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Dit proefschrift beschrijft een serie experimenten aan nanoelectromechanische systemen (NEMS) met koolstof nanobuis bouwstenen. NEMS zijn mechanische objecten met dimensies van enkele nanometers die interacties aangaan met elektronica. Deze systemen zijn de logische opvolger van micromechanische systemen, en beloven een significante verbetering wat betreft operatiefrequenties en dissipatie van energie.

This thesis describes a series of experiments on dynamical characterization of silicon nitride cantilevers. These devices play an important role in micro-and nanoelectromechanical systems (MEMS and NEMS). They consist of a mechanical part, a sensor or actuator, and an electronic part for readout and control. The core of NEMS and MEMS, the so called mechanical part, exists in various shapes. Examples include disk resonators, doubly clamped beams, tuning forks and cantilevers. These mechanical sensors are good candidates for applications in e.g the medical world, and telecommunication. Examples of applications include micro-array biosensors and ultrasensitive mass sensors. On a fundamental level they can be utilized to explore phenomena like the Casimir force and quantum mechanical zero point motion. Mechanical resonators are fabricated through a top-down technique, making use of the bulk material and special micro-machining techniques. Experiments in this thesis are performed on cantilevers, which differ from each other in the clamping point due the release method, and in the accuracy in the pattern definition step. A short description of MEMS, NEMS and the fabrication is described in chapters 1 and 2. The cantilevers are dynamically characterized by measuring their eigenmodes, each with a specific resonance frequency and quality factor. From this information the effective Young's and shear modulus, and the dissipation mechanisms can be determined. The resonance frequency can be measured using an interferometric, capacitive or laser deflection technique. The latter is the most common technique and is used in atomic force microscopes (AFM). We have optimized this technique so that the cantilever deflection due to its thermal mechanical noise is probed. The output signal, the voltage difference generated by the reflected light focused on a two-segment diode, is measured using a spectrum analyser. The Fourier-transformed signal manifests itself as a Lorentzian peak, which contains the necessary information for the characterization. Amplitudes of the order of picometers can be detected with our setup. Details of the measurement technique are described in chapter 3. Chapter 4 describes the resonance frequency behavior as a function of cantilever dimensions. Two vibrational modes are distinguished; flexural and torsional modes, which are independently measured. Also higher order modes for each type of vibration are detected. Depending on the strength of the spring constant seven or more flexural modes and up to three torsional modes are observed. Furthermore we have investigated the dependence of the resonance frequency for different fabrication methods. For cantilevers with no undercut adding an additional length to the nominal length makes the resonance frequency behavior predictable by existing models. For resonance frequency behavior of cantilevers fabricated with no undercut such a correction is not necessary. Finite element simulations support the observations. The resonance frequency of the torsional modes as a function of dimensions is not properly described by commonly used models. It predicts lower frequencies. A different model describing torsional vibrations of airplane-wings, fits to our experimental data. Chapter 5 describes experiments on the behavior of the resonance frequency and quality-factor as a function of gas pressure. The experiments are performed in helium, argon, air and xenon environments. Three pressure regimes are distinguished in the pressure range between 10^{-5} mbar and atmospheric. Depending on the Knudsen number these regimes are known as 'intrinsic', 'molecular' and 'viscous'. Our experimental findings are well fitted by existing theories, for both the first and higher flexural modes. An unexpected slight increase in the resonance frequency in the viscous regime is observed, which is not predicted by the existing models. The increase is due to a slight stiffening of the cantilevers and might be caused by gas adsorption in the near surface. Measurements with higher laser power show a further increase in the anomalous resonance frequency shift. Its origin is not clear since a higher laser power is expected to further heat up the cantilever, and consequently decrease its resonance frequency. Chapter 6 discusses the behavior of Young's modulus as a function of decreasing thickness in the range of 20 to 680 nm. A significant decrease in the Young's modulus is observed for thicknesses below 150 nm, both in the first and second flexural modes. This decrease cannot be explained by neither a double layer and a sandwich model, in which case the extra layer(s) are considered to have a different Young's modulus. With a model including also a surface-elasticity term the experimental data can be understood. An infinitesimal thin layer with a certain surface elasticity, which is determined from a fit through the data, influences the Young's modulus. For thinner cantilevers this influence is even larger because at higher surface-to-volume ratios, surface-processes dominate the bulk properties. Finally chapter 7 describes measurements on the important application of cantilevers as ultrasensitive mass sensors. A cantilever can be considered as a harmonic oscillator so that the resonance frequency can be determined from its spring constant and the effective mass. By measuring the resonance frequency before and after mass loading, the amount of the added mass can be calculated, assuming the spring constant does not change. The first measurements are performed on cantilevers, with a homogeneously evaporated gold coating of 40 nm on top. A measured mass of 390 pg is calculated through resonance frequency shifts from both the first and the second mode. Mass of the gold layer calculated from the volume and mass density is 3 times higher. A possible explanation for this discrepancy is that the total Young's modulus due to the bilayer system is lower than that of bare silicon nitride. A lower effective Young's modulus decreases the resonance frequency and explains partially the mass difference. In a second measurement we performed mass sensing with smaller amounts of mass. For this purpose aminopropyltriethoxysilane (APTES) is selectively coated as a monolayer. These so-called functionalized cantilevers are good candidates for selective mass sensing purposes. As an example, an array of cantilevers, each functionalized with a different coating on a single chip, can be used to simultaneously detect different targets such as DNA, viruses and bacteria. Experimental results on the first three flexural modes and first torsional mode show the same amount of added mass of approximately 10 pg. In contrast to this value, the calculated mass of a monolayer coverage of APTES gives 5 pg. A possible explanation for this difference might be a variation in the spring constant, which was assumed to be constant

This thesis describes three-terminal transport measurements through single molecules. The interest in this field stems from the dream that single molecules will form the building blocks for future nanoscale electronic devices. The advantages are their small size -nanometers-, and their synthetic tailorability which allows the molecules to be designed with built-in functionality. Many efforts in experimental research are nowadays devoted to understand electrical transport though single molecules. Several techniques are used for this purpose: scanning tunneling microscopy (STM), mechanical controllable break junctions (MCBJ), atomic force microscopy (AFM), and shadow evaporation. The method used throughout our work to fabricate nanogaps is named electromigration. We show that after trapping a molecule in the nanogap, a molecule at low temperatures behaves as a quantum dot (QD), i.e., a system where electrons can be placed in discrete energy states. The control over the number of electrons that can sit on the molecule is achieved by the voltage on a third electrode, the gate, which is capacitively coupled to the QD. Transport measurements, which consist of taking current-voltage characteristics as a function of this gate voltage, reveal important spectroscopic information about the molecule.

This thesis describes experiments that were done with a wide range of nano(electro)mechanical systems (NEMS). These devices are promising candidates to study mechanics in the quantum regime. The experiments range from AFM measurements on few-layer graphene nanodrums, electrical detection of flexural modes of suspended carbon nanotubes both at room temperature and at millikelvin temperatures, to position detection of and backaction on a micromechanical resonator that is embedded in a dc SQUID. Continuum mechanical models for the different NEMS are discussed, as well as the concepts that are needed to reach the quantum regime.

In single-molecule junctions, the behavior of a device is determined by the properties of an individual molecule. In this thesis we develop several models to describe both electrical and mechanical effects in such devices, which can be used to design molecules with a specific functionality. We show how the resistance of a molecule varies with its electrostatic environment, in particular due to capacitive interactions with neighboring molecules or metallic grains. A major challenge in the field of molecular electronics is making sure you are measuring the molecule you want to measure. Since molecules are generally flexible entities, they vibrate when current is flowing through them. The spectrum of these vibrations is unique to each species of molecules and we shown how it can be used as a 'molecular fingerprint' to identify single molecules. The electrical and mechanical effects described in this thesis come together in our design for an all-electric single-molecule motor. By applying an oscillating gate field, we can exert a force on a rotor containing a permanent electric dipole moment, and, under the right circumstances, drive it into a unidirectional motion. This rotation can be measured in real-time since the motion of the rotor changes the conductance of the molecule. We show that this approach provides full control over the speed and continuity of motion, thereby combining electrical and mechanical control at the molecular level.

Mechanical sensors are essential tools for the detection of small forces. This thesis presents the dc SQUID as a detector for the displacement of embedded micromechanical resonators. The device geometry and basic operating principle are described. The SQUID displacement detector reaches an excellent resolution, a factor of 1.5 below the standard quantum limit: It can detect one-third of a single vibrational quantum in a 129 kHz resonator. We use the high displacement sensitivity to perform feedback cooling of the temperature of the fundamental resonance mode by using a heterodyne discrete-time scheme. The thesis also studies the SQUID backaction: Because of the strong coupling between the SQUID and the resonator, the SQUID exerts forces on the resonator which change the resonator spring constant and damping depending on the current and flux bias of the SQUID. In the final chapter, the entire SQUID is mechanically suspended to form a torsional resonator. In this geometry, the backaction becomes so strong that the resonators goes into self-sustained oscillation. In conclusion, the results in this thesis show that the dc SQUID is an excellent displacement detector for micro-and nanomechanical resonators, but also that the SQUID-resonator interaction strongly influences the resonator dynamics.

In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like bifurcations, stochastic switching and amplitude-dependent resonance frequencies. The theoretical background of micromechanical systems involving the relevant nonlinearities for beams clamped on one (cantilever) or two sides (clamped-clamped beam) are discussed in chapter 2. First, the linear response of a mechanical resonator is discussed. Then, the linear equations are extended with nonlinear terms accounting for geometric and inertial effects. Specifically, the origin of the Duffing nonlinearity in the equation of motion of a clamped-clamped beam is shown. It is shown that the nonlinearity couples the flexural vibration modes of a beam. Microcantilevers are widely used in mass sensing and force microscopy. At small resonance amplitudes, cantilever motion is described by a harmonic oscillator model, while at high amplitudes, the motions is limited by nonlinearities. In chapter 3, the intrinsic mechanical nonlinearity in microcantilevers is studied. It is shown that although the origin is different, the nonlinearity resembles a Duffing nonlinearity resulting in hysteresis and bistable amplitudes. This bistability is then used to implement a mechanical memory. The bistability of microcantilevers can also be used to study the switching characteristics when noise is applied. Chapter 4 shows the experimental implementation of this stochastic switching of microcantilever motion. It is shown that upon increasing the noise intensity, the switching rate rises exponentially as expected from Kramer's law. However, at higher noise intensities, the switching rate saturates and eventually even decreases, which suggests that the noise influences the dynamical parameters of the system. In chapter 5, we investigate in detail the coupling between the flexural vibration modes of a clamped-clamped beam. The coupling arises from the displacement-induced tension. A theoretical model based on the nonlinearity is developed, which is experimentally verified by driving two modes of the beam at high amplitudes and reading out their motion at the two frequencies. The experiments show that the resonance frequency of one flexural mode depends on the amplitude of another flexural mode and the theory is in excellent agreement with the experiments. The nonlinearity not only couples the flexural modes in a clamped-clamped beam, but we show in chapter 6 that also the cantilever modes are coupled. Here, the mechanism causing the nonlinearity is different, as there is no displacement-induced tension. The microcantilever is driven using a piezo actuator and its motion is read out using an optical setup. At high vibration amplitudes, the resonance frequency of one mode depends on the amplitude of the other modes. The torsional modes also show nonlinear behavior as evidenced by a frequency stiffening of the response. The modal interactions in a microcantilever can also be used in a all-mechanical analogue of a cavity-optomechanics, where one mode is used as a cavity mode, which influences the probe mode. In chapter 7, we show that by exciting at the sum and difference frequencies of the two modes, the $Q$ factor of the probe mode could be suppressed over a wide range. In chapter 8, the interaction between a directly- and parameterically-driven resonance mode is studied. Parametric driving means that the spring constant of the beams is modulated at twice the resonance frequency. Clamped-clamped beams with an integrated piezo-actuator on top, designed for applications as gas sensors, are used in the experiments. First, the parametric amplification and oscillation of the beam is studied, then the motion of a parametrically-driven mode is detected by a change in resonance frequency of the directly-driven mode. There is a linear dependence of the oscillation frequency of the parametrically-driven mode and the resonance frequency of the directly-driven mode. A potential application as a linear frequency converter is suggested.

A carbon nanotube (CNT) is a remarkable material and can be thought of as a single-atom thick cylinder of carbon atoms capped of with a semisphere. This is called a single-walled CNT and, depending on how the cylinder is rolled up, CNTs are either semiconducting or metallic. A CNT is made into a mechanical resonator by suspending it between two electrodes. The CNT is driven into motion electrostatically, and the mechanical motion is detected using the current flowing through the CNT. We use the ultraclean fabrication method, which avoids processing on the CNT by first making the electrodes and the trench and only in the final step growing the CNTs. A suspended CNT resonator can be fabricated without defects, thus reducing mechanical damping. In this Thesis, CNTs are studied as electromechanical resonators. An overview is given of the various optical, microscopy, and electrical methods to detect the mechanical motion of CNT resonators, after which the electrical detection methods are compared in detail. Next, it is shown experimentally and theoretically that their mechanical motion couples strongly to single-electron tunneling, as CNTs become quantum dots at cryogenic temperatures. Mechanical modulation of the single-electron average charge leads to spring softening, damping, and a nonlinear restoring force. Because of their high aspect ratio, CNTs can easily be perturbed into the nonlinear regime. To read out their mechanical motion at high frequencies, a novel high-bandwidth readout scheme is developed and discussed.

During the past decades the downscaling of integrated circuits has been governed by Moore's law, which predicts device dimensions on the order of 10 nm in 2020. Fundamental research in molecular electronics explores the possibility of fabricating such nanoscale devices from single molecules, which offer the prospects of chemical tunability and self-assembly. The experiments that are reported in this Thesis are based on lithographically fabricated mechanically controllable break junctions (MCBJs). These devices enable the formation and tuning of two nanometer-spaced gold electrodes for the electrical characterization of a single molecule. The first part of this Thesis addresses the goal of stable anchoring in single-molecule junctions. An experimental protocol for the trapping of single molecules is established and used to study the influence of established chemical anchoring groups on the electronic properties of single-molecule junctions in vacuum. We then present a new fullerene-based end group that allows for the formation of stable junctions with robust electronic coupling. The second part of this Thesis covers the integration of two-terminal MCBJs with a third electrode (a gate), the potential of which can shift the electronic levels on the molecule. Two types of electrically and mechanically tunable devices are presented and characterized in detail. A nanoscale island in the Coulomb blockade regime serves as a first experimental test system, in which the mechanical and electrical tuning of charge transport is demonstrated.

Semiconductor nanocrystals (NCs), which can have a variety of sizes, shapes and chemical compositions, will be a large and important family of future advanced materials.This thesis focuses on colloidal semiconductor NC solids, also called quantum-dot (QD) solids, which are promising materials for many applications, such as photo-detectors, field-effect transistors, solar cells, light-emitting diodes, and lasers. The thesis presents studies on the charge carrier properties of PbSe QD solids, going through the charge carrier photogeneration, thermalization, diffusion and decay, which together are the ``life and fate'' of the charge carriers. Diverse tools have been utilized to reveal the whole picture of the ``life and fate''. The most important ones are: femtosecond transient absorption spectroscopy (TA) (Chapter 2, 3, 4), picosecond Terahertz spectroscopy (THz) (Chapter 2), the nanosecond time-resolved microwave conductivity technique (TRMC) (Chapter 2-5), and Monte Carlo simulations (Chapter 4).

In this dissertation we discuss ab initio studies of quantum transport through single-molecule devices, using a combination of techniques from quantum chemistry and many-body physics. The molecular transport calculations discussed here are based on the "DFT+NEGF" approach to molecular transport. We first outline the density functional theory (DFT) and non-equilibrium Green's functions (NEGF) formalisms. We discuss the assumptions behind their combined use, as well as consequent limitations to the computational results we have obtained. This has been implemented as a custom, scalable extension of the ADF/BAND quantum chemistry package originally developed in the theoretical chemistry group at the VU University Amsterdam, and currently developed and commercialized by Scientific Computing and Modelling N.V. Using this code, we study chains and more complex chemical systems such as multi-ring phenyl junctions and a class of porphyrin-derivative devices recently studied experimentally. To address the polarization effects suspected to be behind the mechanical gating effects observed in the experiments, we extend our transport method with a complementary approach which accounts for image-charge effects at a metal-molecule interface. We close with a further study of the performance of our main method in relation to approximate transport methods based on simplified treatments of the leads in molecular devices.

Electron transport through single molecule connected to the electrodes is an interesting problem from a fundamental point of view, and because of possible applications. From the theoretical point of view, the hope is that understanding the transport phenomena in such systems enables us to explain measurements and develop devices with new functionalities. In this thesis, different theoretical approaches are presented to address the characteristics of the molecular devices with electrical and optical probes. We have combined the non-equilibrium Green's function formalism with density functional theory (DFT) to address molecular junctions in which Coulomb correlations play a major role. An important issue in the field is the determination of the molecular levels, which contribute to transport. We have investigated the opportunities and limitations of Transition Voltage Spectroscopy (TVS) which has been advocated as a method to determine these molecular level positions without applying large voltages. We also studied a series of molecules, used recently in a self-assembled monolayer experiment, to rationalize the effects of the molecular structure on transport. Finally, we have analyzed the Raman response of several molecules in different charge states and suggested experiments in which these states could be identified using the Raman technique.

As a result of progress in nanotechnology, smaller and smaller electronic circuits can be made. The stage of electrically contacting even a single molecule has now been reached. This stimulates both fundamental and applied research alike. Molecular electronics is hence a booming new field that draws a lot of attention. In this research project we have studied fundamental electrical transport properties of single molecules at low temperatures. In collaboration with chemists, a special kind of molecules has been synthesized for this purpose: molecular magnets. These molecules individually behave as tiny magnets. In this thesis, we describe the effect of the magnetic properties on the conductance of the molecule. Quantum mechanical effects play an important role in this respect. Furthermore, we looked at the conductance of a novel material system: graphene an atomic layer of graphite. Graphene is a semi-metal, in which electrons behave as relativistic, massless particles. By coupling graphene to superconducting electrodes, we were able to induce a supercurrent in graphene. The supercurrent in graphene can be tuned by a gate-electrode and hence the device behaves as a superconducting transistor. Our measurements provide new insights in the properties of this exotic material.