Piezoresistive cantilevers with an integrated bimorph actuator

Scanning Probe Microscopy (SPM) has become of fundamental importance for research in area of micro and nano-technology. The continuous progress in these fields requires ultra sensitive measurements at high speed. The imaging speed limitation of the conventional Tapping Mode SPM is due to the actuation time constant of piezotube feedback loop that keeps the tapping amplitude constant. In order to avoid this limit a deflection sensor and an actuator have to be integrated into the cantilever. In this work has been demonstrated the possibility of realisation of piezoresistive cantilever with an embedded actuator. Piezoresistive detection provides a good alternative to the usual optical laser beam deflection technique. In frames of this thesis has been investigated and modelled the piezoresistive effect in bulk silicon (3D case) for both n- and p-type silicon. Moving towards ultra-sensitive measurements it is necessary to realize ultra-thin piezoresistors, which are well localized to the surface, where the stress magnitude is maximal. New physical effects such as quantum confinement which arise due to the scaling of the piezoresistor thickness was taken into account in order to model the piezoresistive effect and its modification in case of ultra-thin piezoresistor (2D case). The two-dimension character of the electron gas in n-type piezoresistors lead up to decreasing of the piezoresistive coefficients with increasing the degree of electron localisation. Moreover for p-type piezoresistors the predicted values of the piezoresistive coefficients are higher in case of localised holes. Additionally, to the integration of the piezoresistive sensor, actuator integrated into the cantilever is considered as fundamental for realisation of fast SPM imaging. Actuation of the beam is achieved thermally by relying on differences in the coefficients of thermal expansion between aluminum and silicon. In addition the aluminum layer forms the heating micro-resistor, which is able to accept heating impulses with frequency up to one megahertz. Such direct oscillating thermally driven bimorph actuator was studied also with respect to the bimorph actuator efficiency. Higher eigenmodes of the cantilever are used in order to increase the operating frequencies. As a result the scanning speed has been increased due to the decreasing of the actuation time constant. The fundamental limits to force sensitivity that are imposed by piezoresistive deflection sensing technique have been discussed. For imaging in ambient conditions the force sensitivity is limited by the thermo-mechanical cantilever noise. Additional noise sources, connected with the piezoresistive detection are negligible.

Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.

Elektrochemo- und mikromechanisches Verhalten elektronisch leitfähiger Polymere

Intrinsisch leitfähige Polymere sind durch eine Reihe materialspezifischer Eigenschaften gekennzeichnet. In Abhängigkeit des angelegten Potenzials und der chemischen Umgebung zeigen sie elektrochromes Verhalten, Veränderungen der Masse, des Volumens und der elektronischen Leitfähigkeit. Basierend auf diesen Eigenschaften eignen sich halbleitende organische Polymere als funktionales Material für Anwendungen in der Mikro- und Nanotechnologie, insbesondere für miniaturisierte chemische Sensoren und Aktoren. Im Gegensatz zu konventionellen Piezo-Aktoren operieren diese Aktoren z. B. bei Spannungen unterhalb 1 V. Diese Arbeit befasst sich mit den elektrochemomechanischen Eigenschaften der ausgewählten Polymere Polyanilin und Polypyrrol, d. h. mit den potenzialkontrollierten Veränderungen des Volumens, der Struktur und der mechanischen Eigenschaften. Bei diesem Prozess werden positive Ladungen innerhalb der Polymerphase generiert. Um die für den Ladungsausgleich benötigten Gegenionen bereitzustellen, werden alle Messungen in Anwesenheit eines wässrigen Elektrolyten durchgeführt. Der Ladungstransport und die Volumenänderungen werden mit den Methoden der zyklischen Voltammetrie, der elektrochemischen Quarzmikrowaage und der Rastersondenmikroskopie untersucht. Signifikante Ergebnisse können für dünne homogene Polymerschichten erhalten werden, wobei Schichtdicken oberhalb 150 nm aufgrund der insbesondere bei Polyanilin einsetzenden Bildung von Fadenstrukturen (Fibrillen) vermieden werden. Von besonderem Interesse im Rahmen dieser Arbeit ist die Kombination der funktionalen Polymere mit Strukturen auf Siliziumbasis, insbesondere mit mikrostrukturierten Cantilevern. Die zuvor erhaltenen Ergebnisse bilden die Grundlage für das Design und die Dimensionierung der Mikroaktoren. Diese bestehen aus Siliziumcantilevern, die eine Elektrodenschicht aus Gold oder Platin tragen. Auf der Elektrode wird mittels Elektrodeposition eine homogene Schicht Polymer mit Schichtdicken bis zu 150 nm aufgebracht. Die Aktorcharakteristik, die Biegung des Cantilevers aufgrund des angelegten Potenzials, wird mit dem aus der Rastersondenmikroskopie bekannten Lichtzeigerverfahren gemessen. Das Aktorsystem wird hinsichtlich des angelegten Potenzials, des Elektrolyten und der Redox-Kinetik charakterisiert. Die verschiedenen Beiträge zum Aktorverhalten werden in situ während des Schichtwachstums untersucht. Das beobachtete Verhalten kann als Superposition verschiedener Effekte beschrieben werden. Darunter sind die Elektrodenaufladung (Elektrokapillarität), die Veränderungen der Elektrodenoberfläche durch dünne Oxidschichten und die Elektrochemomechanik des Polymers.

Statistical evaluation of texture analysis from the biocrystallization method

The consumers are becoming more concerned about food quality, especially regarding how, when and where the foods are produced (Haglund et al., 1999; Kahl et al., 2004; Alföldi, et al., 2006). Therefore, during recent years there has been a growing interest in the methods for food quality assessment, especially in the picture-development methods as a complement to traditional chemical analysis of single compounds (Kahl et al., 2006). The biocrystallization as one of the picture-developing method is based on the crystallographic phenomenon that when crystallizing aqueous solutions of dihydrate CuCl2 with adding of organic solutions, originating, e.g., from crop samples, biocrystallograms are generated with reproducible crystal patterns (Kleber & Steinike-Hartung, 1959). Its output is a crystal pattern on glass plates from which different variables (numbers) can be calculated by using image analysis. However, there is a lack of a standardized evaluation method to quantify the morphological features of the biocrystallogram image. Therefore, the main sakes of this research are (1) to optimize an existing statistical model in order to describe all the effects that contribute to the experiment, (2) to investigate the effect of image parameters on the texture analysis of the biocrystallogram images, i.e., region of interest (ROI), color transformation and histogram matching on samples from the project 020E170/F financed by the Federal Ministry of Food, Agriculture and Consumer Protection(BMELV).The samples are wheat and carrots from controlled field and farm trials, (3) to consider the strongest effect of texture parameter with the visual evaluation criteria that have been developed by a group of researcher (University of Kassel, Germany; Louis Bolk Institute (LBI), Netherlands and Biodynamic Research Association Denmark (BRAD), Denmark) in order to clarify how the relation of the texture parameter and visual characteristics on an image is. The refined statistical model was accomplished by using a lme model with repeated measurements via crossed effects, programmed in R (version 2.1.0). The validity of the F and P values is checked against the SAS program. While getting from the ANOVA the same F values, the P values are bigger in R because of the more conservative approach. The refined model is calculating more significant P values. The optimization of the image analysis is dealing with the following parameters: ROI(Region of Interest which is the area around the geometrical center), color transformation (calculation of the 1 dimensional gray level value out of the three dimensional color information of the scanned picture, which is necessary for the texture analysis), histogram matching (normalization of the histogram of the picture to enhance the contrast and to minimize the errors from lighting conditions). The samples were wheat from DOC trial with 4 field replicates for the years 2003 and 2005, “market samples”(organic and conventional neighbors with the same variety) for 2004 and 2005, carrot where the samples were obtained from the University of Kassel (2 varieties, 2 nitrogen treatments) for the years 2004, 2005, 2006 and “market samples” of carrot for the years 2004 and 2005. The criterion for the optimization was repeatability of the differentiation of the samples over the different harvest(years). For different samples different ROIs were found, which reflect the different pictures. The best color transformation that shows efficiently differentiation is relied on gray scale, i.e., equal color transformation. The second dimension of the color transformation only appeared in some years for the effect of color wavelength(hue) for carrot treated with different nitrate fertilizer levels. The best histogram matching is the Gaussian distribution. The approach was to find a connection between the variables from textural image analysis with the different visual criteria. The relation between the texture parameters and visual evaluation criteria was limited to the carrot samples, especially, as it could be well differentiated by the texture analysis. It was possible to connect groups of variables of the texture analysis with groups of criteria from the visual evaluation. These selected variables were able to differentiate the samples but not able to classify the samples according to the treatment. Contrarily, in case of visual criteria which describe the picture as a whole there is a classification in 80% of the sample cases possible. Herewith, it clearly can find the limits of the single variable approach of the image analysis (texture analysis).

Zur Erfassung von form- und materialbedingten Oberflächenstrukturen mit Mikro-Deflexions-Ellipsometrie

Die vorliegende Arbeit berichtet über ein neuartiges, kombiniertes Messverfahren zur gleichzeitigen Erfassung von Form und Material einer glänzenden Probenoberfläche. Die Materialerkennung erfolgt über die polarisationsoptische Brechzahlbestimmung im Messpunkt mit Mikroellipsometrie. Die Mikroellipsometrie ist ein fokussierendes Ellipsometer, das aus der Polarisationsänderung, bedingt durch die Wechselwirkung Licht – Materie, die materialcharakteristische komplexe Brechzahl eines reflektierenden Materials ermitteln kann. Bei der fokussierenden Ellipsometrie ist die Anordnung der fokussierenden Optiken von Bedeutung. Die hier vorgestellte ellipsometerexterne Fokussierung vermeidet Messfehler durch optische Anisotropien und ermöglicht die multispektrale ellipsometrische Messung. Für die ellipsometrische Brechzahlbestimmung ist zwingend die Kenntnis des Einfallswinkels des Messstrahls und die räumliche Orientierung der Oberflächenneigung zum Koordinatensystem des Ellipsometers notwendig. Die Oberflächenneigung wird mit einem Deflektometer ermittelt, das speziell für den Einsatz in Kombination mit der Ellipsometrie entwickelt wurde. Aus der lokalen Oberflächenneigung kann die Topographie einer Probe rekonstruiert werden. Der Einfallswinkel ist ebenfalls aus den Oberflächenneigungen ableitbar. Die Arbeit stellt die Systemtheorie der beiden kombinierten Messverfahren vor, außerdem werden Beiträge zu Messunsicherheiten diskutiert. Der experimentelle Teil der Arbeit beinhaltet die separate Untersuchung zur Leistungsfähigkeit der beiden zu kombinierenden Messverfahren. Die experimentellen Ergebnisse erlauben die Schlussfolgerung, dass ein Mikro-Deflexions-Ellipsometer erfolgreich realisierbar ist.

Femtosecond real-time probing of reactions. 13. Multiphoton dynamics of IHgI

Real-time studies of the dynamics were performed on the reaction of HgI_2 in a molecular beam. Excitation was by either one or multi pump photons (311 nm), leading to two separate sets of dynamics, each of which could be investigated by a time-delayed probe laser (622 nm) that ionized the parent molecule and the fragments by REMPI processes. These dynamics were distinguished by combining the information from transients taken at each mass (HgI_2, HgI, I_2, Hg, and I) with the results of pump (and probe) power dependence studies on each mass. A method of plotting the slope of the intensity dependence against the pump-probe time delay proved essential. In the preceding publication, we detailed the dynamics of the reaction initiated by a one photon excitation to the A-continuum. Here, we present studies of higher-energy states. Multiphoton excitation accesses predissociative states of HgI_2, for which there are crossings into the symmetric and asymmetric stretch coordinates. The dynamics of these channels, which lead to atomic (I or Hg) and diatomic (HgI) fragments, are discussed and related to the nature of the intermediates along the reaction pathway.

Femtosecond pump-probe study of the spreading and recurrence of a vibrational wave packet in Na_2

The motion of a vibrational wave packet in the bound A(^1 \summe^+_u) electronic state of the sodium dimer is detected in a femtosecond pump/probe molecular beam experiment. For short times harmonic motion is seen in the total ion yield of Na^+_2 as a function of delay time between the two laser pulses. The spreading of the wave packet results in the loss of the periodic variation of the ion signal. For longer delay times (47 ps) the wave packet regains its initial form which is reflected in the revival structure of the Na^+_2 signal. Time-dependent quantum calculations reproduce the measured effects.

Femtosecond dynamics of molecules and clusters

The real-time dynamics of multiphoton ionization and fragmentation of molecules - Na_2 , Na_3 - and clusters - Na_n, Hg_n - has been studied in molecular beam experiments employing ion and electron spectroscopy together with femtosecond pump-probe techniques. Experiments with Na_2 and Na_3 reveal unexpected features of the dynamics of the absorption of several photons as seen in the one- and three dimensional vibrational wave packet motion in different potential surfaces and in high laser fields. Cluster size dependent studies of physical properties such as absorption resonances, lifetimes and decay channels have been performed using tunable femtosecond light pulses in resonance enhanced multiphoton ionization (REMPI) of the cluster size under investigation. This method failed in ns-laser experiments due to the ultrafast decay of the studied cluster. For Na_n, cluster we find that for cluster sizes n \le 21 molecular excitations and properties prevail over collective excitations of plasmon-like resonances. In the case of Hg_n cluster prompt formation of singly and doubly charged cluster are observed up to n \approx 60. The transient multiphoton ionization spectra show a 'short' time wave packet dynamics, which is identical for singly and doubly charged mercury clusters while the 'long' time fragmentation dynamics is different.

Generic Finite Element Model for Mechanically Consistent Scaling of Composite Beam-to-column Joint with Welded Connection

To study the behaviour of beam-to-column composite connection more sophisticated finite element models is required, since component model has some severe limitations. In this research a generic finite element model for composite beam-to-column joint with welded connections is developed using current state of the art local modelling. Applying mechanically consistent scaling method, it can provide the constitutive relationship for a plane rectangular macro element with beam-type boundaries. Then, this defined macro element, which preserves local behaviour and allows for the transfer of five independent states between local and global models, can be implemented in high-accuracy frame analysis with the possibility of limit state checks. In order that macro element for scaling method can be used in practical manner, a generic geometry program as a new idea proposed in this study is also developed for this finite element model. With generic programming a set of global geometric variables can be input to generate a specific instance of the connection without much effort. The proposed finite element model generated by this generic programming is validated against testing results from University of Kaiserslautern. Finally, two illustrative examples for applying this macro element approach are presented. In the first example how to obtain the constitutive relationships of macro element is demonstrated. With certain assumptions for typical composite frame the constitutive relationships can be represented by bilinear laws for the macro bending and shear states that are then coupled by a two-dimensional surface law with yield and failure surfaces. In second example a scaling concept that combines sophisticated local models with a frame analysis using a macro element approach is presented as a practical application of this numerical model.