Application of the differential transformation method to bifurcation and chaotic analysis of an AFM probe tip

The AFM (atomic force microscope) has become a popular and useful instrument for measuring intermolecular forces with atomic resolution, that can be applied in electronics, biological analysis, and studying materials, semiconductors etc. This paper conducts a systematic investigation into the bifurcation and chaotic behavior of the probe tip of an AFM using the differential transformation (DT) method. The validity of the analytical method is confirmed by comparing the DT solutions for the displacement and velocity of the probe tip at various values of the vibrational amplitude with those obtained using the Runge–Kutta (RK) method. The behavior of the probe tip is then characterized utilizing bifurcation diagrams, phase portraits, power spectra, Poincaré maps, and maximum Lyapunov exponent plots. The results indicate that the probe tip behavior is significantly dependent on the magnitude of the vibrational amplitude. Specifically, the tip motion changes first from subharmonic to chaotic motion, then from chaotic to multi-periodic motion, and finally from multi-periodic motion to subharmonic motion with windows of chaotic behavior as the non-dimensional vibrational amplitude is increased from 1.0 to 5.0.     

A microwave probe nanostructure for atomic force microscopy

An atomic force microscope (AFM) probe on a GaAs wafer was studied as a new microwave probe structure. A waveguide was created by evaporating an Au film on the top and bottom surfaces of the GaAs AFM probe. The fabricated AMF probe’s tip is 8 μm long and has a radius of curvature of about 50 nm. The open structure of the waveguide at the tip of the probe was generated by using focused ion beam (FIB) fabrication. AFM topography of a grating sample was created by using the fabricated microwave AFM probe. The fabricated probe exhibits nanometer-scale resolution, and microwave emission was successfully detected at the tip of the probe by approaching Cr–V steel and Au wire samples.     

Structure modification of M-AFM probe for the measurement of local conductivity

In order to realize the evaluation of electrical properties of materials in nanometer scale, a method to measure the local conductivity of materials was demonstrated. A microwave atomic force microscope (M-AFM) probe which can propagate and emit microwave signals was fabricated. An open structure of a waveguide at the tip of the probe was introduced by focused ion beam fabrication. The M-AFM combined a network analyzer and an AFM was used to measure a sample. The amplitude and phase of the reflection coefficient of the microwave signals were measured, thereby the electrical conductivities of metallic materials were determined. The conductivity obtained by this method is agreement well with that measured by a high-frequency conductometry.     

Properties of M-AFM probe affected by nanostructural metal coatings

In order to develop a new structure microwave probe, the fabrication of the atomic force microscope (AFM) probe on a GaAs wafer was studied and characteristics of the AFM probe with different nanostructural metal coating were evaluated in order to understand the performance of the probe for the topography of materials and the propagation of microwave signals. A waveguide was introduced by the sputtering and the electron beam (EB) evaporation technique on the top and bottom surfaces of the GaAs AFM probe with Au or Al film. The open structure of the waveguide at the tip of the probe was introduced by using focused ion beam fabrication. It was found that the fabricated probes coated with the Au or Al film have nanometer order resolution. Moreover, using the Au-coating probe formed by the EB evaporation technique, microwave emission was detected successfully at the tip of the probe by approaching an Au film sample.     

Mechanical and tribological characterization of a thermally actuated MEMS cantilever

The temperature effect on the mechanical and tribological behaviors of a microelectromechanical systems cantilever is experimentally investigated using an atomic force microscope. A nonlinear variation of the bending stiffness of microcantilevers as a function of temperature is determined. The variation of the adhesion force between the tip of atomic force microscope (AFM) probe (Si₃N₄) and the microcantilever fabricated in gold is monitored at different temperatures. Using the lateral mode operation of atomic force microscope, the influence of temperature on friction coefficient between the tip of AFM probe and microcantilever is presented. Finite element analysis is used to estimate the thermal field distribution in microcantilever and the axial expansion.     

Micromachining of diamond film for MEMS applications

We realized two diamond microdevices: a movable diamond microgripper and a diamond probe for an atomic force microscope (AFM), consisting of a V-shaped diamond cantilever and a pyramidal diamond tip, using a microfabrication technique employing semiconductive chemical-vapor-deposited diamond thin film. The microgripper was fabricated by patterning the diamond thin film onto a sacrificial SiO ₂ layer by selective deposition and releasing the movable parts by sacrificial layer etching. The diamond AFM probe was fabricated by combining selective deposition for patterning a diamond cantilever with a mold technique on an Si substrate for producing a pyramidal diamond tip. The cantilever was then released by removing the substrate. We report the initial results obtained in AFM measurements taken using the fabricated diamond probe. These results indicate that this diamond probe is capable of measuring AFM images. In addition, we have developed the anodic bonding of diamond thin film to glass using Al or Ti film as an intermediate layer for assembly. This bonding technique will allow diamond microstructures to be used in many novel applications for microelectromechanical systems     

基于AFM探针的电晕放电研究

针对扫描探针显微镜与质谱联用系统中的采样方式,提出了利用原子力显微镜(AFM)探针进行电晕放电解吸附的采样方案.运用ANSYS软件对AFM导电探针进行了有限元仿真,电场分析表明间距100 μm加1 kV高压时的AFM探针周围场强在0.32 ～62.4 V/μm间,验证了利用其产生电晕放电的可行性;通过实验观察了电晕放电...     

A methodology for quantitative evaluation of local electrical conductivity: from micron to submicron

The local electrical conductivity of aluminum thin film with dimensions from micron to submicron was quantitatively measured by a four-point atomic force microscope (AFM) technique. The technique is a combination of the principles of four-point probe method and standard AFM. A silicon nitride based AFM probe with a V-shaped two-dimensional sliced structure tip was patterned by using conventional photolithography method. The probe was then etched to four parallel electrodes isolated from each other, for the purpose of performing current input and electrical potential drop measurement. The spacing between electrodes is smaller than 1.0 μm, which facilitates the quantitative electrical conductivity measurement of ultrathin film. The four-point AFM probe technique is capable of measuring surface topography together with local conductivity simultaneously. The technique was applied to a series of 99.999% aluminum thin films with thicknesses from micron to submicron. The repeatable measurements demonstrate the capability of this technique and its possible extension to be used for fast in situ electrical properties characterization of submicron interconnects that widely applied in nanosensors and nanodevices.     

Molecular dynamics prediction of nanofluidic contact angle offset by an AFM

This paper investigates the nano-fluidic contact angle measurement by performing molecular dynamics simulations. The contact angle between a nano-water droplet and a platinum surface is important for the design of the porous catalyst layer in low-temperature fuel cells. The measurement can generally be conducted by an atomic force microscope (AFM). However, the interaction force between the water droplet and the probe tip of the microscope may influence the measurement results. This paper employs the molecular dynamics technique to investigate the offset of the contact angle measurement. Calculations are in two sets, one simulated the water molecules clustering on the platinum surface, and the other involved the AFM measurement of the contact angle. The former case presents the original contact angle between the nano-scale water droplet and the platinum surface; the offset of the contact angle measurement due to intrusion of the AFM probe is predictable from the latter case. For engineering purposes, we present a correlation between the offset angle and the AFM measurement locations.     

Fabrication of AFM probe with CuO nanowire formed by stress-induced method

A novel method has been proposed to fabricate an atomic force microscope (AFM) probe using CuO nanowire and a stress-induced method that can form the nanowire easily. By heating a commercial AFM probe with a film coating of Ta and Cu, a Cu hillock with CuO nanowires on its surface could be formed at the end of the probe. The thickness of the coating films, the heating temperature, and the heating time were investigated to obtain CuO nanowires with a high aspect ratio for use as an AFM probe tip. It was found that a suitable probe tip can be fabricated using the a Cu film thickness of 700 nm, a heating temperature of 380 °C and a heating time of 6 h. Probe tips (~5 μm high) and nanowires of ~25 nm diameter were obtained successfully. In the range evaluated, the measurement resolution of the CuO nanowire probe was slightly worse than that of a commercial AFM probe. However, both probes had almost the same dimensional measurement precision.     

Fabrication of improved piezoresistive silicon cantilever probes for the atomic force microscope

This paper describes an improved design for a monolithic silicon atomic force microscope (AFM) probe using piezoresistive sensing. The probe is V shaped, with a sharp tip at the free end and two piezoresistors at the root, and is fabricated using silicon-on-insulator (SOI) starting material. The maximum sensitivity of the AFM probe is measured to be 4.0(± 0.1) × 10⁻⁷ Å⁻¹, which is larger than that of the previous parallel-arm piezoresistive AFM probe. The measured results are in reasonable agreement with the values predicted by theory. The minimum detectable force and minimum detectable deflection of the AFM probes are predicted to be 1.0 × 10⁻¹⁰ N and 0.29 Å_r.m.s., respectively, using a Wheatstone bridge arrangement biased at a voltage of ± 5 V and bandwidth of 10 Hz–1 kHz.     

基于最大Lyapunov指数的行星齿轮传动系统混沌特性分析

为了分析行星齿轮系统的混沌特性,基于集中参数理论,考虑时变啮合刚度、齿隙和综合啮合误差等非线性因素,建立行星齿轮系统扭转振动模型.采用Runge-Kutta数值解法求解振动方程,利用分岔图和最大Lyapunov指数图分析系统随各种参数变化的分岔与混沌特性.数值仿真得出:随激励频率的增加,系统首先从周期运动进入阵发性混沌,再通过逆倍化分岔由混沌回到周期运动,之后再次通过跳跃激变和倍化分岔由周期运动进入混沌运动,最后通过逆倍化分岔稳定到1周期运动.随阻尼比的增加,系统通过逆倍化分岔由混沌运动进入周期运动.随综合啮合误差幅值、齿隙和刚度幅值分别增加的三种情况下,系统都是通过倍化分岔由周期运动进入混沌运动.随荷载的增加,系统通过跳跃激变和逆倍化分岔由混沌运动进入周期运动.以上分析结果可为行星齿轮系统参数设计提供理论依据.     

Automated scanning probe lithography with n-alkanethiol self-assembled monolayers on Au(111): application for teaching undergraduate laboratories

Controllers for scanning probe instruments can be programmed for automated lithography to generate desired surface arrangements of nanopatterns of organic thin films, such as n-alkanethiol self-assembled monolayers (SAMs). In this report, atomic force microscopy (AFM) methods of lithography known as nanoshaving and nanografting are used to write nanopatterns within organic thin films. Commercial instruments provide software to control the length, direction, speed, and applied force of the scanning motion of the tip. For nanoshaving, higher forces are applied to an AFM tip to selectively remove regions of the matrix monolayer, exposing bare areas of the gold substrate. Nanografting is accomplished by force-induced displacement of molecules of a matrix SAM, followed immediately by the surface self-assembly of n-alkanethiol molecules from solution. Advancements in AFM automation enable rapid protocols for nanolithography, which can be accomplished within the tight time restraints of undergraduate laboratories. Example experiments with scanning probe lithography will be described in this report that were accomplished by undergraduate students during laboratory course activities and research internships in the chemistry department of Louisiana State University. Students were introduced to principles of surface analysis and gained "hands-on" experience with nanoscale chemistry.     

Nonlinear and hysteretic influence of piezoelectric actuators in AFMs on lateral dimension measurement

Piezoelectric actuators that are used in atomic force microscopes (AFM) have undesirable properties. The nonlinear and hysteretic characteristics of piezoelectric actuators introduce geometric deformations in the reconstructed AFM images. Due to these deformations, the quantitative interpretation of the absolute dimensions of surface features is difficult and often not accurate.A real-time measuring ‘Nano-metrological Atomic Force Microscope’ system equipped with an ultra-high resolution three-axis laser interferometer system is developed, in which the undesirable properties of piezoelectric actuators are compensated completely. Using this AFM and a one-dimensional (1D) grating reference standard with pitches of 240 nm, which is one of the widely used reference standards as nano-metrological lateral scales, the influences of nonlinear and hysteretic characteristics of piezoelectric actuators on image reconstruction and lateral dimension measurement are examined and compared quantitatively among three different measurement methods. The three measurement methods are: (1) the relative movement between probe tip and sample is controlled and measured directly by voltage signals applied on the XYZ scanner, the nonlinear and hysteretic characteristics of piezoelectric actuators are not compensated; (2) the relative movement between probe tip and sample is controlled by voltage signals applied on the XYZ scanner, but it is measured accurately by interferometers; (3) the relative movement between probe tip and sample in lateral directions are both controlled and measured accurately by interferometers. According to the comparison results, an accurate displacement control system is key to reduce the influences of undesirable properties of piezoelectric actuators and the developed AFM system with three-axis laser interferometer system is proved to eliminate the nonlinear and hysteretic characteristics of piezoelectric actuators completely.     

A high-stiffness axial resonant probe for atomic force microscopy

A high-stiffness, (>500 N/m) resonant atomic force microscope probe was constructed to allow force measurements in the presence of large force gradients. The probe employs a piezoresistively detected, electrostatically driven resonant beam sensor oriented perpendicularly to the sample surface. This probe is distinguished from shear force microscopy and noncontact atomic force microscopy in that the design allows for a stationary probe tip for improved spatial resolution and measures forces rather than force gradients. Measured results show a force resolution of 9 nN in a 1-kHz bandwidth in air with an oscillation amplitude of 36 nm and a resonance quality of 20. In a 1-mtorr vacuum the force resolution in the same bandwidth improves to 200 pN with a resonance quality of 450 and oscillation amplitude of 53 nm. This resolution is limited by white noise of the piezoresistor, and scales as expected with amplitude and resonance quality     

Impact of features of control systems of the tunneling microscope on the measurement accuracy

A significant number of measurement errors of the surface nanotopography by a tunneling microscope is caused by features of the probe motion control. If the geometry of the needle tip is taken into account in the interpretation of measurements, it is possible to significantly reduce the influence of these errors. It is shown that the shape and size of the tip can be determined from the mathematical model of the scanning process using existing measurements of the nanotopography.     

Multiwalled carbon nanotube AFM probes for surface characterization of micro/nanostructures

A multiwalled carbon nanotube (MWNT) probe was used as a scanning probe in an atomic force microscope (AFM) to obtain surface height maps of micro/nano structures. The surface height maps acquired by the MWNT probe are compared with those by a conventional silicon probe on the four samples: silicon ruler, polymer microchannels, silicon nanomembrane and nanocomposite metal particle (MP) tapes. The results of the silicon ruler, microchannels and membrane samples show that the surface height maps by the MWNT probe have a better resolution than those by a conventional silicon tip due to the sharper tip with the larger aspect ratio of the MWNT. A MWNT probe is especially useful to observe surface height maps of the structures that have larger aspect ratio.Financial support for this work was provided by the National Science Foundation (contract no. ECS-0301056). The authors are grateful to Prof. Derek Hansford and Nick Ferrell of the Micro MD laboratory for providing the samples and fruitful discussions, and Imation Corporation for the samples provided. Work by C.V.N. was supported by a NASA contract to ELORET Corporation.     

Integrated SPM probes with NEMS technology

Two kinds of integrated scanning probe microscope (SPM) probes are developed. The first kind is AFM probes realized with a novel masked–maskless combined etching process. Both the nano-tips for scanning and the bending cantilevers are simultaneously formed with the masked–maskless combined anisotropic etching technique. The simultaneous formation method effectively avoids damage to the previously formed tips when the cantilever shaping is processed. The testing results for the probes show the imaging quality comparable with commercial probes. The second kind of probes is an integrated probe with both a piezoresistive sensor and an electric-heated tip. This kind of probe is used for thermal–mechanical data storage, with the pulse-heated tip for data writing and the piezoresistive sensor for data reading. Nano-sized bumps have been formed by probe scanning on PMMA thin film, resulting in a storage density beyond 30 GB/in.².     

Development of a nanostructural microwave probe based on GaAs

In order to develop a new structural microwave probe, we studied the fabrication of an AFM probe on a GaAs wafer. A waveguide was introduced by evaporating Au film on the top and bottom surfaces of the GaAs AFM probe where a tip 7 μm high with a 2.0 aspect ratio was formed and the dimensions of the cantilever were 250 × 30 × 15 μm. The open structure of the waveguide at the tip of the probe was obtained by FIB fabrication. An AFM image and profile analysis for a standard sample, obtained by the fabricated GaAs microwave probe and a commercial Si AFM probe, indicate that the fabricated probe has a similar capability for measurement of material topography as compared to the commercial probe.     

Cantilever probes for high speed AFM

Since the invention in 1986 atomic force microscopy (AFM) has become the most widely used scanning probe microscopy (Binnig et al. in Phys Rev Lett 56:930–933, 1986). The microscope images the interaction of forces like Van der Waals or Coulomb forces between a sample and the apex of a small tip integrated near the free end of a flexible cantilever. But as all other scanning probe techniques the AFM requires serial data acquisition and suffers therefore from a low temporal resolution. Enhancing the speed to video rate imaging makes high demands on scanner technology, control electronics and on the key feature the cantilever with integrated sharp stylus. For the cantilever probes, fundamental resonance frequencies in the MHz regime are envisaged while the force constant of a few nN/nm shall be maintained. We present different novel AFM probes with ultrashort cantilevers and integrated sharp tips for high speed AFM while focusing on widely dispersed applications and on aspects of mass fabrication.