Vibrational modes of ultrathin carbon nanomembrane mechanical resonators

We report measurements of vibrational mode shapes of mechanical resonators made from ultrathin carbon nanomembranes (CNMs) with a thickness of approximately 1 nm. CNMs are prepared from electron irradiation induced cross-linking of aromatic self-assembled monolayers and the variation of membrane thi...

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Bibliographic Details
Published in:Applied physics letters 2015-02, Vol.106 (6)
Main Authors: Zhang, Xianghui, Waitz, Reimar, Yang, Fan, Lutz, Carolin, Angelova, Polina, Gölzhäuser, Armin, Scheer, Elke
Format: Article
Language:English
Subjects:
Applied physics
CARBON
COMPARATIVE EVALUATIONS
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
CROSS-LINKING
Crosslinking
DISPERSION RELATIONS
Electron irradiation
ELECTRONS
FOURIER TRANSFORMATION
Fourier transforms
IRRADIATION
LIGHT SOURCES
Mathematical models
MEMBRANES
MOLECULES
NANOSTRUCTURES
Orifices
PIEZOELECTRICITY
RADIATION EFFECTS
RESONATORS
Self-assembled monolayers
Self-assembly
Silicon substrates
STRESSES
SUBSTRATES
SURFACES
TIME DEPENDENCE
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Summary:We report measurements of vibrational mode shapes of mechanical resonators made from ultrathin carbon nanomembranes (CNMs) with a thickness of approximately 1 nm. CNMs are prepared from electron irradiation induced cross-linking of aromatic self-assembled monolayers and the variation of membrane thickness and/or density can be achieved by varying the precursor molecule. Single- and triple-layer freestanding CNMs were made by transferring them onto Si substrates with square/rectangular orifices. The vibration of the membrane was actuated by applying a sinusoidal voltage to a piezoelectric disk on which the sample was glued. The vibrational mode shapes were visualized with an imaging Mirau interferometer using a stroboscopic light source. Several mode shapes of a square membrane can be readily identified and their dynamic behavior can be well described by linear response theory of a membrane with negligible bending rigidity. By applying Fourier transformations to the time-dependent surface profiles, the dispersion relation of the transverse membrane waves can be obtained and its linear behavior verifies the membrane model. By comparing the dispersion relation to an analytical model, the static stress of the membranes was determined and found to be caused by the fabrication process.
ISSN:0003-6951
1077-3118
DOI:10.1063/1.4908058