Nonlinear behavior and temperature-dependence of frequency in silicon bulk-mode micromechanical resonators
矽基體振動模式微機械諧振器的非線行為及頻率溫度相關性
Student thesis: Doctoral Thesis
Author(s)
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Detail(s)
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| Award date | 10 Mar 2015 |
Link(s)
| Permanent Link | https://scholars.cityu.edu.hk/en/theses/theses(fb0316a2-e34d-44ef-963e-f5f9603de61f).html |
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| Other link(s) | Links |
Abstract
"Silicon bulk-mode micromechanical (MEMS) resonators, given their high quality factors (Q's), are key elements in high-performance MEMS oscillators, which are reshaping the timing devices market by offering low-cost and fully-integrated solutions. The phase noise (PN) performance and frequency stability over the industrial temperature range (-40°C to 85°C) are two major bottlenecks to realizing high-end application MEMS oscillators. The nonlinearity of the resonator sets a fundamental limit on the PN performance while frequency-temperature dependence needs to be quantitatively examined for improving the frequency stability against temperature change. In this thesis, these two aspects and their correlations are comprehensively explored.
This thesis covers the design, fabrication, and characterization of various single-crystal-silicon (SCS) bulk-mode resonators. These include resonators dominated by longitudinal-waves (like square-extensional and length-extensional mode resonators) as well as resonators dominated by shear-waves (like Lame and face-shear mode resonators). These bulk-mode resonators exhibit very high Q ranging from 10 5~10 6, leading to fQ products in the order of 10 13 and close to the fundamental limit of SCS.
A three-level modeling framework (from bottom to top: material, device, and system levels) is proposed to simulate the nonlinear behavior of MEMS devices. This proposed framework offers the capability to predict the nonlinear behavior of the silicon bulk-mode resonators, dominated by material-nonlinearity, from the atomic structure of the crystal lattice as the basis. Close agreement between simulations and measurements is obtained. In addition, reversed nonlinearity (softening vs. hardening) has been observed in devices with the same physical dimensions but aligned to different crystal orientations, indicating the material nonlinearity is highly orientation dependent. To cancel the undesirable nonlinearity, this thesis describes a novel electronic tuning mechanism that cancels out the nonlinearity in bulk-mode resonators, which is achieved for the first time.
The temperature dependence of frequency in silicon bulk-mode resonators tend to be affected by doping type and concentration. A quantitative study based on free carrier contribution on elastic constants is performed to predict the temperature coefficient of frequency (TCf) of n-type doped resonators with different vibration modes and crystal orientations. The predicted TCf values agree well with the experimental results. The measured TCfs are found to also be orientation dependent and, as expected, can be correlated with the observed nonlinear behaviors.
Finally, to demonstrate the application of silicon bulk-mode resonators for MEMS oscillators, this thesis describes the implementation of 17.6MHz MEMS oscillators based on wafer-level vacuum packaged silicon Lame-mode resonators. The oscillators only require less than 3V bias voltage and show good PN performance of -127dBc/Hz at 1kHz offset. Their PN performance could be further improved by implementing the proposed nonlinearity cancellation concept."
This thesis covers the design, fabrication, and characterization of various single-crystal-silicon (SCS) bulk-mode resonators. These include resonators dominated by longitudinal-waves (like square-extensional and length-extensional mode resonators) as well as resonators dominated by shear-waves (like Lame and face-shear mode resonators). These bulk-mode resonators exhibit very high Q ranging from 10 5~10 6, leading to fQ products in the order of 10 13 and close to the fundamental limit of SCS.
A three-level modeling framework (from bottom to top: material, device, and system levels) is proposed to simulate the nonlinear behavior of MEMS devices. This proposed framework offers the capability to predict the nonlinear behavior of the silicon bulk-mode resonators, dominated by material-nonlinearity, from the atomic structure of the crystal lattice as the basis. Close agreement between simulations and measurements is obtained. In addition, reversed nonlinearity (softening vs. hardening) has been observed in devices with the same physical dimensions but aligned to different crystal orientations, indicating the material nonlinearity is highly orientation dependent. To cancel the undesirable nonlinearity, this thesis describes a novel electronic tuning mechanism that cancels out the nonlinearity in bulk-mode resonators, which is achieved for the first time.
The temperature dependence of frequency in silicon bulk-mode resonators tend to be affected by doping type and concentration. A quantitative study based on free carrier contribution on elastic constants is performed to predict the temperature coefficient of frequency (TCf) of n-type doped resonators with different vibration modes and crystal orientations. The predicted TCf values agree well with the experimental results. The measured TCfs are found to also be orientation dependent and, as expected, can be correlated with the observed nonlinear behaviors.
Finally, to demonstrate the application of silicon bulk-mode resonators for MEMS oscillators, this thesis describes the implementation of 17.6MHz MEMS oscillators based on wafer-level vacuum packaged silicon Lame-mode resonators. The oscillators only require less than 3V bias voltage and show good PN performance of -127dBc/Hz at 1kHz offset. Their PN performance could be further improved by implementing the proposed nonlinearity cancellation concept."
