Ryan C. Tung

Hydrodynamic loading of microcantilevers oscillating near rigid walls

The vibrations of microcantilevers in atomic force microscopes (AFMs) or radio frequency (RF) switches are strongly influenced by the viscous hydrodynamics of the surrounding fluid in the vicinity of a rigid wall. While prior efforts to model this hydrodynamic loading have focused on squeeze film damping effects at high Knudsen and squeeze numbers, the regimes of low Knudsen and squeeze numbers are also very important for which squeeze film models need to be discarded in favor of unsteady Stokes hydrodynamics. We extend the work of Green and Sader [Phys Fluids 17, 073102 (2005); J. Appl. Phys. 98, 114913 (2005)] and present compact semianalytical formulas for the unsteady viscous hydrodynamic function of slender microbeams oscillating near rigid walls, in terms of key nondimensional numbers. Using these closed-form expressions, it becomes possible to predict easily the wet natural frequencies and quality factors of multiple modes of microcantilevers near rigid walls in diverse applications ranging from AF...

Squeeze-film damping of flexible microcantilevers at low ambient pressures: theory and experiment

An improved theoretical approach is proposed to predict the dynamic behavior of long, slender and flexible microcantilevers affected by squeeze-film damping at low ambient pressures. Our approach extends recent continuum gas damping models (Veijola 2004 J. Micromech. Microeng. 14 1109‐18, Gallis and Torczynski 2004 J. Microelectromech. Syst. 13 653‐9), which were originally derived for a rigid oscillating plate near a wall, to flexible microcantilevers for calculating and predicting squeeze-film damping ratios of higher order bending modes at reduced ambient pressures. Theoretical frequency response functions are derived for a flexible microcantilever beam excited both inertially and via external forcing. Experiments performed carefully at controlled gas pressures are used to validate our theoretical approach over five orders of the Knudsen number. In addition, we investigate the relative importance of theoretical assumptions made in the Reynolds-equation-based approach for flexible microelectromechanical systems. (Some figures in this article are in colour only in the electronic version)

Flexural vibration spectra of carbon nanotubes measured using laser Doppler vibrometry

Laser Doppler vibrometry is used to measure the thermal vibration spectra of individual multiwalled carbon nanotubes (MWNTs) under ambient conditions. Since the entire vibration spectrum is measured with high frequency resolution, the resonant frequencies and quality factors of the MWNTs are accurately determined, allowing for estimates of their elastic moduli. Because the diameters of the MWNTs studied are smaller than the wavelength of the vibrometers laser, Mie scattering is used to estimate values for the smallest diameter nanotube or nanowire whose vibration can be measured in this way.

Unified theory of gas damping of flexible microcantilevers at low ambient pressures

Predicting the gas damping of microcantilevers oscillating in different vibration modes in unbounded gas at low pressures is relevant for increasing the sensitivity of microcantilever-based sensors. While existing free-molecular theories are valid only at very high Knudsen numbers, continuum models are valid only at very low Knudsen numbers. We solve the quasisteady Boltzmann equation and compute a closed-form fit for gas damping of rectangular microcantilevers that is valid over four orders of magnitude of Knudsen numbers spanning the free-molecular, the transition, and the low pressure slip flow regimes. Experiments are performed using silicon microcantilevers under controlled pressures to validate the theory.

Characterization of silver–gallium nanowires for force and mass sensing applications

We investigate the mechanical properties of cantilevered silver-gallium (Ag(2)Ga) nanowires using laser Doppler vibrometry. From measurements of the resonant frequencies and associated operating deflection shapes, we demonstrate that these Ag(2)Ga nanowires behave as ideal Euler-Bernoulli beams. Furthermore, radial asymmetries in these nanowires are detected through high resolution measurements of the vibration spectra. These crystalline nanowires possess many ideal characteristics for nanoscale force and mass sensing, including small spring constants (as low as 10(-4) N m(-1)), high frequency bandwidth with resonance frequencies in the 0.02-10 MHz range, small suspended mass (picograms), and relatively high Q-factors (approximately 2-50) under ambient conditions. We evaluate the utility of Ag(2)Ga nanowires for nanocantilever applications, including ultrasmall mass and high frequency bandwidth piconewton force detection.

Estimating residual stress, curvature and boundary compliance of doubly clamped MEMS from their vibration response

Structural parameters of doubly clamped microfabricated beams such as initial curvature, boundary compliance, thickness and mean residual stress are often critical to the performance of microelectromechanical systems (MEMS) and need to be estimated as a part of quality control of the microfabrication process. However, these parameters couple and influence many metrics of device response and thus are very difficult to disentangle and estimate using conventional methods such as the M-test, static mechanical tests, pull-in measurements or dynamic mechanical tests. Here we present a simple, non-destructive experimental method to extract these parameters based on the non-contact measurement of the natural frequencies of the lowest few eigenmodes of the microfabricated beam, and knowledge of Youngs modulus and plan dimensions of the beam alone. The method exploits the fact that certain eigenmodes are insensitive to some of these structural parameters which enable a convenient decoupling and estimation of the parameters. As a result, the method does not require complicated finite element analysis, is insensitive to the gap height and introduces no contact wear or dielectric charging effects. Experiments are performed using laser Doppler vibrometry to measure the natural frequencies of doubly clamped, nickel, RF-MEMS capacitive switches and the method is applied to extract the residual stress, beam thickness, boundary compliance and post-release curvature.

Quantitative Contact Resonance Force Microscopy for Viscoelastic Measurement of Soft Materials at the Solid−Liquid Interface

Viscoelastic property measurements made at the solid-liquid interface are key to characterizing materials for a variety of biological and industrial applications. Further, nanostructured materials require nanoscale measurements. Here, material loss tangents (tan δ) were extracted from confounding liquid effects in nanoscale contact resonance force microscopy (CR-FM), an atomic force microscope based technique for observing mechanical properties of surfaces. Obtaining reliable CR-FM viscoelastic measurements in liquid is complicated by two effects. First, in liquid, spurious signals arise during cantilever excitation. Second, it is challenging to separate changes to cantilever behavior due to the sample from changes due to environmental damping and added mass effects. We overcame these challenges by applying photothermal cantilever excitation in multiple resonance modes and a predictive model for the hydrodynamic effects. We demonstrated quantitative, nanoscale viscoelastic CR-FM measurements of polymers at the solid-liquid interface. The technique is demonstrated on a point-by-point basis on polymer samples and while imaging in contact mode on a fixed plant cell wall. Values of tan δ for measurements made in water agreed with the values for measurements in air for some experimental conditions on polystyrene and for all examined conditions on polypropylene.

Liquid contact resonance atomic force microscopy via experimental reconstruction of the hydrodynamic function

We present a method to correct for surface-coupled inertial and viscous fluid loading forces in contact resonance (CR) atomic force microscopy (AFM) experiments performed in liquid. Based on analytical hydrodynamic theory, the method relies on experimental measurements of the AFM cantilevers free resonance peaks near the sample surface. The free resonance frequencies and quality factors in both air and liquid allow reconstruction of a continuous hydrodynamic function that can be used to adjust the CR data in liquid. Validation experiments utilizing thermally excited free and in-contact spectra were performed to assess the accuracy of our approach. Results show that the method recovers the air frequency values within approximately 6%. Knowledge of fluid loading forces allows current CR analysis techniques formulated for use in air and vacuum environments to be applied to liquid environments. Our technique greatly extends the range of measurement environments available to CR-AFM.

Vibrational shape tracking of atomic force microscopy cantilevers for improved sensitivity and accuracy of nanomechanical measurements

Contact resonance atomic force microscopy (CR-AFM) methods currently utilize the eigenvalues, or resonant frequencies, of an AFM cantilever in contact with a surface to quantify local mechanical properties. However, the cantilever eigenmodes, or vibrational shapes, also depend strongly on tip-sample contact stiffness. In this paper, we evaluate the potential of eigenmode measurements for improved accuracy and sensitivity of CR-AFM. We apply a recently developed, in situ laser scanning method to experimentally measure changes in cantilever eigenmodes as a function of tip-sample stiffness. Regions of maximum sensitivity for eigenvalues and eigenmodes are compared and found to occur at different values of contact stiffness. The results allow the development of practical guidelines for CR-AFM experiments, such as optimum laser spot positioning for different experimental conditions. These experiments provide insight into the complex system dynamics that can affect CR-AFM and lay a foundation for enhanced nanomechanical measurements with CR-AFM.

Hydrodynamic corrections to contact resonance atomic force microscopy measurements of viscoelastic loss tangenta)

We present a method to improve accuracy in measurements of nanoscale viscoelastic material properties with contact resonance atomic force microscope methods. Through the use of the two-dimensional hydrodynamic function, we obtain a more precise estimate of the fluid damping experienced by the cantilever-sample system in contact resonance experiments, leading to more accurate values for the tip-sample damping and related material properties. Specifically, we consider the damping and added mass effects generated by both the proximity of the cantilever to the sample surface and the frequency dependence on the hydrodynamic loading of the system. The theoretical correction method is implemented on experimental contact resonance measurements. The measurements are taken on a thin polystyrene film and are used to determine the viscoelastic loss tangent, tan δ, of the material. The magnitude of the corrections become significant on materials with low tan δ (<0.1) and are especially important for measurements made with the first flexural mode of vibration.