The objective of this research is to present a new model for predicting the piezoresistive effect in microflexures experiencing bending stresses. A linear model describing piezoresistivity exists for members in pure tension and compression. Extensions of this model to more complex loading conditions do not match experimental results. An accurate model of piezoresistivity in complex loading conditions would expand the design possibilities of piezoresistive devices. A new model to predict piezoresistive effects in tension, compression, and more complex loading conditions is proposed. The focus of this research is to verify a unidirectional form of this proposed model for microflexures in tension and bending. Implementation of the unidirectional form of the model involves geometric design, stress analysis, and electrical analysis. One of the ways to implement the model is with finite-element analysis (FEA). The piezoresistive FEA for flexures (PFF) algorithm is an FEA implementation of the unidirectional form of the model for flexures. A case study is then given in which the resistance curves of two test devices are predicted with the PFF algorithm. Results from the PFF implementation of the unidirectional form of the model show a close comparison between analytical prediction and experimental results. This new model could contribute to optimized sensors, feedback control of microdevices, nanopositioning, and self-sensing microdevices.

It has been observed that carbon nanotube (CNT)-polymer nanocomposite material has observable piezoresistive effect, that is to say that changes in applied strain may induce measurable changes in resistance. The first focus of the work is on modeling the piezoresistive response of the CNT-polymer nanocomposites by using computational micromechanics techniques based on finite element analysis. The in-plane, axial, the three dimensional piezoresistive responses of the CNT-polymer nanocomposites are studied by using 2D, axisymmetric, and 3D electromechanically coupled and multiscale finite element models. The microscale mechanisms that may have a substantial influence on the overall piezoresistivity of the nanocomposites, i.e. the electrical tunneling effect and the inherent piezoresistivity of the CNT, are included in microscale RVEs in order to understand their influence on macroscale piezoresistive response in terms of both the normalized change in effective resistivity and the corresponding effective gauge factor under applied strain. The computational results are used to better understand the driving mechanisms for the observed piezoresistive response of the material. The second focus of the work is on modeling the piezoresistive response of fuzzy fiber reinforced polymer composites by applying a 3D multiscale micromechanics model based on finite element analysis. Through explicitly accounting for the local piezoresistive response of the anisotropic interphase region, the piezoresistive responses of the overall fuzzy fiber reinforced polymer composites are obtained. The modeling results not only provide a possible explanation for the small gauge factors as observed in experiments, but also give guidance for the manufacture of fuzzy fiber reinforced polymer composites in order to achieve large, consistent, and predictable gauge factors. The third focus of the work is on modeling the coupled effect between continuum damage and piezoresistivity in the CNT-polymer nanocomposites by using computational micromechanics techniques based on a concurrent multiscale finite element analysis. The results show that there is a good correlation between continuum damage and piezoresistive response of the nanocomposites, which gives theoretical and modeling support for the use of CNT-polymer nanocomposites in structural health monitoring (SHM) applications for damage detections. / Ph. D.

As the world’s population increases, the demand for energy also grows. The strain on our limited resources of fossil fuels is unsustainable in the long term. An alternative, renewable method of energy generation must be implemented. Solar energy has good potential as an environmentally sound, unlimited energy source, but solar devices are not yet able to efficiently store energy for later use. A device has been proposed which uses direct sunlight to split water into hydrogen and oxygen. The hydrogen can then be harvested and stored as fuel, solving the question of how to effectively store energy generated during times of peak sunlight for use when sunlight levels are low. The prototype device incorporates arrays of doped silicon microwires which function as light absorbers and current-carriers, driving the chemical reactions that evolve hydrogen from water. This work aims to quantify and characterize the reduction in microwire resistivity that is achievable through application of silicon’s piezoresistive properties. Silicon displays a change in electrical resistance as a function of applied mechanical strain. This electromechanical effect has been studied extensively in bulk and top-down (etched) microstructures, but studies on microstructures grown bottom-up have been limited. A simple method is presented for piezoresistive characterization of individual, released, bottom-up silicon microwires. It is shown that these n-type microwires display a consistent negative piezoresistive response which increases in magnitude with increasing doping concentration. It was found that harnessing the piezoresistive response of moderately-doped (∼10^17 cm^−3) n-type wires allowed for a maximum observed reduction in resistivity of 49%, which translated to a 1% reduction in overall system resistance of a prototype unit cell of the artificial photosynthesis device, if all other components therein remained unchanged. / February 2015

This work describes a model of the piezoresistive behavior in nanocomposite sensors. These sensors are also called flexible sensors because the polymer matrix allows for large deformations without failure. The sensors have conductive nanoparticles dispersed through an insulative polymer matrix. The insulative polymer gaps between nanoparticles are assumed to be possible locations for electron tunneling. When the distance between two nanoparticles is small enough, electrons can tunnel from one nanoparticle to the next and ultimately through the entire sensor. The evolution of this gap distance with strain is important to understand the overall conductivity of the strain sensor. The gap evolution was modeled in two ways: (1) applying Poisson's contraction to the sensor as a homogenous material, referred to as Simple Poisson's Contraction (SPC) and (2) modeling the nanoparticle-polymer system with Finite Element Analysis (FEA). These two gap evolution models were tested in a random resistor network model where each polymer gap was treated as a single resistor in the network. The overall resistance was calculated by solving the resistor network system. The SPC approach, although much simpler, was sufficient for cases where various orientations of nanoparticles were used in the same sensor. The SPC model differed significantly from the FEA, however, in cases where nanoparticles had specific alignment, e.g. all nanoparticles parallel to the tensile axis. It was also found that the distribution used to determine initial gap sizes for the polymer gaps as well as the mean of that distribution significantly impacted the overall resistivity of the sensor.Another key part of this work was to determine if the piezoresistivity in the sensors follows a percolation type behavior under strain. The conductance versus strain curve showed the characteristic s-curve behavior of a percolative system. The conductance-strain curve was also compared to the effective medium and generalized effective medium equations and the latter (which includes percolation theory) fit the random resistor network much more closely. Percolation theory is, therefore, an accurate way to describe this polymer-nanoparticle piezoresistive system.Finally, the FEA and SPC models were compared against experimental data to verify their accuracy. There are also two design problems addressed: one to find the sensor with the largest gauge factor and another to determine how to remove the characteristic initial spike in resistivity seen in nanocomposite sensors.

This work explores the computational modeling of electromechanical problems using peridynamics and in particular, its application in studying the potential of carbon nanotube (CNT) reinforced nanocomposites for the purpose of sensing deformation and damage in materials. Peridynamics, a non-local continuum theory which was originally formulated for modeling problems in solid mechanics, has been extended in this research to electromechanical fields and applied to study the electromechanical properties of CNT nanocomposites at multiple length scales. Piezoresistivity is the coupling between the electrical properties of a material and applied mechanical loads, more specifically the change in resistance in response to deformation. This can include both, a geometric effect due to change in dimensions as well as the change in resistivity of the material itself. Nanocomposites referred to in this work are materials which consist of CNTs dispersed in a binding polymer matrix. The origins of the extraordinary piezoresistive properties of nanocomposites lie at the nanoscale where the non-local phenomenon of electron hopping plays a significant role in establishing the properties of the nanocomposite along with CNT network formation and inherent piezoresistivity of CNTs themselves. Electron hopping or tunneling allows for a current to flow between neighboring CNTs even when they are not in contact, provided the energy barrier for electrons to hop is small enough. This phenomenon is highly nonlinear with respect to the intertube distance and is also dependent on other factors such as the potential barrier of the polymer matrix. To investigate this in more detail, peridynamic simulations are first employed to study the piezoresistivity at the CNT bundle scale by considering a nanoscale representative volume element (RVE) of CNTs within polymer matrix, and by explicitly modeling electron hopping effects. This is done by introducing electron hopping bonds and it is shown that the conductivity and the non-local length scale parameter in peridynamics (the horizon) can be derived from a purely physics based model rather than assuming an ad-hoc value. Piezoresistivity can be characterized as a function of the deformation and damage within the material and thereby used as an in-situ indicator of the structural health of the material. As such, a material system for which real time in-situ monitoring may be useful is polymer bonded explosives. While these materials are designed for detonation under conditions of a strong shock, they can be damaged or even ignited under certain low magnitude impact scenarios such as during accidental drop or transportation. Since these materials are a heterogeneous system consisting of explosive grains within a polymer matrix binder, it is proposed that CNTs can be dispersed within the binder medium leading to an inherently piezoresistive hybrid nanocomposite bonded explosive material (NCBX) material which can then be monitored for a continuous assessment of deformation and damage within the material. To explore the potential use of CNT nanocomposites for this novel application, peridynamic simulations are carried out at the microscale level, first under quasistatic conditions and subsequently under dynamic conditions to allow the propagation of elastic waves. Peridynamics equations, which can be discretized to obtain a meshless method are particularly suited to this problem as the explicit modeling of crack initiation and propagation at the microscale is essential to understanding the properties of this material. Moreover, many other parameters such as electrical conductivity of the grain and the properties of the grain-binder interface are studied to understand their effect on the piezoresistive response of the material. For example, it is found that conductivity of the grain plays a major role in the piezoresistive response since it affects the preferential pathways of current density depending on the relative ease of flow through grain vs. binder. The results of this work are promising and are two fold. Peridynamics is found to be an effective method to model such materials, both at the nanoscale and the microscale. It alleviates some of difficulties faced by traditional finite element methods in the modeling of damage in materials and can be extended to coupled fields with relative ease. Secondly, simulations presented in this work show that there is much promise in this novel application of nanocomposites in the field of structural health monitoring of polymer bonded explosives. / Ph. D. / CNT reinforced nanocomposites are known to possess extraordinary mechanical, thermal and especially piezoresistive properties. Piezoresistivity is the change in resistivity of a material in response to mechanical deformation, which can possibly be used as a tool to monitor the structural health of a material. One such set of materials are polymer bonded explosives (PBXs), a heterogeneous composite system consisting of explosive grains dispersed within a binding matrix. These materials are susceptible to mechanical insults during transportation and handling, which can damage the material at the microstructural level, decreasing the reliability and usability and may even lead to accidental detonation. It is proposed that doping the binder phase with CNTs will form inherently piezoresistive NCBX materials, whose resistivity can be monitored for microstructural changes. This may help detect and discern these damage processes that can occur on at sub-macroscale length scales, which may pass unnoticed to the naked eye or even to other non-destructive methods which may not be able to detect internal changes in the material. The current work explores the structural health monitoring (SHM) capability of NCBX materials through a recently developed computational method, peridynamics. These materials are virtually tested under various loading conditions through peridynamics simulations and compared to experimental data. The results of this work are two fold; peridynamics is found to be an effective tool to study coupled phenomena such as piezoresistivity and nancomposite piezoresistivity is well suited to monitor microstructural changes in NCBX materials. This is a first step in establishing computational models for SHM in PBX materials and can be used in various other applications ubiquitous in the engineering world such as aircrafts, spacecrafts, bridges, dams among many others.

Cette thèse a été effectuée dans un contexte industriel de forte concurrence en lien avec les capteurs miniatures en silicium, destinés au gigantesque marché dit "consumer", dont l'application phare est le "Smartphone", pour laquelle les fonctionnalités accrues engendrent un besoin en matière de multi-capteurs inertiels dits 10-axes (accéléromètre 3-axes, magnétomètre 3-axes, gyromètre 3-axes et capteur de pression). Tout comme les circuits intégrés, les contraintes de coût de tels capteurs se traduisent par une exigence en termes de densité d'intégration. La technologie M&NEMS (Micro- & Nano- Electro Mechanical Systems) a été développée pour répondre à cette attente. Elle repose sur l'intégration de jauges de contraintes de dimensions nanométriques (~250 nm) avec des structures électromécaniques micrométriques, ce qui prodigue une compacité hors-pair des capteurs, ouvrant la voie à la co-intégration de multi-capteurs sur la même puce de silicium. Toutefois, la nature différente des grandeurs physiques à mesurer impose des contraintes supplémentaires, parfois opposées, ce qui rend leur co-intégration difficile. Partant de ce constat, nous avons exploré et développé, des solutions devant permettre le fonctionnement sous une même pression environnante, d'accéléromètres et de gyromètres à force de Coriolis. Cette problématique de co-intégration, s'étend au-delà du couple accéléromètre-gyromètre. Des questions inhérentes au capteur de pression ainsi qu'aux 3 axes de mesure d'un accéléromètre, sont également traitées dans cette thèse / This thesis was carried out in an industrial context of strong competition in connection with miniature silicon sensors for the huge so-called “consumer” market, where the “Smartphone” is the killer application; its increasing functionality creates a need for the so-called ‘10-axis' inertial multi-sensors (3-axis accelerometer, 3-axis magnetometer, 3-axis gyro sensor and pressure). Similarly to integrated circuits, cost constraints on such sensors translate into a requirement in terms of integration density. The M & NEMS (Micro- & Nano- Electro-Mechanical-Systems) technology has been developed to meet this expectation. It is based on the integration of nanoscale (~ 250 nm) strain gauges together with micrometric electromechanical structures, which ensure unrivaled compactness, paving the way for the co-integration of multiple inertial sensors on the same silicon chip. However, the different nature of the physical quantities to be measured imposes additional constraints, sometimes conflicting, which leads to a difficult co-integration. Based on this observation, we have explored and developed solutions to allow operation under the same ambient pressure, of accelerometers together with Coriolis force based gyroscopes. This issue of co-integration extends beyond the accelerometer-gyroscope couple. Issues inherent to the pressure sensor and to the 3-axis accelerometer measurements, are also addressed in this thesis

Les progrès technologiques de ces dernières années ont permis une très forte intégration des composants de la microélectronique à l'échelle nanométrique. Face aux limites de la miniaturisation classique, les technologies d'intégration en trois dimensions (3D) ouvrent la voie vers des dispositifs miniaturisés hétérogènes avec de nouvelles générations de puces. En parallèle, de nouveaux concepts tels que les nanofils sans jonction et les nanofils en silicium polycristallins permettent à terme d'imaginer des procédés froids et des dispositifs à faible coût permettant une intégration 3D hyperdense sur un CMOS stabilisé. La fabrication de NEMS à base de nanofils polycristallins pour la détection de masse sur CMOS est donc une nouvelle opportunité « More-Than-Moore ». Les capteurs pourraient être disposés en réseau dense en s'inspirant des architectures mémoires et imageurs. L'adressage individuel de chaque NEMS, la possibilité de les fonctionnaliser à la détection de molécules particulières, et la multiplication des capteurs sur une grande surface (« Very Large Integration » (VLSI)) permettraient la mise en œuvre d'un nouveau genre de capteur multi-physique, compact et ultrasensible. Le but de ces travaux de thèse a donc été la fabrication et l'évaluation des performances de NEMS à base de nanofils en poly-silicium. L'enjeu fut de trouver des procédés avec un budget thermique compatible à une intégration sur back-end. Une étude rigoureuse sur les propriétés physico-chimiques de la couche a été corrélée aux performances électriques, mécaniques, ainsi qu'au rendement des NEMS poly-Silicium, ce qui nous a permis de faire une sélection des meilleurs procédés de fabrication. Les NEMS fabriqués à basse température avec une couche active déposée à température ambiante et recristallisée par laser ont montré des performances, que ce soit au niveau de la transduction (piézorésistivité), ou de la stabilité du résonateur compétitives par rapports aux références monocristallines. / Recently, technological advances lead to a very large scale integration (VLSI) of microelectronics components at the nanoscale. Faced with the traditional miniaturization limits, the three dimensions (3D) integration open the door to heterogeneous miniaturized devices, with new chip generations. At the same time, new concepts such as junctionless nanowires and polycrystalline silicon nanowires allow to imagine low temperature processes and low-cost devices for a 3D integration on a stabilized CMOS. Poly-silicon nanowire based NEMS on CMOS for mass detection is a new "More-Than-Moore" opportunity. The NEMS could be arranged in a dense network like memory and image sensor architectures. The individual addressing of each NEMS, the functionalization for the detection of specific molecules within a large area (VLSI), allow the implementation of a new type of Multi-physics sensors, compact and highly sensitive. The purpose of this thesis has been the manufacturing and the performance evaluation of poly-silicon nanowire based NEMS. The challenge was to find the best processes with a back-end compatible thermal budget. A rigorous study of the layer physicochemical properties has been correlated with the electrical, mechanical performances and the yield of poly-silicon NEMS. This allowed us to make a selection of the best fabrication processes. NEMS manufactured at very low temperature with an active layer deposited at room temperature and recrystallized by a laser annealing exhibited high performances in terms of transduction (piezoresistivity) and frequency stability comparable to monocrystalline references. Polycrystalline silicon.

<div>Sensing of mechanical state is critical in diverse fields including biomedical implants, intelligent robotics, consumer technology interfaces, and integrated structural health monitoring among many others. Recently, materials that are self-sensing via the piezoresistive effect (i.e. having deformation-dependent electrical conductivity) have received much attention due to their potential to enable intrinsic, material-level strain sensing with lesser dependence on external/ad hoc sensor arrays. In order to effectively use piezoresistive materials for strain-sensing, however, it is necessary to understand the deformation-resistivity change relationship. To that end, many studies have been conducted to model the piezoresistive effect, particularly in nanocomposites which have been modified with high aspect-ratio carbonaceous fillers such as carbon nanotubes or carbon nanofibers. However, prevailing piezoresistivity models have important limitations such as being limited to microscales and therefore being computationally prohibitive for macroscale analyses, considering only simple deformations, and having limited accuracy. These are important issues because small errors or delays due to these challenges can substantially mitigate the effectiveness of strain-sensing via piezoresistivity. Therefore, the first objective of this thesis is to develop a conceptual framework for a piezoresistive tensorial relation that is amenable to arbitrary deformation, macroscale analyses, and a wide range of piezoresistive material systems. This was achieved by postulating a general higher-order resistivity-strain relation and fitting the general model to experimental data for carbon nanofiber-modified epoxy (as a representative piezoresistive material with non-linear resistivity-strain relations) through the determination of piezoresistive constants. Lastly, the proposed relation was validated experimentally against discrete resistance changes collected over a complex shape and spatially distributed resistivity changes imaged via electrical impedance tomography (EIT) with very good correspondence. Because of the generality of the proposed higher-order tensorial relation, it can be applied to a wide variety of material systems (e.g. piezoresistive polymers, cementitious, and ceramic composites) thereby lending significant potential for broader impacts to this work. </div><div><br></div><div>Despite the expansive body of work on direct current (DC) transport, DC-based methods have important limitations which can be overcome via alternating current (AC)-based self-sensing. Unfortunately, comparatively little work has been done on AC transport-deformation modeling in self-sensing materials. Therefore, the second objective of this thesis is to establish a conceptual framework for the macroscale modeling of AC conductivity-strain coupling in piezoresistive materials. For this, the universal dielectric response (UDR) as described by Joncsher's power law for AC conductivity was fit to AC conductivity versus strain data for CNF/epoxy (again serving as a representative self-sensing material). It was found that this power law does indeed accurately describe deformation-dependent AC conductivity and power-law fitting constants are non-linear in both normal and shear strain. Curiously, a piezoresistive switching behavior was also observed during this testing. That is, positive piezoresistivity (i.e. decreasing AC conductivity with increasing tensile strain) was observed at low frequencies and negative piezoresistivity (i.e. increasing AC conductivity with increasing tensile strain) was observed at high frequencies. Consequently, there exists a point of zero piezoresistivity (i.e. frequency at which AC conductivity does not change with deformation) between these behaviors. Via microscale computational modeling, it was discovered that changing inter-filler tunneling resistance acting in parallel with inter-filler capacitance is the physical mechanism of this switching behavior.</div>

A model that accurately describes the transient and steady-state response of thermal microactuators is desirable to provide guidance for design and operation. However, modeling the full response of thermal actuators is challenging due to the temperature-dependent material properties and nonlinear deformations that must be included to obtain accurate results. To meet these challenges a three-dimensional multi-physics nonlinear finite-element model was developed using commercial code. The Thermomechanical Inplane Microactuator (TIM) was chosen as a candidate application to validate the model. TIMs were fabricated using the SUMMiT V™ process and their response was measured using a high-speed camera. The TIMs were modeled and the model output was compared to the experimental data. The finite-element model predicts the steady-state response to within 0.74 percent and the transient response, as described by the time constant, to within 42 percent. The usefulness of the model was further demonstrated by its predicting that response time and energy consumption can be reduced by actuating thermal microactuators with short-duration high-voltage pulses. This behavior was verified through testing. Feedback control has proven useful in improving reliability and performance for a variety of systems. However there has been limited success implementing feedback control on surface micromachined MEMS devices. The inherent difficulties in sensing microscale phenomena complicate the development of an economical transducer that can accurately monitor the states of a surface micromachined system. We have demonstrated a simple and effective sensing strategy that uses the piezoresistive property of the polysilicon thin film of which surface micromachined MEMS devices are fabricated. The states of the device are monitored by measuring the change in resistance of flexible members which deflect as the device moves. Measurement of the output displacement of an in-plane thermal actuator is presented as a candidate application. The thermal actuator is constructed of angled pairs of expansion legs that are connected to a center shuttle. As current flows through the legs they heat up and expand. The expansion causes the center shuttle to displace in the direction the legs are angled. The center shuttle is also connected to a pair of sensing legs. Theses legs are identical to the expansion legs except that they are angled in the opposite direction. Three other leg pairs are electrically connected to the sensing legs in a Wheatstone bridge configuration. An excitation voltage is applied to the bridge, and as the sensing legs deflect with the center shuttle displacement, the resistance change across the legs can be determined by measuring the voltage across the bridge. While there still is a noise issue to be dealt with, this setup provides adequate signal strength to implement feedback control using off-chip analog circuitry. Implementation of proportional/integral control on the system is successfully demonstrated.

The objective of this work is to demonstrate the feasibility of on-chip sensing of bistable mechanism state using the piezoresistive properties of polysilicon, thus eliminating the need for electrical contacts. Changes in position are detected by observing changes in resistance across the mechanism. Sensing the state of bistable mechanisms is critical in their various applications. The research in this thesis advances the modeling techniques of MEMS devices which use piezoresistivity for position sensing. A fully compliant bistable micro mechanism was designed, fabricated, and tested to demonstrate the feasibility of this sensing technique. Testing results from two fabrication processes, Fairchild's SUMMiT IV and MUMPs, are compared. The Fairchild mechanism was then integrated into various Wheatstone bridge configurations to show the advantages of bridges and to demonstrate various design layouts. Repeatable and detectable results were found with independent mechanisms and with those integrated into Wheatstone bridges. Finite element models were constructed for the different Wheatstone bridges which were used to predict piezoresistive trends. A bistable mechanism for high-acceleration sensing was designed using uncertainty analysis optimization. The piezoresistive effects for this mechanism were also modeled. Discussion concerning nonvolatile memory applications is also presented.