Contrast inversion in electrostatic force microscopy imaging of trapped charges: tip-sample distance and dielectric constant dependence

We present a numerical and analytical study of the behavior of both electrostatic force and force gradient created by a charge trapped below the surface of a dielectric on an atomic force microscope tip as a function of the dielectric constant and tip-sample distance. As expected, the force decreases monotonously when the dielectric constant increases. However, a maximum in the dielectric constant dependence of the force gradient is found. This maximum occurs in the typical experimental parameters' range and depends on the tip-sample distance and the sample thickness. The analytical study permits us to understand the physical origin of this phenomenon and is in good agreement with the numerical simulation for small tip-sample distances. We also report a study exemplifying a possible contrast inversion in electrostatic force microscopy (EFM) signals while scanning, at different heights, two charges trapped in a sample having heterogeneous dielectric domains. In addition to this particular contrast inversion effect, this study can be considered as a way to gain insight into the mechanisms of EFM image formation as a function of the dielectric constant and tip-sample.     

Tapping-mode scanning force microscopy: Metallic tips and samples

The operation of a tapping-mode scanning force microscope using a metallic tip and metallic sample, with a bias voltage applied between the two, is modelled as a driven nonlinear oscillator, where metal-metal adhesion and electric forces are taken into account. The model, which applies to the case where the sample indentation by the tip is minimal, shows that one can obtain a good estimate of the tip-sample contact time from the tip-sample current.     

Effects of nonlinear forces on dynamic mode atomic force microscopy and spectroscopy

In this paper, we describe the effects of nonlinear tip-sample forces on dynamic mode atomic force microscopy and spectroscopy. The jumps and hysteresis observed in the vibration amplitude (A) versus tip-sample distance (h) curves have been traced to bistability in the resonance curve. A numerical analysis of the basic dynamic equation was used to explain the hysteresis in the experimental curve. It has been found that the location of the hysteresis in the A-h curve depends on the frequency of the forced oscillation relative to the natural frequency of the cantilever.     

Buckling dynamics of imperfect Elastica subject to various loading conditions

Buckling dynamics of a pinned-pinned flexible imperfect beam attached to a sliding mass is investigated using nonlinear Elastica theory. Initially straight flexible buckling beam having pinned end boundary conditions loaded at one of its end with curved imperfection is considered. Large deflection analysis of flexible beam is studied using nonlinear Elastica theory. Imperfection analysis of the flexible beam is investigated considering the imperfection as an initial curvature. The governing differential equations are expressed in terms of nonlinear functions that are typical of flexible beams, generally leading to highly implicit relationships involving elliptic integrals and functions. Dynamic simulation of the flexible beam is studied using numerical simulation procedures with various types of loading (step, ramp, and sinusoidal) assuming this member buckles in its first mode. Dynamic response of the imperfect buckling Elastica has been obtained by using numerical Runge-Kutta methods. Load deflection characteristics of flexible beams are presented in polynomial curve fits. The polynomial curve fits obtained from nonlinear inextensible exact beam theory may then be used as the nonlinear lumped system stiffness. The buckling Elastica may find applications in compliant mechanism design. The motivation behind this research is not only to present the dynamic behavior of the buckling beam considering the magnitude of the imperfection but also to provide a tool to design new types of compliant mechanisms. Original compliant mechanism designs are presented demonstrating where the buckling dynamics of imperfect Elastica or flexible curved beams might be needed in mechanism design and synthesis.     

Nonlinear effects in varactor-tuned resonators

This paper describes the effects of RF power level on the performance of varactor-tuned resonator circuits. A variety of topologies are considered, including series and parallel resonators operating in both unbalanced and balanced modes. As these resonators were designed to produce oscillators with minimum phase noise, the initial small signal insertion loss was set to 6 dB and, hence, QL/Q0 = 1/2. To enable accurate analysis and simulation, S parameter and PSPICE models for the varactors were optimized and developed. It is shown that these resonators start to demonstrate nonlinear operation at very low power levels demonstrating saturation and lowering of the resonant frequency. On occasion squegging is observed for modified bias conditions. The nonlinear effects are dependent on the unloaded Q (Q0), the ratio of loaded to unloaded Q (QL/Q0), the bias voltage, and circuit configurations with typical nonlinear effects occurring at -8 dBm in a circuit with a loaded Q of 63 and a varactor bias voltage of 3 V. Analysis, simulation, and measurements that show close correlation are presented.     

STM Observations of 2D Kr and Xe Adsorbed on Graphite

Crystalline structures of two dimensional rare-gas solids physisorbed on a graphite surface are studied with a low-temperature scanning tunneling microscope (STM) at T=4 K. We have obtained atomically resolved STM images of monolayer krypton (Kr) for the first time as well as those of xenon (Xe). It was observed that the 2D structure of Xe is destroyed with small tip-sample separation. Distinct changes in the local density of states were observed in tunneling spectra after the adsorption. For a multi-layer Xe film, a characteristic telegraph pattern of the tunneling current was also observed, which probably indicates single atom dynamics.     

Nonlinear Dynamic Analysis of Electrostatically Actuated Resonant MEMS Sensors Under Parametric Excitation

Electrostatically actuated resonant microelectromechanical systems (MEMS) sensors have gotten significant attention due to their geometric simplicity and broad applicability. In this paper, nonlinear responses and dynamics of the electrostatically actuated MEMS resonant sensors under two-frequency parametric and external excitations are presented. The presented model and methodology enable simulation of the steady-state dynamics of electrostatic MEMS undergoing small motions. Response and dynamics of the MEMS resonator to a combination resonance are studied. The responses of the system at steady-state conditions and their stability are investigated using the method of multiple scales. The results showing the effect of varying the dc bias, the squeeze film damping, cubic stiffness, and ac excitation amplitude on the frequency response curves, resonant frequencies and nonlinear dynamic characteristics are given in detail. Frequency response, resonant frequency and peak amplitude are examined for variation of the dynamic parameters involved. This investigation provides an understanding of the nonlinear dynamic characteristics of microbeam-based resonant sensors in MEMS     

Characterization of surface stiffness and probe-sample dissipation using the band excitation method of atomic force microscopy: a numerical analysis

Recently Jesse and co-workers introduced the band excitation atomic force microscopy (BE-AFM) method (Jesse et al 2007 Nanotechnology 18 435503), in which the cantilever probe is excited in a continuum frequency band in order to measure its response at all frequencies in the band. Analysis of the cantilever response using the damped harmonic oscillator model provides information on the stiffness and level of dissipation at the tip-sample junction as the sample is scanned. Since its introduction, this method has been used in magnetic, electromechanical, thermal and molecular unfolding applications, among others, and has given rise to a new family of scanning probe microscopy techniques. Additionally, the concept is applicable to any field in which measurement of the frequency response of harmonic oscillators is relevant. In this paper we present an analytical and numerical analysis of the excitation signals used in BE-AFM, as well as of the cantilever response under different conditions. Our analysis is performed within the context of viscoelastic characterization. We discuss subtleties in the cantilever dynamics, provide guidelines for implementing the method effectively and illustrate the use of simulation in interpreting the results.     

A History of the Photographic Lens

Abstract

We investigate the transient and the steady-state behaviour of the photon statistics of a single-atom laser, consisting of a three-level Λ system, driven by an incoherent external pump field and strongly coupled to a single mode of an optical cavity. For several limiting cases we are able to obtain analytical results. A comparison with standard multi-atom laser theory reveals a surprisingly good agreement down to very small intracavity photon numbers. Under appropriate operating conditions a calculation of the second-order intensity correlation function yields sub-Poissonian statistics as well as strong antibunching induced by the nonlinear dynamics of the atom.     

Electrical scanning probe microscopy of an integrated blocking layer

Scanning probe microscopy was performed on an integrated blocking layer system developed for hybrid organic solar cells. A nanocomposite consisting of titania and an amphiphilic triblock copolymer ((PEO)MA-PDMS-MA(PEO)) was prepared by sol-gel chemistry. After plasma treatment and annealing of a spin casted film of 30-100 nm thickness a granular structure with a typical titania grain diameter of 20 nm was found. Conductive scanning force microscopy revealed that on top of almost every grain on the surface there is an increased conductivity compared to the average value. The correlation of grains and conductivity indicated that titania particles formed interconnecting paths through the film. For the resistivity of these pathways we found that effects of tip-sample and sample-electrode resistivity dominate. Additionally, conductive scanning force microscopy revealed non-conducting structures attributed to the thermal treatment. Kelvin probe microscopy of pristine samples on one side and plasma treated plus annealed samples on the other side showed that there is a shift in work function (0.8 +/- 0.2 eV) as expected for the transition of amorphous to anatase titania.     

Investigation of the different stable states of the cantilever oscillation in an atomic force microscope

We present an algorithm which allows us to identify all possible stable states of the cantilever oscillation of an AFM operated in the intermittent contact mode within the harmonic approximation. The oscillatory states are qualified as quasi-free, net-attractive and net-repulsive solutions. Using a generic model for the tip-sample interaction the influence of a number of important experimental parameters on the state of oscillation is systematically studied. The analysis gives conditions under which an AFM can be operated in a chosen state. As an exemplary experimental application we compare selected measurements on a semicrystalline polymer acquired in the net-repulsive and the net-attractive mode with simulations based on the approach introduced here. The experiments indicate that a small indentation below one nanometer in the net-attractive mode is enough to produce phase contrast.     

小波能量平均线性化法

为解非线性多自由度系统窄随机响应问题，本文提出小波能量平均线性化法，典型算例证明其简单有效，误差较小。     

Atomic-resolution imaging in liquid by frequency modulation atomic force microscopy using small cantilevers with megahertz-order resonance frequencies

In this study, we have investigated the performance of liquid-environment FM-AFM with various cantilevers having different dimensions from theoretical and experimental aspects. The results show that reduction of the cantilever dimensions provides improvement in the minimum detectable force as long as the tip height is sufficiently long compared with the width of the cantilever. However, we also found two important issues to be overcome to achieve this theoretically expected performance. The stable photothermal excitation of a small cantilever requires much higher pointing stability of the exciting laser beam than that for a long cantilever. We present a way to satisfy this stringent requirement using a temperature controlled laser diode module and a polarization-maintaining optical fiber. Another issue is associated with the tip. While a small carbon tip formed by electron beam deposition (EBD) is desirable for small cantilevers, we found that an EBD tip is not suitable for atomic-scale applications due to the weak tip-sample interaction. Here we show that the tip-sample interaction can be greatly enhanced by coating the tip with Si. With these improvements, we demonstrate atomic-resolution imaging of mica in liquid using a small cantilever with a megahertz-order resonance frequency. In addition, we experimentally demonstrate the improvement in the minimum detectable force obtained by the small cantilever in measurements of oscillatory hydration forces.     

Dynamics of an elastic multibody chain: part a—body motion equations

In this paper—the first of a series describing the dynamics of an arbitrary multibody system—motion equations governing a set of individual bodies in a chain configuration are discussed. A chain consisting entirely of rigid bodies is considered first. Motion equations for a typical body of arbitrary shape and arbitrary mass distribution are then briefly summarized. Finally, the geometrical constraints necessary to connect the individual bodies into a chain are derived.

Large translational and rotational motions are permitted at the joints connecting contiguous bodies. In other words, both prismatic and revolute joints are included, alone and in combination. As well, the interbody force constraints required to ensure that equal but opposite forces and torques exist at each joint are developed. The resulting expressions are amenable to the introduction of constraint and control forces at the chain joints. This permits the number of actively controlled degrees of freedom at any specific joint to be arbitrarily specified. The equations are fully nonlinear in the 'rigid' velocities for all individual chain bodies.

The analysis is then extended to the case of a chain consisting of an arbitrary number of elastic bodies. Each elastic body is assumed to possess an arbitrary stiffness distribution, although structural deformations are assumed to be small.     

Mechanical manifestations of rare atomic jumps in dynamic force microscopy

The resonance frequency and the excitation amplitude of a silicon cantilever have been measured as a function of distance to a cleaved KBr(001) surface with a low-temperature scanning force microscope (SFM) in ultrahigh vacuum. We identify two regimes of tip-sample distances. Above a site-dependent critical tip-sample distance reproducible data with low noise and no interaction-induced energy dissipation are measured. In this regime reproducible SFM images can be recorded. At closer tip-sample distances, above two distinct atomic sites, the frequency values jump between two limiting curves on a timescale of tens of milliseconds. Furthermore, additional energy dissipation occurs wherever jumps are observed. We attribute both phenomena to rarely occurring changes in the tip apex configuration which are affected by short-range interactions with the sample. Their respective magnitudes are related to each other. A specific candidate two-level system is also proposed.     

Methods derived from nonlinear dynamics for analysing heart rate variability

Methods from nonlinear dynamics (NLD) have shown new insights into heart rate (HR) variability changes under various physiological and pathological conditions, providing additional prognostic information and complementing traditional time- and frequency-domain analyses. In this review, some of the most prominent indices of nonlinear and fractal dynamics are summarized and their algorithmic implementations and applications in clinical trials are discussed. Several of those indices have been proven to be of diagnostic relevance or have contributed to risk stratification. In particular, techniques based on mono- and multifractal analyses and symbolic dynamics have been successfully applied to clinical studies. Further advances in HR variability analysis are expected through multidimensional and multivariate assessments. Today, the question is no longer about whether or not methods from NLD should be applied; however, it is relevant to ask which of the methods should be selected and under which basic and standardized conditions should they be applied.     

Effective Hamiltonians in quantum optics: a systematic approach

A general and systematic method for obtaining eiective Hamiltonians that describe diierent nonlinear optical processes is discussed. The method exploits the existence of a nonlinear deformation of the usual su(2) algebra that arises as the dynamical symmetry of the original model. When some physical parameter, dictated by the process under consideration, becomes small, a diagonal eiective Hamiltonian is obtained immediately, that correctly represents the dynamics for arbitrary states and long times. The technique is extended to su(3) and su(N), finding the corresponding eiective Hamiltonians when some resonance conditions are fulfilled.     

Floating tip nanolithography

We demonstrate noncontact, high quality surface modification of soft and hard materials with spatial resolution of approximately 20 nm. The nanowriting is based on the interaction between the surface and the tip of a standard atomic force microscope illuminated by a focused femtosecond laser beam and hovering (at ambient conditions) 1-4 nanometers above the surface without touching it. Field enhancement at the tip-sample gap or high tip temperature are identified as the causes of material ablation.     

Analytical formulation of small signal stability analysis of power systems with nonlinear load models

It is now recognized that both load dynamics and generating unit dynamics contribute significantly to the limitation of loadability of power systems. In this paper, we take a static nonlinear load representation and different combinations of machine and exciter dynamic models to develop a comprehensive linearized model to study small signal stability. In particular we monitor the Hopf bifurcation instability and through participation factor analysis we identify the relevant state variables.     

Cantilever arrays with self-aligned nanotips of uniform height

Cantilever arrays are employed to increase the throughput of imaging and manipulation at the nanoscale. We present a fabrication process to construct cantilever arrays with nanotips that show a uniform tip-sample distance. Such uniformity is crucial, because in many applications the cantilevers do not feature individual tip-sample spacing control. Uniform cantilever arrays lead to very similar tip-sample interaction within an array, enable non-contact modes for arrays and give better control over the load force in contact modes. The developed process flow uses a single mask to define both tips and cantilevers. An additional mask is required for the back side etch. The tips are self-aligned in the convex corner at the free end of each cantilever. Although we use standard optical contact lithography, we show that the convex corner can be sharpened to a nanometre scale radius by an isotropic underetch step. The process is robust and wafer-scale. The resonance frequencies of the cantilevers within an array are shown to be highly uniform with a relative standard error of 0.26% or lower. The tip-sample distance within an array of up to ten cantilevers is measured to have a standard error around 10 nm. An imaging demonstration using the AFM shows that all cantilevers in the array have a sharp tip with a radius below 10 nm. The process flow for the cantilever arrays finds application in probe-based nanolithography, probe-based data storage, nanomanufacturing and parallel scanning probe microscopy.