Noise analysis of geometrically complex mechanical structures using the analogy between electrical circuits and mechanical systems

Cataloged from PDF version of article.Random fluctuations of displacement or velocity in mechanical systems can be calculated by using the analogy between electrical circuits and mechanical systems. The fluctuation-dissipation theorem expresses the relation between the generalized mechanical admittance and the noise in velocity. Similarly, correlation of mechanical noise can be calculated by using the generalized Nyquist theorem which states that the current noise correlation between two ports in an electrical circuit is dictated by the real part of the transadmittance. In this article, we will present the determination of the mechanical transadmittance and we will use the mechanical transadmittance to calculate the noise correlation on geometrically complex structures where it is not possible to approximate the noise by using the simple harmonic oscillator model. We will apply our method to atomic force microscope cantilevers by means of finite element method tools. The application of the noise correlation calculation method to rectangular cantilever beams shows some interesting results. We found that on the resonance frequencies, the correlation coefficient takes values 1 (full correlation) and -1 (anti-correlation) along the cantilever axis depending on the mode shapes of the structure. (C) 1999 American Institute of Physic

Analysis and design of interdigital cantilever as a displacement sensor

Cataloged from PDF version of article.The interdigital ~ID! cantilever with two sets of interleaving fingers is an alternative to the conventional cantilever used in the atomic force microscope ~AFM!. In this paper we present a detailed analysis of the interdigital cantilever and its use as a sensor for the AFM. In this study, we combine finite element analysis with diffraction theory to simulate the mechanically induced optical response of the ID. This model is used to compare this system with the optical lever detector as used in conventional instruments by analyzing the ratio of signal to noise and overall performance. We find that optical detection of the cantilever motion with interdigital fingers has two advantages. When used in conjunction with arrays of cantilevers it is far easier to align. More importantly, it is immune to laser pointing noise and thermally excited mechanical vibrations and this improves the sensitivity as compared to the optical lever. © 1998 American Institute of Physics

Two dimensional micromechanical bimorph arrays for detection of thermal radiation

Cataloged from PDF version of article.We demonstrate that two-dimensional arrays of micromechanical bimorphs can be used as thermal sensors to image infrared (IR) radiation. A density of 100 pixels per mm(2) is achieved by coiling a bimorph beam into the shape of a flat spiral. Temperature variations of a given spiral are converted to modulations of visible light by illuminating the spiral array with a visible source. The optical properties of the spiral resemble a Fresnel zone plate when light reflected off neighboring rings of the spiral is focused. When a spiral is heated through the absorption of IR radiation, thermally induced bending of the bimorph degrades the focusing efficiency by distorting the spiral. This reduces the optical intensity at the focal point. Arrays of spirals can be monitored with a commercial CCD camera. At 40 Hz, the temperature resolution and noise equivalent power of a 75 mu m diam spiral are 50 mu K/root Hz and 20 nW/root Hz, respectively, and the thermal response time is 270 mu s. (C) 1997 American Institute of Physics

Centimeter scale atomic force microscope imaging and lithography

Cataloged from PDF version of article.We present a 4 mm2 image taken with a parallel array of 10 cantilevers, an image spanning 6.4 mm taken with 32 cantilevers, and lithography over a 100 mm2 area using an array of 50 cantilevers. All of these results represent scan areas that are orders of magnitude larger than that of a typical atomic force microscope (0.01 mm2). Previously, the serial nature and limited scan size of the atomic force microscope prevented large scale imaging. Our design addresses these issues by using a modular micromachined parallel atomic force microscope array in conjunction with large displacement scanners. High-resolution microscopy and lithography over large areas are important for many applications, but especially in microelectronics, where integrated circuit chips typically have nanometer scale features distributed over square centimeter areas. © 1998 American Institute of Physics

Automated parallel high-speed atomic force microscopy

Cataloged from PDF version of article.An expandable system has been developed to operate multiple probes for the atomic force microscope in parallel at high speeds. The combined improvements from parallelism and enhanced tip speed in this system represent an increase in throughput by over two orders of magnitude. A modular cantilever design has been replicated to produce an array of 50 cantilevers with a 200 μm pitch. This design contains a dedicated integrated sensor and integrated actuator where the cells can be repeated indefinitely. Electrical shielding within the array virtually eliminates coupling between the actuators and sensors. The reduced coupling simplifies the control electronics, facilitating the design of a computer system to automate the parallel high-speed arrays. This automated system has been applied to four cantilevers within the array of 50 cantilevers, with a 20 kHz bandwidth and a noise level of less than 50 Å. For typical samples, this bandwidth allows us to scan the probes at 4 mm/s. © 1998 American Institute of Physic

Parallel atomic force microscopy with optical interferometric detection

Cataloged from PDF version of article.We have developed an atomic force microscope that uses interferometry for parallel readout of a cantilever array. Each cantilever contains a phase sensitive diffraction grating consisting of a reference and movable set of interdigitated fingers. As a force is applied to the tip, the movable set is displaced and the intensity of the diffracted orders is altered. The order intensity from each cantilever is measured with a custom array of siliconphotodiodes with integrated complementary metal–oxide–semiconductor amplifiers. We present images from five cantilevers acquired in the constant height mode that reveal surface features 2 nm in height. The interdigital method for cantilever array readout is scalable, provides angstrom resolution, and is potentially simpler to implement than other methods. © 2001 American Institute of Physic

Characterization and imaging with lamb wave lens at gigahertz frequencies

Lamb wave lenses with conical refracting surfaces are fabricated for use at 400 MHz and 1 GHz. The conical surfaces are ground and polished with mechanical means and they are sufficiently smooth for the frequencies of interest. The wide bandwidth of transducers allow frequency tuning necessary for Lamb wave lenses. The fabricated lenses show the expected V(Z) performance. At high frequencies the attenuation in the coupling medium can be very high, but due to the smaller wavelength the resolution is better and defocus distance can be reduced. Inherently higher leaky wave sensitivity of Lamb wave lens enables a good V(Z) characterization ability at higher frequencies as compared to the conventional spherical lens. Subsurface imaging with these Lamb wave lenses gives satisfactory results for layered structures. Chosen object has leaky wave modes within the angular coverage of the lens. The images exhibit a resolution close to the diffraction limit. Experimental V(Z) curves obtained with these lenses along with images are presented

A nanomechanical resonator shuttling single electrons at radio frequencies

We observe transport of electrons through a metallic island on the tip of a nanomechanical pendulum. The resulting tunneling current shows distinct features corresponding to the discrete mechanical eigenfrequencies of the pendulum. We report on measurements covering the temperature range from 300 K down to 4.2 K. We explain the I-V curve, which differs from previous theoretical predictions, with model calculations based on a Master equation approach.Comment: 5 pages, 4 jpeg-figure

High-speed tapping mode imaging with active Q control for atomic force microscopy

Cataloged from PDF version of article.The speed of tapping mode imaging with the atomic force microscope(AFM) has been increased by over an order of magnitude. The enhanced operation is achieved by (1) increasing the instrument’s mechanical bandwidth and (2) actively controlling the cantilever’s dynamics. The instrument’s mechanical bandwidth is increased by an order of magnitude by replacing the piezotube z-axis actuator with an integrated zinc oxide (ZnO)piezoelectric cantilever. The cantilever’s dynamics are optimized for high-speed operation by actively damping the quality factor (Q) of the cantilever. Active damping allows the amplitude of the oscillating cantilever to respond to topography changes more quickly. With these two advancements, 80μm×80 μm high-speed tapping mode images have been obtained with a scan frequency of 15 Hz. This corresponds to a tip velocity of 2.4 mm/s. © 2000 American Institute of Physic

Integration of through-wafer interconnects with a two-dimensional cantilever array

Cataloged from PDF version of article.High-density through-wafer interconnects are incorporated in a two-dimensional (2D) micromachined cantilever array. The design addresses alignment and density issues associated with 2D arrays. Each cantilever has piezoresistive deflection sensors and high-aspect ratio silicon tips. The fabrication process and array operation are described. The integration of cantilevers, tips, and interconnects enables operation of a high-density 2D scanning probe array over large areas. (C) 2000 Elsevier Science S.A. All rights reserved