Rajashree Baskaran

Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor

Abstract Parametric resonance has been well established in many areas of science, including the stability of ships, the forced motion of a swing and Faraday surface wave patterns on water. We have previously investigated a linear parametrically driven torsional oscillator and along with other groups have mentioned applications including mass sensing, parametric amplification, and others. Here, we thoroughly investigate the design of a highly sensitive mass sensor. The device we use to carry out this study is an in-plane parametrically resonant oscillator. We show that in this configuration, the nonlinearities (electrostatic and mechanical) have a large impact on the dynamic response of the structure. This result is not unique to this oscillator—many MEMS oscillators display nonlinearities of equal importance (including the very common parallel plate actuator). We report the effects of nonlinearity on the behavior of parametric resonance of a micro-machined oscillator. A nonlinear Mathieu equation is used to model this problem. Analytical results show that nonlinearity significantly changes the stability characteristics of parametric resonance. Experimental frequency response around the first parametric resonance is well validated by theoretical analysis. Unlike parametric resonance in the linear case, the jumps (very critical for mass sensor application) from large response to zero happen at additional frequencies other than at the boundary of instability area. The instability area of the first parametric resonance is experimentally mapped. Some important parameters, such as damping co-efficient, cubic stiffness and linear electrostatic stiffness are extracted from the nonlinear response of parametric resonance and agree very well with normal methods.

Tunable Microelectromechanical Filters that Exploit Parametric Resonance

Background: This paper describes an analytical study of a bandpass filter that is based on the dynamic response of electrostatically-driven MEMS oscillators. Method of Approach: Unlike most mechanical and electrical filters that rely on direct linear resonance for filtering, the MEM filter presented in this work employs parametric resonance. Results: While the use of parametric resonance improves some filtering characteristics, the

Contact transfer of aligned carbon nanotube arrays onto conducting substrates

The authors demonstrate the fabrication of different architectures of carbon nanotubes on conducting substrates via contact transfer of nanotubes using low temperature solders. Lithographically patterned multiwalled carbon nanotube arrays grown on silica substrates by chemical vapor deposition methods are transferred onto solder coated substrates. Both negative and positive patterns can be obtained by changing the printing parameters. Good wetting and electrical contacts are confirmed by measuring their field emission properties. This method can be used to construct nanotube structures of different shapes and dimensions over large areas on substrates of choice and could be a feasible process to integrate nanotubes into various devices.

Silicon oxide thickness-dependent growth of carbon nanotubes

Recent discovery of substrate-selective growth of carbon nanotubes on SiO2 in exclusion to Si, has opened up the possibility of organizing nanotubes on Si/SiO2 patterns in premeditated configurations for building devices. Here, we report the strong dependence of nanotube growth on the SiO2 layer thickness, and the utility of this feature to build three-dimensional architectures. Our results show that there is no detectable nanotube growth on SiO2 layers with thickness (TSiO2) less than ∼5–6 nm. For 6 nm 50 nm. We grew nanotubes with multiple lengths at close proximity in a single step by using substrates with regions of different TSiO2. Such processing strategies would be attractive for creating nanotube mesoscale architectures for device applications.

Mechanical domain coupled mode parametric resonance and amplification in a torsional mode micro electro mechanical oscillator

In this paper, we experimentally demonstrate non-degenerate parametric resonance in a torsional micro electro mechanical (MEM) oscillator with two interacting mechanical modes of oscillation. The parametric oscillation results from a displacement-dependent electrostatic force generated in both the modes of oscillation. There is a decoupling of the input and the output frequencies in this mode of operation where the system responds at the primary natural frequency when driven at the sum of the first two mechanical modes. This can be implemented in many commonly used MEM oscillator configurations including the cantilever beam geometry. In this mode of operation, single oscillator non-degenerate parametric amplifiers as well as resonant mode sensors based on the frequency selectivity of parametric resonance can be implemented.

Tuning the dynamic behavior of parametric resonance in a micromechanical oscillator

We describe how to significantly change the dynamic behavior of parametric resonance in a micromechanical oscillator. By varying the voltage amplitude of applied electrical signal, the frequency response of the first order parametric resonance changes dramatically. We attribute this variation to the tuning of effective cubic stiffness of the oscillator, which is a contribution of both structural and electrical cubic stiffness. This phenomenon is well explained by the first-order perturbation analysis of nonlinear Mathieu equation.

Controlling Liquid Drops with Texture Ratchets

Controlled vibration selectively propels multiple microliter-sized drops along microstructured tracks, leading to simple microfluidic systems that rectify oscillations of the three-phase contact line into asymmetric pinning forces that propel each drop in the direction of higher pinning.

Understanding mechanical domain parametric resonance in microcantilevers

In this paper we present a mathematical model for the dynamics of an electrostatically actuated micro-cantilever. For the common case of cantilevers excited by a periodic voltage, we show that the underlying linearized dynamics are those of a periodic system described by a Mathieu equation. We present experimental results that confirm the validity of the model, and in particular illustrate that parametric resonance phenomena occur in capacitively actuated micro-cantilevers. The combined parametric/harmonic mode of operation is investigated as well and experimental data are provided.

High-Speed Flex-Circuit Chip-to-Chip Interconnects

High-speed chip-to-chip interconnect utilizing flex-circuit technology is investigated for extending the lifetime of copper-based system-level channels. Proper construction of the flex ribbon is shown to improve the raw bandwidth over standard FR-4 boards by about three times. Active testing results from a 130-nm CMOS test vehicle show the potential of up to two times higher data rates. The next-generation test vehicle with 90-nm CMOS circuits gives improved voltage and timing margins at 20 Gb/s. In an interconnect limited case a channel with 36 in (91.4 cm) of flex runs at 18.2 Gb/s data rate at a bit-error ratio (BER) of better than 10-12. The channel includes two 90-nm CMOS test chips, two organic flip-chip package substrates, and two flex connectors; crosstalk is not included in this experiment. High-speed connector solutions, including results from a ldquosplit socketrdquo assembly test vehicle, are discussed in detail. The characterization of two top-side flex connector prototypes demonstrates their basic durability and good high-frequency performance. Samples survive 100 mating cycles at an average contact resistance of less than 30 mOmega, adequate for high-speed signaling. Measured differential insertion loss is less than 1.5 dB up to 10 GHz and less than 3.5 dB up to 20 GHz. Near-end and far-end crosstalk measurements indicate that the connectors exceed crosstalk specifications.

Parametrically Excited MEMS-Based Filters

In this paper we describe the dynamics of MEMS oscillators that can be used as frequency filters. The unique feature of these devices is that they use parametric resonance, as opposed to the usual linear resonance, for frequency selection. However, their response in the parametric resonance zone has some undesirable features from the standpoint of filter performance, most notably that their bandwidth depends on the amplitude of the input and the nonlinear nature of the response. Here we provide a brief background on filters, a MEMS oscillator that overcomes some of the deficiencies, and we offer a description of how one might utilize a pair of these MEMS oscillators to build a band-pass filter with nearly ideal stopband rejection. These designs are made possible by the fact that MEMS devices are highly tunable, which allows one to build in system features to achieve desired performance.