Quantum size aspects of the piezoresistive effect in ultra thin piezoresistors

Proximal probe sensors with an ability to detect extremely small forces (10(-15)-10(-18)N) play significant role in scanning probe microscopy applications. The detection of extremely low forces, require producing micromachined cantilevers with as small as possible spring constants, which is considered by the optimization of the sensor design. In the last year many papers describing the fabrication process of producing ultrathin cantilevers (below 100nm) with integrated piezoresistors for deflection read-out have been published. In the case of such cantilevers the required thickness of piezoresistors is in the range of 50nm. From a quantum mechanical point of view, an electrical carrier transport confinement in direction perpendicular to the cantilever surface can be expected and in this manner we have to consider the quantum size effect.The goal of the project described in this paper is to calculate and determine the piezoresistive coefficients in p type Si thin (under 50nm) piezoresistors taking into account the quantum size effect and to compare them with the corresponding coefficients for bulk material. The calculation of the band structure will use the mathematical apparatus of an exact analytical diagonalization six-band k.p model, modified with the envelope function approximation.The behaviour of the thin piezoresistors employed as integrated deflection read-out will be also discussed. Moreover, critical issues in the realization of piezoresistors formed by MOS transistor channel will be presented.     

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.     

Monitoring the chemical changes in Pd induced by hydrogen absorption using microcantilevers

The reactivity of the palladium shaped as a microcantilever is investigated as a function of the hydrogen stoichiometry. A small cell holding the microcantilever is designed to monitor the deflection and the flexural resonance response from high vacuum to a hydrogen gas pressure of several bars. The measurements show that the Young's modulus is accurate if the cantilever is thick enough to be described by a continuum mechanics approach. The orientation distribution function of the palladium grains determined by X-ray diffraction enables to correlate Young's modulus measured using microcantilevers with the elastic constant tensor issued from the literature. The surface stress induced by the dissociation of H(2) in palladium surface depends mainly on the cantilever cross-section. Cantilever response was found to be extremely sensitive to both the palladium lattice expansion induced by the insertion of hydrogen atoms into octahedral sites of palladium and the electronic affinity between palladium and hydrogen.     

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.     

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.     

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.     

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.     

Improving tapping mode atomic force microscopy with piezoelectric cantilevers

This article summarizes improvements to the speed, simplicity and versatility of tapping mode atomic force microscopy (AFM). Improvements are enabled by a piezoelectric microcantilever with a sharp silicon tip and a thin, low-stress zinc oxide (ZnO) film to both actuate and sense deflection. First, we demonstrate self-sensing tapping mode without laser detection. Similar previous work has been limited by unoptimized probe tips, cantilever thicknesses, and stress in the piezoelectric films. Tests indicate self-sensing amplitude resolution is as good or better than optical detection, with double the sensitivity, using the same type of cantilever. Second, we demonstrate self-oscillating tapping mode AFM. The cantilever's integrated piezoelectric film serves as the frequency-determining component of an oscillator circuit. The circuit oscillates the cantilever near its resonant frequency by applying positive feedback to the film. We present images and force-distance curves using both self-sensing and self-oscillating techniques. Finally, high-speed tapping mode imaging in liquid, where electric components of the cantilever require insulation, is demonstrated. Three cantilever coating schemes are tested. The insulated microactuator is used to simultaneously vibrate and actuate the cantilever over topographical features. Preliminary images in water and saline are presented, including one taken at 75.5 μm/s—a threefold improvement in bandwidth versus conventional piezotube actuators.     

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.     

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.     

基于微悬臂梁的传感技术研究

本文对基于微悬臂梁的传感技术从四方面展开讨论,分别介绍了微悬臂梁的制造工艺,修饰技术,激励、检测和控制技术,以及与其它电路的工艺集成技术。微悬臂梁在液体中,工作在动态模式时,品质因数的提高问题一直是国内外研究的焦点。本文的重点便是介绍国际上最新出现的两种品质因子控制技术,一种是对微悬臂梁的材料进行了改进,使其在水溶液的品质因数达到40,另一种是把液体环境转移到悬臂梁内部,使其在水溶液中的品质因数达到700。     

曲面过载保护的新型高g值冲击硅微机械加速度传感器的设计

给出一种测量高g值冲击加速度的硅微机械加速度传感器的结构和动力学模型，此传感器为整体式悬臂梁结构，采用硅微机械加工技术制作，便于封装和大批量低成本制造，其敏感方向在硅片平面内，两个压敏电阻分布在悬臂梁的顶端，两个完全相同的悬壁梁沿相反方向分布，四个压敏电阻构成惠斯通全桥连接，悬臂梁的过载保护采用上下两个曲面，一方面有效地提高悬壁梁的过载保护能力，另一方面调节加速度传感器的压膜阻尼，使之接近临界阻尼，有效抑制自由振动模态，提高测量精度。     

Resonance-mode effect on microcantilever mass-sensing performance in air

This research investigates the air drag damping effect of the micromachined cantilevers in different resonance modes on the quality factor, which are operated in ambient air. Based on a simplified dish-string model for air drag force acting on the resonant cantilever, the air drag damping properties of the cantilevers vibrating in different modes are analyzed with theoretic vibration mechanics, which is complemented and further confirmed with finite-element simulation. Four kinds of integrated cantilevers, which resonate in the first flexural mode, the second flexural mode, the first torsional mode, and the second torsional mode, respectively, are designed and fabricated by using micromachining techniques. Finally, biomolecular sensing experiments are carried out to verify the theoretical results obtained before. From both the modeling and experimental results, it can be seen that damping characteristics of the torsional cantilever resonators are generally better than that of the flexural ones, and quality factor of the cantilever resonator in a higher-frequency mode is always superior to that in a lower-frequency one. Among the four kinds of microcantilever resonators operated in our experiments, the one operated in the second flexural modes exhibits the highest Q factor and the best biomass sensing performance.     

Uncooled IR imaging using optomechanical detectors

In this study, we present an uncooled infrared imaging detector using knife-edge filter optical readout method. The tilt angle change of each cantilever in a focal plane array (FPA) can be simultaneously detected with a resolution of 10(-5) degrees. A deformation magnifying substrate-free microcantilever unit is specially designed. The multi-fold legs of microcantilever are interval metal coated to form a thermal deformation magnifying structure. Thermal and thermomechanical performance of this microcantilever unit are modeled and analyzed. An FPA with 100 x 100 pixels is fabricated and thermal images of human body are obtained by this detector.     

Manipulation of microcantilever oscillations

Experimental observation of self-sustaining oscillations via a delayed feedback system is presented for a rectangular silicon microcantilever. The system is modeled as one and two-dimensional damped oscillator and the resulting delay differential equations are studied in frequency and time domain. The shortcomings of each model are outlined, and an improved formulation of the dynamics of the cantilever is presented.     

IR imaging using uncooled microcantilever detectors

Uncooled bimaterial microcantilever detectors were fabricated and used to obtain infrared (IR) images of objects at temperatures ranging from room temperature to a few hundred degrees C. Images were obtained using both single 50 micro m x 50 micro m microcantilever IR detectors and arrays of microcantilever detectors. Thermal radiation from the target object was imaged onto the detector and the resulting temperature change caused microcantilever bending due to the bimaterial effect. This micromechanical bending was measured using two different non-contact optical readout techniques and IR images were obtained. A smaller size (20 micro m x 20 micro m) microcantilever IR detector was also used to capture IR images of near room temperature objects.     

基于特征模型的压电悬臂板振动控制

航天器上悬臂板型挠性附件在扰动作用下将引起包括弯曲和扭转模态的振动,这将影响系统的稳定性和控制精度,尤其是在平衡点附近低频模态频率上的小幅值残余振动很难快速抑制。为了快速抑制压电智能挠性悬臂板系统,包括弯曲和扭转模态的振动,提出采用基于特征模型的非线性黄金分割自适应控制,组合非线性切换逻辑积分阻尼器算法。首先,优化配置压电传感器和驱动器实现了悬臂板的弯曲和扭转模态在检测和驱动上的解耦;其次,设计并建立压电挠性悬臂板试验平台,进行试验模态辨识并获得了悬臂板系统弯曲和扭转振动的模态频率和频响特性;最后,进行压电智能悬臂板的弯曲和扭转振动模态主动振动几种方法试验的比较研究。试验结果表明,采用的控制方法能够快速地抑制压电智能挠性悬臂板的振动。     

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.     

Motion video image processing (MVIP) method for measuring microfluidic–structure interactions

In microsystem applications, many microstructures are submerged in fluid and their performances are directly influenced by the microfluidic–structure interactions. Characterizations of such interactions in microfluidic devices such as micropumps, microvalves, micro-viscometers, and biomedical related microfluidic chips, are essential to seek enhanced designs and design guidance. In this study, a hybrid microfluidic test chip with integrated microcantilever is fabricated on a polymer platform using soft lithography method for characterization of microcantilever–fluid interactions. A measurement technique based on the motion video image capture and processing (MVIP) is developed to measure the static and dynamic deflections of the microcantilever subjected to forces due to fluid within the microchannel. A peristaltic pump was used to generate fluid flows across the channel, which caused a pressure differential loading of the microstructure. The images of motion were processed to characterize the motion in terms of deflection, velocity and acceleration of the structure under different flow conditions. The validity of the proposed MIP method is illustrated through comparisons with finite element model of the microcantilever. The images acquired from the proposed MVIP method were further analyzed to estimate deflection mode shapes and natural frequencies of the microcantilever under fluid interactions.     

Shape effects of micromechanical cantilever sensor

Microcantilever has been increasingly used as microsensor thanks to its fast response, low cost and parallel implementation in large quantity. The principle of sensing lies in the positive correlation between the resonant frequency of microcantilever and the target mass loading. The shape of cantilever determines the resonant frequency. Therefore it plays a vital role in microsensing. In the present study three basic geometric shapes (rectangle, triangle and half-ellipse) with innovative inner cut are investigated. The micro-cantilever beams are cut to external aspect ratios of 0.5, 1, and 2, and inner cut at aspect ratios of 0, 0.5, 1, and 2, with equal sensing area. Both numerical and experimental analysis indicates that the low-aspect-ratio cantilever with high-aspect-ratio inner cut achieved high sensitivity. The half-ellipse being the highest followed by the rectangle. The results are useful for optimal shape design of a micromechanical cantilever sensor.