Lynn Khine

High-Q bulk-mode SOI square resonators with straight-beam anchors

In this paper, the performance of 6.35 MHz Lame-mode square resonators with different dimensions of straight-beam anchor supports is presented, with quality factor values exceeding one million in ambient pressures as high as 150 Pa. A maximum Q value of 1.70 million was experimentally measured for some of the square resonators at a vacuum pressure of 36 µTorr. The Q values of square resonators were relatively independent of pressure at levels below 100 Pa, which suggests that Q is pressure limited due to air damping only when pressures become higher than 100 Pa. Dimensions of straight-beam anchors placed at the four corners of the square resonator lead to tradeoffs among achievable Q, power handling capabilities and motional resistance. Longer anchor beams generally provide good signal-to-noise performance of a square resonator at lower dc bias; however, the resonator goes into the nonlinear regime at lower ac–dc drive amplitudes, which means reduced power handling capability. The benefit of shorter anchors is that the resonator is able to operate in a linear mode under high drive conditions. Depending on the type of application, anchor dimensions can be chosen such that the resonators performance is optimal in terms of a quality factor, motional resistance and power handling. The resonators were fabricated using the silicon-on-insulator multi-user MEMS process from MEMSCAP.

6Mhz Bulk-Mode Resonator with Q Values Exceeding One Million

In this paper, we report a 6.3 MHz Lame-mode square resonator with fully differential drive and sense electronics, exhibiting quality factor, Q values exceeding 1 million in ambient pressures as high as 100 Pa. A maximum Q value of 1.6 million was experimentally measured at vacuum pressure of 36 muTorr. It was also experimentally observed that the Q value for the bulk mode resonator was relatively independent for pressures below 100 Pa suggesting that the Q is pressure limited for pressure higher than 100 Pa. This resonator was fabricated using SOIMUMPs process from MEMSCAP.

Nonlinearity in micromechanical free–free beam resonators: modeling and experimental verification

In this paper, we present a systematic characterization and modeling technique for the micromechanical free?free beam resonator to analyze its nonlinear vibration behavior. Different from the conventional FEM-based approach whose simulation accuracy is usually limited around 60?70%, the proposed modeling method is able to accurately identify both the mechanical and electrostatic nonlinear parameters from just a few preliminary experimental observations. The nonlinear equation of motion is then numerically solved, demonstrating both the spring hardening and softening effects in the system. The simulated nonlinear behavior of the resonator under different driving conditions is validated by comparing them with the experimental data. In addition, based on the verified nonlinear model, design guidelines such as the nonlinearity cancellation are also highlighted. Although this work focuses on the free?free beam resonators, the proposed modeling approach can be applied to any other electrostatically driven microresonator to reveal different intrinsic nonlinear properties of the device.

12.9MHz Lame-Mode Differential SOI Bulk Resonators

In this paper, differentially driven 12.9 MHz square resonators in Lame mode with two different types of anchor - T-anchor and straight beam anchor are presented in an attempt to investigate how the anchor design influences the quality factor, Q values. These square resonators operated in a vacuum pressure of 36 muTorr exhibited Q values of 807,000 and 404,000, respectively. This difference in Q values for the two resonators is probably due to differing energy losses in their respective anchors. These resonators were fabricated using SOIMUMPs process from MEMSCAP.

Nonlinear behavior of Lamé-mode SOI bulk resonator

In this paper, we report for the first time the detailed analysis of the nonlinear behavior of a Lame-mode SOI bulk resonator. The measured resonant frequency of the resonator was 6.35 MHz with a quality factor of 1.7 million in the ambient pressure of 0.02 Pa. We used the two-step semi-analytic approach to characterize the model parameters of the resonator and the nonlinear model of the resonator was verified by the experimental results. Our study shows that the Lame-mode bulk resonator has three orders of magnitude larger maximum energy storage capability than the flexural beam resonator, leading to improved overall phase noise performance of the resonator-based oscillator.

Characterization of SOI Lamé-mode square resonators

Characterization of Lame-mode square resonators with different straight-beam anchor lengths, structural layer thickness, and number of anchor support reveals that there is likely an optimal range of anchor designs that provide high quality factor (Q) above one million, along with low motional resistance. Shorter anchor length restricts resonator vibrations and motional resistance could be increased by 3.5 times compared to resonators with longer anchor length. Two-anchor support design is able to achieve higher Qpsilas but results in higher motional resistance compared to four-anchor support. When structural thickness is reduced from 25 mum to 10 mum, Q gets degraded but still maintained above one million.

Behavioural modelling and system-level simulation of micromechanical beam resonators

This paper presents a behavioural modelling technique for micromechanical beam resonators that enables the simulation of MEMS resonator model in Analog Hardware Description Language (AHDL) format within a system-level circuit simulation. A 1.13 MHz clamped-clamped beam and a 10.4 MHz free-free beam resonators have been modelled into Verilog-A code and successfully simulated with Spectre in Cadence. Analysis has shown that both models behave well and their electrical characteristics are in agreement with the theory.