Dynamic thermomechanical response of bimaterial microcantilevers to periodic heating by infrared radiation

This paper investigates the dynamic thermomechanical response of bimaterial microcantilevers to periodic heating by an infrared laser operating at a wavelenegth of 10.35 μm. A model relates incident radiation, heat transfer, temperature distribution in the cantilever, and thermal expansion mismatch to find the cantilever displacement. Experiments were conducted on two custom-fabricated bimaterial cantilevers and two commercially available bimaterial microcantilevers. The cantilever response was measured as a function of the modulation frequency of the laser over the range of 0.01-30 kHz. The model and the method of cantilever displacement calibration can be applied for bimaterial cantilever with thick coating layer. The sensitivity and signal-to-noise of bimaterial cantilevers were evaluated in terms of either total incident power or incident flux. The custom-fabricated bimaterial cantilevers showed 9X or 190X sensitivity improvement compared to commercial cantilevers. The detection limit on incident flux is as small as 0.10 pW μm(-2) Hz(-1/2).     

Study of thermal and acoustic noise interferences in low stiffness atomic force microscope cantilevers and characterization of their dynamic properties

The atomic force microscope (AFM) is a powerful tool for the measurement of forces at the micro/nano scale when calibrated cantilevers are used. Besides many existing calibration techniques, the thermal calibration is one of the simplest and fastest methods for the dynamic characterization of an AFM cantilever. This method is efficient provided that the Brownian motion (thermal noise) is the most important source of excitation during the calibration process. Otherwise, the value of spring constant is underestimated. This paper investigates noise interference ranges in low stiffness AFM cantilevers taking into account thermal fluctuations and acoustic pressures as two main sources of noise. As a result, a preliminary knowledge about the conditions in which thermal fluctuations and acoustic pressures have closely the same effect on the AFM cantilever (noise interference) is provided with both theoretical and experimental arguments. Consequently, beyond the noise interference range, commercial low stiffness AFM cantilevers are calibrated in two ways: using the thermal noise (in a wide temperature range) and acoustic pressures generated by a loudspeaker. We then demonstrate that acoustic noises can also be used for an efficient characterization and calibration of low stiffness AFM cantilevers. The accuracy of the acoustic characterization is evaluated by comparison with results from the thermal calibration.     

Mass determination and sensitivity based on resonance frequency changes of the higher flexural modes of cantilever sensors

Micro- and nanocantilevers are increasingly employed as mass sensors. Most studies consider the first flexural mode and adsorbed masses that are either discretely attached or homogeneously distributed along the entire length of the cantilever. We derive general expressions that allow for the determination of the total attached mass with any mass distribution along the cantilever length and all flexural modes. The expressions are valid for all cantilevers whose flexural deflection can be described by a one-dimensional function. This approach includes the most common types of microcantilevers, namely, rectangular, picket, and V-shaped. The theoretical results are compared with experimental data up to the fourth flexural mode obtained from thermal noise spectra of rectangular and V-shaped cantilevers.     

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.     

Expanded beam deflection method for simultaneous measurement of displacement and vibrations of multiple microcantilevers

Here we present an extension of optical beam deflection (OBD) method for measuring displacement and vibrations of an array of microcantilevers. Instead of focusing on the cantilever, the optical beam is either focused above or below the cantilever array, or focused only in the axis parallel to the cantilevers length, allowing a wide optical line to span multiple cantilevers in the array. Each cantilever reflects a part of the incident beam, which is then directed onto a photodiode array detector in a manner allowing distinguishing between individual beams. Each part of reflected beam behaves like a single beam of roughly the same divergence angle in the bending sensing axis as the incident beam. Since sensitivity of the OBD method depends on the divergence angle of deflected beam, high sensitivity is preserved in proposed expanded beam deflection (EBD) method. At the detector, each spot's position is measured at the same time, without time multiplexing of light sources. This provides real simultaneous readout of entire array, unavailable in most of competitive methods, and thus increases time resolution of the measurement. Expanded beam can also span another line of cantilevers allowing monitoring of specially designed two-dimensional arrays. In this paper, we present first results of application of EBD method to cantilever sensors. We show how thermal noise resolution can be easily achieved and combined with thermal noise based resonance frequency measurement.     

Finite element calculations and fabrication of cantilever sensors for nanoscale detection

Finite element analysis (FEA) is used to study the effect of geometric variations on the properties of rectangular cantilevers and U-shaped Joule-heated cantilevers. Simulations of locally thinned cantilevers as well as of cantilevers modified by the implementing of a hole or a side cut are compared with fabricated cantilevers, which are tuned by focused ion beam (FIB) milling. By locally thinning the cantilevers, the resonance frequency and the spring constant are reduced. For a hole, the internal stress is increased while for a side cut, the lateral spring constant is decreased. Good agreement between the measured and the simulated resonance frequencies is observed. Simulations of the current density and the temperature distributions attained during the passage of current through a doped silicon layer are performed to optimize the design of Joule-heated cantilevers (U-shaped) for thermal gravimetric applications. A very uniform temperature distribution over a region near the apex can be realized by slitting the U-shaped cantilever. In such a way, the heating power can be minimized by effecting only a small variation in the geometry of a U-shaped cantilever. A simple fabrication process for the fabrication of Joule-heated cantilevers is presented, which consists mainly of a uniform conductive p-doped layer.     

基于变分贝叶斯的DR/UTP组合导航滤波方法

针对水下无人航行器(UUV)的航位推算导航方法(DR)和水下应答器(UTP)组合导航系统中传统滤波器因观测噪声统计模型不准确或未知而出现的滤波器发散问题,提出了一种基于变分贝叶斯的平方根容积卡尔曼滤波算法,该算法利用变分贝叶斯方法对DR/UTP组合导航系统的状态和时变观测噪声进行估计,并引入自适应调节因子来提高对观测噪声的逼近精度,然后利用平方根容积卡尔曼滤波对系统状态进行更新。仿真结果表明,该滤波算法能够较好地跟踪UUV的DR/UTP组合导航系统外部观测噪声方差的不断变化,可有效提高对DR/UTP组合导航系统各参数的估计精度。     

Kinetostatic model of spring constant ratios for an AFM cantilever with end extended mass

In previous work we showed that the kinetostatic method is very effective in computing the increase in value of the spring constants of an AFM free (with or without added mass) and supported rectangular cantilever for higher mode oscillations relative to their values for natural vibration. We have considered in all previous cases that added mass is a concentrated one. However, the additional mass may be an extended one particularly in the case of a V-shaped cantilever. In this article we consider the influence of the constituent beam’s (leg’s) mutual skew and the altered position of the nodal points in the case when the attached extended triangular (trapezoid) mass of the V-shaped cantilever has a significant moment of rotational inertia and a center of this mass gravity located beyond the constituent beam end. We show that considering these effects in using the kinetostatic model yields results for the ratios of the spring constants at higher modes of oscillation and their values at the first frequency natural vibration for a V-shaped cantilever which are in good agreement with the thermomechanical noise amplitudes obtained by other researchers. This should prove helpful for the proper calibration of V-shaped cantilevers whose application with higher modes oscillation provides increased measurement sensitivity.     

Exploiting cantilever curvature for noise reduction in atomic force microscopy

Optical beam deflection is a widely used method for detecting the deflection of atomic force microscope (AFM) cantilevers. This paper presents a first order derivation for the angular detection noise density which determines the lower limit for deflection sensing. Surprisingly, the cantilever radius of curvature, commonly not considered, plays a crucial role and can be exploited to decrease angular detection noise. We demonstrate a reduction in angular detection shot noise of more than an order of magnitude on a home-built AFM with a commercial 450 μm long cantilever by exploiting the optical properties of the cantilever curvature caused by the reflective gold coating. Lastly, we demonstrate how cantilever curvature can be responsible for up to 45% of the variability in the measured sensitivity of cantilevers on commercially available AFMs.     

Nondestructive and noncontact method for determining the spring constant of rectangular cantilevers

We present here an experimental setup and suggest an extension to the long existing added-mass method for the calibration of the spring constant of atomic force microscope cantilevers. Instead of measuring the resonance frequency shift that results from attaching particles of known masses to the end of cantilevers, we load them with water microdrops generated by a commercial inkjet dispenser. Such a device is capable of generating drops, and thus masses, of extremely reproducible size. This makes it an ideal tool for calibration tasks. Moreover, the major advantage of water microdrops is that they allow for a nearly contactless calibration: no mechanical micromanipulation of particles on cantilevers is required, neither for their deposition nor for removal. After some seconds the water drop is completely evaporated, and no residues are left on the cantilever surface or tip. We present two variants: we vary the size of the drops and deposit them at the free end of the cantilever, or we keep the size of the drops constant and vary their position along the cantilever. For the second variant, we implemented also numerical simulations. Spring constants measured by this method are comparable to results obtained by the thermal noise method, as we demonstrate for six different cantilevers.     

Distortion in the thermal noise spectrum and quality factor of nanomechanical devices due to finite frequency resolution with applications to the atomic force microscope

The thermal noise spectrum of nanomechanical devices is commonly used to characterize their mechanical properties and energy dissipation. This spectrum is measured from finite time series of Brownian motion of the device, which is windowed and Fourier transformed. Here, we present a theoretical and experimental investigation of the effect of such finite sampling on the measured device quality factor. We prove that if no spectral window is used, the thermal noise spectrum retains its original Lorentzian distribution but with a reduced quality factor, indicating an apparent enhancement in energy dissipation. A simple analytical formula is derived connecting the true and measured quality factors - this enables extraction of the true device quality factor from measured data. Common windows used to reduce spectral leakage are found to distort the (true) Lorentzian shape, potentially making fitting problematic. These findings are expected to be of particular importance for devices with high quality factors, where spectral resolution can be limited in practice. Comparison and validation using measurements on atomic force microscope cantilevers are presented.     

Accurate determination of spring constant of atomic force microscope cantilevers and comparison with other methods

We present calibration results of commercial AFM cantilevers using the KRISS nanoforce calibrator (NFC) that can determine traceably spring constants with an uncertainty better than 1%, along with the results obtained from other four calibration methods: the dimensional method, the cantilever-on-cantilever method, the Sader method, and the thermal noise method. Two types (contact and tapping mode) of beam-shaped AFM cantilevers with nominal spring constants of 0.9 N m⁻¹ and 42 N m⁻¹, respectively, were investigated in this study. Because of its small uncertainty, the NFC method was used to assess the uncertainties of other four methods through comparisons between values obtained from other methods and those from the NFC method for the same cantilever. Results from other methods were generally in good agreement with those from the NFC method within the uncertainties of other methods claimed in other literatures, but values obtained from the Sader method were differed by up to 40% from the NFC values, which is 2 times worse than the known uncertainty.     

七桥混合耦连油气悬架车辆仿真与试验

将某七桥车辆的油气悬架系统混合耦连并对其原理和结构进行分析,建立了整车十七自由度动力学模型。基于整车结构和数学模型,以Simulink为主平台,搭建了整车的Simulink/AMESim联合仿真模型,仿真激励为白噪声法生成的相关性路面时域模拟信号。确定所需仿真参数后,进行整车的联合仿真和实际道路试验研究,得到了40 km/h和60 km/h车速下的对比曲线。对比结果显示,质心加速度均方根和功率谱密度峰值的仿真数据与试验数据的相对误差小于8%,仿真结果与试验结果基本吻合,说明所建立的整车模型具有较高的准确性,可以作为整车特性研究的依据。     

Microfabricated torsion levers optimized for low force and high-frequency operation in fluids

We developed a mass production fabrication process for making symmetrically supported torsion cantilevers/oscillators with highly compliant springs. These torsion probes offer advantages in atomic force microscopy (AFM) because they are small, have high optical gain, do not warp and can be made with two independent axes. Compared to traditional AFM cantilevers, these probes have higher frequency response, higher Q, lower noise, better optics (since the mirror does not bend) and two data channels. Soft small levers with sub-pN force resolution can resonate cleanly above 10 kHz in water. When fabricated with a ferromagnetic coating on the rigid reflecting pad, they can be driven magnetically or serve as high-resolution magnetometers. Asymmetric levers can be tapping mode probes or high-resolution accelerometers. The dual axis gimbaled probes with two orthogonal axes can operate on a standard AFM with single beam illumination. These probes can be used as self-referencing, drift free, cantilevers where one axis senses the substrate position and the other the sample position. These levers can be optimized for differential contrast or high-resolution friction imaging.     

Diffusion anisotropy of Ag and In on Si(1 1 1) surface studied by UHV-SEM

Anisotropic features of Ag and In electromigration on clean and Au-precovered Si(1 1 1) surfaces were studied by in situ scanning electron microscopy in ultrahigh vacuum. It was noted that the migration direction of Ag was determined by both applied direct-current direction and step orientation on the substrate surface; on an Si(1 1 1) surface with steps inclined with respect to the current direction, the electromigration direction shows an apparent deviation from the accurate current direction. On clean and Au-precovered Si(1 1 1) surfaces with various coverages of Au (within submonolayer range), the migration behaviors of Ag and In drastically changed with Au coverages and showed different diffusion anisotropy (either thermal diffusion and electromigration) depending on the adsorbate surface structures. Particularly, on a beta-square root of 3 x square root of 3-Au surface of one monolayer Au coverage, In migrated with the highest mobility across the step bands, whereas In showed only a slow movement on the 7 x 7 clean surface due to a migration barrier at step edges. This result implied that the beta-square root of 3 x square root of 3-Au surface phase served as an intermediate layer for In adatoms migration. On the contrary, Ag showed negligible migration on the beta-square root of 3 x square root of 3-Au surface, while the 7 x 7 surface was the substrate for appreciable migration of Ag atoms. The results are discussed in terms of step-edge barriers in migration and on-terrace migration.     

光寻址电位传感器的噪声分析与信号处理方法研究

鉴于光寻址电位传感器(LAPS)的响应信号较弱,传统的抽取频域基波分量的方法易受信号漂移和随机噪声的影响,提出了一种基于频域分量均方根和卡尔曼滤波的两步信号处理方法。基于光寻址电位传感器件的理论模型构建了其等效电路模型,推导得到输出信号的表达式,分析了漂移与噪声产生的原因及其抑制方法。通过实验检测了不同pH值的溶液,并采集了系统输出的光电流信号。求取信号傅里叶变换后频域中的基波分量、二次谐波分量、三次谐波分量的谱线幅值的均方根,然后对归一化电流-偏压(I-V)特性曲线进行卡尔曼滤波。实验结果表明,相对于单纯抽取基波分量的方法,基于频域分量均方根和卡尔曼滤波的两步信号处理方法使检测结果的均方差(MSE)降低了97%,显著减少了信号漂移和随机噪声对检测结果的影响。     

Spring constant calibration of atomic force microscopy cantilevers with a piezosensor transfer standard

We describe a method to calibrate the spring constants of cantilevers for atomic force microscopy (AFM). The method makes use of a "piezosensor" composed of a piezoresistive cantilever and accompanying electronics. The piezosensor was calibrated before use with an absolute force standard, the NIST electrostatic force balance (EFB). In this way, the piezosensor acts as a force transfer standard traceable to the International System of Units. Seven single-crystal silicon cantilevers with rectangular geometries and nominal spring constants from 0.2 to 40 Nm were measured with the piezosensor method. The values obtained for the spring constant were compared to measurements by four other techniques: the thermal noise method, the Sader method, force loading by a calibrated nanoindentation load cell, and direct calibration by force loading with the EFB. Results from different methods for the same cantilever were generally in agreement, but differed by up to 300% from nominal values. When used properly, the piezosensor approach provides spring-constant values that are accurate to +/-10% or better. Methods such as this will improve the ability to extract quantitative information from AFM methods.     

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.     

The Time Resolution of a Vacuum Fission Chamber

The process of the formation of a signal by a vacuum fission chamber (VFC) under the irradiation by a short-duration pulsed neutron flux is considered for the first time. It is shown that the collection time of charge carriers in the VFC with plane–parallel electrodes does not exceed 0.4 ns at a supply voltage of >100 V and that the square of the VFC pulse width is inversely proportional to the supply voltage. The minimum detectable flux densities for fast and thermal neutrons are estimated at 5 × 10¹⁰ and 10⁸ cm^–2 s^–1, respectively, at a noise current of 10^–3 A for the electronic equipment.     

基于ASRCKF算法的锂电池SOC估算

针对平方根容积卡尔曼滤波(SRCKF)估算SOC时需要准确获得系统状态及测量噪声协方差这一缺陷,将基于电池模型输出电压残差序列的协方差匹配思想引入平方根容积卡尔曼滤波,提出了自适应平方根容积卡尔曼滤波算法(ASRCKF)。以18650型锂电池为实验对象,建立了戴维南等效电路模型,采用递推最小二乘法辨识电池模型参数,最后,利用UDDS电池实验数据对ASRCFK算法进行了仿真。实验结果表明,传统的SRCKF算法估算SOC产生的均方根误差为3.41%;而提出的ASRCKF算法估算SOC产生的均方根误差仅为0.97%,与传统算法相比具有更高的精度,对噪声的适应能力更强。