arXiv subjects

David B. Haviland

Publications and source records attributed to David B. Haviland.

At least 37 records · Page 2Linked to original sources

arXiv2018

Intermodulation spectroscopy as an alternative to pump-probe for the measurement of fast dynamics at the nanometer scale

We present an alternative approach to pump-probe spectroscopy for measuring fast charge dynamics with an atomic force microscope (AFM). Our approach is based on coherent multifrequency lock-in measurement of the intermodulation between a mechanical drive and an optical or electrical excitation. In response to the excitation, the charge dynamics of the sample is reconstructed by fitting a theoretical model to the measured frequency spectrum of the electrostatic force near resonance of the AFM cantilever. We discuss the time resolution, which in theory is limited only by the measurement time, but in practice is of order one nanosecond for standard cantilevers and imaging speeds. We verify the method with simulations and demonstrate it with a control experiment, achieving a time resolution of $20~\mathrm{ns}$ in ambient conditions, limited by thermal noise.

cond-mat.mes-hall↗

arXiv2018

Calibrating torsional eigenmodes of micro cantilevers for dynamic measurement of frictional forces

Non-invasive thermal noise calibration of both torsional and flexural eigenmodes is performed on numerous cantilevers of 10 different types. We show that for all tipless and short-tipped cantilevers, the ratio of torsional to flexural mode stiffness is given by a constant, times the ratio of their resonant frequencies. By determining this constant we enable a calibration of the torsional eigenmode, starting from a calibration of the flexural eigenmode. Our results are well motivated from beam theory and we verify them with finite element simulation.

cond-mat.mtrl-sci↗

arXiv2018

On modeling and measuring viscoelasticity with dynamic Atomic Force Microscopy

The interaction between a rapidly oscillating atomic force microscope tip and a soft material surface is described using both elastic and viscous forces with a moving surface model. We derive the simplest form of this model, motivating it as a way to capture the impact dynamics of the tip and sample with an interaction consisting of two components: interfacial or surface force, and bulk or volumetric force. Analytic solutions to the piece-wise linear model identify characteristic time constants, providing a physical explanation of the hysteresis observed in the measured dynamic force quadrature curves. Numerical simulation is used to fit the model to experimental data and excellent agreement is found with a variety of different samples. The model parameters form a dimensionless impact-rheology factor, giving a quantitative physical number to characterize a viscoelastic surface that does not depend on the tip shape or cantilever frequency.

physics.app-ph↗

arXiv2017

Background force compensation in dynamic atomic force microscopy

Background forces are linear long-range interactions of the cantilever body with its surroundings that must be compensated for in order to reveal tip-surface force, the quantity of interest for determining material properties in atomic force microscopy. We provide a mathematical derivation of a method to compensate for background forces, apply it to experimental data, and discuss how to include background forces in simulation. Our method, based on linear-response theory in the frequency domain, provides a general way of measuring and compensating for any background force and it can be readily applied to different force reconstruction methods in dynamic AFM.

cond-mat.mes-hall↗

arXiv2016

Imaging high-speed friction at the nanometer scale

Friction is a complicated phenomenon involving nonlinear dynamics at different length and time scales[1, 2]. The microscopic origin of friction is poorly understood, due in part to a lack of methods for measuring the force on a nanometer-scale asperity sliding at velocity of the order of cm/s.[3, 4] Despite enormous advance in experimental techniques[5], this combination of small length scale and high velocity remained illusive. Here we present a technique for rapidly measuring the frictional forces on a single asperity (an AFM tip) over a velocity range from zero to several cm/s. At each image pixel we obtain the velocity dependence of both conservative and dissipative forces, revealing the transition from stick-slip to a smooth sliding friction[1, 6]. We explain measurements on graphite using a modified Prandtl-Tomlinson model that takes into account the damped elastic deformation of the asperity. With its greatly improved force sensitivity and very small sliding amplitude, our method enables rapid and detailed surface mapping of the full velocity-dependence of frictional forces with less than 10~nm spatial resolution.

cond-mat.mes-hall↗

arXiv2016

A virtual instrument to standardise the calibration of atomic force microscope cantilevers

Atomic force microscope (AFM) users often calibrate the spring constants of cantilevers using functionality built into individual instruments. This is performed without reference to a global standard, which hinders robust comparison of force measurements reported by different laboratories. In this article, we describe a virtual instrument (an internet-based initiative) whereby users from all laboratories can instantly and quantitatively compare their calibration measurements to those of others - standardising AFM force measurements - and simultaneously enabling non-invasive calibration of AFM cantilevers of any geometry. This global calibration initiative requires no additional instrumentation or data processing on the part of the user. It utilises a single website where users upload currently available data. A proof-of-principle demonstration of this initiative is presented using measured data from five independent laboratories across three countries, which also allows for an assessment of current calibration.

physics.ins-det↗

arXiv2014

Determining surface properties with bimodal and multimodal AFM

Conventional dynamic atomic force microscopy (AFM) can be extended to bimodal and multimodal AFM in which the cantilever is simultaneously excited at two ore more resonance frequencies. Such excitation schemes result in one additional amplitude and phase images for each driven resonance, and potentially convey more information about the surface under investigation. Here we present a theoretical basis for using this information to approximate the parameters of a tip-surface interaction model. The theory is verified by simulations with added noise corresponding to room-temperature measurements.

cond-mat.mes-hall↗

arXiv2014

Intermodulation electrostatic force microscopy for imaging surface photo-voltage

We demonstrate an alternative to Kelvin Probe Force Microscopy for imaging surface potential. The open-loop, single-pass technique applies a low-frequency AC voltage to the atomic force microscopy tip while driving the cantilever near its resonance frequency. Frequency mixing due to the nonlinear capacitance gives intermodulation products of the two drive frequencies near the cantilever resonance, where they are measured with high signal to noise ratio. Analysis of this intermodulation response allows for quantitative reconstruction of the contact potential difference. We derive the theory of the method, validate it with numerical simulation and a control experiment, and we demonstrate its utility for fast imaging of the surface photo-voltage on an organic photo-voltaic material.

cond-mat.mes-hall↗

arXiv2014

Dynamic Calibration of Higher Eigenmode Parameters of a Cantilever in Atomic Force Microscopy Using Tip-Surface Interactions

We present a theoretical framework for the dynamic calibration of the higher eigenmode parameters (stiffness and optical lever responsivity) of a cantilever. The method is based on the tip-surface force reconstruction technique and does not require any prior knowledge of the eigenmode shape or the particular form of the tip-surface interaction. The calibration method proposed requires a single-point force measurement using a multimodal drive and its accuracy is independent of the unknown physical amplitude of a higher eigenmode.

physics.ins-det↗

arXiv2013

Quantum Phase Slips in one-dimensional Josephson Junction Chains

We have studied quantum phase-slip (QPS) phenomena in long one-dimensional Josephson junction series arrays with tunable Josephson coupling. These chains were fabricated with as many as 2888 junctions, where one sample had a tunable weak link in the middle. Measurements were made of the zero-bias resistance, $R_0$, as well as current-voltage characteristics (IVC). The finite $R_0$ is explained by QPS and shows an exponential dependence on $\sqrt{E_J/E_C}$ with a distinct change in the exponent at $R_0=R_Q=h/4e^2$. When $R_0 > R_Q$ the IVC clearly shows a remnant of the Coulomb blockade, which evolves to a zero-current state with a sharp critical voltage as $E_J$ is tuned to a smaller value. The zero-current state below the critical voltage is due to coherent QPS and we show that these are enhanced at the central weak link. Above the critical voltage a negative differential resistance is observed which nearly restores the zero-current state.

cond-mat.mes-hall↗

arXiv2013

Reconstruction of Tip-Surface Interactions with Multimodal Intermodulation Atomic Force Microscopy

We propose a theoretical framework for reconstructing tip-surface interactions using the intermodulation technique when more than one eigenmode is required to describe the cantilever motion. Two particular cases of bimodal motion are studied numerically: one bending and one torsional mode, and two bending modes. We demonstrate the possibility of accurate reconstruction of a two-dimensional conservative force field for the former case, while dissipative forces are studied for the latter.

cond-mat.mes-hall↗

arXiv2013

Phase-sticking in one-dimensional Josephson Junction Chains

We studied current-voltage characteristics of long one dimensional Josephson junction chains with Josephson energy much larger than charging energy, $E_J \gg E_C$. In this regime, typical IV curves of the samples consist of a supercurrent branch at low bias voltages followed by a voltage-independent chain current branch, $I_{Chain}$ at high bias. Our experiments showed that $I_{Chain}$ is not only voltage-independent but it is also practically temperature-independent up to $T_C$. We have successfully model the transport properties in these chains using a capacitively shunted junction model with nonlinear damping.

cond-mat.mes-hall↗

arXiv2013

Simultaneous quantitative imaging of surface and magnetic forces

We demonstrate quantitative force imaging of long-range magnetic forces simultaneously with near-surface van-der-Waals and contact-mechanics forces using intermodulation atomic force microscopy. Magnetic forces at the 200 pN level are separated from near-surface forces at the 30 nN level. Imaging of these forces is performed in both the contact and non-contact regimes of near-surface interactions.

cond-mat.mes-hall↗

arXiv2013

Effect of material stiffness on intermodulation response in dynamic atomic force microscopy

We perform simulations and experiments on an oscillating atomic force microscope cantilever approaching a surface, where the intermodulation response of the cantilever driven with two pure harmonic tones is investigated. In the simulations, the tip and surface interact with a conservative nonlinear force, and the parameter space of approach distance and surface stiffness is explored. Approach experiments are carried out on three surfaces with widely varying stiffness. Qualitative similarities between simulations and experiment can be seen, but quantitative comparison is difficult due to the overly idealized tip-surface force model used in the simulation.

cond-mat.mes-hall↗

arXiv2013

Polynomial force approximations and multifrequency atomic force microscopy

We present polynomial force reconstruction from experimental intermodulation atomic force microscopy (ImAFM) data. We study the tip-surface force during a slow surface approach and compare the results with amplitude-dependence force spectroscopy. Based on polynomial force reconstruction we generate high-resolution surface property maps of polymer blend samples. The polynomial method is described as a special example of a more general approximataive force reconstruction, where the aim is to determine model parameters which best approximate the measured force spectrum. This approximative approach is not limited to spectral data and we demonstrate how is can adapted to a force quadrature picture.

cond-mat.mes-hall↗

arXiv2013

Interaction imaging with amplitude-dependence force spectroscopy

Knowledge of surface forces is the key to understanding a large number of processes in fields ranging from physics to material science and biology. The most common method to study surfaces is dynamic atomic force microscopy (AFM). Dynamic AFM has been enormously successful in imaging surface topography, even to atomic resolution, but the force between the AFM tip and the surface remains unknown during imaging. Here, we present a new approach that combines high accuracy force measurements and high resolution scanning. The method, called amplitude-dependence force spectroscopy (ADFS) is based on the amplitude-dependence of the cantilever's response near resonance and allows for separate determination of both conservative and dissipative tip-surface interactions. We use ADFS to quantitatively study and map the nano-mechanical interaction between the AFM tip and heterogeneous polymer surfaces. ADFS is compatible with commercial atomic force microscopes and we anticipate its wide-spread use in taking AFM toward quantitative microscopy.

cond-mat.mes-hall↗

arXiv2013

Interpreting motion and force for narrow-band intermodulation atomic force microscopy

Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic force microscopy that probes the nonlinear tip-surface force by measurement of the mixing of multiple tones in a frequency comb. A high $Q$ cantilever resonance and a suitable drive comb will result in tip motion described by a narrow-band frequency comb. We show by a separation of time scales, that such motion is equivalent to rapid oscillations at the cantilever resonance with a slow amplitude and phase or frequency modulation. With this time domain perspective we analyze single oscillation cycles in ImAFM to extract the Fourier components of the tip-surface force that are in-phase with tip motion ($F_I$) and quadrature to the motion ($F_Q$). Traditionally, these force components have been considered as a function of the static probe height only. Here we show that $F_I$ and $F_Q$ actually depend on both static probe height and oscillation amplitude. We demonstrate on simulated data how to reconstruct the amplitude dependence of $F_I$ and $F_Q$ from a single ImAFM measurement. Furthermore, we introduce ImAFM approach measurements with which we reconstruct the full amplitude and probe height dependence of the force components $F_I$ and $F_Q$, providing deeper insight into the tip-surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface.

cond-mat.mes-hall↗

arXiv2013

Tip-surface interactions in dynamic atomic force microscopy

In atomic force microscopy (AFM) tip-surface interactions are usually considered as functions of the tip position only, so-called force curves. However, tip-surface interactions often depend on the tip velocity and the past tip trajectory. Here, we introduce a compact and general description of these interactions appropriate to dynamic AFM where the measurement of force is restricted to a narrow frequency band. We represent the tip-surface interaction in terms of a force disk in the phase space of position and velocity. Determination of the amplitude dependence of tip-surface forces at a fixed static probe height allows for a comprehensive treatment of conservative and dissipative interactions. We illuminate the fundamental limitations of force reconstruction with narrow band dynamic AFM and we show how the amplitude dependence of the Fourier component of the force at the tip oscillation frequency, gives qualitative insight into the detailed nature of the tip-surface interaction. With minimal assumptions this amplitude dependence force spectroscopy allows for a quantitative reconstruction of the effective conservative tip-surface force as well as a position-dependent damping factor. We demonstrate this reconstruction on simulated intermodulation AFM data.

cond-mat.mes-hall↗