Frequency Of Cantilever Research Articles

Study of the sensitivity of the first four flexural modes of an AFM cantilever with a sidewall probe

The resonant frequency and sensitivity of flexural vibration for an atomic force microscope (AFM) cantilever with a sidewall probe have been analyzed. A closed-form expression for the sensitivity of vibration modes has been obtained using the relationship between the resonant frequency and contact stiffness of cantilever and sample. The results show that a sidewall scanning AFM is more sensitive when the contact stiffness is lower and that the first mode is the most sensitive. However, the high-order modes become more sensitive than the low-order modes as the contact stiffness increases. The resonance frequency of an AFM cantilever is low when contact stiffness is small. However, the frequency rapidly increases as contact stiffness increases. In addition, it can be found that the effects of the vertical extension on the sensitivity and the resonant frequency of an AFM cantilever are significant. Decreasing the length of vertical extension can increase the resonance frequency and sensitivity of mode 1 when the contact stiffness is small. However, the situation is reverse when the contact stiffness becomes large.

Microelectromechanical Resonator Characterization Using Noncontact Parametric Electrostatic Excitation and Probing

A noncontact electrostatic probing technique using a scanning probe microscopy cantilever is shown to actuate and detect the resonant behavior of a micromachined resonator. The method is capable of characterizing a resonator with resonant frequency much greater than that of the cantilever. The coupled oscillator model developed for this system describes the resonant response of the test resonator as detected through the probe, including the fourth-power dependence on the probe drive voltage. The veracity of this model is demonstrated through comparison with experimental data obtained from a test resonator with a resonant frequency ten times greater than the resonant frequency of the probe cantilever. This technique yields a straightforward determination of the resonant frequency and quality factor of a micromachined resonator, avoiding limitations due to optical interference and any reliance on a supporting circuitry.

Adaptive control of force microscope cantilever dynamics

Magnetic resonance force microscopy (MRFM) and other emerging scanning probe microscopies entail the detection of attonewton-scale forces. Requisite force sensitivities are achieved through the use of soft force microscope cantilevers as high resonant-Q micromechanical oscillators. In practice, the dynamics of these oscillators are greatly improved by the application of force feedback control computed in real time by a digital signal processor (DSP). Improvements include increased sensitive bandwidth, reduced oscillator ring up/down time, and reduced cantilever thermal vibration amplitude. However, when the cantilever tip and the sample are in close proximity, electrostatic and Casimir tip-sample force gradients can significantly alter the cantilever resonance frequency, foiling fixed-gain narrow-band control schemes. We report an improved, adaptive control algorithm that uses a Hilbert transform technique to continuously measure the vibration frequency of the thermally-excited cantilever and seamlessly adjust the DSP program coefficients. The closed-loop vibration amplitude is typically 0.05 nm. This adaptive algorithm enables narrow-band formally-optimal control over a wide range of resonance frequencies, and preserves the thermally-limited signal to noise ratio (SNR).

Tip-sample distance control using photothermal actuation of a small cantilever for high-speed atomic force microscopy

We have applied photothermal bending of a cantilever induced by an intensity-modulated infrared laser to control the tip-surface distance in atomic force microscopy. The slow response of the photothermal expansion effect is eliminated by inverse transfer function compensation. By regulating the laser power and regulating the cantilever deflection, the tip-sample distance is controlled; this enables much faster imaging than that in the conventional piezoactuator-based z scanners because of the considerably higher resonant frequency of small cantilevers. Using this control together with other devices optimized for high-speed scanning, video-rate imaging of protein molecules in liquids is achieved.

Flexural vibration frequency of atomic force microscope cantilevers using the Timoshenkobeam model

The modal frequencies of flexural vibration for an atomic force microscope (AFM)cantilever have been evaluated using the Timoshenko beam theory, and a closed-formexpression for the frequencies of vibration modes has been obtained. In the analysis, theeffect of the ratios of different cantilever dimensions on frequency for the cantilever werestudied. The results show that increasing the ratio of cantilever thickness andlength decreases the vibration frequency. Increasing the ratio of the tip lengthand cantilever length also increases the frequency. In addition, results using theBernoulli–Euler beam theory and the Timoshenko beam theory are compared. It can befound that the Timoshenko beam theory is able to predict the frequencies offlexural vibration of the higher modes with higher contact stiffness for the AFMcantilever.

Atomic resolution in noncontact AFM by probing cantilever frequency shifts

Rutile TiO 2 (0 0 1) quantum dots (or nano-marks) in different shapes were used to imitate uncleaved material surfaces or materials with rough surfaces. By numerical integration of the equation of motion of cantilever for silicon tip scanning along the [1 1 0] direction over the rutile TiO 2 (0 0 1) quantum dots in ultra high vacuum (UHV), scanning routes were explored to achieve atomic resolution from frequency shift image. The tip–surface interaction forces were calculated from Lennard–Jones (12-6) potential by the Hamaker summation method. The calculated results showed that atomic resolution could be achieved by frequency shift image for TiO 2 (0 0 1) surfaces of rhombohedral quantum dot scanning in a vertical route, and spherical cap quantum dot scanning in a superposition route.

On the Fundamental Transverse Vibration Frequency of a Free-Free Thin Beam With Identical End Masses

Current research in vibration-based energy harvesting and in microelectromechanical system technology has focused renewed attention on the vibration of beams with end masses. This paper shows that the commonly accepted and frequently quoted fundamental natural frequency formula for a beam with identical end masses is incorrect. It is also shown that the higher mode frequency expressions suggested in the referred work (Haener, J., 1958, “Formulas for the Frequencies Including Higher Frequencies of Uniform Cantilever and Free-Free Beams With Additional Masses at the Ends,” ASME J. Appl. Mech. 25, pp. 412) are also incorrect. The correct characteristic (frequency) equation is derived and nondimensional comparisons are made between the results of the previously published formula and the corrected formulation using Euler–Bernoulli beam assumptions. The previous formula is shown to be accurate only for the extreme case of very large end mass to beam mass ratios. Curve fitting is used to report alternative first order and second order polynomial ratio expressions for the first natural frequency, as well as for the frequencies of some higher modes.

Finite-element vibration analysis of tapping-mode atomic force microscopy in liquid

Investigation of morphology and mechanical properties of biological specimens using atomic force microscopy (AFM) often requires its operation in liquid environment. Due to the hydrodynamic force, the vibration of AFM cantilevers in liquid shows dramatically different dynamic characteristics from that in air. A good understanding of the dynamics of AFM cantilevers vibrating in liquid is needed for the interpretation of scanning images, selection of AFM operating conditions, and evaluation of sample's mechanical properties. In this study, a finite element (FE) model is used for frequency and transient response analysis of AFM cantilevers in tapping mode (TM) operated in air or liquid. Hydrodynamic force exerted by the fluid on AFM cantilevers is approximated by additional mass and hydrodynamic damping. The additional mass and hydrodynamic damping matrices corresponding to beam elements are derived. With this model, numerical simulations are performed for an AFM cantilever to obtain the frequency and transient responses of the cantilever in air and liquid. The comparison between our simulated results and the experimentally obtained ones shows good agreement. Based on the simulations, different characteristics of cantilever dynamics in air and liquid are discussed.

Analytical 3-D p-element for quadrilateral plates—Part 1: Thick isotropic plate structures

An analytical three-dimensional (3-D) p-version element for the vibration analysis of arbitrary quadrilateral thick plates is presented. With the additional hierarchical shape functions and analytically integrated element matrices, the computed accuracy is considerably improved. The computed natural frequencies of cantilever and simply supported square plates show that the convergence rate of the present element is very fast with respect to the number of hierarchical terms and it can predict very accurate modes. The element is applicable to the free vibration analysis of quadrilateral, polygonal plates as well as 3-D space structures. The continuous wavelet transform (CWT) is applied for the identification of damping ratios. Based on the Rayleigh damping model, the damped vibration response is obtained. A simple experiment is performed to verify the predicted vibration responses. The results show that the proposed element is also efficient for the vibration response analysis of plates.

Analysis of nano-chemical mapping performed by an AFM-based (“AFMIR”) acousto-optic technique

In this paper, we analyze in detail a new method of infrared micro-spectroscopy, which aims at performing “chemical mapping” of various objects with sub-wavelength lateral resolution by using the infrared vibrational signature characterizing different molecular species. Its principle consists in an atomic force microscope tip, probing the local transient deformation induced by an infrared pulsed laser tuned at a sample absorbing wavelength. The cantilever oscillates at resonant frequencies, which amplitudes can be correlated with local absorption. We show that the system acts as an amplifier of extremely small motions induced by optical absorption and that different frequencies provide different informations, leading to a full description of the sample deformation. We estimate also the influence of the light confinement in the sample and exemplify the accuracy of the method by mapping Escherichia coli bacteria at different cantilever frequencies.

Mechanical characteristics and applications of diamondlike-carbon cantilevers fabricated by focused-ion-beam chemical vapor deposition

Diamondlike-carbon (DLC) cantilevers were fabricated with a commercially available focused-ion-beam chemical-vapor-deposition (FIB-CVD) system using a beam of 30keV Ga+ ions, and the mechanical characteristics of the cantilevers were measured. Vibration frequency of the cantilevers was passively measured using scanning electron microscopy. Resonant frequency of DLC cantilevers fabricated at 0.1–0.5pA beam current was found to be constant. The equivalent spring constant of the cantilevers was identified by squeezing the tip of a Si3N4 cantilever and a DLC cantilever together. Using the measured displacement, the spring constant of the DLC cantilever was calculated as (1.1±0.2)×10−2N∕m. Furthermore, Young’s modulus and the density of the DLC cantilevers were measured to be 187±32GPa and (3.8±0.7)×103kg∕m3, respectively. The DLC cantilevers were used as mass sensors in an ultrasensitive sensing application. A small amount of DLC was deposited on the tip of a DLC cantilever as a mass adhesion by FIB-CVD at 0.5pA beam current. As a result, the authors were able to measure a small amount of mass shift in the femtogram range using a DLC cantilever.

Quantitative analysis of tip–sample interaction in non-contact scanning forcespectroscopy

Quantitative characterization of tip–sample interaction in scanning force microscopy isfundamental for optimum image acquisition as well as data interpretation. In this work wediscuss how to characterize the electrostatic and van der Waals contribution to tip–sampleinteraction in non-contact scanning force microscopy precisely. The spectroscopic techniquepresented is based on the simultaneous measurement of cantilever deflection, oscillationamplitude and frequency shift as a function of tip–sample voltage and tip–sampledistance as well as on advanced data processing. Data are acquired at a fixedlateral position as interaction images, with the bias voltage as fast scan, andtip–sample distance as slow scan. Due to the quadratic dependence of the electrostaticinteraction with tip–sample voltage the van der Waals force can be separated from theelectrostatic force. Using appropriate data processing, the van der Waals interaction, thecapacitance and the contact potential can be determined as a function of tip–sampledistance. The measurement of resonance frequency shift yields very high signal tonoise ratio and the absolute calibration of the measured quantities, while theacquisition of cantilever deflection allows the determination of the tip–sample distance.

Anomalous resonance in a nanomechanical biosensor

The decrease in resonant frequency (-Deltaomega(r)) of a classical cantilever provides a sensitive measure of the mass of entities attached on its surface. This elementary phenomenon has been the basis of a new class of bio-nanomechanical devices as sensing components of integrated microsystems that can perform rapid, sensitive, and selective detection of biological and biochemical entities. Based on classical analysis, there is a widespread perception that smaller sensors are more sensitive (sensitivity approximately -0.5omega(r)/m(C), where m(C) is the mass of the cantilever), and this notion has motivated scaling of biosensors to nanoscale dimensions. In this work, we show that the response of a nanomechanical biosensor is far more complex than previously anticipated. Indeed, in contrast to classical microscale sensors, the resonant frequencies of the nanosensor may actually decrease or increase after attachment of protein molecules. We demonstrate theoretically and experimentally that the direction of the frequency change arises from a size-specific modification of diffusion and attachment kinetics of biomolecules on the cantilevers. This work may have broad impact on microscale and nanoscale biosensor design, especially when predicting the characteristics of bio-nanoelectromechanical sensors functionalized with biological capture molecules.

Fluid viscosity determination by means of uncalibrated atomic force microscopy cantilevers

In this letter it has been proved that the vibrating resonance frequency of an atomic force microscope cantilever is strictly characterized by its thickness (α), while its width/thickness ratio (β) appears to be a less sensitive parameter that can be approximated to a constant. We therefore propose a data analysis method that, by accounting for a constant β, allows for the determination of the value of α and consequently to calculate η. This method of monitoring viscosity has the advantage of requiring short measurement times on very small sample volumes, thereby avoiding laborious, time-consuming cantilever calibration.

A self-excited micro cantilever biosensor actuated by PZT using the mass micro balancing technique

A micro biosensor, which can be applied to a Lab-On-a-Chip (LOC), is developed in order to detect biomaterials such as protein or DNA. The biomaterials are detected by mass micro-balancing technique, which measures the change of the resonant frequency of the sensor structure. The sensor structure consists of a micro cantilever actuated by piezoelectric PZT film. The PZT film is designed to act as both a sensor and an actuator. The geometry of the micro cantilever is determined so as to maximize the sensitivity of the sensor, and environmental effects such as added mass effect in liquid are also considered in the structural analysis. The micro cantilever is 100 μm in length, 30 μm in width and 5 μm in thickness, and the PZT film thickness and length are 2.5 and 50 μm, respectively. The first resonant frequency of the PZT micro cantilever is 1.2 ∼ 1.3 MHz. Lastly the fabricated micro-biosensor using the self-excited PZT-micro cantilever is tested by detecting the human insulin-anti human insulin binding protein, the poly T-sequence DNA, the K20-Thiol DNA and the K40-Thiol DNA in air.

Size-Related Plasticity Effects in AFM Silicon Cantilever Tips

ABSTRACTWe are developing dynamic atomic force microscopy (AFM) techniques to determine nanoscale elastic properties. Atomic force acoustic microscopy (AFAM) makes use of the resonant frequencies of an AFM cantilever while its tip contacts the sample surface at a given static load. Our methods involve nanosized silicon probes with tip radius R ranging from approximately 10 nm to 150 nm. The resulting radius of contact between the tip and the sample is less than 20 nm. However, the contact stress can be greater than a few tens of GPa, exceeding the theoretical yield strength of silicon by a factor of two to four. Our AFAM experiments indicate that, contrary to expectation, tips can sometimes withstand such stresses without fracture. We subjected ten tips to the same sequence of AFAM experiments. Each tip was brought into contact with a fused quartz sample at different static loads. The load was systematically increased from about 0.4 μN to 6 μN. Changes in tip geometry were observed in images acquired in a scanning electron microscope (SEM) between the individual AFAM experiments. All of the tips with R < 10 nm broke during the first AFAM experiments at static loads less than 1.6 μN. Tips with R > 40 nm plastically deformed under such loads. However, a group of tips with R from 25 nm to 30 nm neither broke nor deformed during the tests. In order to reach higher contact stresses, two additional tips with similar values of R were used in identical experiments on nickel and sapphire samples. Although the estimated stresses exceeded 40 GPa, we did not observe any tip fracture events. Our qualitative observations agree with more systematic studies performed by other groups on various nanostructures. The results emphasize the necessity of understanding the mechanics of nanometer-scaled bodies and the impact of size effects on measurements of mechanical properties on such scales.

Optimal design of micro-force sensor for wire bonding with high acceleration and frequent movement

The wire bonding is the mostly used process in chip packaging, which requires micro-force sensor and micro-force control to perform the bonding task with high frequency no less than 15Hz. This paper presents a new strategy of active control methodology based on the linear motor (used as actuator). The novel methodology of optimal design for the 0.001N-resolution micro-force sensor under the condition of high acceleration and fast movements is detailedly elaborated on the basis of analyzing the influence of the acceleration on force sensor. The transfer function between the bracket input and the output force of the double-beam cantilever force sensor is finally derived. The experiments proved that the intrinsic frequency of the double-beam cantilever is much higher than that of the single-beam cantilever with same sensitivity, which improved the system bandwidth and effectively solved the contradiction between the high sensitivity requirements of softness and the high accuracy position control requirements of rigidity of the micro-force sensor system.

Effect of gold coating on the Q-factor of a resonant cantilever

The resonance frequency and the Q-factor of the fundamental and higher order flexural modes of silicon dioxide microcantilevers have been characterized at different pressures and for different thicknesses of gold coating. We present the experimental results and discuss the effect of the gold film on the performance and sensitivity of the cantilevers when used as mass sensors. An almost linear relationship between the Q-factor and the resonance frequency of the uncoated cantilevers is observed, implying that a higher sensitivity can be attained by actuation at higher order resonant modes. We also find that even a thin gold coating may reduce Q-factors by more than an order of magnitude.

Amplitude-mode electrostatic force microscopy in UHV: Quantification of nanocrystal charge storage

Charge storage in Si and Ge dots $(8--60\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ has been studied via electrostatic force microscopy (EFM) in UHV using a nontraditional amplitude-mode (AM) inversion method to detect cantilever frequency shift and surface potential. Specifics of the AM technique are discussed relating to resonance curve inversion, nonlinear tip-surface coupling, and force vs force gradient ``nulling'' to extract surface potentials. Single dots were charged via contact electrification with the atomic force microscopy (AFM) tip, followed by EFM, to quantitatively determine how the dot charging level depends on injection bias and dot size. Correlating surface potential with dot charge is addressed by calculating the dipole-dipole, dipole-charge, and capacitive forces acting on the AFM tip in a rigorous manner. For this, the tip-substrate capacitive interaction was studied in detail to account for tip geometry and screening effects due to the dot dielectric volume. In every instance, the change in surface potential measured above a charged dot was seen to be carrier-type dependent and vary linearly with injection bias, where the charging efficiency (${e}^{\ensuremath{-}}∕\mathrm{V}$ applied bias) was determined by only the dot-substrate contact area. Charging efficiencies for small dots $(8\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ were $\ensuremath{\sim}10\phantom{\rule{0.2em}{0ex}}{e}^{\ensuremath{-}}∕\mathrm{V}$ and larger dots $(50--60\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ showed $\ensuremath{\sim}200--400\phantom{\rule{0.2em}{0ex}}{e}^{\ensuremath{-}}∕\mathrm{V}$, agreeing well with the predicted single ${e}^{\ensuremath{-}}$ charging behavior of the tip-dot-substrate double tunnel junction (orthodox theory). These experiments demonstrate that AM-EFM can quantitatively measure charge near the level of single electrons---so long as tip shape and screening effects (perturbation of the tip-substrate electric field by the nanostructure being interrogated) are understood and incorporated into models for static charge determination.

Atomic force microscope anodization lithography using pulsed bias voltage synchronizedwith resonance frequency of cantilever

An applied bias voltage between the atomic force microscope tip and the substrate is one ofthe important factors related to the growth of oxide patterns. A pulse modulator was usedto apply a pulsed bias voltage that synchronizes with the resonance frequency of thecantilever between the tip and the substrate in tapping mode. The height of the protrudedoxide structure was increased for short duration times of the pulsed bias due to thereduction of built-up space charge in oxide. The aspect ratio of patterns using pulsed biasvoltage was about two times higher than that using continuous bias voltage. This studyrevealed that the pulsed bias has an advantage for obtaining a higher aspect ratiopattern than the continuous bias by reducing the effect of space charge in oxide.