Cantilever Thickness Research Articles

Characterization of a roof tile-shaped out-of-plane vibrational mode in aluminum-nitride-actuated self-sensing micro-resonators for liquid monitoring purposes

This Letter reports on an advanced out-of-plane bending mode for aluminum-nitride (AlN)-actuated cantilevers. Devices of different thickness were fabricated and characterized by optical and electrical measurements in air and liquid media having viscosities up to 615 cP and compared to the classical out-of-plane bending and torsional modes. Finite element method eigenmode analyses were performed showing excellent agreement with the measured mode shapes and resonance frequencies. Quality factors (Q-factor) and the electrical behavior were evaluated as a function of the cantilever thickness. A very high Q-factor of about 197 was achieved in deionized water at a low resonance frequency of 336 kHz, being up to now, the highest quality factor reported for cantilever sensors in liquid media. Compared to the quality factor of the common fundamental out-of-plane bending mode, a 5 times higher Q-factor was achieved. Furthermore, the strain related conductance peak of the roof tile-shaped mode is superior. Compared to any out-of-plane bending mode, this combination of most beneficial properties is unique and make this mode superior for a large variety of resonator-based sensing applications.

Rapid microcantilever-thickness determination by optical interferometry

Silicon microcantilevers are widely used in scanning-probe microscopy and in cantilever-sensing applications. However, the cantilever thickness is not well controlled in conventional lithography and, since it is also difficult to measure, it is the most important undefined factor in mechanical variability. An accurate method to measure this parameter is thus essential. We demonstrate the capability to measure microcantilever thicknesses rapidly (>1 Hz) and accurately (±2 nm) by optical interferometry. This is achieved with standard microscopy equipment and so can be implemented as a standard technique in both research and in batch control for commercial microfabrication. In addition, we show how spatial variations in the thickness of individual microcantilevers can be mapped, which has applications in the precise mechanical calibration of cantilevers for force spectroscopy.

A new investigation for double tapered atomic force microscope cantilevers by considering the damping effect

The resonant frequency of flexural vibration for a double tapered atomic force microscope (AFM) cantilever has been investigated by considering the damping effect. In this paper the effects of the contact position, contact stiffness, height of the tip, thickness of the beam, the height and breadth taper ratios of cantilever, the angle between the cantilever and the sample surface and damping parameter based on Timoshenko beam theory on the non‐dimensional frequency and sensitivity have been studied. The differential Quadrature method (DQM) is employed to solve the nonlinear differential equations of motion. The results show that the resonant frequency decreases when Timoshenko beam parameter or cantilever thickness increases and high order modes are more sensitive to it. The first frequency is sensitive only in the lower range of contact stiffness, but the higher order modes are sensitive to the contact stiffness in a larger range. Increasing the tip height increases the sensitivity of the vibrational modes in a limited range of normal contact stiffness. Increasing the lateral contact stiffness increases the sensitivity to the normal contact stiffness after critical normal contact stiffness, but when the normal contact stiffness is lower than critical normal contact stiffness, the situation is reversed. By increasing the lateral damping parameter, the resonant frequency and sensitivity to the contact stiffness decrease. Furthermore, by increasing the breadth taper ratio, the frequency increases.

Flexural vibrations of double tapered atomic force microscope cantilevers studied by considering the contact position and using the differential quadrature method

The resonant frequency of flexural vibrations for a double tapered atomic force microscope (AFM) cantilever has been investigated by using the Timoshenko beam theory. In this paper, the effects of various parameters on the dimensionless frequency of vibrations of the AFM cantilever have been studied. The differential quadrature method (DQM) is employed to solve the nonlinear differential equations of motion. The results show that the resonant frequency decreases when the Timoshenko beam parameter or the cantilever thickness increases, and high-order modes are more sensitive to it. The first frequency is sensitive only in the lower range of contact stiffness, but the higher-order modes are sensitive to the contact stiffness in a larger range. Increasing the tip height increases the sensitivity of the vibrational modes in a limited range of normal contact stiffness. Furthermore, with increasing the breadth taper ratio, the frequency increases. The DQM results are compared with the exact solution for a rectangular AFM cantilever.

Theory of magnetoelectric effect in multilayer nanocomposites on a substrate: Resonant bending-mode response

Resonant bending-mode magnetoelectric (ME) coefficients of magnetostrictive-piezoelectric multilayer cantilevers are calculated analytically using a model developed for arbitrary multilayers on a substrate. Without quality factor effects the ME coefficient maxima in the four-dimensional parameter space of layer numbers, layer sequences, piezoelectric volume fractions, and substrate thicknesses are found to be essentially constant for nonzero substrate thickness. Global maxima occur for bilayers without substrates. Vanishing magnetoelectric response regions result from voltage cancellation in piezoelectric layers or absence of bending-mode excitation. They are determined by the neutral plane position in the multilayer stack. With Q-factor effects dominated by viscous air damping ME coefficients strongly increase with cantilever thickness primarily due to increasing resonance frequencies. The results yield a layer specific prediction of ME coefficients, resonance frequencies, and Q-factors in arbitrary multilayers and thus distinction of linear-coupling and Q-factor effects from exchange interaction, interface, or nonlinear ME effects.

Study on the Electromechanical Coupling Performance of Bimorph Piezoelectric Cantilever

In order to accurately predict the electromechanical coupling performance of bimorph piezoelectric cantilever structure. Based on Euler-Bernoulli beam assumption, the expression of output voltage response of the bimorph piezoelectric cantilever is written, the output voltage curve of unit acceleration excitation are obtained, the law of the output voltage influenced by the structure parameters of the cantilever beam length, width and thickness of the metal beam and the piezoelectric layer are analyzed, the results will play an important theoretical and engineering significance in the development of high efficient piezoelectric energy harvesting device.

Experimental Investigation of Piezoelectric Bimorph Cantilever on Vibration Energy Harvesting Performance

The bimorph piezoelectric cantilever model for vibration energy harvesting was established to analyse its natural frequency and generating performance according to Euler-Bernoulli theory. The influence of the length and thickness of piezoelectric cantilever on natural frequency and generating voltage was discussed by computing the cantilever equivalent stiffness. Experimental investigation was performed to measure its natural frequency and output generating voltage of bimorph piezoelectric cantilever, and the effect of cantilever with different proof mass and structural parameters on generating performance was also analysed. Theoretical results of bimorph piezoelectric cantilever are compared with experimental results qualitatively, good correlations are observed.

Development of Miniaturized Walking Biological Machines

The quest to ‘forward-engineer’ and fabricate biological machines remains a grand challenge. Towards this end, we have fabricated locomotive “bio-bots” from hydrogels and cardiomyocytes using a 3D printer. The multi-material bio-bot consisted of a ‘biological bimorph’ cantilever structure as the actuator to power the bio-bot, and a base structure to define the asymmetric shape for locomotion. The cantilever structure was seeded with a sheet of contractile cardiomyocytes. We evaluated the locomotive mechanisms of several designs of bio-bots by changing the cantilever thickness. The bio-bot that demonstrated the most efficient mechanism of locomotion maximized the use of contractile forces for overcoming friction of the supporting leg, while preventing backward movement of the actuating leg upon relaxation. The maximum recorded velocity of the bio-bot was ~236 µm s−1, with an average displacement per power stroke of ~354 µm and average beating frequency of ~1.5 Hz.

Impact of silicon nitride thickness on the infrared sensitivity of silicon nitride–aluminum microcantilevers

This paper investigates how silicon nitride thickness impacts the performance of silicon nitride–aluminum bimaterial cantilever infrared sensors. A model predicts cantilever behavior by considering heat transfer within and from the cantilever, cantilever optical properties, cantilever bending mechanics, and thermomechanical noise. Silicon nitride–aluminum bimaterial cantilevers of different thicknesses were designed and fabricated. Cantilever sensitivity and noise were measured when exposed to infrared laser radiation. For cantilever thickness up to 1200nm, thicker silicon nitride results in improved signal to noise ratio due to increased absorptivity and decreased noise. The best cantilever had an incident flux sensitivity of 2.1×10−3VW−1m2 and an incident flux signal to noise ratio of 406Hz1/2W−1m2, which is more than an order of magnitude improvement compared to the best commercial cantilever.

The flexural vibration of V shaped atomic force microscope cantilevers by using the Timoshenko beam theory

AbstractThe resonant frequency of flexural vibration for a V shaped atomic force microscope (AFM) cantilever has been investigated using the Timoshenko beam theory. Generally, three different regions are considered for V shaped cantilevers, one region with constant cross section and height and two double tapered regions. In this paper, the effects of the different parameters on the non‐dimensional frequency and sensitivity to the contact stiffness have been studied. The differential quadrature method (DQM) is applied to solve the nonlinear differential equations of motion. The results show that the resonant frequency decreases when Timoshenko beam parameter or cantilever thickness increases and high order modes are more sensitive to it. The first frequency is sensitive only in the lower range of contact stiffness, but the high order frequencies are sensitive to the contact stiffness in a larger range. It is possible to increase the range of sensitivity to the contact stiffness by increasing the width ratio for the first mode. By increasing both height and breadth taper ratios the resonant frequency increases. The resonant frequency is sensitive to the width ratio and by increasing this ratio, the resonant frequency decreases, but critical contact stiffness increases and finally the variations of the height and breadth taper ratios and width ratio are affected on the sensitivity to the contact stiffness. We show that the sensitivity to the contact stiffness can be increased by the variations of height taper ratio and this matter has never been investigated formerly.

Cantalever Protection Aluminum Profiles Extrusion Die Design Method and Numerical Simulation

In order to improve the service life of extrusion dies with long cantilever structure, a design scheme of porthole die for half-hollow profiles with long cantilever was introduced. Using numerical simulation method, compared with conventional method for the half-hollow porthole design method of a typical profile die model, the equilibrium of the material flow at the outlet, the stress and deformation of the die were analyzed in detail. With selection of the cantilever thickness shrinkage as the objective function, experiment was done to verify the result of simulating analysis. The results indicated that there was only little difference for the equilibrium of material flow between the two design schemes, but the stress load and deformation of the design scheme were greatly improved.

PZT Thin Films from Bulk PZT for Vibration Power Harvester Applications

The objective of this work was the development of a technology for the fabrication of piezoelectric PZT thin films from bulk PZT on silicon wafer for micro power harvester applications. With the lapping technique, the thickness of bulk PZT was reduced from 300µm to 10µm at the top data. KOH etching for silicon was used to thin the thickness of silicon cantilever from 300µm to 15µm at the top data. The piezoelectric coefficient d31 was measured to be -12pC/N. Resonance frequency measurements on a 4mmX1mmX0.06mm cantilever resulted in a value of 430Hz, and the voltage output was around 0.68V at 1g acceleration. The result shows that the fabrication process is quite feasible.

Sensitivity of V-shaped atomic force microscope cantilevers based on a modified couple stress theory

A relationship based on a modified couple stress theory is developed to investigate the flexural sensitivity of a V-shaped cantilever of an atomic force microscope (AFM) taking into account the normal interaction force between the cantilever tip and the sample surface. An approximate solution to the flexural vibration problem is obtained using the Rayleigh–Ritz method. The results show that the sensitivity of the V-shaped AFM cantilever using the modified couple stress theory is smaller than that using the classical beam theory for the lower contact stiffness. However, when the contact stiffness becomes higher, the situation is reversed. Furthermore, as the ratio of cantilever thickness to internal material length scale parameter decreases, the sensitivity of the cantilever decreases.

Effect of focused ion beam milling on microcantilever loss

Micro-scale cantilevers such as those used in the atomic force microscope are now being applied to the accurate measurement of novel forces such as the Casimir force. The measurements are done in dynamic mode and higher sensitivity can be achieved by using cantilevers with lower force constants. One method to produce a low force constant cantilever is to reduce the thickness of a conventional AFM cantilever by focused ion beam (FIB) milling. Here we show that this method leads to a typical reduction of the resonance quality factor by 40–50%. Reduction of the thickness by FIB milling therefore does not necessarily result in improved force sensitivity, with a decreased quality factor negating any improvement from the lower force constant. If the increased loss is due to the FIB damage layer then it is shown that this layer is ∼30 nm thick and the complex part of Young's modulus of the layer is in the range 205–270 MPa. In the measurements reported here no trend in the quality factor has been observed with either dose rate of the milling or with the total mill depth.

Sensitivity analysis of the nanoparticles on substrates using the atomic force microscope with rectangular and V-shaped cantilevers

The dynamic model of the nanoparticles pushing on a substrate based on the atomic force microscope with a rectangular cantilever (RC) and a V-shaped cantilever (VSC), which includes 12 nonlinear and coupled equations, has been analysed, by using the graphical and automatic differential sensitivity analysis (SA) methods, and the sensitive and non-sensitive parameters and their sensitive ranges have been identified. The results indicate that the output variables of manipulation are very sensitive to the cantilever's dimensions. The two parameters, length and thickness of cantilever, are very sensitive, which the results of the graphic SA confirm. In addition, the results of the graphic SA show that the degree of sensitivity depends on the apparent values of input parameters, such that by changing the magnitude of a specific parameter, it could be possible to increase or decrease the sensitivity. Moreover, the results indicate that, in general, by changing the cantilever from RC to VSC, the sensitivity to geometrical dimensions decreases, and through the proper selection, the effect of cantilever geometry on manipulation could be controlled.

A High-Speed Single Crystal Silicon AFM Probe Integrated with PZT Actuator for High-Speed Imaging Applications

A new high speed AFM probe has been proposed and fabricated. The probe is integrated with PZT actuated cantilever realized in bulk silicon wafer using heavily boron doped silicon as an etch stop layer. The cantilever thickness can be accurately controlled by the boron diffusion process. Thick SCS cantilever and integrated PZT actuator make it possible to be operated at high speed for fast imaging. The resonant frequency of the fabricated probe is 92.9 kHz and the maximum deflection is 5.3 <TEX>${\mu}m$</TEX> at 3 V. The fabricated probe successfully measured the surface of standard sample in an AFM system at the scan speed of 600<TEX>${\mu}m$</TEX>/sec.

Nanosensitive Silicon Microprobes for Mechanical Detection and Measurements

Nanosensitive mechanical microprobes with CMOS transistors, inverters, inverters cascades and ring oscillators, integrated on the thin silicon cantilevers are presented. Mechanical stress shifts linear, steep switching fragment of the inverters’ electrical characteristics. Microprobes were fabricated with use of the standard CMOS technology (3.5 μm design rules, one level polysilicon gate and one level of the metal interconnections) and relief MEMS technique. Control of the silicon cantilever thickness was satisfactory in the range above the few micrometers. Several computer simulations were done to analyze and optimize transistors location on the cantilever, in respect to the mechanical stress distribution. Results of the microprobes electromechanical tests confirm high deflection sensitivity 1.2 - 1.8 mV/nm and force sensitivity 2.0 - 2.4 mV/nN, both in nano ranges. Microprobes, with the ring oscillators revealed sensitivities 5 - 8 Hz/nm. These microprobes seem to be appropriate for applications in precise chemical and biochemical sensing.

Anisotropic response of glassy splay-bend and twist nematic cantilevers to light and heat

A gradient of director through the thickness of a nematic glass cantilever gives a gradient in the large distortions such materials suffer in response to temperature or illumination changes. We first sketch, within isotropic elasticity, how such gradients cause these cantilevers to respond by bending. We then derive the response within the anisotropic elasticity expected for uniaxial solids. Because, in general, spontaneously bending cantilevers have regions of elongation and contraction (with respect to their neutral state), internal stresses are generated, the magnitude of which depends on the anisotropic, fourth rank modulus tensor and in particular on its local alignment arising from the director's spatial distribution. We show that despite elastic complexity, bend is simply linear in the anisotropy of thermo-optical response, with a slope depending on the structure of the modulus tensor, justifying the previous literature on spontaneously bending cantilevers. We also explicitly consider two important director distributions--splay-bend and twist. Splay-bend cantilevers have no anticlastic (double-bend, saddle) response in the isotropic case or for some values of the anisotropic modulus tensor. Twist cantilevers have maximal anticlasticity in the isotropic case which we show to be weakly modified by anisotropy of elastic moduli.

On the calibration of rectangular atomic force microscope cantilevers modified by particle attachment and lamination

A simple but effective method for estimating the spring constant of commercially available atomic force microscope (AFM) cantilevers is presented, based on estimating the cantilever thickness from knowledge of its length, width, resonant frequency and the presence or absence of an added mass, such as a colloid probe at the cantilever apex, or a thin film of deposited material. The spring constant of the cantilever can then be estimated using standard equations for cantilever beams. The results are compared to spring constant calibration measurements performed using reference cantilevers. Additionally, the effect of the deposition of Cr and Ti thin films onto rectangular Si cantilevers is investigated.

ANN Modeling for the Drop Impact Dynamics of Mobile Hard Disk

In view of complexity internal structure of mobile hard disk and according to the principle of quality equivalent, a finite element model of mobile hard disk was established. Finite element simulation with dropping impact of mobile hard disk was made based on uniform design. A neural network model of nonlinear mapping relations was established between shell thickness，actuator arm thickness, cantilever thickness and pivot bearings stiffness of mobile hard disk with shell stress，disk interface stress and space with head and disk. The difference is less of the prediction values with the ANN(artificial neutral network) and the simulation datum with the FEM(finite element method). This indicates that the method is effective and may provide theory evidence for optimization crashworthiness design.