Cheng Tu

A semi-analytical modeling approach for laterally-vibrating thin-film piezoelectric-on-silicon micromechanical resonators

In this paper, we propose an analytical model that more accurately captures the electro-mechanical behavior of laterally-vibrating extensional-mode thin-film piezoelectric-on-silicon resonators. The proposed modeling approach considers the actual vibration mode shape of the resonator instead of relying on simplified modal functions such as assuming that the displacements occur only within the plane of fabrication and follow a sine function in the vibration plane. Out-of-plane and planar deviations in the mode shape from an ideal sine function arise from differences in the acoustic velocities between the piezoelectric film and underlying silicon. The proposed model allows more accurate prediction of the key lumped parameters in both the mechanical (e.g. equivalent point force associated with the reverse piezoelectric effect, effective stiffness) and electrical domain (i.e. motional capacitance) as a function of electrode coverage. Compared to an existing 1D approximation model proposed in a seminal work, the lumped parameters derived from the proposed model show notably closer agreement with 3D coupled-domain finite element (FE) simulations and also the measured results from fabricated devices. The semi-analytical nature of our modeling approach relies on the details of the mode shape provided. As such, our model has the benefit of allowing increasing levels of precision as desired depending on the amount of detail that is included in the FE modal analysis.

VHF-band biconvex AlN-on-silicon micromechanical resonators with enhanced quality factor and suppressed spurious modes

This paper reports experimental results demonstrating the use of biconvex-edge designs to enhance the quality factor (Q) in aluminum nitride (AlN)-on-silicon micromechanical resonators. The proposed biconvex design serves to confine the acoustic energy to the center of the resonators, thus reducing out-of-plane bending on the supporting tethers that contribute to acoustic energy leakage, thereby enhancing Q. We here demonstrate that the biconvex design concept can be scaled and applied across a range of operating frequencies from 70 to 141 MHz with the notable effect of boosting Q relative to conventional flat-edge designs. Our measurements of several resonators have shown that the biconvex designs result in an increase in Q by 4–10 times compared to conventional flat-edge designs. In addition, we have also investigated the effect of using different lengths of supporting tethers on Q for both biconvex and flat-edge designs. From the measurement results of devices under test, we have found that the variation in Q as a function of tether length was insignificant compared to the increase in Q going from a flat-edge to biconvex design. As such, the level of enhancement for Q using the biconvex design is much more significant compared to varying the geometry of the support structures. Interestingly, the biconvex shape causes a modal split that gives rise to an additional anti-symmetric mode not found in the flat-edge design. We show experimentally that this spurious anti-symmetric mode can be suppressed by over 54 dB by applying a novel center-loaded electrode design that matches the strain field pattern of the desired symmetric mode. Close agreements between the 3D coupled-domain finite element simulations and the measured results of fabricated devices have been obtained for the resonant frequencies and motional capacitances.

Increased dissipation from distributed etch holes in a lateral breathing mode silicon micromechanical resonator

Etch holes are commonly used design features when fabricating silicon-on-insulator micromechanical resonators to realize free standing structures. This paper shows that including etch-holes in a square-extensional mode resonator results in marked reduction of quality factor (Q) by 75%. The cause of this drop is explained by our finite element model used to theoretically estimate Q. These theoretical estimates agree well with measurement results. Our analyses show that anchor loss is dominant in a plain structure while etch holes increase thermoelastic damping to the point where both dissipation factors become comparable in determining the actual Q.

Study on thermoelastic dissipation in bulk mode resonators with etch holes

This paper aims to investigate the primary cause for marked drops in quality factor (by over 98%) of a bulk mode resonator as a result of introducing etch holes into the structure. We show that thermoelastic damping (TED) appears to be the dominant cause of energy dissipation. The resonator is fabricated in single-crystal silicon (SCS). According to finite-element (FE) analysis, the uniform isochoric property of the Lamé mode is no longer preserved when etch holes are introduced. This results in marked drop in quality factor (Q) by 98.5% for the Lamé mode and 75.7% for the extensional from measurements. FE analysis based on coupled thermoelastic equations is used to compute the the thermal gradients that give rise to TED when etch holes are added to the resonator.

High-Q low impedance UHF-band ALN-ON-SI mems resonators using quasi-symmetrical Lamb wave modes

This paper describes the phase velocity dispersion characteristics of Lamb waves propagating in AlN-on-Si plates, which achieves high quality factor (Q > 10000) and low motional resistance (R_m <; 50 Ω) at 260 MHz in air by using the fundamental quasi-symmetrical (QS₀) mode. We have found that the ratio of the Si layer thickness (h_Si) over the acoustic wavelength (λ) sets a limit for the QS₀ mode resonance at higher frequencies as increasing the ratio of h_Sl/λ reduces the electromechanical coupling for the QS₀ mode while enhancing the spurious quasi-antisymmetrical (QA₀) mode. Lastly, we also experimentally demonstrate that using multiple tethers helps suppress spurious modes.

Planar ring-shaped phononic crystal anchoring boundaries for enhancing the quality factor of Lamb mode resonators

We report the use of planar ring-shaped phononic crystals (PnCs) as anchor boundaries of very-high-frequency band piezoelectric-on-silicon Lamb mode resonators for the purpose of enhancing their quality factor (Q). Here, we exploit the acoustic bandgap associated with the PnC anchoring boundaries to reduce acoustic energy leakage out of the micromechanical resonator. The proposed approach provides greater mechanical robustness (by merit of interlocking the cells in a matrix) and the possibility of electrical routing through the PnC cells. We experimentally show enhancements in Q by a factor of three using the proposed approach of hybridizing planar ring-shaped PnCs with micromechanical resonators. The effect of these PnCs on resonator Q is further corroborated by their effects in suppressing transmission when incorporated into a delay line.

Effect of curvature and electrode coverage on the quality factor of biconvex ALN-on-Si MEMS resonators

This paper analyzes for the first time the effect of incrementally varying the curvature of a MEMS contour mode resonator on its quality factor (Q). The change in curvature is analyzed in terms of the change in width of the acoustic cavity. Our experimental results show that the change in width of the acoustic cavity should be at least half the acoustic wavelength (λ) of the resonant cavity to achieve optimal and consistent improvement in Q. However, curving beyond λ drastically reduces coupling while providing little improvement in Q. We also examine the impact of electrode coverage for Q-enhanced biconvex resonators: Narrowing the width of the electrodes tends to increase Q but shortening the length reduces Q slightly.

Probing anchor losses in AlN-on-Si contour mode MEMS resonators through laser Doppler vibrometry

We present the novel application of high frequency laser Doppler vibrometry to measure the underlying mechanism leading to anchor loss that now limits the quality factor of low impedance contour mode aluminum nitride (AlN) on silicon resonators. We applied the technique to two resonators designed to have largely different quality factors (2100 vs. 12000) in order to correlate the findings from laser vibrometer measurements to anchor loss. We show that the vibrometer measurements are in close harmony with findings from finite element analysis. These results allow us to move beyond pure simulations in the course of analyzing anchor losses in AlN-on-Si contour mode resonators.

Etch-hole-assisted energy dispersion for enhancing quality factor in silicon bulk acoustic resonators

This paper empirically demonstrates how the quality factor (Q) of a width-extensional mode single-crystal silicon bulk-acoustic-resonator (SiBAR) can be enhanced by three times by strategic placement of holes on the structure. The holes serve to disperse the strain energy field concentrated primarily around the nodal lines, ultimately re-distributing strain energy away from the anchors. This in turn reduces anchor loss and thus enhances Q. These results agree well with our finite-element (FE) simulations. We envisage that the concepts reported herein can be extended to even higher performance resonators like piezoelectric aluminum nitride contour mode resonators.

Anomalous DC-current-induced attenuation of Q factor in a silicon contour mode micromechanical resonator

In this work, we report the experimental observation of quality factor (Q) variation in piezoresistively sensed silicon micromechanical resonators vibrating in a lateral contour mode. By fine tuning the bias current, the gradual descending and ascending trend of Q is distinctively observable. It shows a drastic drop in Q by nearly one order of magnitude (from 105 to 104) at a certain bias current level. The observed Q variation is replicable even when applying a capacitive sensing configuration with bias current running through. This anomaly is consistently detected from multiple die samples including resonators aligned along both <;110> and <;100> crystal orientations in the (100) plane. A detailed quantitative study is currently underway.