Quality factor of micro cantilevers transduced by piezoelectric lead zirconate titanate film

The quality factors (Q-factor) of micro cantilevers transduced by piezoelectric lead zirconate titanate (PZT) film under atmospheric pressure conditions were investigated and discussed. It was found that Q-factors increased with thicker PZT film. Due to air damping, shorter cantilevers resulted in preferred larger Q-factors. The Q-factor was found to be as high as 450 for a 150-μm long PZT cantilever when using 1.04-μm thick PZT film as the electromechanical conversion medium. Differences in the measured Q-factors when using integrated PZT film self-excitation and external PZT vibrator actuation indicate that energy dissipation induced by the electromechanical coupling in PZT thin films was noteworthy even under atmospheric pressure conditions. Moreover, the mechanical properties of the PZT film were found contribute significantly to decreases of the Q-factor.     

Polymer-based cantilevers with integrated electrodes

An innovative release method of polymer cantilevers with embedded integrated metal electrodes is presented. The fabrication is based on the lithographic patterning of the electrode layout on a wafer surface, covered by two layers of SU-8 polymer: a 10-/spl mu/m-thick photo-structured layer for the cantilever, and a 200-/spl mu/m-thick layer for the chip body. The releasing method is based on dry etching of a 2-/spl mu/m-thick sacrificial polysilicon layer. Devices with complex electrode layout embedded in free-standing 500-/spl mu/m-long and 100-/spl mu/m-wide SU-8 cantilever were fabricated and tested. We have optimized major fabrication steps such as the optimization of the SU-8 chip geometry for reduced residual stress and for enhanced underetching, and by defining multiple metal layers [titanium (Ti), aluminum (Al), bismuth (Bi)] for improved adhesion between metallic electrodes and polymer. The process was validated for a miniature 2/spl times/2 /spl mu/m/sup 2/ Hall-sensor integrated at the apex of a polymer microcantilever for scanning magnetic field sensing. The cantilever has a spring constant of /spl cong/1 N/m and a resonance frequency of /spl cong/17 kHz. Galvanometric characterization of the Hall sensor showed an input/output resistance of 200/spl Omega/, a device sensitivity of 0.05 V/AT and a minimum detectable magnetic flux density of 9 /spl mu/T/Hz/sup 1/2/ at frequencies above 1 kHz at room temperature. Quantitative magnetic field measurements of a microcoil were performed. The generic method allows for a stable integration of electrodes into polymers MEMS and it can readily be used for other types of microsensors where conducting metal electrodes are integrated in cantilevers for advanced scanning probe sensing applications.     

Air-bearing sliders and plane-plane-concave tips for atomic forcemicroscope cantilevers

This paper explores strategies for fabricating and maintaining a sharp atomic force microscope (AFM) tip suitable for AFM data storage applications. To this end, AFM cantilevers have been incorporated into micromachined sled carriers and air-bearing sliders. These supports act to limit the maximum loading force on the AFM tip and allow for improved vibration immunity for the AFM cantilever in comparison to macroscopic loading schemes. Readback from a patterned rotating disk has been demonstrated using these devices. Silicon-carbide AFM cantilevers with diamond tips have been fabricated in a process compatible with that of the sleds and sliders. Molded silicon-nitride tips defined by the intersection of three surfaces have also been fabricated for AFM cantilevers. The molds for plane-plane-concave tips are defined by two silicon {111} planes and a silicon-dioxide curved surface. By geometry, the three surfaces necessarily have a unique intersection point, which may improve the consistency in sharpness of these tips relative to conventional pyramidal tips     

Theoretical analysis of the sensing and actuating effects of piezoelectric multimorph cantilevers

The paper presents the modeling of two types of piezoelectric microcantilevers, the two-layer and two-segment piezoelectric cantilevers, in which the two piezoelectric parts perform sensor and actuator functions, respectively. An analytic model is proposed to evaluate the sensing and actuating effects of multiporph microcantilevers formed of several layers or segments of piezoelectric materials. The analytical model is used to analyze the tip deflection of the cantilever and the piezoelectric charge generated on the sensor element as a function of the microcantilever geometry. The cantilevers of sensing and actuation are compared for the different working situations of the two-layer and two-segment cantilevers. The theoretical results can be used to optimize the design of the piezoelectric cantilever structures.     

Silicon cantilevers with piezo-resistive measuring bridge for tactile line measurement

In this article a variety of applications of a microelectromechanical system (MEMS) including a cantilever with an integrated piezo-resistive bridge is described. With the low-noise integrated piezo-resistive bridge a resolution in the nanometer range is possible. This sensor obtains a typical resolution in the vertical displacement of 2 nm (due to noise floor Δf = 1.6 kHz). Due to the low spring constant of D = 1 to 10 N/m, measurements with contact forces of <100 μN can be realized. This allows a non-destructive examination of polymer structures. Furthermore, the sensor is characterized by a high eigenfrequency (>2.7 kHz), a slight mass (≈0.1 mg) and a measuring velocity of up to 10 mm/s. The important applications of the MEMS cantilever are fast inline control of building panels, measurement of optical structures, inside measurement of fuel injection nozzle micro holes. Furthermore, it is possible to provide different tip geometries (e.g. cone or ball) at the end of the cantilever for an ideal surface measurement.     

Silicon nitride cantilevers with oxidation-sharpened silicon tips for atomic force microscopy

High-resolution atomic force microscopy (AFM) of soft or fragile samples requires a cantilever with a low spring constant and a sharp tip. We have developed a novel process for making such cantilevers from silicon nitride with oxidation-sharpened silicon tips. First, we made and sharpened silicon tips on a silicon wafer. Next, we deposited a thin film of silicon nitride over the tips and etched it to define nitride cantilevers and to remove it from the tips so that they protruded through the cantilevers. Finally, we etched from the back side to release the cantilevers by removing the silicon substrate. We characterized the resulting cantilevers by imaging them with a scanning electron microscope, by measuring their thermal noise spectra, and by using them to image a test sample in contact mode. A representative cantilever had a spring constant of /spl sim/0.06 N/m, and the tip had a radius of 9.2 nm and a cone angle of 36/spl deg/ over 3 /spl mu/m of tip length. These cantilevers are capable of higher resolution imaging than commercially available nitride cantilevers with oxidation-sharpened nitride tips, and they are especially useful for imaging large vertical features.     

1/f noise considerations for the design and process optimization ofpiezoresistive cantilevers

Piezoresistive cantilevers are limited by two major noise sources: Johnson noise, which is independent of frequency, and conductance fluctuation noise, which has a 1/f spectrum. The 1/f fluctuations of piezoresistive cantilevers are shown to vary inversely with the total number of carriers in the piezoresistor, as formulated by Hooge in 1969. Therefore, while 1/f noise is reduced for large heavily doped cantilevers, sensitivity considerations favor thin lightly doped cantilevers. Balancing these conflicting constraints produces optima for many design and processing parameters. For a cantilever with specified spring constant and bandwidth requirements, optima are identified for the beam thickness and length, and it is shown that the legs should be between 1/3 and 2/3 of the total length with a doping depth that is 1/3 of the beam thickness. Additionally, an optimal doping concentration is identified as a function of the cantilever volume and the measurement bandwidth. Annealing reduces 1/f noise, but causes a loss in sensitivity due to dopant diffusion, and an optimal anneal is computed with a typical diffusion length 10^-8 cm. The analysis, methods, and some of the conclusions of this paper are also applicable to other types of piezoresistive sensors     

Systematic generation of nonlinear discretized dynamic equilibrium equations of spinning cantilevers

The Rayleigh-Ritz procedure, in conjunction with any admissible trial solution in terms of undetermined functions of time and known yet unspecified coordinate functions of space, is systematized to obtain the coefficient matrices of the second order nonlinear ordinary differential equations of dynamic equilibrium of a spinning cantilever with initial geometric imperfections. In the functional second order nonlinear strain-displacement and velocity-displacement relationships are used, and the material is assumed linearly elastic. Systematic forms for the discretized energy density expressions are provided. The fact that the coordinate functions are represented parametrically serves to unify the discretization approaches. The choice of the coordinate functions includes both sets of continuous and piecewise continuous functions employed in the conventional Rayleigh-Ritz method and the finite element method, respectively. A computer program for the systematic generation of the coefficient matrices involved in the governing equations is described. The degree of the nonlinearity, the type and number of the coordinate functions, the ordering of the vetor representing the complete list of the undetermined functions of time, the imperfection functions, and the time independent forcing functions are taken as parameters of the program for the complete simulation.     

Microfabrication of oxidation-sharpened silicon tips on siliconnitride cantilevers for atomic force microscopy

We have developed a novel process for the microfabrication of atomic force microscope (AFM) cantilevered tips from silicon-on-insulator (SOI) wafers. The tip and cantilever are made of crystalline silicon and low-stress silicon nitride, respectively. This choice of materials allows us to sharpen the tips by oxidation sharpening without affecting the cantilever. We evaluated their performance in contact mode during imaging of artificial nanostructures and compared them to commercially available ones. The images acquired with our tips feature superior resolution on those samples     

Out-of-plane deformation and pull-in voltage of cantilevers with residual stress gradient: experiment and modelling

The out-of-plane deformation and the pull-in voltage of electrostatically actuated cantilevers with a residual stress gradient, is investigated in the length range 100–300 µm. Measured pull-in voltages are compared with calculations, which are obtained using previously proposed analytical expressions and a finite element method (FEM) modelling. In particular, a simplified model of the residual stress distribution inside cantilevers is formulated that enables FEM simulation of measured out-of-plane deformations and pull-in voltages for all lengths of fabricated cantilevers. The presented experimental results and FEM model are exploitable in the design of cantilever-based microelectromechanical systems, in order to provide a reliable prediction of the influence of residual stress gradient on device shape and pull-in voltage.

     

6-MHz 2-N/m piezoresistive atomic-force microscope cantilevers withINCISIVE tips

Piezoresistive atomic force-microscope (AFM) cantilevers with lengths of 10 μm, displacement sensitivities of (ΔR/R)/A 1.1×10^-5, displacement resolutions of 2×10^-3 A/√Hz, mechanical response times of less than 90 ns, and stiffnesses of 2 N/m have been fabricated from a silicon-on-insulator (SOI) wafer using a novel frontside-only release process. To reduce mass, the cantilevers utilize novel inplane crystallographically defined silicon variable aspect-ratio (INCISIVE) tips with radius of curvature of 40 A. The cantilevers have been used in an experimental AFM data-storage system to read back data with an areal density of 10 Gb/cm ². Four-legged cantilevers with both imaging and thermomechanical surface modification capabilities have been used to write 2-Gb/cm² data at 50 kb/s on a spinning polycarbonate sample and to subsequently read the data. AFM imaging has been successfully demonstrated with the cantilevers. Some cantilever designs have sufficient displacement resolution to detect their own mechanical-thermal noise in air. The INCISIVE tips also have applications to other types of sensors     

Michell cantilevers constructed within trapezoidal domains—Part III: force fields

This paper complements the analysis of geometric properties of the Hencky nets within the Michell cantilevers constructed in the trapezoidal domains by providing the analytical formulae for the force fields. The force field analysis introduces a new division of the cantilever domain and enables an alternative method for computing the optimal weights.     

A microvalve for lab-on-a-chip applications based on electrochemically actuated SU8 cantilevers

Increasing the complexity and functionality of Lab-on-a-Chip devices requires integrated valves for internal flow regulation. The device introduced in this work is an electrochemical SU8 microvalve, featuring a cantilevered structure that seals an adjacent channel under the action of a growing electrolysis bubble. The valve is based on previously reported movable microcantilevers embedded in microchannels. As opposed to membrane valves moving perpendicular to the substrate, the cantilever valve is patterned next to the channel and closes it by moving horizontally, dramatically reducing footprint. Its compact, monolithic and 2D construction reduces assembly problems and results in negligible increase in dead volume (14.5 nl). Besides, its location in the way of the channels avoids the need for auxiliary filling ports or separate working media for actuation. Effective sealing with negligible leakage at 20 kPa has been achieved. The valve also displays passive flow regulation induced by the pressure differential generated across the valve chamber under flow conditions (42-72% flow decrease).     

Low-stiffness silicon cantilevers with integrated heaters andpiezoresistive sensors for high-density AFM thermomechanical datastorage

Single-crystal silicon cantilevers 1 μm thick have been demonstrated for use in high-density atomic-force microscopy (AFM) thermomechanical data storage. Cantilevers with integrated piezoresistive sensors were fabricated with measured sensitivities ΔR/R up to 7.5×10^-7 per Å in close agreement with theoretical predictions. Separate cantilevers with integrated resistive heaters were fabricated using the same basic process. Electrical and thermal measurements on these heating devices produced results consistent with ANSYS simulations. Geometric variants of the cantilever were also tested in order to study the dependence of the thermal time constant on device parameters. Depending on the design, time constants as low as 1 μs were achieved. A thermodynamic model was developed based on the cantilevers geometry and material properties, and the model was shown to predict device behavior accurately. A comprehensive understanding of cantilever functionality enabled us to optimize the cantilever for high-speed thermomechanical recording     

Design and optimization of parylene nanomechanical cantilevers with integrated piezoresistors for surface-stress based biochemical sensing

The sensitivity of surface-stress based cantilever sensor can be significantly increased by using polymer as the cantilever material. In our previous research, parylene nanomechanical cantilevers with integrated poly-crystal silicon piezoresistors have already been developed for biochemical applications. However, parylene cantilevers exhibit different behaviors compared with their more rigid counterparts. In this paper, a new analytical model has been developed and verified using finite element simulations. The design optimization has also been discussed based on the new analytical model, resulting in several useful design guidelines that are unique to parylene or more generally to polymer cantilevers with integrated poly-crystal or single-crystal silicon piezoresistors for surface stress sensing.     

Narrow-band filtering by means of triangular meta-material resonators based on RF MEMS cantilevers in CPW configuration

Microsystem Technologies - Triangular resonators, designed by using Radio Frequency Micro Electro Mechanical Systems (RF MEMS) cantilevers in coplanar waveguide (CPW) configuration, have been...     

Direct comparison of stylus and resonant methods for determining Young's modulus of single and multilayer MEMS cantilevers

As microelectromechanical systems (MEMS) become more complex and is produced in even greater numbers it becomes increasingly important to have a full understanding of the mechanical properties of the commonly used MEMS materials. One of the most important properties for MEMS is the Young's modulus. This work describes the direct comparison of two methods often used for measuring the Young's modulus of thin film materials using micro-cantilever test structures: a load-deflection method and a resonant frequency method. The comparison was carried out for a range of materials, different cantilever geometries as well as for single and multilayer materials. It was found that both methods produce results that agree with each other and also agree with the values most often given in the literature.     

Michell cantilevers constructed within trapezoidal domains—Part I: geometry of Hencky nets

The present paper is the first part of the four-part work on Michell cantilevers transmitting a given point load to a given segment of a straight-line support, the feasible domain being a part of the half-plane contained between two fixed half-lines. The axial stress σ in the optimal cantilevers is assumed to be bounded by −σ _C ≤σ≤σ _T , where σ _C and σ _T represent the allowable compressive and tensile stresses, respectively. The work provides generalization of the results of the article of Lewiński et al. (Int J Mech Sci 36:375–398, 1994a) to the case of σ _T ≠σ _C . The present, first part of the work concerns the analytical formation of the Hencky nets or the lines of fibres filling up the interior of the optimal cantilevers corresponding to an arbitrary position of the point of application of the given concentrated force.