Dynamic force microscopy with quartz tuning forks at high oscillation amplitudes

Polythiophene molecules adsorbed on a highly oriented pyrolytic graphite surface were studied by combined dynamic scanning tunneling microscopy (STM) and frequency modulation atomic force microscopy (FM-AFM) with a quartz tuning fork sensor operating in Qplus mode and equipped with a Pt/Ir tip. Upon completing a careful sub-angström oscillation amplitude calibration of the probe, experiments were conducted in an ultra high vacuum at room temperature. By selecting the tip/surface distance regulation parameter, one can select the type of simultaneous information obtained in an area. For distance regulation based on the mean tunneling current, dynamic STM images together with maps of tip/surface force gradient were obtained. FM-AFM images with maps of the tunneling current were also acquired when the distance regulation was based on the frequency shift. Comparison between these images reveals interesting features. For example the tip which operates in STM mode with ultra low current (<10 pA) generates different interaction forces above molecules or graphite. Changes in energy dissipation processes as small as tens of millielectronvolts per cycle were recorded when the tip oscillates above the polymer or on the graphite surface. Hence data demonstrates that a stiff piezoelectric tuning fork of several kilonewtons/meters working as an AFM/STM probe with sub-angström amplitude can characterize weakly adsorbed molecules.

Quartz tuning fork (QTF) sensors offer an attractive alternative to traditional silicon microcantilevers for sensing applications in dynamic atomic force microscopy (DAFM). The QTF sensor consists of two identical, weakly-coupled tines with a sharp tip affixed to the distal end of one tine. The fundamental anti-phase mode of the QTF achieves a stable resonant frequency with a high Quality factor making it ideal for DAFM applications in which a small shift in the resonant frequency is linked to a tip-sample force. The addition of the tip-sample force also breaks the symmetry of the QTF leading to a classic eigenvalue veering scenario. The eigenvalue veering and accompanying mode localization phenomena violate the standard DAFM modeling assumptions which treat the addition of the tip-sample force as a small perturbation to a single-degree-of-freedom oscillator. We find that the eigenvalue veering can contribute a systematic error in force measurements on the order of 20%. Methodology for correcting the systematic error caused by eigenvalue veering is proposed.

The main purpose of this thesis is to explore a new concept of SNOM probes. In order to produce more reliable and reproducible tips, we propose to graft a single gold particle of 60 nm diameter onto the aperture of a SNOM probe. The expected advantage of such a design is a better control of the light distribution at the probe aperture, a higher light transmission by the probe and an increase of the achievable resolution in the near-field. Indeed, the single and spherical metal particle below the tip apex is responsible for a redistribution of the electromagnetic energy below the tip, the particle acting as a nano-antenna that scatters the exciting field. The present work focuses on optimizing the parameters, through numerical simulations and practical realizations. From a theoretical point of view, simulations using Maxwell's formalism have been carried out in the field of localized and unlocalized surface plasmons, suggesting the a nanoparticle grafted at the SNOM tip aperture should lead to a field enhancement. Simple models are exploited to understand the influence of the particle's dielectric profile, size and shape on the scattering properties, with the aim of exploiting resonant plasmon effects to increase the optical performance of near field probes. The results are compared to other simulations based on the Finite Dimension Time Domain method (FDTD). From an experimental point of view, a new SNOM head based on low coherence interferometry using an optical fiber is proposed to measure extremely small SNOM tips oscillation amplitudes, both in air and aqueous environments. It allows characterizing the SNOM-tip oscillation modes and amplitudes on the one hand, and, on the other hand, performing topographical measurements with a high precision both in dry and aqueous environments with typical SNOM tip vibration amplitudes of 50-100 pm. Furthermore, two methods are proposed to graft one single gold particle at the aperture of a SNOM tip. First, a chemical process based on the use of thiosilane molecules to attach one single gold particle on the silica aperture of a tip is presented. Second, the electron beam induced deposition allows depositing gold nanostructures embedded in a carbon matrix at the SNOM tip end. Finally, light scattering by individual nanometer-sized gold particles attached at the apex of fiber-based probes for near field optical microscopy is experimentally investigated. This grafted single nanoparticle at the tip apex produces an enhancement of the light throughput, both in the near and the far field, a homogenization of the diffracted light polarization and a higher accuracy of the optical contrast. The dependence of the light scattering by one single gold nanoparticle on the wavelength, the shape and the surrounding medium dielectric profile is theoretically described and experimentally investigated in the presented work, demonstrating that the plasmon resonances play a crucial role in the light scattering process in the context of scanning near-field optical microscopy.

Propagation of Gaussian X-ray laser beam is presented in collisional quantum plasma and the beam width oscillation is studied along the propagation direction. It is noticed that due to energy absorption in collisional plasma, the laser energy drops to an amount less than the critical value of the self-focusing effect and consequently, the laser beam defocuses. It is found that the oscillation amplitude of the laser spot size enhances while passing through collisional plasma. For the greater values of collision frequency, the beam width oscillates with higher amplitude and defocuses in a shallower plasma depth. Also, it is realized that in a dense plasma environment, the laser self-focusing occurs earlier with the higher oscillation amplitude, smaller laser spot size and more oscillations.

The dissipative processes that occur with immersing a vibrating tuning fork in superfluid helium are investigated. The tuning forks resonance width Δf of frequencies from 32 to 97 kHz was measured in the temperature range from 0.2 to 2.5 K and He II pressure from SVP to 24.9 atm. Some of the tuning forks were in the original can (closed tuning fork), and for some tuning forks the can was either completely or partially removed (opened fork). We found that for the open tuning forks two dissipation mechanisms are clearly revealed in the temperature dependence of Δf, namely, acoustic radiation and scattering of ballistic thermal excitations at low temperatures, and viscous friction at high temperatures. At low temperatures (below ∼ 0.8 K) acoustic dissipation dominates, and the model of quadrupole oscillator for a tuning fork can be applied. We found that acoustic radiation for closed tuning forks is less effective and appears at lower temperatures. The first experimental data on dissipative processes in the quartz tuning fork–He II system at increased liquid pressures are obtained. It is shown that, for high frequency tuning forks the resonance bandwidth decreases with increasing pressure, i.e., with increasing wavelength of sound λ, according to the law λ−5. At low frequencies and low temperatures, with increasing mean free path of thermal excitations the resonance bandwidth is well described by the model of ballistic scattering.

The quartz tuning fork has recently become a popular experimental tool for investigations of both classical and quantum turbulence in cryogenic helium. Its increased use in low-temperature experiments and a number of puzzling results obtained in the past have led to many questions concerning the interaction of multiple tuning forks or the interaction of tuning forks with other oscillators. We report measurements performed in He II at low temperatures around 360 mK, on the mutual interaction of tuning forks placed in the same volume of fluid, and examine the responsible mechanisms in an effort to discriminate between acoustic coupling and interaction via quantized vortices. To this end, the interaction of two tuning forks is investigated by analyzing their recorded resonance curves, looking for any nonelectrical crosstalk. Further, the force-velocity characteristics of a detector tuning fork are measured for different operating velocities of a generator tuning fork. As a complementary measurement, the intensity of sound waves is recorded using a set of miniature receivers. We confirm the current knowledge on acoustic emission by tuning forks in He II and verify properties of their radiation patterns. We conclude that in our experiment the interaction is almost entirely mediated by sound waves.

We present the results of simultaneous scanning-tunneling and frequency-modulated dynamic atomic force microscopy measurements with a qPlus setup. The qPlus sensor is a purely electrical sensor based on a quartz tuning fork. If both the tunneling current and the force signal are to be measured at the tip, a cross-talk of the tunneling current with the force signal can easily occur. The origin and general features of the capacitive cross-talk will be discussed in detail in this contribution. Furthermore, we describe an experimental setup that improves the level of decoupling between the tunneling-current and the deflection signal. The efficiency of this experimental setup is demonstrated through topography and site-specific force/tunneling-spectroscopy measurements on the Si(111) 7×7 surface. The results show an excellent agreement with previously reported data measured by optical interferometric deflection.

Glycerol-extracted fibres from Lethocerus flight muscle were subjected to large-amplitude sinusoidal oscillation in a solution containing Mg-ATP and Ca 2+ at room temperature, under conditions designed to eliminate the effects of diffusion of nucleotides into and out of the fibre. They produced work up to 4 to 8 % peak-to-peak oscillation amplitude at 1.5 to 2.5 Hz and up to lower amplitudes at higher frequencies; freshly extracted fibres produced work at higher amplitudes than aged fibres. The mean tension in the muscle was shown to be critical for work production. Provided this parameter was maintained constant, the mean fibre length, Ca 2+ concentration and ADP concentration could be varied considerably without loss of oscillatory work; these factors are therefore not in themselves critical for oscillation. The tension/length relationship of relaxed fibres is non-linear at high amplitudes of oscillation. Oscillatory tension/length loops are not elliptical at high amplitude and change shape when mean tension and frequency are changed. Linear control theory cannot be used to analyse performance at high amplitudes. At the upper limit of mechanical performance the oscillation amplitude and work-per-cycle performed by the freshly extracted fibres were similar to those of live flight muscle, and the active tension generated was similar to that from other maximally activated striated muscles. Calculation suggests that most or all of the myosin in the muscle was activated in each cycle of oscillation. The limits of performance are therefore probably present in life and are characteristics of the entire contractile material; their possible significance is discussed.

We report a sub-terahertz scattering-type scanning near-field microscope (sub-THz s-SNOM) which uses a 6 mm long metallic tip driven by a quartz tuning fork as the near-field probe. Under continuous-wave illumination by a 94 GHz Gunn diode oscillator, terahertz near-field images are obtained by demodulating the scattered wave at both the fundamental and the second harmonic of the tuning fork oscillation frequency together with the atomic-force-microscope (AFM) image. The terahertz near-field image of a gold grating with a period of 2.3 µm obtained at the fundamental modulation frequency agrees well with the AFM image. The experimental relationship between the signal demodulated at the fundamental frequency and the tip-sample distance is well fitted with the coupled dipole model indicating that the scattered signal from the long probe is mainly contributed by the near-field interaction between the tip and the sample. This near-filed probe scheme using quartz tuning fork can adjust the tip length flexibly to match the wavelength over the entire terahertz frequency range and allows for operation in cryogenic environment.

The performance of a scanning force microscope (SFM) operated in the dynamic mode at high oscillation amplitudes is determined by the response of the system to a given set of interaction forces between the probing tip and the sample surface. To clarify the details of the cantilever/tip dynamics two different aspects were investigated in experiment and computer simulation. First, the interaction forces dominating the oscillatory motion of the probe were varied by applying an additional electrostatic force field. It is shown that such variations in the attractive part of the interaction potential can cause a switching between two different oscillation states and thereby significantly contribute to the contrast obtained from phase imaging. Secondly, the interaction forces were kept constant but the system response itself was varied by modifying the effective quality factor of the oscillating cantilever with an active feedback circuit. This provides a means to influence the transition from the attractive to the partly repulsive interaction regime, i.e. the onset of the intermittent contact or tapping mode. Operating an SFM in the dynamic mode at high amplitudes (> 10 nm) offers the possibility of minimizing the contact time of the probing tip with the sample surface and thereby reduce lateral or friction forces involved in the scanning process. It also allows the collection of additional data related to different sample properties by recording the phase shift between the force driving the cantilever and its oscillation. In the last few years these features of operating the SFM in the dynamic mode [1, 2] were shown to be very useful to characterize several different kinds of sample surfaces, e.g. thin organic films, polymers, biological samples or even liquid droplets [3]. Although this has led to a steady increase in the number of possible applications, there are still several details of the interaction process between the tip and the sample that need further clarification. The overall goal must be to relate the experimentally accessible data, such as the amplitude and ∗ Corresponding author phase signal, more or less directly to specific sample properties, such as topography, elasticity and viscoelasticity. Because highly nonlinear interaction forces are involved when the oscillating tip is in close proximity to a solid surface, the analysis of the dynamic system becomes quite complex. Therefore supplementary computer simulations based on proper mathematical models are useful to investigate the details of the interaction process. Basically, the equation of motion describing the dynamic properties of the probing tip has to be solved in such a way that the influence of different parameters characterizing the probe as well as the sample surface can be examined. There have been several reports recently on different approaches to this problem, providing analytical [4] as well as numerical [5–11] solutions. Most of them are based on the point-mass model, but there are also approaches which describe the complete flexural motion of the cantilever beam supporting the probing tip, as this becomes more relevant when the system is driven well above its resonance frequency [12]. Thus by simulating the dynamic system one can gain useful information on the complex interaction process of the oscillating tip and the sample surface. 1 Experimental and simulation methods The simulation results presented here are all based on the point-mass model with the interaction forces being derived from MYD/BHW calculations [11, 13, 14] and applying the Verlet algorithm [15] to solve the equation of motion numerically. All experiments were performed with a NanoScope III MultiMode stage (Digital Instruments) equipped with an additional lock-in amplifier (EG&G Instruments, Princeton Applied Research, Model 5302) to measure the phase lag between the driving force and the cantilever response quantitatively. Rectangular cantilevers made of doped silicon (Nanosensors) with a nominal length of L = 125 μm were used. By analogy with measurements of quasistatic forcedistance curves in contact mode, the amplitude and phase shift as a function of the z-position were quantitatively investigated in the dynamic mode by means of simulation and

A theoretical-experimental framework for the analysis of the dynamic response of a QEPAS tuning fork device immersed in a fluid medium

We demonstrate a scanning near-field microwave microscope (NSMM) in the liquid environment using a tuning fork shear-force feedback method to control the distance between tip and sample. Only the probe tip for the NSMM is immersed in water. The dry part of the probe is attached to one prong of a quartz tuning fork and directly coupled to a high-quality dielectric resonator at an operating frequency f=4.5–5.5GHz. This distance control method is independent of the local microwave characteristics. The amplitude of the tuning fork was used as a set point of the distance control parameter in the liquid. To demonstrate the distance regulation system, we present the NSMM images of a copper film in air and liquid without and with readjustment of the distance set point, as well as an image of a DNA film in buffer solution. Imaging under buffer environments is of particular interest for future studies of biomolecular association reactions on solid supports.

The force sensor is key to the performance of atomic force microscopy (AFM).\nNowadays, most AFMs use micro-machined force sensors made from silicon, but\npiezoelectric quartz sensors are applied at an increasing rate, mainly in\nvacuum. These self sensing force sensors allow a relatively easy upgrade of a\nscanning tunneling microscope to a combined scanning tunneling/atomic force\nmicroscope. Two fundamentally different types of quartz sensors have achieved\natomic resolution: the 'needle sensor' that is based on a length extensional\nresonator and the 'qPlus sensor' that is based on a tuning fork. Here, we\ncalculate and measure the noise characteristics of these sensors. We find four\nnoise sources: deflection detector noise, thermal noise, oscillator noise and\nthermal drift noise. We calculate the effect of these noise sources as a factor\nof sensor stiffness, bandwidth and oscillation amplitude. We find that for self\nsensing quartz sensors, the deflection detector noise is independent of sensor\nstiffness, while the remaining three noise sources increase strongly with\nsensor stiffness. Deflection detector noise increases with bandwidth to the\npower of 1.5, while thermal noise and oscillator noise are proportional to the\nsquare root of the bandwidth. Thermal drift noise, however, is inversely\nproportional to bandwidth. The first three noise sources are inversely\nproportional to amplitude while thermal drift noise is independent of the\namplitude. Thus, we show that the earlier finding that quoted optimal\nsignal-to-noise ratio for oscillation amplitudes similar to the range of the\nforces is still correct when considering all four frequency noise\ncontributions. Finally, we suggest how the signal-to-noise ratio of the sensors\ncan be further improved and briefly discuss the challenges of mounting tips.\n

We report here a chemical sensor based on detecting the mechanical response of a thin (approximately 10-microm) polymer wire stretched across the two prongs of a wristwatch quartz tuning fork (QTF). When the fork is set to oscillate, the wire is stretched and compressed by the two prongs. The stretching/compression force changes upon adsorption of analyte molecules onto/into the polymer wire, which is detected by the QTF with pico-Newton force sensitivity. An array of such sensors with different polymer wires is used for simultaneous detection of several analytes and for improvement of pattern recognition. The low cost (approximately 10 cent) of the QTF, together with that an array of QTFs can be driven to oscillate simultaneously and their resonance frequencies detected with the same circuit, promises a high performance, low cost, and portable sensor for detecting various chemical vapors. We demonstrate here detection of parts-per-billion-level water, ethylnitrobenzene, and ethanol vapors using the QTF arrays.

A theoretical model describing the acoustic coupling between two resonator tubes in spectrophones exploiting custom-made quartz tuning forks (QTFs) is proposed. The model is based on an open-end correction to predict the optimal tube length. A calculation of the sound field distribution from one tube exit allowed for the estimation of the optimal radius as a function of the QTF prong spacing and the sound wavelength. The theoretical predictions have been confirmed using experimental studies employing a custom QTF with a fundamental flexural mode resonance frequency of 15.8 kHz and a quality factor of 15,000 at atmospheric pressure. The spacing between the two prongs was 1.5 mm. Spectrophones mounting this QTF were implemented for the quartz-enhanced photoacoustic detection of water vapor in air in the mid-infrared spectral range.