Luke A. Beardslee

Thermal Excitation and Piezoresistive Detection of Cantilever In-Plane Resonance Modes for Sensing Applications

Thermally excited and piezoresistively detected bulk-micromachined cantilevers vibrating in their in-plane flexural resonance mode are presented. By shearing the surrounding fluid rather than exerting normal stress on it, the in-plane mode cantilevers exhibit reduced added fluid mass effects and improved quality factors in a fluid environment. In this letter, different cantilever geometries with in-plane resonance frequencies from 50 kHz to 2.2 MHz have been tested, with quality factors as high as 4200 in air and 67 in water.

Liquid-Phase Chemical Sensing Using Lateral Mode Resonant Cantilevers

Liquid-phase operation of resonant cantilevers vibrating in an out-of-plane flexural mode has to date been limited by the considerable fluid damping and the resulting low quality factors (Q factors). To reduce fluid damping in liquids and to improve the detection limit for liquid-phase sensing applications, resonant cantilever transducers vibrating in their in-plane rather than their out-of-plane flexural resonant mode have been fabricated and shown to have Q factors up to 67 in water (up to 4300 in air). In the present work, resonant cantilevers, thermally excited in an in-plane flexural mode, are investigated and applied as sensors for volatile organic compounds in water. The cantilevers are fabricated using a complementary metal oxide semiconductor (CMOS) compatible fabrication process based on bulk micromachining. The devices were coated with chemically sensitive polymers allowing for analyte sorption into the polymer. Poly(isobutylene) (PIB) and poly(ethylene-co-propylene) (EPCO) were investigated as sensitive layers with seven different analytes screened with PIB and 12 analytes tested with EPCO. Analyte concentrations in the range of 1-100 ppm have been measured in the present experiments, and detection limits in the parts per billion concentration range have been estimated for the polymer-coated cantilevers exposed to volatile organics in water. These results demonstrate significantly improved sensing properties in liquids and indicate the potential of cantilever-type mass-sensitive chemical sensors operating in their in-plane rather than out-of-plane flexural modes.

An analytical model of a thermally excited microcantilever vibrating laterally in a viscous fluid

To achieve higher quality factors (Q) for microcantilevers used in liquid-phase sensing applications, recent studies have explored the use of the lateral (in-plane) flexural mode. In particular, we have recently shown that this mode may be excited electrothermally using integrated heating resistors near the micro-cantilever support, and that the resulting increase in Q helps to make low-ppb limits of detection a possibility in liquids. However, because the use of electrothermally excited, liquid-phase, microcantilever-based sensors in lateral flexure is relatively new, theoretical models are lacking. Therefore, we present here a new analytical model for predicting the vibratory response of these devices. The model is also used to successfully confirm the validity of our previously derived Q formula, which was based on a single-degree-of-freedom (SDOF) model and a harmonic tip force. Comparisons with experimental data show that the present model and, thus, the analytical formula provide excellent Q estimates for sufficiently thin beams vibrating laterally in water and reasonable upper-bound estimates for thicker beams.

Mass-sensitive detection of gas-phase volatile organics using disk microresonators.

The detection of volatile organic compounds (VOCs) in the gas phase by mass-sensitive disk microresonators is reported. The disk resonators were fabricated using a CMOS-compatible silicon micromachining process and subsequently placed in an amplifying feedback loop to sustain oscillation. Sensing of benzene, toluene, and xylene was conducted after applying controlled coatings of an analyte-absorbing polymer. An analytical model of the resonators chemical sensing performance was developed and verified by the experimental data. Limits of detection for the analytes tested were obtained, modeled, and compared to values obtained from other mass-sensitive resonant gas sensors.

Lateral-Mode Vibration of Microcantilever-Based Sensors in Viscous Fluids Using Timoshenko Beam Theory

To more accurately model microcantilever resonant behavior in liquids and to improve lateral-mode sensor performance, a new model is developed to incorporate viscous fluid effects and Timoshenko beam effects (shear deformation, rotatory inertia). The model is motivated by studies showing that the most promising geometries for lateral-mode sensing are those for which Timoshenko effects are most pronounced. Analytical solutions for beam response due to harmonic tip force and electrothermal loadings are expressed in terms of total and bending displacements, which correspond to laser and piezoresistive readouts, respectively. The influence of shear deformation, rotatory inertia, fluid properties, and actuation/detection schemes on resonant frequencies (fres) and quality factors (Q) are examined, showing that Timoshenko beam effects may reduce fres and Q by up to 40% and 23%, respectively, but are negligible for width-tolength ratios of 1/10 and lower. Comparisons with measurements (in water) indicate that the model predicts the qualitative data trends, but underestimates the softening that occurs in stiffer specimens, indicating that support deformation becomes a factor. For thinner specimens, the model estimates Q quite well, but exceeds the observed values for thicker specimens, showing that the Stokes resistance model employed should be extended to include pressure effects for these geometries.

Geometrical optimization of resonant cantilevers vibrating in in-plane flexural modes

The influence of the beam geometry on the quality factor and resonance frequency of resonant silicon cantilever beams vibrating in their fundamental in-plane flexural mode has been investigated in air and water. Compared to cantilevers vibrating in their out-of-plane flexural mode, utilizing the in-plane mode results in reduced damping and reduced mass loading by the surrounding fluid. Quality factors as high as 4,300 in air and 67 in water have been measured for cantilevers with a 12 µm thick silicon layer. This is in comparison to Q-factors up to 1,500 in air and up to 20 in water for cantilevers vibrating in their fundamental out-of-plane bending mode. Based on the experimental data, design guidelines are established for beam dimensions that ensure maximal Q-factors and minimal mass loading by the surrounding fluid.

Timoshenko Beam Model for Lateral Vibration of Liquid-Phase Microcantilever-Based Sensors

Dynamic-mode microcantilever-based devices are potentially well suited to biological and chemical sensing applications. However, when these applications involve liquid-phase detection, fluid-induced dissipative forces can significantly impair device performance. Recent experimental and analytical research has shown that higher in-fluid quality factors (Q) are achieved by exciting microcantilevers in the lateral flexural mode. However, experimental results show that, for microcantilevers having larger width-to-length ratios, the behaviors predicted by current analytical models differ from measurements. To more accurately model microcantilever resonant behavior in viscous fluids and to improve understanding of lateral-mode sensor performance, a new analytical model is developed, incorporating both viscous fluid effects and “Timoshenko beam” effects (shear deformation and rotatory inertia). Beam response is examined for two harmonic load types that simulate current actuation methods: tip force and support rotation. Results are expressed in terms of total beam displacement and beam displacement due solely to bending deformation, which correspond to current detection methods used with microcantilever-based devices (optical and piezoresistive detection, respectively). The influences of the shear, rotatory inertia, and fluid parameters, as well as the load/detection scheme, are investigated. Results indicate that load/detection type can impact the measured resonant characteristics and, thus, sensor performance, especially at larger values of fluid resistance.

Damping and mass sensitivity of laterally vibrating resonant microcantilevers in viscous liquid media

The effect of liquid viscosity and density on the characteristics of laterally excited microcantilevers is investigated and compared to transversely excited microcantilevers. When immersed into a viscous liquid medium such as water from air, the resonant frequency of laterally (in-plane) vibrating microcantilevers is shown to decrease by only 5–10% as compared to ∼50% reduction for transversely (out-of-plane) vibrating microcantilevers. Furthermore, as the viscosity of the medium increases the resonant frequency of a laterally vibrating beam is shown to decrease at a slower rate than that of a transversely vibrating beam. The decreased viscous damping also leads to increases in the quality factor of the system by a factor of 4–5 compared to beams vibrating transversely. The mass sensitivities of laterally vibrating beams are also theoretically predicted to be roughly two orders of magnitude larger in water for some cantilever geometries. The increase in the quality factor and mass sensitivity indicate that operating in the in-plane flexural mode (lateral vibration) will decrease the limit of detection compared to operating in the more common out-of-plane flexural mode (transverse vibration). These improvements in device characteristics indicate that microcantilevers excited laterally are more suited for operating in media of high viscosities.

Thermally actuated silicon tuning fork resonators for sensing applications in air

This paper introduces an electrothermally actuated, piezoresistively detected, silicon-based tuning fork geometry as a suitable platform for resonant sensing applications in air. Operated at their fundamental tuning fork mode (fTF ≈ 400 kHz), in which the two tines oscillate with 180° phase shift to each other, the devices exhibit Q-factors of 4000-4200 in air. By properly choosing the locations of the integrated excitation resistors as well as the four piezoresistors forming a Wheatstone bridge, output signals stemming from low-frequency out-of-plane vibration modes of the microstructure are successfully suppressed. As a result, the tuning forks can be easily embedded into an amplifying feedback loop, achieving short-term frequency stabilities in air as low as 0.02 ppm (0.008 Hz) for gate times of 1 sec. Coated with a chemically sensitive polymer film, the tuning forks were used as mass-sensitive sensors with detection limits in the low-ppm range for toluene.

On the relative sensitivity of mass-sensitive chemical microsensors

In this work, the chemical sensitivity of mass-sensitive chemical microsensors with a uniform layer sandwich structure vibrating in their lateral or in-plane flexural modes is investigated. It is experimentally verified that the relative chemical sensitivity of such resonant microsensors is -to a first order- independent of the microstructures in-plane dimensions and the flexural eigenmode used, and only depends on the layer thicknesses and densities as well as the sorption properties of the sensing film. Important implications for the design of mass-sensitive chemical microsensors are discussed, whereby the designer can focus on the layer stack to optimize the chemical sensitivity and on the in-plane dimensions and mode shape to optimize the resonators frequency stability.