMPs process. 102 BIBLIOGRAPHY [1] M. L. Hammock, A. Chortos, B. C.-K. Tee, J. B.-H. 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