Effects of temperature and pressure on microcantilever resonance response

The variation in resonance response of microcantilevers was investigated as a function of pressure (10(-2)-10(6)Pa) and temperature (290-390K) in atmospheres of helium (He) and dry nitrogen (N(2)). Our results for a silicon cantilever under vacuum show that the frequency varies in direct proportion to the temperature. The linear response is explained by the decrease in Young's modulus with increasing the temperature. However, when the cantilever is bimaterial, the response is nonlinear due to differential thermal expansion. Resonance response as a function of pressure shows three different regions, which correspond to molecular flow regime, transition regime, and viscous regime. The deflection in flow transition regime resulting from thermal variation has minimal effect on frequency. The frequency variation of the cantilever is caused mainly by changes in the mean free path of gas molecules.     

纳米硬度计研究多晶硅微悬臂梁的弹性模量

利用纳米硬度计通过微悬臂梁的弯曲试验来测量其力学特性是一种简便而有效的方法,具有很高的载荷分辨率,可精确测量微悬臂梁纳米级弯曲形变。运用该方法在研究微悬臂梁的弯曲形变过程中,必须考虑压头在微悬臂梁上的压入以及微悬臂沿宽度方向的挠曲。微悬臂梁采用普通的集成电路工艺(IC)制造。试验研究表明,多晶硅微悬臂梁的纯挠曲与载荷成很好的线性关系,呈现弹性变形,通过该线性关系可计算得到梁的弹性模量。测得的多晶硅微悬臂梁的弹性模量为156±(2.9%-6.3%)GPa。     

A femtogram resolution mass sensor platform, based on SOI electrostatically driven resonant cantilever. Part I: electromechanical model and parameter extraction

A microcantilever based platform for mass detection in the femtogram range has been integrated in the doped top silicon layer of a SOI substrate. The on-plane fundamental resonance mode of the cantilever is excited electrostatically and detected capacitively by means of two parallel placed electrodes in a two port configuration. An electromechanical model of the cantilever-electrodes transducer and its implementation in a SPICE environment are presented. The model takes into account non-linearities from variable cantilever-electrode gap, fringing field contributions and real deflection shape of the cantilever for the calculation of the driving electrostatic force. A fitting of the model to the measured S(21) transmitted power frequency response is performed to extract the characteristic sensor parameters as Young modulus, Q factor, electrical parasitics and mass responsivity.     

Deconvolution of damping forces with a nonlinear microresonator

We report a fully electrical microcantilever device that utilizes capacitance for both actuation and detection and show that it can characterize various gases with a bare silicon microcantilever. We find the motion of the cantilever as it rings down when the oscillating force is removed, by measuring the voltage induced by the oscillating capacitance in the microcantilever∕counterelectrode system. The ringdown waveform was analyzed using an iterative numerical algorithm to calculate the oscillator motion, modeling the cantilever∕electrode capacitance to calculate the electrostatic force. We find that nonlinearity in the motion of the cantilever is not necessarily a disadvantage. After calibration, we simultaneously measure viscosity and density of several gaseous mixtures, yielding viscosities within ±2% and densities within ±6% of NIST values.     

Microthermogravimetry using a microcantilever hot plate with integrated temperature-compensated piezoresistive strain sensors

This paper reports thermogravimetric analysis of nanogram samples of paraffin using a microcantilever hot plate. The microcantilever hot plate has an integrated temperature-controlled heater and integrated temperature-compensated strain-sensing piezoresistors. The microcantilever vibration amplitude was measured using either a laser and a position sensitive photodiode, or using the piezoresistors. The cantilever resonance was measured as the cantilever was heated, such that the analyte mass could be measured as a function of temperature. Both optical and piezoresistive methods were employed to generate thermogravimetric curves for analytes in the range of 1-3 ng, and the results of the two methods compared well.     

Energy dissipation and frequency shift of a damped dynamic force microscopy

The closed-form solution of the transient response of damped dynamic force microscopy subjected to the nonlinear interatomic force is derived. The frequency shift and the decay rate of a V-typed probe can be determined easily and precisely by the proposed method. If the taper ratio is zero, a uniform cantilever is obtained. Moreover, the transient response of a non-uniform cantilever can be determined also in the same way. The complex Young's modulus is used to describe the viscoelastic material property. In the modulus, the loss factor is introduced. The relation between the Q-factor and the loss factor is discussed. Moreover, the relation between the energy dissipation and the frequency shift is revealed. Finally, the effects of several parameters on the Q-factor, the frequency shift and the decay rate are investigated. The proposed method can be easily applied to investigate the tapping mode of AFM.     

硅微构件的弹性模量和残余内应力的测试

叙述了利用硅悬臂梁和两端固定梁微构件进行硅微薄膜材料的弹性模量和残余内应力的测试方法。本方法利用简单的光学装置,通过测量悬臂梁和两端固定梁的一阶谐振频率,分别求弹性模量和残余内应力。本方法测量系统简单,试样制作方便。本试验获得（100）面<110>方向单晶硅微薄膜的弹性模量为128GPa,残余内应力为74.7MPa.     

Micromechanical sensor for studying heats of surface reactions, adsorption, and cluster deposition processes

We present a newly designed highly sensitive micromechanical sensor devoted to thermodynamic studies involving supported clusters. The thermally sensitive element of the sensor consists of a micromachined silicon cantilever array, onto which a thin metal film is evaporated. Due to the difference between the thermal expansion coefficients of silicon and the metal employed, thermal bending is observed when heat is exchanged with the cantilever. The sensitivity and the response time of the cantilever are studied as a function of the film material (gold or aluminum) and the thickness of the metal film. With our routinely prepared cantilevers, a minimum power of 120 nW is measurable with a submillisecond response time, corresponding to a limit of detection in the femtojoule range. The high sensitivity of the sensor is demonstrated by measuring the heat exchange which occurs during the deposition of clusters on the cantilever. Experimentally, we illustrate the 1,3-butadiene hydrogenation reaction using a cluster model catalysts created by soft-landing palladium clusters onto the cantilever surface.     

3D mechanical measurements with an atomic force microscope on 1D structures

We have developed a simple method to characterize the mechanical properties of three dimensional nanostructures, such as nanorods standing up from a substrate. With an atomic force microscope the cantilever probe is used to deflect a horizontally aligned nanorod at different positions along the nanorod, using the apex of the cantilever itself rather than the tip normally used for probing surfaces. This enables accurate determination of nanostructures' spring constant. From these measurements, Young's modulus is found on many individual nanorods with different geometrical and material structures in a short time. Based on this method Young's modulus of carbon nanofibers and epitaxial grown III-V nanowires has been determined.     

Microfabricated silicon dioxide cantilever with subwavelength aperture

We have developed a microfabricated SiO₂ cantilever with subwavelength aperture for scanning near-field optical microscopy (SNOM), to overcome the disadvantages of conventional optical fibre probes such as low reproducibility and low optical throughput. The microcantilever, which has a SiO₂ cantilever and an aperture tip near the end of the cantilever, is fabricated in a reproducible batch process. The circular aperture with a diameter of 100–150 nm is formed by a focused ion-beam technique. Incident light is directly focused on the aperture from the rear side of the cantilever using a focusing objective, and high optical throughput (10⁻² to 10⁻³) is obtained. The microcantilever can be operated as a SNOM probe in contact mode or in dynamic mode.     

多晶硅微机械抗粘附结构参数设计

讨论了在大气环境或有液体的环境下，表面张力对微加工悬臂梁结构粘附的影响，以及真空条件下Casimir量子力对微机械薄膜微腔结构的稳定性和粘附的影响。建立了Casimir量子力作用下粘附问题的实际粗糙模型理论。对不同表面力作用下的抗粘附结构研究结果表明，微悬臂梁和薄膜微腔结构的稳定性和粘附与材料的弹性特性，材料的表面特性、结构的长度、厚度以及构件与基本之间的间隙有关，而与结构的宽度无关。给出了抗粘附结构参数设计的对数坐标图。     

Analytical and experimental study of mismatch strain-induced microcantilever behavior during deposition

A model of mechanical behavior of microcantilever due to mismatch strain during deposition of MEMS structures is analytically derived and experimentally verified. First, a microcantilever, modeled as an Euler-Bernoulli beam, is subjected to deposition of another material and a linear ordinary differential equation which considers the throughthickness variation of the mismatch strain is derived. Second, the deposition analysis is experimentally verified by electroplating of nickel onto an AFM cantilever beam. The deflection of the AFM cantilever is measured in-situ as a function of the deposited thin film thickness through the optical method of Atomic Force Microscopy and the mismatch strain with the through-thickness variation is determined from the experiment results. The usefulness of these equations is that they are indicative of the real time behavior of the structures, i.e. it predicts the deflection of the beam continuously during deposition process.     

Wide frequency range capacitive detection of loss in a metallic cantilever using resonance and relaxation modes

The impedance of a capacitor which embraces a charged cantilever is used to measure the mechanical properties of the cantilever material. The technique has been tested with an amorphous metallic specimen, but is applicable for many other solids. The material damping can be measured at the resonance frequency of the cantilever via the width of the resonance curve or by recording the ring-down behavior. Additionally, several decades in frequency are accessible below the resonance frequency, where values as low as nu=0.03 Hz are achieved easily. The data are analyzed with a single equation that captures the damping at all frequencies in terms of the material specific Young's modulus E and its loss angle tan delta=E"/E'.     

Micromechanical measurement of active sites on silicon nitride using surface free energy variation

We have investigated chemical reactions between adsorbed water and active sites on a silicon nitride surface as a function of temperature and relative humidity using microcantilevers. Effects that might produce a change in the response of the microcantilever, such as a mass adsorption, surface tension of the adsorbed water, and changes in thermal conductivity, were systematically investigated. It is shown that the judicious choice of experimental conditions could make these effects essentially inconsequential in comparison with the instrument response produced by the change in free surface energy of the microcantilever due to the chemical reactions. Using this method, the variation in free surface energy when changing from dry to high humidity conditions was found and the number of active sites that reacted was estimated. This method may be extended to other problems for use in determining surface free energy change and thus the density of reactant sites under different conditions of interest.     

Effective mass and flow patterns of fluids surrounding microcantilevers

An analytical approach to determine the streamlines of fluid flow adjacent to the surfaces of vibrating cantilevers is presented. Fluid flow over the top and bottom surfaces of a microcantilever is established by solving two-dimensional Navier-Stokes equations for viscous flow. The x and y velocity components are used to establish streamlines for absolute fluid motion. These streamlines show a central stagnation core perpendicular and central to the cantilever surface extending along the full length of cantilevers, which most likely accounts for the added mass effect (induced mass) of fluid media around vibrating microcantilevers.     

薄膜的力学测试技术

对薄膜力学性能的测试方法、技术以及所取得的主要成果进行简要的综合介绍。     

An embedded polymer piezoresistive microcantilever sensor

We have developed a new type of chemical microsensor based on piezoresistive microcantilever technology. In this embedded polymer microsensor, a piezoresistive microcantilever is partially "embedded" into a polymeric material. Swelling of the polymer upon analyte exposure is measured as a simple resistance change in the embedded cantilever. Arrays of these sensors, each employing a different polymeric material, provide for the identification of a wide range of chemical vapor analytes. Advantages of this system over previous "surface" piezoresistive microcantilever chemical sensors include enhanced mechanical simplicity (no mechanical approach necessary), greater resistance to shock or movement, and lower cost.     

A bi-material microcantilever temperature sensor based on optical readout

As one of the simplest MEMS sensors, microcantilever can sense temperature faster and more sensitively than traditional thermometers as its small size and low thermal mass. In this paper, an Au/SiNx bi-material microcantilever temperature sensor based on optical readout is presented. The deflection of the cantilever varies with the change of temperature due to the differences in thermal expansion coefficients between gold and silicon nitride. Then, the temperature could be accurately measured by detecting the deflection of the cantilever with optical lever method. By experiments, the theoretical model is verified and the temperature characteristics of the sensor are also determined. With a commercial microcantilever, the temperature resolution of the sensor is tested to be 0.02 K when 25 mm length of optical arm set. By optimizing the microcantilever parameters, the temperature resolution of the sensor could be 0.1 mK. High sensitivity makes it suitable for some special precise temperature measurements.     

范德华力对硅基微悬臂梁抗粘附稳定性的影响

通过在硅微悬臂梁与基底表面上涂覆低表面能的憎水性OTS(CH3(CH2)17SiCl3)膜,以除去接触面间的表面张力;把梁与基底均接地,以除去接触面间的静电力,研究仅有范德华力作用时,硅微悬臂梁结构的抗粘附稳定性.根据两接触面均为粗糙表面的微观实际接触模型,在接触表面产生塑性变形的情况下,计算范德华粘附能大小,并分析表面形貌对其影响,得到粗糙表面接触的微梁抗粘附临界长度.     

A novel method of temperature compensation for piezoresistive microcantilever-based sensors

Microcantilever with integrated piezoresistor has been applied to in situ surface stress measurement in the field of biochemical sensors. It is well known that piezoresistive cantilever-based sensors are sensitive to ambient temperature changing due to highly temperature-dependent piezoresistive effect and mismatch in thermal expansion of composite materials. This paper proposes a novel method of temperature drift compensation for microcantilever-based sensors with a piezoresistive full Wheatstone bridge integrated at the clamped ends by subtracting the amplified output voltage of the reference cantilever from the output voltage of the sensing cantilever through a simple temperature compensating circuit. Experiments show that the temperature drift of microcantilever sensors can be significantly reduced by the method.