Vibration Analysis of Piezoelectric Microcantilever Sensors

The main objective of this dissertation is to comprehensively analyze vibration characteristics of microcantilever-based sensors with application to ultra small mass detection and low dimensional materials characterization. The first part of this work focuses on theoretical developments and experimental verification of piezoelectric microcantilevers, commercially named Active Probes, which are extensively used in most today\u27s advanced Atomic Force Microscopy (AFM) systems. Due to special geometry and configuration of Active Probes, especially multiple jump discontinuities in their cross-section, a general and comprehensive framework is introduced for forced vibration and modal analysis of discontinuous flexible beams. More specifically, a general formulation is obtained for the characteristics matrix using both boundary and continuity conditions. The formulation is then reduced to the special case of Active Probes with intentional geometrical discontinuities. Results obtained from experiment are compared with the commonly used uniform beam model as well as the proposed discontinuous beam model. It is demonstrated that a significant enhancement on sensing accuracy of Active Probes can be achieved using the proposed discontinuous beam model compared to a uniform model when a multiple-mode operation is desired. In the second part of this dissertation, a comprehensive dynamic model is proposed for vector Piezoforce Microscopy (PFM) system under applied electrical loading. In general, PFM is considered as a suspended microcantilever beam with a tip mass in contact with a piezoelectric material. The material properties are expressed in two forms; Kelvin-Voigt model for viscoelstic representation of the material and piezoelectric force acting on the tip as a result of response of material to applied electric field. Since the application of bias voltage to the tip results in the surface displacement in both normal and in-plane directions, the microcantilever is considered to vibrate in all three directions with coupled transversal/longitudinal and lateral/torsional motions. In this respect, it is demonstrated that the PFM system can be governed by a set of partial differential equations along with non-homogeneous and coupled boundary conditions. Using the method of assumed modes, the governing ordinary differential equations of the system and its state-space representation are derived under applied external voltage. The formulation is then reduced to vertical PFM, in which low dimensional viscoelestic and piezoelectric properties of periodically poled lithium niobate (PPLN) material can be detected. For this purpose, the experimental and theoretical frequency responses along with a minimization strategy for the percentage of modeling error are utilized to obtain optimal spring constant of PPLN. Finally, the step input responses of experiment and theory are used to estimate the piezoelectric and damping coefficients of PPLN. Overall in this dissertation, a precise dynamic model is developed for piezoelectric microcantilever for ultra small mass detection purpose. This model can also be utilized in AFM systems to replace laser-based detection mechanism with other alternative transductions. Moreover, a comprehensive model is proposed for PFM system to simultaneously detect low dimensional viscoelastic and piezoelectric properties of materials. This model can also be utilized for data storage purpose in ferroelectric materials

Electromechanical Investigation of Low Dimensional Nanomaterials for NEMS Applications

Successful operation of Nano-ElectroMechanical Systems (NEMS) critically depends on their working environment and component materials' electromechanical properties. It is equally important that ambient or liquid environment to be seriously considered for NEMS to work as high sensitivity sensors with commercial viabilities. Firstly, to understand interaction between NEMS oscillator and fluid, transfer function of suspended gold nanowire NEMS devices in fluid was calculated. It was found that NEMS's resonance frequency decreased and energy dissipation increased, which constrained its sensitivity. Sensitivity limit of NEMS oscillators was also considered in a statistical framework. Subsequently, suspended gold nanowire NEMS devices were magnetomotively actuated in vacuum and liquid. Secondly, electromechanical properties of gold nanowires were carefully studied and the observed size effect was found to agree with theory, which predicted small changes of electromechanical property compared with bulk gold materials. Finally, it is well recognized that continuous development of new NEMS devices demands novel materials. Mechanical properties of new two-dimensional hexagonal Boron Nitride films with a few atomic layers were studied. Outlook of utilizing ultrathm BN films in next generation NEMS devices was discussed

Characterization of a home-built low temperature scanning probe microscopy system

The continuing advancement of technology is the driving force behind science and fundamental research. Scanning probe instruments still have a major impact in nanoscience and technology, because they provide a link between the macroscopic world and the atomic scale. The key to a reliable performance of experiments at the nanometer scale is the instrumentation, that allows probe positioning ranging from micrometers to Ångstroms with sub atomic precisions. A new type of scanning probe microscopy (SPM) system operating in ultra high vacuum (UHV) and at liquid Helium (LHe) temperature was developed. This offers the advantages that even reactive surfaces remain clean over time periods of several days, permitting long time experiments. Moreover, these experiments this low temperature scanning probe microscopy (LTSPM) system is the implementation of a focussing Fabry Perot interferometer (fFPi) that allows the following features: - Small amplitude operations and stiff cantilevers require sensors with high deflection sensitivity. With the fFPi in this low temperature SPM system, a deflection sensitivity of 4fm/ sqrt(Hz) at 1MHz can be obtained. - Wide detection bandwidth (DC-10MHz) enables the operation of higher flexural oscillation modes as well as the torsional modes of the cantilever. - A laser spot size of 3µm allows the use of ultra small cantilevers with the dimensions 1/10 of conventional cantilevers. - Photothermal excitation of cantilevers avoids undesirable mechanical vibrations near the cantilever resonance frequency. - Simultaneous flexural and torsional force detection provides quantitative studies of frictions and thus, atom manipulations by atomic force microscopy (AFM). - The combination of both types of microscopes (simultaneous AFM/STM) reveals more information than a scanning tunneling microscopy (STM) or AFM alone. A series of measurements on Si(111)7x7, herringbone superstructure of Au(111) and highly oriented pyrolytic graphite (HOPG) provides information regarding imaging performance of the system. Among these performance tests are atomically resolved scans at three different operating temperatures in STM mode. In non-contact atomic force microscopy (nc-AFM) mode, imaging was performed with the cantilever driven at the fundamental and 2nd oscillation mode. Additional measurements were performed with the fFPi in order to quantify the impact of the laser cooling effects (radiation pressure and photothermal effects) on the oscillating cantilever at three different operating temperatures. The aim of this work is the development, implementation and characterization of a new low temperature scanning probe microscope with an ultra sensitive and high bandwidth fFPi deflection sensor, suitable for nc-AFM operations with small, simultaneous flexural and torsional cantilever oscillation modes. Furthermore, expected upgrades will allow simultaneous nc-AFM/STM operations. Keywords: low temperature home-built simultaneous STM/ nc-AFM, tip-sample gap stability, PLL and self-excitation, highly oriented pyrolytic graphite (HOPG), reconstructed Si(111)7x7, herringbone superstructure, focussing Fabry-Perot interferometer, cantilever cooling, radiation pressure and photothermal effects. Der kontinuierliche, technologische Fortschritt ist die treibende Kraft hinter Wissenschaft und Grundlagenforschung. Rasterkraft und -tunnel Instrumente haben immer noch einen bedeutenden Einfluss auf die Nanotechnologie und -wissenschaft, weil sie eine Verbindung zwischen der makroskopischen Welt und den atomaren Massstäben darstellen. Der Schlüssel für eine zuverlässige Ausführung von Experimenten mit Nanometer Massstäben ist die Instrumentierung, die eine Spitzenpositionierung von Mikrometer bis Ångstroms mit subatomarer Präzision erlaubt. Ein neuartiges Rasterspitzen Mikroskop (SPM) System wurde entwickelt, das im Ultra Hoch Vakuum (UHV) und bei flüssig Helium Temperaturen arbeitet. Dies bietet Vorteile weil sogar reaktive Oberflächen über eine Dauer von einigen Tagen sauber bleiben, was eine längere Experimentierphase zulässt. Zusätzlich zeigen diese Experimente bei tiefen Temperaturen weitere Vorteile wie kleine Driftwerte und tiefe Piezo Kriechraten. Der Ansatz bei diesem Tieftemperatur Rasterspitzen Mikroskop System ist die Implementierung eines fokussierenden Fabry Perot Interferometers das die folgenden Eigenschaften vorweist: - Der Betrieb bei kleinen Amplituden und mit steifen Cantilever setzt Sensoren mit einer hohen Ablenkempfindlichkeit voraus. Mit diesem fokussierenden Fabry Perot Interferometer (fFPi) kann eine Ablenkempfindlichkeit von 4fm/ sqrt(Hz) bei 1MHz erreicht werden. - Detektion mit einer grossen Bandbreite (DC-10MHz) erlauben einen Betrieb von Cantilever mit flexuralen und torsionalen Oszillation Modi. - Ein Laser mit einem Brennpunkt von 3µm lässt einen Betrieb mit einem ultra kleinen Cantilever zu, der 1/10 so gross ist wie ein konventioneller Cantilever. - Photothermische Anregung eines Cantilevers vermeidet unerwünschte mechanische Vibrationen rund um die Resonanzfrequenz. - Gleichzeitige flexural und torsional Kraftdetektion erlauben quantitative Untersuchungen von Reibungen und daher atomare Manipulationen mit Rasterkraft Mikroskopie (AFM). - Die Kombination und simultanen Betrieb von beiden Rasterspitzen Mikroskopen (AFM/STM) zeigen mehr Information als ein Raster Tunnel Mikroskop (STM) alleine. Eine Serie von Messungen mit Si(111)7x7, Herringbone Superstrukturen auf Au(111) und Highly Oriented Pyrolytic Graphite (HOPG) geben Information bezüglich der Leistungen des Systems preis. Einige dieser Leistungstests sind atomar aufgelöste Abbildungen bei drei unterschiedlichen Betriebstemperaturen im STM Betriebsart. Im nicht-Kontakt AFM (nc-AFM) Betriebsart, Abbildungen sind ausgeführt worden auf der Grundschwingung und der zweiten Oberschwingung. Zusätzliche Messungen wurden mit dem fFPi ausgeführt um den Einfluss der Laserkühlung auf den oszillierenden Cantilever bei drei unterschiedlichen Betriebstemperaturen zu quantifizieren. Das Ziel dieser Arbeit ist die Entwicklung, Implementation und Charakterisierung eines neuen Tieftemperatur Rasterspitzen Mikroskops mit einem ultra-empfindlichen und Breitband fokussierenden Fabry Perot Interferometer Ablenk Sensor, geeignet für den nicht-Kontakt AFM Betrieb mit kleinen, simultanen flexural und torsional Cantilever Schwingungsmodi. Naheliegende Erweiterungen des Systems gewährleisten einen simultan nc-AFM/STM Betrieb. Schlüsselwörter: Tieftemperatur simultan nc-AFM/STM aus Eigenbau, Spitzen-Probe Spalt Stabilität, PLL und Eigenanregungsbetrieb, Highly Oriented Pyrolytic Graphite (HOPG), reconstrukturiertes Si(111)7x7, Herringbone Superstruktur, fokussierenden Fabry Perot Interferometer, Cantilever Kühlung, Strahlendruck und photothermische Effekte

Optical direct detection of thermal vibrations of ultralow stiffness micro-nano structures.

A direct detection optical vibrometer is constructed around an 850 nm laser and a quadrant photodetector (QPD). The limit of detection is 0.2 fW which corresponds to a minimum amplitude of 0.1 Å. The vibrometer is used to measure the thermal vibration spectra of low stiffness micromechanical structures have nanometer features. One structure measured is a cantilevered 30 μm diameter glass fiber. Vibration amplitudes as low as 1.1 Å are measured. The thermal vibration spectra show fundamental resonances at 80-250 Hz and a signal to noise ratio (SNR) of 23-55 dB. Young’s modulus of glass in the cantilevers, estimated from the spectra, agree to within 3 % of the manufacturer’s value, which is somewhat more accurate than force-elongation measurements made of 50-100 mm long fibers which differ by 5 %. Mass changes due to adhering small drops of liquids to the tip of the fiber cantilevers shifts the resonant frequency with a sensitivity of 120 ng. The mass detection limit would decrease by 2-3 orders by increasing the length of the time series data. The intended purpose of the vibrometer development is the measurement of the thermal vibration of polymer bead-on-string (BOS) fibers with enough sensitivity to detect time-varying changes in the spectra that relate to molecular-level and temperature dependent changes, such as evaporation, solidification, crystallization and strain-dependent chain reorganizations of the polymer material. Time dependent variations in the BOS spectra are observed in vibrometer measurements that, if attributable to material properties, would represent 2.5-5.2 % change in elastic modulus, 20-40 % loss in water mass due to evaporation, with the minimum detectable change in these properties being 0.06 % for the measured spectra. The vibrometer provides an important tool for the real-time study of changing properties of BOS fibers, as well as other low stiffness microstructures, especially those composed of polymers and other soft mater

Non-ambiguous recovery of Biot poroelastic parameters of cellular panels using ultrasonic waves

a b s t r a c t The inverse problem of the recovery of the poroelastic parameters of open-cell soft plastic foam panels is solved by employing transmitted ultrasonic waves (USW) and the Biot-Johnson-Koplik-Champoux-Allard (BJKCA) model. It is shown by constructing the objective functional given by the total square of the difference between predictions from the BJKCA interaction model and experimental data obtained with transmitted USW that the inverse problem is ill-posed, since the functional exhibits several local minima and maxima. In order to solve this problem, which is beyond the capability of most off-the-shelf iterative nonlinear least squares optimization algorithms (such as the Levenberg Marquadt or Nelder-Mead simplex methods), simple strategies are developed. The recovered acoustic parameters are compared with those obtained using simpler interaction models and a method employing asymptotic phase velocity of the transmitted USW. The retrieved elastic moduli are validated by solving an inverse vibration spectroscopy problem with data obtained from beam-like specimens cut from the panels using an equivalent solid elastodynamic model as estimator. The phase velocities are reconstructed using computed, measured resonance frequencies and a time-frequency decomposition of transient waves induced in the beam specimen. These confirm that the elastic parameters recovered using vibration are valid over the frequency range of study

Mechanical compression of coiled carbon nanotubes

Carbon nanotubes are molecular-scale tubes of graphitic carbon that possess many unique properties. They have high tensile strength and elastic modulus, are thermally and electrically conductive, and can be structurally modified using well established carbon chemistries. There is global interest in taking advantage of their unique combination of properties and using these interesting materials as components in nanoscale devices and composite materials. The goal of this research was the correlation of the mechanical properties of coiled carbon nanotubes with their chemical structure. Individual nanocoils, grown by chemical vapor deposition, were attached to scanning probe tip using the arc discharge method. Using a scanning probe microscope the nanocoils are repeatedly brought into and out of contact with a chemically-modified substrate. Precise control over the length (or area) of contact with the substrate is achievable through simultaneous monitoring the cantilever deflection resonance, and correlating these with scanner movement. The mechanical response of nanocoils depended upon the extent of their compression. Nonlinear response of the nanocoil was observed consistent with compression, buckling, and slip-stick motion of the nanocoil. The chemical structure of the nanocoil and its orientation on the tip was determined using scanning and transmission electron microscopy. The mechanical stiffness of eighteen different nanocoils was determined in three ways. In the first, the spring constant of each nanocoil was computed from the slope of the linear response region of the force-distance curve. The assumptions upon which this calculation is based are: 1) under compression, the cantilever-nanocoil system can be modeled as two-springs in series, and 2) the nanocoil behaves as an ideal spring as the load from the cantilever is applied. Nanocoil spring constants determined in this fashion ranged from 6.5x10-3 to 5.16 TPa for the CCNTs understudy. In the second, the spring constant of the nanocoil was computed from measuring the critical force required to buckle the nanocoil. The critical force method measured the force at the point where the nanocoil-cantilever system diverges from a linear region in the force curve. Nanocoil spring constants determined in this fashion ranged from 1.3x10-5 to 10.4 TPa for the CCNTs understudy. In the third, the spring constant of each nanocoil was computed from the thermal resonance of the cantilever-nanocoil system. Prior to contact of the nanocoil with the substrate, the effective spring constant of the system is essentially that of the cantilever. At the point of contact and prior to buckling or slip-stick motion, the effective spring constant of the system is modeled as two springs in parallel. Nanocoil spring constants determined in this fashion ranged from 2.7x10-3 to 0.03 TPa for the CCNTs understudy. Using the thermal resonance of the cantilever system a trend was observed relating nanocoil structure to the calculated modulus. Hollow, tube-like nanostructures had a higher measured modulus than solid or fibrous structures by several orders of magnitude. One can conclude that the structure of carbon nanocoils can be determined from using their mechanical properties. This correlation should significantly contribute to the knowledge of the scientific and engineering community. It will enable the integration of carbon nanocoils in microelectromechanical (MEMS) or nanoelectromechanical systems (NEMS) as resonators, vibration dampers, or any other application in which springs are used within complex devices.Ph.D.Committee Chair: Lawrence Bottomley; Committee Member: Aldo Ferri; Committee Member: E. Kent Barefield; Committee Member: Levent Degertekin; Committee Member: Robert Whetten; Committee Member: Satish Kumar; Committee Member: Zhong Lin Wan

Multi-Eigenmode Control for Improved Tracking Speed in Multifrequency Atomic Force Microscopy

Die Sensoren von Rasterkraftmikroskopen sind mechanische Schwinger, die zur zeitgleichen Aufnahmevon Topographie und Materialeigenschaften genutzt werden können. Besonders wichtig sinddie Bildrastergeschwindigkeit und Kraftsensitivität, die oft einen Kompromiss benötigen. In dieserArbeit wird ein neuartiger Multi-Eigenmode Kompensator basierend auf einem Zustandsschätzervorgestellt, der die dynamischen Eigenschaften jeder Cantilever-Resonanz unabhängig voneinandermodifizieren kann. Dargelegt wird die Modellierung, Kompensator-Design und Implementierungsstrategiein ein digitales System. Als Erstes wird der Kompensator zur Modifikation desQ Faktors einzelner Eigenmoden genutzt. Somit kann die Abbildungsrate um das 20-fache erhöhtwerden. Die Modifikation der natürlichen Frequenz erlaubt die Abbildung von Proben mitvollständig verschobenen Resonanzen. Moderne Mehrfachfrequenz-Abbildungsverfahren nutzenhöheren Eigenmoden, um bessere Abbildungsraten und Materialsensitivitäten zu erreichen. Beieiner Methode werden die angeregten höheren Harmonischen extrahiert, die beim Rastern einerOberfläche im Fourier-Spektrum entstehen. Eine andere Methode regt die erste und höhere Eigenmodengleichzeitig an. In Experimenten wird der Kompensator in Kombination mit beiden Abbildungsverfahrengenutzt, um speziell den Q Faktor der ersten beiden transversalen Eigenmoden gleichzeitigzu beeinflussen. Experimente zeigen, dass beste Abbildungsraten und Materialkontrastemit geringen Q Faktoren in der ersten und hohen Q Faktoren in der zweiten Eigenmode erreichtwerden. Eine Erweiterung des Kompensators erlaubt die Hochgeschwindigkeits-Demodulationvon Cantilever-Amplituden ohne Einsatz eines Lock-in Verstärkers, was anhand von Abbildungenmit der ersten Eigenmode gezeigt wird. Eine weitere Möglichkeit zur Verbesserung des Materialkontrastesbasiert auf der strukturellen Modifikation des Cantilevers. Mit Hilfe einer Ionenfeinstrahlanlagewird Material an bestimmten Bereichen des Cantilevers entfernt, so dass die erste undhöheren Eigenmoden aufeinander abgestimmt werden. Die Bestimmung von Form und Ort derMaterialentfernung wird entweder durch Simulationen im Voraus oder mit einem in situ Ansatzerreicht. Die extrahierten höheren harmonischen Signale des harmonischen Cantilevers zeigen eindeutlich verstärktes Signal von bis zu 10 % im Vergleich zur ersten Resonanz.Atomic Force Microscope probes are mechanical beams that can be used to simultaneously maptopography and material properties. In particular the imaging speed and force sensitivity aremajor concerns that often require a trade-off approach. In this work, a novel estimator basedmulti-eigenmode compensator is introduced to modify the dynamics of each resonance independently.Modeling, compensator design, implementation strategy in a digital system and validationin experiments will be presented. A single-eigenmode version of the compensator is used to modifythe Q factor of the first three eigenmodes separately. Using higher eigenmodes in combinationwith a modified Q factor leads to a 20-fold increase in image acquisition rates. The modificationof the natural frequency (F control) allows imaging at resonance frequencies that are not naturalto the cantilever. The emerging multifrequency Atomic Force Microscopy utilizes higher eigenmodesto improve imaging speed and force sensitivity concurrently. One method actuates the firsteigenmode for topography imaging and records the excited higher harmonics to map a sample’snanomechanical properties. To enhance the higher frequencies’ response two or more eigenmodesare actuated simultaneously, where the higher eigenmodes are used to quantify the nanomechanics.In experiments, the compensator is used to specifically modify the Q factors of the cantilever’sfirst two transversal eigenmodes concurrently in both imaging schemes. The experiments indicatemost enhanced material contrast and imaging rate with low Q factors in the first eigenmode andhigh Q factors in the higher eigenmode. An extension of the compensator allows for a high speedLock-in amplifier free amplitude demodulation, which is used for topography imaging with the firstresonance. A different technique for improving material property sensitivity is presented basedon structural modifications of the cantilever. Focused Ion Beam milling is used to remove massfrom specific areas in the cantilever such that the first and higher eigenmodes are tuned towardseach other. The shape and location of mass removal is determined either by simulation beforehandor through an in-situ approach. Higher harmonics of the harmonic active cantilevers indicate asignificant response of up to 10% in respect to the first resonance/harmonic