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Study of the out-of-plane vibrational modes in thin-film amorphous silicon micromechanical disk resonators
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10.1063/1.4803681
/content/aip/journal/jap/113/17/10.1063/1.4803681
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/17/10.1063/1.4803681

Figures

Image of FIG. 1.
FIG. 1.

Schematic representation of the shape of the vibrational modes of a plate. The dashed lines represent the nodal diametral and radial lines.

Image of FIG. 2.
FIG. 2.

(a) Resonance frequency as a function of disk radius of an a-Si:H disk in the cases of a plate (  = 3.196) and membrane (  = 2.405), according to Eq. (2) ( = 3 m) (b).

Image of FIG. 3.
FIG. 3.

(a) Schematic of cross section of disk resonator. (b) SEM micrograph of a thin-film silicon microresonator fabricated on a glass substrate with one pair of actuation electrodes.

Image of FIG. 4.
FIG. 4.

Resonance peaks of a 200 m diameter disk resonator measured in vacuum with in-phase actuation (top) and anti-phase actuation (bottom).

Image of FIG. 5.
FIG. 5.

Tension parameter as a function of the disk radius for the first vibrational mode (0,1) in the plate-like ( < 2) and membrane-like ( > 20) limits.

Image of FIG. 6.
FIG. 6.

Resonance frequency as a function of the inverse disk radius for a-Si:H resonator modes (0,1) and (0,2) measured in vacuum (10 Pa).

Image of FIG. 7.
FIG. 7.

Nonlinear vibrations effect due to large deformation at high bias voltage for a 100-m radius disk.

Image of FIG. 8.
FIG. 8.

Quality factor measured in vacuum as a function of the resonance frequency for a-Si:H disk resonators with radius that ranges from 50 m to 113 m.

Image of FIG. 9.
FIG. 9.

Quality factor as a function of resonance frequency for the families of modes with multiple number of radial nodes (100 m radius disk resonator).

Image of FIG. 10.
FIG. 10.

Resonance frequency variation relative to unannealed state (top) and quality factor (bottom) for a series of 6 successive 1 h annealing steps at 250 °C.

Image of FIG. 11.
FIG. 11.

Quality factor variation as a function of time for modes (0,1), (1,1)a, (1,1)b, and (0,2) of a 100 m radius disk resonator.

Tables

Generic image for table
Table I.

Values of () for a disk clamped along the edges in the limit of negligible tension .

Generic image for table
Table II.

Values of () for a disk clamped along the edges in the limit of high tension .

Generic image for table
Table III.

Non-degenerated frequencies of modes (1,1) and (2,1) of a 125 m radius disk.

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/content/aip/journal/jap/113/17/10.1063/1.4803681
2013-05-02
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Study of the out-of-plane vibrational modes in thin-film amorphous silicon micromechanical disk resonators
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/17/10.1063/1.4803681
10.1063/1.4803681
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