Yafei Li and Clark Nguyen

EECS Department, University of California, Berkeley

Technical Report No. UCB/EECS-2018-60

May 11, 2018

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2018/EECS-2018-60.pdf

The growing need for high performance but low power microelectromechanical system (MEMS) devices capable of operating at various frequency regimes, including high frequency (HF), very high frequency (VHF) and ultra-high frequency (UHF), fuels an increasing demand for resonators with simultaneous high quality factor (Q) and high electromechanical coupling, as gauged by the motional-to-static capacitive ratio (C_x/C_o). Capacitive-gap transduced resonators have already posted some of the highest disk C_x/C_o-Q products to date at HF and low-VHF. Attaining similar performance at the high-VHF and UHF ranges, however, if more difficult, as it requires electrode-to-resonator gaps considerably smaller than previously demonstrated. This thesis explores a method that raises C_x/C_o without excessive gap-scaling by hollowing out a disk resonator structure, which reduces the dynamic mass and stiffness of the structure. Since C_x/C_o goes as the reciprocal of mass and stiffness, a hollow disk can have considerably stronger electromechanical coupling than a solid one at the same frequency. This work introduces two types of hollow disks: asymmetric and symmetric. In an asymmetric hollow disk, a thin sidewall ring protrudes upward from the edges of an inner disk that itself anchors to the substrate via a center stem. The inner disk still vibrates in the radial contour mode in the radial direction. However, a few nonidealities influence this asymmetric structure, including transverse vibration of the inner disk and reduction of the nominal resonance frequency. The sidewall vibrates in a radial cantilever mode, which boosts C_x/C_o even higher. In addition, the negative capacitance (-C_e) in the equivalent circuit does not always equal the static capacitance (C_o). As a result, an 80 MHz asymmetric radial contour hollow disk achieves C_x/C_o=0.142% and C_x/C_e=0.358% with a 148 nm electrode-to-resonator gap and a 20 V DC bias, while a solid disk only has C_x/C_o=0.015% with the same resonance frequency, gap spacing, and DC bias. In a symmetric hollow disk, the sidewall ring protrudes in both upwards and downwards directions along the inner disk edges. As long as the stem anchor is small, the symmetry eliminates vertical vibration nonidealities, allowing for even better performance. Unfortunately, post-fabrication stress gradients rendered testable only a large-stemmed 98 MHz symmetric hollow disk. Although its large stem compromised its mode shape, this device still achieves C_x/C_o=0.261% and C_x/C_e=0.430% with a 50 nm electrode-to-resonator gap and a 7 V DC bias, both higher than achievable by a similar frequency solid disk. C_e is only 0.442C_o, which makes its parallel frequency (f_p) is parabolically dependent on DC bias.

Advisors: Clark Nguyen

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BibTeX citation:

@mastersthesis{Li:EECS-2018-60,
    Author= {Li, Yafei and Nguyen, Clark},
    Title= {Hollow Disk Electromechanical Coupling Cx/Co Boosting},
    School= {EECS Department, University of California, Berkeley},
    Year= {2018},
    Month= {May},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2018/EECS-2018-60.html},
    Number= {UCB/EECS-2018-60},
    Abstract= {The growing need for high performance but low power microelectromechanical system (MEMS) devices capable of operating at various frequency regimes, including high frequency (HF), very high frequency (VHF) and ultra-high frequency (UHF), fuels an increasing demand for resonators with simultaneous high quality factor (Q) and high electromechanical coupling, as gauged by the motional-to-static capacitive ratio (C_x/C_o). Capacitive-gap transduced resonators have already posted some of the highest disk C_x/C_o-Q products to date at HF and low-VHF. Attaining similar performance at the high-VHF and UHF ranges, however, if more difficult, as it requires electrode-to-resonator gaps considerably smaller than previously demonstrated. 
This thesis explores a method that raises C_x/C_o without excessive gap-scaling by hollowing out a disk resonator structure, which reduces the dynamic mass and stiffness of the structure. Since C_x/C_o goes as the reciprocal of mass and stiffness, a hollow disk can have considerably stronger electromechanical coupling than a solid one at the same frequency. This work introduces two types of hollow disks: asymmetric and symmetric.
In an asymmetric hollow disk, a thin sidewall ring protrudes upward from the edges of an inner disk that itself anchors to the substrate via a center stem. The inner disk still vibrates in the radial contour mode in the radial direction. However, a few nonidealities influence this asymmetric structure, including transverse vibration of the inner disk and reduction of the nominal resonance frequency. The sidewall vibrates in a radial cantilever mode, which boosts C_x/C_o even higher. In addition, the negative capacitance (-C_e) in the equivalent circuit does not always equal the static capacitance (C_o). As a result, an 80 MHz asymmetric radial contour hollow disk achieves C_x/C_o=0.142% and C_x/C_e=0.358% with a 148 nm electrode-to-resonator gap and a 20 V DC bias, while a solid disk only has C_x/C_o=0.015% with the same resonance frequency, gap spacing, and DC bias.
In a symmetric hollow disk, the sidewall ring protrudes in both upwards and downwards directions along the inner disk edges. As long as the stem anchor is small, the symmetry eliminates vertical vibration nonidealities, allowing for even better performance. Unfortunately, post-fabrication stress gradients rendered testable only a large-stemmed 98 MHz symmetric hollow disk. Although its large stem compromised its mode shape, this device still achieves C_x/C_o=0.261% and C_x/C_e=0.430% with a 50 nm electrode-to-resonator gap and a 7 V DC bias, both higher than achievable by a similar frequency solid disk. C_e is only 0.442C_o, which makes its parallel frequency (f_p) is parabolically dependent on DC bias.},
}

EndNote citation:

%0 Thesis
%A Li, Yafei 
%A Nguyen, Clark 
%T Hollow Disk Electromechanical Coupling Cx/Co Boosting
%I EECS Department, University of California, Berkeley
%D 2018
%8 May 11
%@ UCB/EECS-2018-60
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2018/EECS-2018-60.html
%F Li:EECS-2018-60