# Thermally actuated silicon tuning fork resonators for sensing applications in air

Luke Beardslee, Jonathan Lehmann, Christopher Carron, Jin-Jyh Su, Fabien Josse, Isabelle Dufour, Oliver Brand

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## ► To cite this version:

Luke Beardslee, Jonathan Lehmann, Christopher Carron, Jin-Jyh Su, Fabien Josse, et al. Thermally actuated silicon tuning fork resonators for sensing applications in air. IEEE MEMS 2012 Conference, 2012, Paris, France. pp.1-4, 10.1109/MEMSYS.2012.6170261. [hal-00636029]

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https://hal.science/hal-00636029v1

Submitted on 12 Feb 2026

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# THERMALLY ACTUATED SILICON TUNING FORK RESONATORS
## FOR SENSING APPLICATIONS IN AIR

L.A. Beardslee¹, J. Lehmann¹, C. Carron¹, J.-J. Su¹, F. Josse², I. Dufour³, and O. Brand¹*

¹School of Electrical and Computer Engineering, Georgia Institute of Technology, USA

²Dept. of Electrical and Computer Engineering, Marquette University, USA

³Université de Bordeaux, IMS, FRANCE

## ABSTRACT

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 ($f_{TF} \approx 400$ 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.

## INTRODUCTION

The basic two-pronged tuning fork (TF) structure was invented 300 years ago and is still widely used to tune musical instruments because of its pure tone. One of the main advantages of the tuning fork is that the moments generated by the vibrating tines cancel each other at the base. This minimizes the support loss compared to e.g. single-cantilever geometries [1] with the same dimensions as one of the TF tines. Piezoelectric, quartz-based two-pronged TFs are used as frequency standards in many applications, including wristwatches. Besides, quartz-based TF are employed in AFM applications [2]. In addition, electrostatically excited silicon-based TFs [3] have been investigated as MEMS resonators and in gyroscopes. In the latter applications, the TF is generally operated in vacuum; operation in air typically introduces significant damping associated with squeezed film effects in the narrow electrostatic transduction gaps.

In this work, we demonstrate that a simple electrothermal actuation and piezoresistive detection scheme works efficiently in air provided that the integrated resistors are properly placed on the TF. This way, the thermally actuated TF resonators become a promising platform for sensing applications in air, e.g. as mass-sensitive chemical sensors [4].

## TUNING FORK DESIGN

Figure 1 shows SEM micrographs of the fabricated TF chip containing eight tuning forks and a close-up of one tuning fork resonator with integrated p-type silicon resistors for electrothermal excitation and piezoresistive detection of flexural vibrations. Each TF tine has a length

and width of 400 and 60 µm, respectively. The tuning forks are fabricated on epi-wafers and released by a combination of anisotropic wet etching from the back of the wafer using an electrochemical etch stop technique (to define a thin membrane that dictates the resonator thickness) and reactive ion etching from the wafer front (to define the lateral resonator dimensions) [1,5]. The thickness of the n-type epitaxial layer defines the silicon thickness of the resonator, either 8 µm or 20 µm in this work (the data presented here are for 20 µm thick devices only). During resonator fabrication, p-doped silicon resistors are created using a solid diffusion source; typical resistance values for each resistor are 500-700 Ohms and aluminum lines are used as interconnects. The resonator surface is covered with a 0.7 µm thick thermal oxide and a 1.2 µm thick passivation layer consisting of PECVD silicon oxide and nitride films.

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<figure><img src="image_4.png" /><figcaption>Figure 1: SEM photographs of (a) chip with eight tuning forks and (b) close-up of one silicon tuning fork with integrated resistors for electrothermal actuation and piezoresistive detection; each tine is 400 µm long, 60 µm wide and 20 µm thick.</figcaption></figure>

The excitation and detection resistors are placed so that the desired TF mode, in which the two tines oscillate against each other (in the plane of the chip) with 180° phase shift, is preferentially excited and/or detected. To this end, two heating resistors are located on opposite
sides of the two tines (Figure 2a). If both heating resistors are driven with the same excitation signal (the TFs are excited with an AC voltage superimposed on a DC offset), in-plane flexural modes in which the two tines vibrate with 180° phase shift (such as the desired TF mode), but also out-of-plane modes in which the two tines oscillate in phase are primarily excited (see Figure 3). However, signals stemming from these out-of-plane modes are effectively suppressed by the piezoresistors due to their proper placement (Figures 2a and 2b) in a Wheatstone bridge configuration. Considering the stress distribution associated with an out-of-plane mode where the two tines oscillate in phase (see Figure 2c), all four resistors exhibit similar resistance changes, thus generating –to a first order– no output signal. In a similar way, out-of-plane modes in which the two tines vibrate with 180° phase shift also generate ideally no output signal. However, in case of the desired TF mode (Figure 2c), resistors 2 and 3 exhibit a positive resistance change, while resistors 1 and 4 exhibit a negative resistance change (and vice-versa), thus generating a Wheatstone bridge signal. Finally, a temperature increase of the TF stemming e.g. from the dc power dissipation in the heating resistors again creates –to a first order– no bridge output signal, as all four resistances change in a similar way.

<figure><img src="image_5.png" /><figcaption>Figure 2: (a) Schematic of the tuning fork design with location of heating resistors and piezoresistors and (b) resistor arrangement in driving and read-out circuit. EX1 and EX2 denote the heating resistors. (c) Stress distribution in length direction on the surface of TF for 1st out-of-plane flexural mode and tuning fork mode (blue color indicates compressive stress, yellow/red color indicates tensile stress).</figcaption></figure>

## RESONATOR CHARACTERISTICS

To characterize the efficiency of the electrothermal actuation scheme, the out-of-plane and in-plane vibration amplitudes were measured optically using a Polytec MSA-500 vibration analyzer. For a driving voltage of $V_{ac} = 1$ V$_p$ superimposed on $V_{dc} = 1$ V, Figure 3 depicts the

measured out-of-plane vibration amplitude at the tip of one of the TF tines as a function of frequency. The individual resonance modes, as obtained by finite element simulations using COMSOL, are shown in the same figure together with the experimentally determined Q-factors. The desired TF mode at 419 kHz exhibits (as expected) only a small out-of-plane vibration component with a peak amplitude of 0.3 nm. Using the in-plane measurement capabilities of the MSA-500, the in-plane vibration amplitude of the TF mode was extrapolated to be 170 nm for the same excitation voltages (see Figure 4 for an in-plane measurement with $V_{dc} = 4$ V and $V_{ac} = 4$ V$_p$).

Besides the desired TF mode, several lower frequency out-of-plane modes are also excited. As expected from the heating resistor layout, out-of-plane flexural mode shapes with both tines vibrating in phase (at 38.4 kHz and 278.3 kHz) are most efficiently excited. It should be noted, however, that even for the first (out-of-plane) mode the out-of-plane vibration amplitude is only 170 nm, i.e. similar to the in-plane amplitude at the TF mode, despite the fact that the frequency is an order of magnitude lower; this demonstrates the efficiency of the heating resistors in exciting the desired in-plane TF mode.

<figure><img src="image_6.png" /><figcaption>Figure 3: Out-of-plane vibration amplitude at the tip of the tuning fork tines vs. frequency measured optically using a Polytec MSA-500. The grey line represents a coarse frequency scan, while the solid lines are high-resolution measurements around the resonance modes. For reference, the in-plane vibration amplitude at the TF mode ($f_{TF} = 419$ kHz) is approx. 170 nm for the same driving voltages. The additional modes at 111.5 kHz and 363.3 kHz correspond to fundamental in-plane and torsional modes of the whole microstructure. OOP-S and OOP-AS refer to flexural out-of-plane modes in which the two tines vibrate in phase and out of phase, respectively.</figcaption></figure>

Figure 5 shows the (amplified) piezoresistive output signal generated by the Wheatstone bridge biased at 3V as
a function of frequency. Between 100 kHz and 1MHz, only one resonance mode at 418.2 kHz is visible, corresponding to the TF mode. The frequency is slightly lower than the optically measured one (Figure 3), since the power applied to the piezoresistors slightly increases the TF temperature, lowering its stiffness and thus its resonance frequencies. Comparison of Figs. 3 and 5 clearly shows the effectiveness of the piezoresistive read-out scheme in suppressing signals from the unwanted out-of-plane modes while detecting the desired tuning fork mode. Thus, the layout of the piezoresistors on the TF surface facilitates operation of the microresonator in closed-loop operation, where the TF is the frequency-determining element in an amplifying feedback loop.

<figure><img src="image_7.png" /><figcaption>Figure 4: In-plane vibration amplitude (triangles) and phase (circles) at the tip of the TF tines measured using a Polytec MSA-500 as a function of frequency around the TF mode; the open symbols are measured at one tine, while the closed symbols are measured simultaneously at the other tine; the 180° phase shift between open and closed symbols is characteristic for the TF mode. Heating voltages are $V_{ac} = 4 V_p$ and $V_{dc} = 4 V$.</figcaption></figure>

From the 3-dB bandwidths of the amplitude transfer characteristics shown in Figures 3 and 5(b), Q-factors in the range of 4000-4200 in air are obtained for the TF-mode at ≈ 419 kHz. In contrast, individual cantilevers with the same dimensions as the TF tines (tested for comparison) yield Q-factors of 3000-3300 for their fundamental in-plane mode ($f_{IP} ≈ 440$ kHz). The Q-factor of cantilevers vibrating in a flexural mode in air is limited by viscous losses to the surrounding media [6], but also support losses, which become increasingly important for shorter cantilevers [7,8]. While the viscous losses to the surrounding fluid remain unchanged going from an individual cantilever to a tuning fork design, support losses are reduced because the moments generated by the vibrating tines cancel each other at the base, thus increasing the overall Q-factor by about 30%.

The high Q-factors obtained in air are a prerequisite for obtaining excellent short-term frequency stabilities when the resonator is operated in closed loop, which directly affects the achievable frequency resolution when using the resonators in a sensing application. Embedding the TFs in an amplifying feedback loop allows them to be continuously driven at their TF-mode with short-term

frequency stabilities in air (measured by the Allan variance method) as low as 0.02 ppm ($2×10^{-8}$) for a 1 second gate time.

<figure><img src="image_8.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 5: (a) Piezoresistive amplitude transfer characteristic of tuning fork resonator in the range of 100-1000 kHz and (b) close-up of the transfer characteristic (amplitude and phase) around the TF mode; the reference voltage for the amplitude axis is 1V. For both measurements, the Wheatstone bridge is biased at 3 V.</figcaption></figure>

## CHEMICAL SENSING BEHAVIOR

To demonstrate the suitability of the thermally actuated tuning forks for sensing applications in air, 20 µm thick tuning forks were coated with poly(isobutylene) (PIB) films as a chemically sensitive material and exposed to different toluene concentrations in a gas mixing system (using nitrogen as carrier gas) [9]. Figure 6 shows an SEM micrograph of the tuning fork after spray-coating with the PIB film. Actual film thicknesses were estimated using SEM and by partially coating a reference sample and measuring the PIB thickness using a contact profilometer.

Figure 7 shows the frequency change of a PIB-coated 20 µm thick TF exposed to different toluene concentrations in nitrogen. After each analyte exposure, the microresonator is subjected to a flow of pure nitrogen carrier gas for 10 minutes. In the measured concentration range from 800-6400 ppm, the frequency change is linear with
the toluene concentration and the measured chemical sensitivity is approximately 0.05 Hz/ppm for the tested PIB thickness (≈ 3 µm) and PIB/toluene combination. The chemical sensitivity can be further improved by decreasing the silicon thickness of the resonator and increasing the polymer film thickness. With polymer coating and gas flow over the TF, the short-term frequency stability increases to approx. 0.06 ppm; assuming that a frequency change three times the noise level can be detected, the estimated limit of detection for toluene is 1.5 ppm.

<figure><img src="image_10.png" /><figcaption>Figure 6: SEM micrograph of 20 µm thick tuning fork resonator after spray-coating with PIB (polyisobutylene) sensing film.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 7: Frequency change of tuning fork resonator coated with an approx. 3 µm thick poly(isobutylene) film subject to subsequent exposures to different toluene concentrations (800-1600-3200-6400-3200-1600-800 ppm) using N₂ as carrier gas; the resonance frequency of the TF mode is 394.6 kHz with polymer coating.</figcaption></figure>

The chemical sensor sensitivity can be estimated using finite element simulations and published data for the partition coefficient of toluene in PIB (K=1030, [9]). Assuming a 3 µm PIB film, the gravimetric sensitivity (frequen cy change per polymer density change) of the 20 µm TF is simulated using COMSOL as 11 Hz/(kg m⁻³). With an analyte sensitivity (polymer density change per change in analyte concentration) [9] of 4.2×10⁻³ (kg m⁻³)/ppm for PIB/toluene, the expected chemical sensitivity becomes 0.047 Hz/ppm, which is very close to the experimental value. During the experiment, the TF temperature is slightly elevated above room temperature because of the thermal power dissipation and, thus, the partition coeffi-

cient is likely smaller than the literature value. The fact that the measured chemical sensitivity still matches the theoretical value might indicate that the actual PIB thickness is larger than 3 µm.

ACKNOWLEDGEMENTS

The authors would like to thank the staff of the Georgia Tech Nanotechnology Research Center for their help. This work has been funded in part by the National Science Foundation under award ECCS-0824017.

REFERENCES

[1] L.A. Beardslee, A.M. Addous, S.M. Heinrich, F. Josse, I. Dufour, O. Brand, "Thermal excitation and piezoresistive detection of cantilever in-plane resonance modes for sensing applications," *J. Microelectromechanical Systems*, vol. 19, pp. 1015-1017, 2010.

[2] T. Akiyama, N.F. de Rooij, U. Staufer, M. Detterbeck, D. Braendlin, S. Waldmeier, M. Scheidiger, "Implementation and characterization of a quartz tuning fork based probe consisted of discrete resonators for dynamic mode atomic force microscopy," *Review of Scientific Instruments*, vol. 81, pp. 063706, 2010.

[3] R.N. Candler, M.A. Hopcroft, B. Kim, W.-T. Park, R. Melamud, M. Agarwal, G. Yama, A. Partridge, M. Lutz, T.W. Kenny, "Long-term and accelerated life testing of a novel single-wafer vacuum encapsulation for MEMS resonators," *J. Microelectromechanical Systems*, vol. 15, 2006, pp. 1446-1456, 2006.

[4] K.M. Goeders, J.S. Colton, L.A. Bottomley, "Microcantilevers: Sensing chemical interactions via mechanical motion," *Chemical Reviews*, vol. 108, pp. 522-542, 2008.

[5] J.H. Seo, O. Brand, "High Q-factor in-plane mode resonant microsensor for gaseous/liquid environment," *J. Microelectromechanical Systems*, vol. 17, pp. 483-493, 2008.

[6] S.M. Heinrich, R. Maharjan, I. Dufour, F. Josse, L. Beardslee, O. Brand, "An analytical model of a thermally excited microcantilever vibrating laterally in a viscous fluid," in *Proc. IEEE Sensors 2010 Conference*, Waikoloa, Hawaii, 2010, pp. 1399-1404.

[7] K. Naeli, O. Brand, "Dimensional considerations in achieving large quality factors for silicon resonant cantilevers in air," *J. Appl. Phys.*, vol. 105, pp. 014908-1-10, 2009.

[8] F. Lochon, I. Dufour, D. Rebière, "A microcantilever chemical sensors optimization by taking into account losses", *Sensors and Actuators B*, vol. 118, pp. 292-296, 2006.

[9] S.B. Truax, K.S. Demirci, L.A. Beardslee. Y. Luzinova, A. Hierlemann, B. Mizaikoff, O. Brand, "Mass-sensitive detection of gas-phase volatile organics using disk microresonators," *Analytical Chemistry*, vol. 83, pp. 3305-3311, 2011.

CONTACT

*Oliver Brand, Phone: +1-404-894-9425; E-mail: oliver.brand@ece.gatech.edu