纳米黏弹性测量中谐振抑制方法研究

针对压痕测量软材料中悬臂梁谐振导致测量数据存在较大误差的问题,提出一种在宽带纳米黏弹性测量中抑制悬臂梁谐振的方法。基于z轴动态特性设计一种陷波器类型的前置滤波器,并对输入驱动电压进行滤波;设计基于最小均方误差准则(LMS)的自适应滤波器,参考赫兹接触模型对软材料的复蠕变量进行滤波,进而在输入环节和测量环节消除谐振影响。通过二甲基硅氧烷(PDMS)样本的黏弹性测量实验,验证悬臂梁谐振抑制方法的有效性。     

Low-force AFM nanomechanics with higher-eigenmode contact resonance spectroscopy

Atomic force microscopy (AFM) methods for quantitative measurements of elastic modulus on stiff (>10?GPa) materials typically require tip-sample contact forces in the range from hundreds of nanonewtons to a few micronewtons. Such large forces can cause sample damage and preclude direct measurement of ultrathin films or nanofeatures. Here, we present a contact resonance spectroscopy AFM technique that utilizes a cantilever's higher flexural eigenmodes to enable modulus measurements with contact forces as low as 10?nN, even on stiff materials. Analysis with a simple analytical beam model of spectra for a compliant cantilever's fourth and fifth flexural eigenmodes in contact yielded good agreement with bulk measurements of modulus on glass samples in the 50-75?GPa range. In contrast, corresponding analysis of the conventionally used first and second eigenmode spectra gave poor agreement under the experimental conditions. We used finite element analysis to understand the dynamic contact response of a cantilever with a physically realistic geometry. Compared to lower eigenmodes, the results from higher modes are less affected by model parameters such as lateral stiffness that are either unknown or not considered in the analytical model. Overall, the technique enables local mechanical characterization of materials previously inaccessible to AFM-based nanomechanics methods.     

动水力简化计算方法对圆形桥墩传递函数的影响

刚性柱法、莫里森法和基频近似法是可供工程应用的不可压缩无粘性水体地震动水力的简化计算方法。为研究上述方法的差异性，将基于不可压缩无粘性水体辐射理论推导的考虑结构变形的精确解作为标准，从频域传递函数的角度，对各简化方法进行比较分析。以水中悬臂圆柱墩为例，选取2个尺寸参数并设计了84种不同尺寸的桥墩，输入脉冲激励得到墩顶节点的位移传递函数、墩底节点的剪力和弯矩传递函数，提取各传递函数的前两阶共振峰幅值和共振频率，基于标准解结果求得3种简化方法的误差。通过分析误差的范围及变化趋势，发现刚性柱法所得共振峰幅值更精确，基频近似法所得共振周期更精确，莫里森法误差受参数的影响显著。此外，基频近似法所得共振峰幅值大多偏小，而莫里森法所得幅值和周期大多偏大。     

Higher-order electromechanical response of thin films by contact resonance piezoresponse force microscopy

Piezoresponse scanning force microscopy (PFM) has turned into an established technique for imaging ferroelectric domains in ferroelectric thin films. At least for soft cantilevers, the piezoresponse signal is not only dependent on the elastic properties of the material under investigation but also on the elastic properties of the cantilever. Due to this dependency, the cantilever response and, therefore, the measured properties depend on the frequency of the small alternating current (AC) testing voltage. At the contact resonance, the cantilever response is maximum, and this increased sensitivity can be used to detect very small signals or to decrease the voltage applied to the sample. We have shown that by using the hysteretic ferroelectric switching, it is possible to separate the signal into its components (viz. electromechanical and electrostatic contributions). Additionally, the measurement frequency can be tuned such that the second and third harmonics of the electromechanical response can be detected at the cantilever resonance, providing information about the higher-order electromechanical coefficients. We assume that this nonlinear behavior seen in local and macroscopic measurements is rooted in the nonlinearity of the dielectric permittivity. Our results are of crucial importance for the study of ferroelectric and electromechanical properties of nanostructures.     

Lorentz force actuation of a heated atomic force microscope cantilever

We report Lorentz force-induced actuation of a silicon microcantilever having an integrated resistive heater. Oscillating current through the cantilever interacts with the magnetic field around a NdFeB permanent magnet and induces a Lorentz force that deflects the cantilever. The same current induces cantilever heating. With AC currents as low as 0.2 mA, the cantilever can be oscillated as much as 80 nm at resonance with a DC temperature rise of less than 5 °C. By comparison, the AC temperature variation leads to a thermomechanical oscillation that is about 1000 times smaller than the Lorentz deflection at the cantilever resonance. The cantilever position in the nonuniform magnetic field affects the Lorentz force-induced deflection, with the magnetic field parallel to the cantilever having the largest effect on cantilever actuation. We demonstrate how the cantilever actuation can be used for imaging, and for measuring the local material softening temperature by sensing the contact resonance shift.     

Dynamic and contact analysis of a bimodal ultrasonic motor

A bimodal ultrasonic motor, which operates with only one power amplifier, uses two simultaneously excited modes to drive the rotor; a longitudinal mode and a flexural mode. The equations of motion describing the vibrations and contact behavior are derived by Hamilton's principle and the geometry constraint. The Lagrange multiplier method is used to treat the frictional contact problem. The finite element method and numerical integration scheme are used to simulate the dynamic responses of this system with and without contact. Some important factors are studied for the bimodal ultrasonic motor design. The factors include structure design, amplitude of input voltage, phase displacement, exciting frequency, and contact behavior.     

Multifrequency imaging in the intermittent contact mode of atomic force microscopy: beyond phase imaging

The cantilever dynamics in single-frequency scanning probe microscopy (SPM) are undefined due to having only two output variables, which leads to poorly understood image contrast. To address this shortcoming, generalized phase imaging scanning probe microscopy (GP-SPM), based on broad band detection and multi-eigenmode operation, is developed and demonstrated on diamond nanoparticles with different functionalization layers. It is shown that rich information on tip-surface interactions can be acquired by separating the response amplitude, instant resonance frequency, and quality factor. The obtained data allow high-resolution imaging even in the ambient environment. By tuning the strength of tip-surface interaction, different surface functionalizations can be discerned.     

原子力声显微镜成像及分析

超声检测技术与原子力显微技术相结合,构成原子力声显微镜(AFAM),能够实现样品内部纳米结构的测量,并分析如局域弹性模量、刚度等力学性能.本文在传统的原子力显微镜(AFM)的基础上初步构建了AFAM,利用AFM轻敲模式下的微悬臂梁振动激励信号来驱动样品背面的压电超声换能器,并利用轻敲模式控制系统中的锁相环检测经过样品后由探针收集的振动信号,形成振幅及相位图像.这种AFAM方法不需外接信号发生器、锁相放大器及相关控制电路,从而避免AFM内、外部的仪器及控制电路的不同步而引起的AFAM振幅/相位与形貌图像间的偏移.此外,还分析了形貌结构对AFAM振幅图像的影响,为进一步研究AFAM亚表面成像奠定了基础.     

Amplitude modulation drive to rectangular-plate linear ultrasonic motors with vibrators dimensions 8 mm x 2.16 mm X 1 mm

In this paper, to exploit the contribution from not only the stators but also from other parts of miniature ultrasonic motors, an amplitude modulation drive is proposed to drive a miniature linear ultrasonic motor consisting of two rectangular piezoelectric ceramic plates. Using finite-element software, the first longitudinal and second lateral-bending frequencies of the vibrator are shown to be very close when its dimensions are 8 mm x 2.16 mm x 1 mm. So one single frequency power should be able to drive the motor. However, in practice the motor is found to be hard to move with a single frequency power because of its small vibration amplitudes and big frequency difference between its longitudinal and bending resonance, which is induced by the boundary condition variation. To drive the motor effectively, an amplitude modulation drive is used by superimposing two signals with nearly the same frequencies, around the resonant frequency of the vibrators of the linear motor. When the amplitude modulation frequency is close to the resonant frequency of the vibrator's surroundings, experimental results show that the linear motor can move back and forward with a maximum thrust force (over 0.016 N) and a maximum velocity (over 50 mm/s).     

Experimental and numerical investigations for the free vibration of cantilever trapezoidal plates

Abstract

Based on the advantages of non‐contact and full field measurement, the optical technique called amplitude‐fluctuation electronic speckle pattern interferometry (AFESPI) with an out‐of‐plane setup is employed to investigate the free vibration of cantilever trapezoidal plates with various taper ratios and sweep‐back angles. Twenty different plate configurations are analyzed, including triangular and trapezoidal plates, and the first seven vibration modes of each plate are measured. The AF‐ESPI method is very convenient for measuring vibrating objects because no contact is required in contrast to classical modal analysis using accelerometers. Based on the fact that clear fringe patterns will appear only in resonance, both resonant frequencies and corresponding mode shapes can be obtained experimentally using the present technique. Numerical calculations by finite element method are also performed and the results are compared with the experimental measurements. Excellent agreements are obtained for both results of resonant frequencies and mode shapes. The influences of taper ratios and sweep‐back angles on the vibration behavior of cantilever trapezoidal plates are also demonstrated in terms of the dimensionless frequency parameter.     

Nanoscale mapping of contact stiffness and damping by contact resonance atomic force microscopy

In this work, a new procedure is demonstrated to retrieve the conservative and dissipative contributions to contact resonance atomic force microscopy (CR-AFM) measurements from the contact resonance frequency and resonance amplitude. By simultaneously tracking the CR-AFM frequency and amplitude during contact AFM scanning, the contact stiffness and damping were mapped with nanoscale resolution on copper (Cu) interconnects and low-k dielectric materials. A detailed surface mechanical characterization of the two materials and their interfaces was performed in terms of elastic moduli and contact damping coefficients by considering the system dynamics and included contact mechanics. Using Cu as a reference material, the CR-AFM measurements on the patterned structures showed a significant increase in the elastic modulus of the low-k dielectric material compared with that of a blanket pristine film. Such an increase in the elastic modulus suggests an enhancement in the densification of low-k dielectric films during patterning. In addition, the subsurface response of the materials was investigated in load-dependent CR-AFM point measurements and in this way a depth dimension was added to the common CR-AFM surface characterization. With the new proposed measurement procedure and analysis, the present investigation provides new insights into characterization of surface and subsurface mechanical responses of nanoscale structures and the integrity of their interfaces.     

Modelling oscillatory flexure modes of an atomic force microscope cantilever in contact mode whilst imaging at high speed

Understanding the modal response of an atomic force microscope is important for the identification of image artefacts captured using contact-mode atomic force microscopy (AFM). As the scan rate of high speed AFM increases, these modes present themselves as ever clearer noise patterns as the frequency of cantilever vibration falls under the frequency of pixel collection. An Euler-Bernoulli beam equation is used to simulate the flexural modes of the cantilever of an atomic force microscope as it images a hard surface in contact mode. Theoretical results are compared with experimental recordings taken in the high speed regime, as well as previous analytical results. It is shown that the model can capture the mode shapes and resonance properties of the first four eigenmodes.     

Measuring phase shifts and energy dissipation with amplitude modulation atomic force microscopy

By recording the phase angle difference between the excitation force and the tip response in amplitude modulation AFM it is possible to image compositional variations in heterogeneous samples. In this contribution we address some of the experimental issues relevant to perform phase contrast imaging measurements. Specifically, we study the dependence of the phase shift on the tip-surface separation, interaction regime, cantilever parameters, free amplitude and tip-surface dissipative processes. We show that phase shift measurements can be converted into energy dissipation values. Energy dissipation curves show a maximum (～10?eV/cycle) with the amplitude ratio. Furthermore, energy dissipation maps provide a robust method to image material properties because they do not depend directly on the tip-surface interaction regime. Compositional contrast images are illustrated by imaging conjugated molecular islands deposited on silicon surfaces.     

共振频率可调式非线性压电振动能量收集器

振动能量回收技术能够将环境中的机械振动能转换成电能,进而为微功耗装置供电,具有良好的应用前景。设计了一种利用压电材料的新型振动能量收集器,该机电耦合结构由一对非对称压电悬臂梁组成,悬臂梁末端固定有永磁体,利用永磁体产生的非线性力,实现了悬臂梁共振频率与外界激振频率的匹配调节。提出了该结构的理论模型,借助Matlab/Simulink数值分析软件对理论模型进行了仿真分析,并通过实验进行了验证。实验结果表明外界激励加速度幅值为3 m/s~2的时,结构即能实现较大频带范围内的频率匹配调节,频带范围不低于6.5Hz,最大回收功率不低于2 mW。     

Thermomagnetic fluctuations and hysteresis loops of magnetic cantilevers for magnetic resonance force microscopy

We have used frequency-shift cantilever magnetometry to study individual nickel magnets patterned at the end of ultra-sensitive silicon cantilevers for use in magnetic resonance force microscopy (MRFM). We present a procedure for inferring a magnet's full hysteresis curve from the response of cantilever resonance frequency versus magnetic field. Hysteresis loops and small-angle fluctuations were determined at 4.2 K with an applied magnetic field up to 6 T for magnets covering a range of dimensions and aspect ratios. Compared to magnetic materials with higher anisotropy, we find that nickel is preferable for MRFM experiments on nuclear spins at high magnetic fields.     

A method to quantitatively measure the elastic modulus of materials in nanometer scale using atomic force microscopy

A method is proposed for quantitatively measuring the elastic modulus of materials using atomic force microscopy (AFM) nanoindentation. In this method, the cantilever deformation and the tip-sample interaction during the early loading portion are treated as two springs in series, and based on Sneddon's elastic contact solution, a new cantilever-tip property α is proposed which, together with the cantilever sensitivity A, can be measured from AFM tests on two reference materials with known elastic moduli. The measured α and A values specific to the tip and machine used can then be employed to accurately measure the elastic modulus of a third sample, assuming that the tip does not get significantly plastically deformed during the calibration procedure. AFM nanoindentation tests were performed on polypropylene (PP), fused quartz and acrylic samples to verify the validity of the proposed method. The cantilever-tip property and the cantilever sensitivity measured on PP and fused quartz were 0.514?GPa and 51.99?nm?nA(-1), respectively. Using these measured quantities, the elastic modulus of acrylic was measured to be 3.24?GPa, which agrees well with the value measured using conventional depth-sensing indentation in a commercial nanoindenter.     

Mechanical manifestations of rare atomic jumps in dynamic force microscopy

The resonance frequency and the excitation amplitude of a silicon cantilever have been measured as a function of distance to a cleaved KBr(001) surface with a low-temperature scanning force microscope (SFM) in ultrahigh vacuum. We identify two regimes of tip-sample distances. Above a site-dependent critical tip-sample distance reproducible data with low noise and no interaction-induced energy dissipation are measured. In this regime reproducible SFM images can be recorded. At closer tip-sample distances, above two distinct atomic sites, the frequency values jump between two limiting curves on a timescale of tens of milliseconds. Furthermore, additional energy dissipation occurs wherever jumps are observed. We attribute both phenomena to rarely occurring changes in the tip apex configuration which are affected by short-range interactions with the sample. Their respective magnitudes are related to each other. A specific candidate two-level system is also proposed.     

陷波滤波器谐振抑制参数优化方法

针对伺服系统谐振抑制中,陷波滤波器的深度和宽度不合理而使谐振抑制不理想的问题,提出陷波滤波器谐振抑制参数优化方法。利用速度偏差的FFT变换得到谐振频谱图,以最大幅值处的频率确定陷波频率;在频谱图上以曲线任意点的幅值与最大幅值的比值确定深度参数,并且以所对应的频率与谐振频率的宽度确定宽度参数;为了保证参数的合理性,以滤波后谐振频率处的幅值为适应度,利用改进粒子群优化算法对陷波深度和宽度参数进行优化,避免因噪声干扰和负载变化而使陷波参数陷入局部最优。实验结果表明：该方法能在线分析机械谐振并且匹配最优参数,可以大幅度降低机械谐振。     

The role of nonlinear dynamics in quantitative atomic force microscopy

Various methods of force measurement with the atomic force microscope are compared for their ability to accurately determine the tip-surface force from analysis of the nonlinear cantilever motion. It is explained how intermodulation, or the frequency mixing of multiple drive tones by the nonlinear tip-surface force, can be used to concentrate the nonlinear motion in a narrow band of frequency near the cantilever's fundamental resonance, where accuracy and sensitivity of force measurement are greatest. Two different methods for reconstructing tip-surface forces from intermodulation spectra are explained. The reconstruction of both conservative and dissipative tip-surface interactions from intermodulation spectra are demonstrated on simulated data.     

四参数正弦波组合式拟合算法

提出了一种组合式四参数正弦曲线拟合方法。首先,使用已知频率的三参数正弦拟合算法进行频率搜索,构造出一维搜索迭代正弦拟合算法,获得幅度、频率、相位、直流分量4个参数。然后,以其作为初始值,使用四参数搜索迭代方式,获得最终的正弦拟合结果。该方法可以适用于多周期和残周期序列情况,具有明确的收敛域,可以保证在任何情况下获得总体最优的收敛拟合结果。仿真和实测实验,均验证了所述方法的有效性与可行性。