Hadi Najar

High quality factor nanocrystalline diamond micromechanical resonators limited by thermoelastic damping

We demonstrate high quality factor thin-film nanocrystalline diamond micromechanical resonators with quality factors limited by thermoelastic damping. Cantilevers, single-anchored and double-anchored double-ended tuning forks, were fabricated from 2.5 μm thick in-situ boron doped nanocrystalline diamond films deposited using hot filament chemical vapor deposition. Thermal conductivity measured by time-domain thermoreflectance resulted in 24 ± 3 W m−1 K−1 for heat transport through the thickness of the diamond film. The resonant frequencies of the fabricated resonators were 46 kHz–8 MHz and showed a maximum measured Q ≈ 86 000 at fn = 46.849 kHz. The measured Q-factors are shown to be in good agreement with the limit imposed by thermoelastic dissipation calculated using the measured thermal conductivity. The mechanical properties extracted from resonant frequency measurements indicate a Youngs elastic modulus of ≈788 GPa, close to that of microcrystalline diamond.

Hemispherical wineglass resonators fabricated from the microcrystalline diamond

We present the development of millimeter scale 3D hemispherical shell resonators fabricated from the polycrystalline diamond, a material with low thermoelastic damping and very high stiffness. These hemispherical wineglass resonators with 1.1 mm diameter are fabricated through a combination of micro-electro discharge machining (EDM) and silicon micromachining techniques. Using piezoelectric and electrostatic excitation and optical vibration measurement, the elliptical wineglass vibration mode is determined to be at 18.321 kHz, with the two degenerate wineglass modes having a relative frequency mismatch of 0.03%. A study on the effect of the size and misalignment of the anchor and resonator’s radius variation on both the average frequency and frequency mismatch of the 2θ elliptical vibration modes is carried out. It is shown that the absolute frequency of a wineglass resonator will increase with the anchor size. It is also demonstrated that the fourth harmonic of radius variation is linearly related to the frequency mismatch. (Some figures may appear in colour only in the online journal)

Quadrature FM gyroscope

A dual mass vibratory gyroscope sensor demonstrates the quadrature frequency modulated (QFM) operating mode, where the frequency of the circular orbit of a proof mass is measured to detect angular rate. In comparison to the mode-matched open loop rate mode, the QFM mode receives the same benefit of improved SNR but without the penalties of unreliable scale factor and decreased bandwidth. A matched pair of gyroscopes, integrated onto the same die, is used for temperature compensation, resulting in 6 ppb relative frequency tracking error, or an Allan deviation of 370 deg/hr with a 70 kHz resonant frequency. The integrated CMOS electronics achieve a capacitance resolution of 0.1 zF/rt-Hz with nominal 6 fF sense electrodes.

Micromachining 3D hemispherical features in silicon via micro-EDM

This paper presents an investigation of micro electrical discharge machining (μEDM) as a viable method for micromachining 3D shapes in silicon. The approach integrates a two-step μEDM process with standard silicon microfabrication techniques to create smooth and axisymmetric 3D hemispherical structures with eccentricity, ε ~ 0.11 and a radius variation <; 2%. Through the selection of ultrahard polycrystalline diamond as the μEDM electrode, the low tool wear allows for high throughput machining of 200 wells in silicon within a short total processing time of 80 min. Feasibility of the approach is demonstrated in the fabrication of millimeter scale hemispherical shell structures using the machined silicon features as a mold.

Impact of doping and microstructure on quality factor of CVD diamond micromechanical resonators

The effect of doping and microstructure is explored on CVD diamond MEMS resonators. Hundreds of surface micromachined double ended tuning fork (DETF) resonators were fabricated in nanocrystalline diamond (NCD) and microcrystalline diamond (MCD) films deposited using hot filament CVD technique with varying levels of Boron doping. High resistivity (1926 MΩ·cm) NCD cantilevers and DETF demonstrated impressive Q-factors of 232,562 at f = 61.86 kHz and Q = 201,435 at f = 263.66 kHz, respectively. These Qs are the highest Q-factors yet reported for diamond resonators and the highest for cantilevers fabricated from any polycrystalline material. Higher boron doping resulted in reduced Q due to defect losses. Higher surface loss was observed in both MCD and NCD as doping increased. Observed Q-factors were almost the same for MCD and NCD at frequencies near 10 MHz.

Microcrystalline diamond cylindrical resonators with quality-factor up to 0.5 million

We demonstrate high quality-factor 1.5 mm diameter batch-fabricated microcrystalline diamond cylindrical resonators (CR) with quality-factors limited by thermoelastic damping (TED) and surface loss. Resonators were fabricated 2.6 and 5.3 μm thick in-situ boron-doped microcrystalline diamond films deposited using hot filament chemical vapor deposition. The quality-factor (Q) of as-fabricated CRs was found to increase with the resonator diameter and diamond thickness. Annealing the CRs at 700 °C in a nitrogen atmosphere led to a three-fold increase in Q, a result we attribute to thinning of the diamond layer via reaction with residual O2 in the annealing furnace. Post-anneal Q exceeding 0.5 million (528 000) was measured at the 19 kHz elliptical wineglass modes, producing a ring-down time of 8.9 s. A model for Q versus diamond thickness and resonance frequency is developed including the effects of TED and surface loss. Measured quality factors are shown to agree with the predictions of this model.

Batch-fabricated high Q-factor microcrystalline diamond cylindrical resonator

This paper reports a 1.5 mm batch-fabricated polycrystalline diamond Cylindrical Resonator (CR) for gyroscope applications. The device is fabricated in a cylindrical shape using silicon on insulator (SOI) wafers and deep reactive ion etching (DRIE), which allows flexibility of choosing different geometries and materials for the resonator structure. A quality factor (Q) of 313,100 is measured at the 23 kHz 2 theta elliptical wineglass modes, producing a ring-down time of 4.32 seconds. Annealing CRs at 700 °C in a nitrogen atmosphere improved Q from 75,000 to over 300,000. The highly symmetric fabrication results in CRs with an excellent frequency mismatch of 3 Hz (130 ppm) between the 2 theta degenerate wineglass modes without applying any tuning voltage.

Quality Factor in Polycrystalline Diamond Micromechanical Flexural Resonators

This paper reports an investigation into the various dissipation mechanisms that can affect polycrystalline diamond micromechanical resonators. Double-ended tuning fork and cantilever resonators were fabricated from 1-5-μm thick microcrystalline diamond films. It is shown that the quality factor of the low frequency (<;500 kHz) resonators is limited by surface loss, whereas the thermoelastic damping limits the quality factor of the higher frequency resonators. In resonators where surface loss is the dominant effect, the dependence of quality factor on resonator thickness is demonstrated. The addition of a lossy surface layer of Al2O3 deposited via atomic layer deposition is shown to degrade quality factor, and an experiment that further demonstrates the effect of surface dissipation and results in a reduction in quality factor that scales with the thickness of the Al2O3 layer. Heat treatment of cantilever resonators in N2 for various times up to 660 min is used to modify the resonator surface and is shown to result in a threefold increase in quality factor up to 365 000 at 26.6 kHz.

Increased thermal conductivity polycrystalline diamond for low-dissipation micromechanical resonators

This paper reports an investigation of microcrystalline diamond (MCD) films deposited under different conditions to increase thermal conductivity and therefore mechanical quality factor (Q) in micromechanical resonators. Through a study of different deposition conditions, we demonstrate a three-fold increase in thermal conductivity and quality factor. Quality factor measurements were conducted on double ended tuning fork resonators, showing Q = 241,047 at fn = 246.86 kHz after annealing, the highest Q reported for polycrystalline diamond resonators. We further present a study of the unique microstructure of hot filament chemical vapor deposition (HFCVD) diamond films and relate growth conditions to observed microstructural defects.