V-shaped Cantilever Research Articles

Piezoelectric based V-shape cantilever beam design of energy harvester for biomedical applications

AbstractThis research paper exhibits the design of a V-shaped cantilever beam as a micro Energy Harvester (EH) having Piezoelectric (PZT) as its energy source for biomedical applications. PZT source based materials have the ability to convert the mechanical energy into electrical energy. Low-power biomedical devices mostly operate using electrical energy (i.e. batteries). But batteries are treated as a bio-hazard due to the massive use of biomedical applications. To overcome this toxic bio-hazard, the proposed PZT based V-shaped cantilever beam of micro EH can solve the limitations. To perform the experimental work, the cantilever beam design parameters - length, width and thickness have been considered and simulated using COMSOL Multiphysics to get the resonant frequency of 156.19 Hz which is lower than previous research work. It was observed that the obtained lower resonant frequency can be converted into AC voltage (mV) using PZT material. To convert the output AC voltage (mV) into DC voltage, a circuit of an Ultra-Low-Power (ULP) EH will be designed in LTSPICE software. Finally, the integration of the both V-shape cantilever beam and the ULP EH circuit will be implemented in PCB hardware to generate the output power (10 µW), will be stored in super-capacitor for biomedical devices-pacemaker.

Determination of calibration parameters of cantilevers of arbitrary shape by finite element analysis

The use of atomic force microscopy in nanomechanical measurements requires accurate calibration of the cantilever's spring constant (kc) and the optical lever sensitivity (OLS). The thermal method, based on the cantilever's thermal fluctuations in fluids, allows estimation of kc in a fast, non-invasive mode. However, differences in the cantilever geometry and mounting angle require the knowledge of three correction factors to get a good estimation of kc: the contribution of the oscillation mode to the total amplitude, the shape difference between the free and end-loaded configurations, and the tilt of the cantilever with respect to the measured surface. While the correction factors for traditional rectangular and V-shaped cantilever geometries have been reported, they must be determined for cantilevers with non-traditional geometries and large tips. Here, we develop a method based on finite element analysis to estimate the correction factors of cantilevers with arbitrary geometry and tip dimensions. The method relies on the numerical computation of the effective cantilever mass. The use of the correction factor for rectangular geometries in our model cantilever (PFQNM-LC) will lead to values underestimated by 16%. In contrast, experiments using pre-calibrated cantilevers revealed a maximum uncertainty below 5% in the estimation of the OLS, verifying our approach.

Design of V-shaped cantilevers for enhanced multifrequency AFM measurements.

As the application of atomic force microscopy (AFM) in soft matter characterization has expanded, the use of different types of cantilevers for these studies have also increased. One of the most common types of cantilevers used in soft matter imaging is V-shaped cantilevers due to their low normal spring constant. These types of cantilevers are also suitable for nanomanipulation due to their high lateral spring constants. The combination of low normal spring constant and high lateral spring constants makes V-shaped cantilevers promising candidates for imaging soft matter. Although these cantilevers are widely used in the field, there are no studies on the static and dynamic behavior of V-shaped cantilevers in multifrequency AFM due to their complex geometry. In this work, the static and dynamic properties of V-shaped cantilevers are studied while investigating their performance in multifrequency AFM (specifically bimodal AFM). By modeling the cantilevers based on Timoshenko beam theory, the geometrical dimensions such as length, base width, leg width and thickness are studied. By finding the static properties (mass, spring constants) and dynamic properties (resonance frequencies and quality factors) for different geometrical dimensions, the optimum V-shaped cantilever that can provide the maximum phase contrast in bimodal AFM between gold (Au) and polystyrene (PS) is found. Based on this study, it is found that as the length of the cantilever increases the 2nd eigenmode phase contrast decreases. However, the base width exhibits the opposite relationship. It is also found that the leg width does not have a monotone relationship similar to length and base width. The phase contrast increases for the range of 14 to 32 µm but decreases afterwards. The thickness of a V-shaped cantilever does not play a major role in defining the dynamics of the cantilever compared to other parameters. This work shows that in order to maximize the phase contrast, the ratio of second to first eigenmode frequencies should be minimized and be close to a whole number. Additionally, since V-shaped cantilevers are mostly used for soft matter imaging, lower frequency ratios dictate lower spring constant ratios, which can be advantageous due to lower forces applied to the surface by the tip given a sufficiently high first eigenmode frequency. Finally, two commercially available V-shaped cantilevers are theoretically and experimentally benchmarked with an optimum rectangular cantilever. Two sets of bimodal AFM experiments are carried out on Au-PS and PS-LDPE (polystyrene and low-density polyethylene) samples to verify the simulation results.

Comparison Between Torsional Spring Constants of Rectangular and V-Shaped AFM Cantilevers

The properties of force-sensing micro-cantilevers are of fundamental importance for measurements employing atomic force microscopy (AFM) techniques. Due to the well-known arguments of Sader, it is generally accepted that V-shaped cantilevers are more sensitive to lateral forces than rectangular ones. We present results of numerical (finite element modelling) and experimental comparison between torsional spring constants of rectangular and V-shaped commercial AFM cantilevers. As representative example of such beams, we considered AFM probes available commercially. In particular, we tested scaled-up models of V-shaped cantilevers which had the same geometrical shapes as commercial AFM cantilevers. Both the rectangular and the V-shaped larger scale models were made of the same material; they had the same length, thickness, normal spring constant, as well as the same location and shape of the tip base. In the experiments and the simulations, an external lateral load was applied to the free end of the tip. A good agreement between the experimental work and finite element method (FEM) simulations was observed. The results show that the torsional spring constant of the V-shape cantilevers considered here was greater than that of the equivalent rectangular beams by up to 45%. The discrepancy with the results from Sader should be caused by differences in both the load transfer scheme and the geometrical shapes of the V-shaped beams.

Analysis of Dynamic Behavior of V-Shaped Atomic Force Microscope Cantilever in Contact and Tapping Modes by Considering Various Immersion Surroundings

In atomic force microscope (AFM) as a powerful device for scanning the samples, a cantilever is used to sense the variations of its dynamic characteristics due to the tip–sample interaction. Theoretical models that can accurately simulate the surface-coupled dynamics of the cantilever are necessary for quantifiable and qualitative explanation and understanding of measured results. 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 paper, the amplitude of frequency response functions (FRF) of vertical and rotational movements for a V-shaped atomic force microscope beam immersed in various surroundings has been surveyed for the first time. For rising the precision of theoretical model, we have considered all needful details for the beam and sample. The amplitude of FRF of vertical and rotational movements and resonant frequency of beam have been surveyed by supposing cantilever thickness, breadth and length, the angle between cantilever and sample surface, tip height and normal and lateral tip–sample interaction force. In this study, carbon tetrachloride (CCL4), methanol, acetone, water and air have been considered as surroundings. The results show that an increase in the tip–sample interaction force considerably raises the amount of resonant frequency. By increasing the liquid viscosity, the amplitude of FRF for vertical and rotational movements and resonant frequency reduce. Moreover, the amplitude of FRF of vertical and rotational movements is reduced by raising the rectangular and tapered parts lengths, but increased by raising the rectangular part breadth and cantilever thickness. The resonant frequency goes down by increasing the rectangular and tapered parts lengths and rectangular part breadth, but increases by rising the cantilever thickness. In this paper, we have tried to model the realistic dynamic behavior of V-shaped AFM beam in contact and tapping modes with the most accuracy. Results show good agreement. Based on the experimental results, the present theoretical model can forestall better the realistic behavior of tapping mode than the contact mode for V-shaped AFM cantilever. Based on the complexity of the V-shaped AFM cantilever, this study has been done for the first time in both of the contact and tapping modes.

A MEMS Accelerometer Based on Wavelength Modulation Using an Integrated Blazed Grating

This paper reports a microelectromechanical systems (MEMS) optical fiber accelerometer with an integrated blazed grating as a wavelength modulation component. The accelerometer includes a V-shaped cantilever beam, a vertically symmetrical proof mass, and an integrated blazed grating. The accelerometer prototype is fabricated with bulk micromachining processes and is tested. The bandwidth of the accelerometer is 200 Hz. The optical sensitivity and nonlinearity of the measure range ±5.2 g are 1.63 nm/g at 100 Hz and 0.06%, respectively. The x- and y-axes cross-axis sensitivities are 2% and 4.5%, respectively. In the full temperature range of -20 °C-200 °C, the temperature sensitivity is 2.8 pm/°C. Thanks to the above-mentioned characteristics, the proposed MEMS accelerometer could have a wide range of applications, such as rail traffic and attitude heading sensing applications.

Phase transformation induced modulation of the resonance frequency of VO2/TiO2 coated microcantilevers

AbstractHere we present an investigation into the phase change mechanism and detection methods of the metal-insulator transition of vanadium dioxide (VO2). We are able to detect the onset of the phase transition, and track it to completion using both the mechanical and electrical response by depositing VO2/TiO2 layers onto microcantilever devices by pulsed laser deposition. The resonance frequency of v-shaped cantilevers was shown to increase by up to 41 % upon deposition of VO2 as detected by laser Doppler vibrometry. Such a large increase in resonance frequency is ascribed to high tensile stress imparted onto the cantilever during the deposition process. The insulator-metal transition manifested as a 5 % increase in the resonance frequency as a result of lattice compression, resulting in additional tensile stress in the more ordered metallic phase. Electrically, the transition was confirmed by over three orders magnitude decrease in resistance upon heating past the transition. The metal-insulator transition was measured with an accuracy of a few °C when comparing the two methods, however, the transition was much sharper in the mechanical response.

Stiffness modelling of various types of atomic force microscopy cantilevers in 3D and validation of the models by finite element method

In the manipulations of nanoparticles in different environments, the manipulation dynamics have to be modeled precisely and the critical force and time of manipulation have to be computed. A dynamic manipulation modeling can be performed two- or three-dimensionally; and a three-dimensional modeling process is obviously more exact and complicated. In order to precisely model, in three dimensions, the dynamics of a nano-manipulation is performed by an atomic force microscope, where the stiffness values of various atomic force microscope cantilevers need to be calculated and modeled correctly. The cantilevers of an atomic force microscope are classified into three general groups (rectangular, V-shaped, and dagger-shaped) and each of these types is used for the manipulation of nanoparticles with particular characteristics. Also, in addition to the important application of stiffness in the dynamic modeling of a manipulation process, this model is very much needed in computing the critical force and time of manipulation, which are the two key parameters in the first phase of a manipulation. Due to the importance of the three-dimensional stiffness modeling of atomic force microscope cantilevers, first, the three-dimensional stiffness values of rectangular, V-shaped, and dagger-shaped cantilevers have been determined. The extracted stiffness models have then been validated by means of the finite element method. The comparisons between the stiffness values along different directions for the three mentioned types of cantilevers indicate that the V-shaped cantilever has the highest lateral stiffness, the dagger-shaped cantilever has the least amount of normal stiffness, and the rectangular cantilever enjoys the highest torsional stiffness.

Shape Design Optimization of Unimorph Piezoelectric Cantilever Energy Harvester

The most promising method for micro scale energy scavenging is via vibration energy harvesting which converts mechanical energy to electrical energy. Using piezoelectric cantilevers is the most common method for vibration energy harvesting. Changing the shape of the cantilevers can lead to changing the generated output voltage and power. In this work vibration energy harvesting via piezoelectric resonant unimorph cantilevers is studied and new design for obtaining more efficient piezoelectric energy harvester is suggested. This study provides comprehensive analysis of the output voltage relationships and deducing a considerable precise rule of thumb for calculating resonance frequency in cantilever-type unimorph piezoelectric energy harvesters using Rayleigh method. The analytical formula, is then analyzed and verified by FEM simulation in ABAQUS. The analytical data was found to be very close to simulation data. A key finding is that among all the unimorph trapezoidal V-shaped cantilever beams with uniform thickness, the triangular tapered cantilever, can lead to highest resonance frequency and by increasing the ratio of the trapezoidal bases, the resonance frequency decreases. These new findings provide guidelines on system parameters that can be manipulated for more efficient performance in different ambient source conditions.

Modeling and simulation of critical force and time in 3D manipulations using rectangular, V-shaped and dagger-shaped cantilevers

Abstract The AFM-based nanorobots are extensively used nowadays for transferring and displacing various nano particles. Because of not being able to simultaneously perform and observe a manipulation operation, simulating the motion dynamics of nano particles in a manipulation operation has greatly attracted the attention of many researchers. This paper has focused on the 3D modeling of motion dynamics by using different cantilevers (rectangular, V-shaped and dagger-shaped) and has simulated the kinematics and dynamics of a manipulation operation. In order to validate the results, by gradually reducing the 3D parameters, the obtained results have been compared with the 2D manipulation results. The simulations have been extended to the rolling, sliding and spinning motion modes. Also, the first critical force and time for the sliding motion mode and the second critical force and time for the spinning motion mode have been simulated for all three types of cantilevers (rectangular, V-shaped and dagger-shaped). By employing the algorithm presented in this paper, it is possible to carry out precise manipulations of nano particles by means of the three mentioned cantilevers. At the end, all the effective geometrical and operational parameters have been investigated.

Improvements in energy harvesting capabilities by using different shapes of piezoelectric bimorphs

The small amount of power needed by microelectronic devices opens up the possibility to convert part of the vibration energy present in the environment into electrical energy, using several methods. One such method is to use piezoelectric material as an additional layer in cantilever beams to harvest vibration energy for self-powered sensors. The geometry of a piezoelectric cantilever beam will greatly affect its vibration energy harvesting ability. Tapering and changing the configuration as ways to increase the generated output power of cantilever piezoelectric energy harvesters have gained popularity in recent years. In this work vibration energy harvesting via piezoelectric resonant bimorph cantilevers is studied and new designs for obtaining optimal piezoelectric energy harvesters are suggested. This paper deduces a very precise and simple analytical formula that can be used as a rule of thumb for calculating the resonant frequency of bimorph trapezoidal V-shaped cantilevers using the Rayleigh–Ritz method. This analytical formula is then analyzed using MATLAB as well as finite element methods and validated by ABAQUS simulation. Also, mathematical derivations for the output voltage of bimorph piezoelectric energy harvesters are presented and validated by simulation and experimental results. These formulas provide a new perspective that, among all the bimorph trapezoidal V-shaped cantilever beams with uniform thickness, the bimorph triangular tapered cantilever can lead to the highest resonant frequency and therefore maximum sensitivity, and by increasing the ratio of the trapezoidal bases the sensitivity decreases. Also, the output voltage and strain distribution show that the triangular cantilever has the highest efficiency and power density.

Sobol method application in dimensional sensitivity analyses of different AFM cantilevers for biological particles

Due to the more delicate nature of biological micro/nanoparticles, it is necessary to compute the critical force of manipulation. The modeling and simulation of reactions and nanomanipulator dynamics in a precise manipulation process require an exact modeling of cantilevers stiffness, especially the stiffness of dagger cantilevers because the previous model is not useful for this investigation. The stiffness values for V-shaped cantilevers can be obtained through several methods. One of them is the PBA method. In another approach, the cantilever is divided into two sections: a triangular head section and two slanted rectangular beams. Then, deformations along different directions are computed and used to obtain the stiffness values in different directions. The stiffness formulations of dagger cantilever are needed for this sensitivity analyses so the formulations have been driven first and then sensitivity analyses has been started. In examining the stiffness of the dagger-shaped cantilever, the micro-beam has been divided into two triangular and rectangular sections and by computing the displacements along different directions and using the existing relations, the stiffness values for dagger cantilever have been obtained. In this paper, after investigating the stiffness of common types of cantilevers, Sobol sensitivity analyses of the effects of various geometric parameters on the stiffness of these types of cantilevers have been carried out. Also, the effects of different cantilevers on the dynamic behavior of nanoparticles have been studied and the dagger-shaped cantilever has been deemed more suitable for the manipulation of biological particles.

An investigation into resonant frequency of trapezoidal V-shaped cantilever piezoelectric energy harvester

Power supply is a bottle-neck problem of wireless micro-sensors, especially where the replacement of batteries is impossible or inconvenient. Now piezoelectric material is being used as an additional layer in cantilever beams to harvest vibration energy for self-powered sensors. However, the geometry of a piezoelectric cantilever beam will greatly affects its vibration energy harvesting ability. This paper deduces a remarkably precise analytical formula for calculating the fundamental resonant frequency of trapezoidal V-shaped cantilevers using Rayleigh---Ritz method. This analytical formula, which is very convenient for mechanical energy harvester design based on Piezoelectric effect, is then analyzed using MATLAB as well as finite element methods and validated by ABAQUS simulation. This formula raises a new perspective that, among all the trapezoidal V-shaped cantilevers with uniform thickness, the simplest triangular tapered cantilever, can lead to maximum resonant frequency and highest sensitivity and by increasing the ratio of the trapezoidal bases, the sensitivity decreases.

Numerical study of the hydrodynamic drag force in atomic force microscopy measurements undertaken in fluids

When atomic force microscopy (AFM) is employed for in vivo study of immersed biological samples, the fluid medium presents additional complexities, not least of which is the hydrodynamic drag force due to viscous friction of the cantilever with the liquid. This force should be considered when interpreting experimental results and any calculated material properties. In this paper, a numerical model is presented to study the influence of the drag force on experimental data obtained from AFM measurements using computational fluid dynamics (CFD) simulation. The model provides quantification of the drag force in AFM measurements of soft specimens in fluids.The numerical predictions were compared with experimental data obtained using AFM with a V-shaped cantilever fitted with a pyramidal tip. Tip velocities ranging from 1.05 to 105μm/s were employed in water, polyethylene glycol and glycerol with the platform approaching from a distance of 6000nm. The model was also compared with an existing analytical model. Good agreement was observed between numerical results, experiments and analytical predictions. Accurate predictions were obtained without the need for extrapolation of experimental data. In addition, the model can be employed over the range of tip geometries and velocities typically utilized in AFM measurements.

A Novel V-Shaped Cross Section Cantilever Sensor for Monitoring Concentrated Masses With Improved Detecting Sensitivity and Measuring Accuracy

Mass detection sensitivity and measuring accuracy of resonant mass sensors are mainly dependent on the analyte position, the resonant frequency, and the effective mass of the cantilever. For measuring concentrated masses or particles, a novel mass sensor incorporating V-shaped cross section cantilever was proposed by locating the analyte at predefined positions for both improving the mass detecting sensitivity and reducing the measuring deviation. The theoretical model for analyzing the mass detection sensitivity was established. With the same geometric dimension, the proposed sensor's sensitivities obtained theoretically and experimentally are 6.75×104 and 6.34×104 Hz/g, which are nearly 2.20 times as great as that of the custom made cantilever with a rectangular cross section. Thus, the feasibility of the proposed sensitivity improving method was adequately validated.

Determination of the spring constants of the higher flexural modes of microcantilever sensors

A method for the simultaneous calibration of the spring constants of all flexural modes of microcantilevers is presented. It is based on a flow of gas from a microchannel that interacts with the microcantilever. The gas flow causes a measurable shift in the resonance frequencies of thermal noise spectra of the flexural modes. From the magnitude of the frequency shifts of the individual modes the spring constants can be determined with high accuracy and precision. The method is non-invasive and does not risk damage to the cantilever. Experimental data are presented for several V-shaped and rectangular cantilevers with nominal fundamental spring constants in the range of 0.03–1.75 N m−1. The spring constants of the fundamental modes compare favorably to those obtained using the Sader method. The higher modes of oscillation are readily calibrated with experimental uncertainties of 5–10%.

Calibration of atomic force microscope cantilevers using standard and inverted static methods assisted by FIB-milled spatial markers

Static methods to determine the spring constant of AFM cantilevers have been widely used in the scientific community since the importance of such calibration techniques was established nearly 20 years ago. The most commonly used static techniques involve loading a trial cantilever with a known force by pressing it against a pre-calibrated standard or reference cantilever. These reference cantilever methods have a number of sources of uncertainty, which include the uncertainty in the measured spring constant of the standard cantilever, the exact position of the loading point on the reference cantilever and how closely the spring constant of the trial and reference cantilever match. We present a technique that enables users to minimize these uncertainties by creating spatial markers on reference cantilevers using a focused ion beam (FIB). We demonstrate that by combining FIB spatial markers with an inverted reference cantilever method, AFM cantilevers can be accurately calibrated without the tip of the test cantilever contacting a surface. This work also demonstrates that for V-shaped cantilevers it is possible to determine the precise loading position by AFM imaging the section of the cantilever where the two arms join. Removing tip-to-surface contact in both the reference cantilever method and sensitivity calibration is a significant improvement, since this is an important consideration for AFM users that require the imaging tip to remain in pristine condition before commencing measurements. Uncertainties of between 5 and 10% are routinely achievable with these methods.

V 형상을 가지는 원자현미경 Cantilever의 정량적 마찰력 교정

Atomic force microscopy (AFM) has been used as a tool, not only for imaging surfaces, but also for measuring surface forces and mechanical properties at the nano-scale. Force calibration is crucial for quantitatively measuring the forces that act between the AFM probe of a force sensing cantilever and a sample. In this work, the lateral force calibrations of a V-shaped cantilever were performed using the finite element method, multiple pivot loading, and thermal noise methods. As a result, it was shown that the multiple pivot loading method was appropriate for the lateral force calibration of a V-shaped cantilever. Further, through crosschecking of the abovementioned methods, it was concluded that the thermal noise method could be used for determining the lateral spring constants as long as the lateral deflection sensitivity was accurately determined. To obtain the lateral deflection sensitivity from the sticking portion of the friction loop, the contact stiffness should be taken into account.

FORCE TRANSDUCER MODELING OF RECTANGULAR, V–SHAPED, AND DAGGER CANTILEVER PROBES BASED ON ATOMIC FORCE MICROSCOPY

Real-time monitoring of the nano-particle manipulation process by atomic force microscope (AFM) is almost impossible since the manipulator of the AFM is used as either the imaging or manipulation tool at a given instant. As one approach to this problem, researchers scan the area where the target particle exists, before and after the nano-manipulation. Thus, by using some fixed reference features, the new relative position of the particle is obtained from the images. However, this imaging is offline, and unexpected problems during nano-manipulation process cannot be detected. In this article, force transducer of the AFM rectangular, V-shaped, and dagger cantilevers, which convert the three-dimensional deflections measured by the detection system to corresponding three-dimensional force, are modeled and compared. So there would be a feedback from the real-time force system during nano-manipulation process, which can be utilized for better understanding and reliable handling of nano-particles. Furthermore, the manipulation forces are affected directly by spring constants of cantilever. Hence, the cantilever is the most significant and sensitive component of the AFM. Therefore, variations of the lateral, longitudinal, and normal spring constants of the mentioned cantilever for different geometrical parameters are analyzed and discussed.

Interlaboratory round robin on cantilever calibration for AFM force spectroscopy

Single-molecule force spectroscopy studies performed by Atomic Force Microscopes (AFMs) strongly rely on accurately determined cantilever spring constants. Hence, to calibrate cantilevers, a reliable calibration protocol is essential. Although the thermal noise method and the direct Sader method are frequently used for cantilever calibration, there is no consensus on the optimal calibration of soft and V-shaped cantilevers, especially those used in force spectroscopy. Therefore, in this study we aimed at establishing a commonly accepted approach to accurately calibrate compliant and V-shaped cantilevers. In a round robin experiment involving eight different laboratories we compared the thermal noise and the Sader method on ten commercial and custom-built AFMs. We found that spring constants of both rectangular and V-shaped cantilevers can accurately be determined with both methods, although the Sader method proved to be superior. Furthermore, we observed that simultaneous application of both methods on an AFM proved an accurate consistency check of the instrument and thus provides optimal and highly reproducible calibration. To illustrate the importance of optimal calibration, we show that for biological force spectroscopy studies, an erroneously calibrated cantilever can significantly affect the derived (bio)physical parameters. Taken together, our findings demonstrated that with the pre-established protocol described reliable spring constants can be obtained for different types of cantilevers.