(Color online) (a) Bright-field optical microscope image of a typical set of released UNCD cantilever resonator beams with an overhang. As a result of optical interference, the free standing UNCD and UNCD on silicon substrate show a color contrast (see the online version). (b) SEM image of a single cantilever beam. FIB milling was conducted at the cantilever base to reduce or eliminate any overhang, as indicated. Portions of the UNCD appear with darker contrast simply due to charging of a previously SEM-imaged region.
(Color online) Representative data for the frequency shift relative to the low temperature limiting value and the absolute resonant frequency (inset) as a function of temperature for the fundamental and the first harmonic for a typical UNCD cantilever (in this case, 460 μm long with no overhang). Measurements were obtained on three different levers with varying lengths (350 μm to 460 μm) and overhangs (no overhang to 30 μm overhang). This particular cantilever has had more data points and a broader temperature range over which the data has been collected, and hence these data are used for calculations, but results were consistent between cantilevers. These plots include data points taken during both heating and cooling cycles (individual cantilevers have gone through at least three cycles), and are reproducible. Heating and cooling rates were approximately 1 K/min. Higher order modes of the cantilevers also show a similar relative temperature dependence in terms of frequency and, hence, modulus.
(Color online) Temperature dependence of Young’s modulus (relative to the low temperature limiting value) of UNCD (squares) and single crystal diamond (triangles6 and circles7) averaged over all directions. Also shown are an Einstein oscillator fit and a Grüneisen–Debye fit for the UNCD data. The Grüneisen–Debye fit, derived for the low temperature limit, diverges at higher temperatures, as expected.
(Color online) A comparison of dissipation as a function of temperature for carbon based resonators. Lever 1 (black squares) had no overhang (the resonant frequency shift of this cantilever is shown in Fig. 2), and Lever 2 (red squares) had an overhang of ∼30 μm (the initial overhang was reduced to this value using FIB). Data include both heating and cooling measurements; no hysteresis is evident. Also plotted are data of UNCD fixed-fixed beams (5 MHz, flexural),26 NCD paddle oscillators (∼5.5 KHz, torsional),25 NCD fixed-fixed beams (13.7 MHz, flexural),30 ta-C paddle oscillators (∼5.5 KHz, torsional),24 cantilevers (∼60 KHz, flexural)29 and single crystal diamond (SCD) dome resonators (50 MHz, flexural).32 Inset: UNCD cantilever data on a linear scale indicating the change in slope.
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