Slava Krylov

Attogram detection using nanoelectromechanical oscillators

We report on the fabrication of nanometer-scale mass sensors with subattogram sensitivity. Surface micromachined polycrystalline silicon and silicon nitride nanomechanical oscillators were used to detect the presence of well-defined mass loading. Controlled deposition of thiolate self-assembled monolayers on lithographically defined gold dots were used for calibrated mass loading. We used a dinitrophenyl poly(ethylene glycol) undecanthiol-based molecule (DNP-PEG4-C11thiol) as a model ligand for this study. Due to the fact that the gold mass is attached at the distance l0 from the end x=l of the cantilever beam, an additional moment evolves in the boundary condition of the oscillator, which was taken into consideration through the rotational inertia of the attached mass. We showed that the corresponding correction of the frequency is on the order of γ(l0/l), where γ is the attached mass normalized to the mass of the beam. The rotational inertia correction to the frequency is on the order of γ(l0/l)2. The a...

The pull-in behavior of electrostatically actuated bistable microstructures

The results of theoretical and experimental investigation of an initially curved clamped–clamped microbeam actuated by a distributed electrostatic force are presented. Reduced-order Galerkin and consistently constructed lumped models of the shallow Euler–Bernoulli arch were built and verified by numerical analysis, and the influence of various parameters on the stability was investigated. Due to the unique combination of generic mechanical and electrostatic nonlinearities, the voltage–deflection characteristic of the device may have two maxima implying the existence of sequential snap-through buckling and pull-in instability and of bistability of the beam. The first critical voltage can be higher or lower than the second one, while the stable deflections are significantly larger than in a straight beam. The minimal initial elevation required for the appearance of the snap-through in the electrostatically actuated beam is smaller than in the case of uniform deflection-independent loading; a closed-form approximation of this elevation was evaluated. The devices were fabricated from silicon on insulator (SOI) wafer using deep reactive ion etching and in-plane responses were characterized by means of optical and scanning electron microscopy. Model results obtained for the actual dimensions of the device were in good agreement with the experimental data.

Pull-in Dynamics of an Elastic Beam Actuated by Continuously Distributed Electrostatic Force

A detailed study of the transient nonlinear dynamics of an electrically actuated micron scale beam is presented. A model developed using the Galerkin procedure with normal modes as a basis accounts for the distributed nonlinear electrostatic forces, nonlinear squeezed film damping, and rotational inertia of a mass carried by the beam. Special attention is paid to the dynamics of the beam near instability points. Results generated by the model and confirmed experimentally show that nonlinear damping leads to shrinkage of the spatial region where stable motion is realizable. The voltage that causes dynamic instability, in turn, approaches the static pull-in value.

Optical excitation of nanoelectromechanical oscillators

We report a method of optical excitation of nanomechanical cantilever-type oscillators. The periodic driving signal with a controlled modulation amplitude was provided by a 415 nm diode laser, wherein the laser spot was located at some distance away from the clamped end of the cantilever. The measured resonant response of the cantilever was obtained at distances in excess of 160μm with varying oscillator dimensions. The effectiveness of the driving mode is studied for different combinations of materials, namely Si–SiO2 and Si3N4–SiO2. These observations were considered within the theoretical framework of the mechanism of heat transfer. We show that measurable amplitudes of vibrations can be obtained at temperature changes much less than 1°.

Stabilization of electrostatically actuated microstructures using parametric excitation

Electrostatically actuated microstructures are inherently nonlinear and can become unstable. Pull-in instability is encountered as a basic instability mechanism. We demonstrate that the parametric excitation of a microstructure by periodic (ac) voltages may have a stabilizing effect and permits an increase of the steady (dc) component of the actuation voltage beyond the pull-in value. An elastic string as well as a cantilever beam are considered in order to illustrate the influence of fast-scale excitation on the slow-scale behavior. The main conclusions about the stability are drawn using the simplest model of a parametrically excited system described by Mathieu and Hills equations. Theoretical results are verified by numerical analysis of microstructure subject to nonlinear electrostatic forces and performed by using Galerkin decomposition with undamped linear modes as base functions. The parametric stabilization of a cantilever beam is demonstrated experimentally.

Young’s modulus and density measurements of thin atomic layer deposited films using resonant nanomechanics

Material properties of atomic layer deposited (ALD) thin films are of interest for applications ranging from wear resistance to high-k dielectrics in electronic circuits. We demonstrate the ability to simultaneously measure Young’s modulus (E) and density (ρ) of 21.2–21.5 nm ALD hafnia, alumina, and aluminum nitride ultrathin films by observing vibrations of nanomechanical cantilever beams. The nanomechanical structures were fabricated from a 250 nm thick single crystal silicon layer with varying length and width ranging from 6 μm to 10 μm and 45 nm to 1 μm, respectively. Our approach is based on an optical excitation and interferometric detection of in-plane and out-of plane vibrational spectra of single crystal silicon cantilevers before and after a conformal coating deposition of an ALD thin film. In conjunction with three-dimensional numerical finite element analysis, measurements of resonance carried out prior to the ALD revealed that while the influence of clamping compliance arising from the underc...

Higher order correction of electrostatic pressure and its influence on the pull-in behavior of microstructures

In close gap electrostatic microactuators modeling, distributed forces are commonly approximated using a parallel capacitor formula, adequate when the distance between electrodes is much smaller than their length. In the present work, using the perturbation theory, we develop simple expressions for electrostatic pressure with higher order corrections, mainly related to the curvature and slope of the electrode. These approximate expressions are validated through a comparison with analytical solutions for simple geometries as well as numerical results. The influence of the higher order correction on the pull-in behavior is illustrated for a large deflection model of a one-dimensional membrane (string), subjected to electrostatic and uniform mechanical pressure. An analytical solution is built and compared with the numerical solution obtained by the collocation method. The initial curvature of the string has a strong influence on the pull-in behavior. In the case of the nonlinear deflection-dependent tensile force, string bistability is possible.

Excitation of large-amplitude parametric resonance by the mechanical stiffness modulation of a microstructure

In this work we report on an approach allowing efficient parametric excitation of large-amplitude stable oscillations of a microstructure operated by a parallel-plate electrode, and present results of a theoretical and experimental investigation of the device. The frame-type structure, fabricated from a silicon on insulator (SOI) substrate using deep reactive ion etching (DRIE), consists a pair of cantilever-type suspensions connected at their ends by a link. The time-varying electrostatic force applied to the link by a parallel-plate electrode is transformed into a periodic tension of the beams, resulting in the modulation of their flexural stiffness and consequently the mechanical parametric excitation of the structure. The lateral compliance of the beams allows for large-amplitude in-plane oscillations in the direction parallel to the electrode while high axial stiffness prevents undesirable instabilities. The lumped model of the device, considered as an assembly of geometrically nonlinear massless flexures and a rigid massive link and built using the Rayleigh?Ritz method, predicted the feasibility of the excitation approach. The fabricated devices were operated in ambient air conditions by a combination of a steady (dc) and time-dependent (ac) components of voltage and the large-amplitude responses, up to 75 ?m, in the vicinity of the principal parametric and primary resonances were registered by means of video acquisition and image processing. The shapes of the experimental resonant curves were consistent with those predicted by the model. The location and size of the instability regions on the frequency?voltage plane (parametric tongues) were quantitatively in good agrement with the model results. Theoretical and experimental results indicate that the suggested approach can be efficiently used for excitation of various types of microdevices where stable resonant operation combined with robustness and large vibrational amplitudes are desirable.

Theoretical and experimental investigation of optically driven nanoelectromechanical oscillators

The actuation of biologically functional micro- and nanomechanical structures using optical excitation is an emerging arena of research that couples the fields of optics, fluidics, electronics, and mechanics with potential for generating novel chemical and biological sensors. In our work, we fabricated nanomechanical structures from 200 and 250 nm thick silicon nitride and single crystal silicon layers with varying lengths and widths ranging from 4 to 12 μm and 200 nm to 1 μm, respectively. Using a modulated laser beam focused onto the device layer in close proximity to the clamped end of a cantilever beam, we concentrate and guide the impinging thermal energy along the device layer. Cantilever beams coupled to chains of thermally isolated links were used to experimentally investigate energy transport mechanisms in nanostructures. The nature of the excitation was studied through steady-periodic axisymmetric thermal analysis by considering a multilayered structure heated using a modulated laser source. Res...

Efficient parametric excitation of silicon-on-insulator microcantilever beams by fringing electrostatic fields

Large amplitude flexural vibrations have been excited in single layer silicon-on-insulator micromechanical cantilever beams in ambient air environment. Our driving approach relies on a single co-planar electrode located symmetrically around the actuated grounded cantilever. Electrostatic forces are created via tailored asymmetries in the fringing fields of deformed mechanical states during their electric actuation, with strong restoring forces acting in a direction opposite to the deflection. This results in an effective increase in the structure stiffness in its elastic regime. The devices had been fabricated using deep reactive ion etching based process and their responses were characterized in a laser Doppler vibrometer under ambient conditions. Harmonic voltages applied to the electrode result in the periodic modulation of the effective stiffness and lead to strong parametric excitation of the structure. As opposed to close gap actuators, where high-amplitude drives are severely limited by pull-in ins...