thin film monitoring with silicon bulk acoustic resonators - IEEE Xplore

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Joshua E-Y. Lee, Behraad Bahreyni, and Ashwin A. Seshia. Department of Engineering. University of Cambridge. Cambridge, United Kingdom joshlee@cantab.
Thin Film Monitoring with Silicon Bulk Acoustic Resonators Joshua E-Y. Lee, Behraad Bahreyni, and Ashwin A. Seshia Department of Engineering University of Cambridge Cambridge, United Kingdom [email protected] important figure of merit for resonant sensors. The use of bulk mode resonators as platforms for mass sensing was previously demonstrated by [5], wherein a silicon beam structure was operated in the length-extensional resonance mode with a Q of 4000 in air and a mass resolution of about 1 pico-gram. The use of a square plate structure for the sensing platform offers the advantage of a larger capture area for a given mass flux density in addition to enhanced electrical interfacing. We have previously reported a mass sensor based on a square-plate resonator that has been excited in the square-extensional mode resonator [6]. This resonator had a Q of almost 15000 in air and over a million in vacuum, and a mass equivalent noise of 125 pg/cm2 was demonstrated. Apart from the extensional mode, square resonator may also be excited to resonate in the wine glass mode, at a lower frequency relative to the extensional mode. Since volume is conserved in the wine glass mode, losses due to thermoelastic damping will be lower, thus potentially leading to higher Q in vacuum.

Abstract—This paper reports a single-crystal silicon mass sensor based on a square-plate resonant structure excited in the wine glass bulk acoustic mode at a resonant frequency of 2.065 MHz and an impressive quality factor of 4 million at 12 mtorr pressure. Mass loading on the resonator results in a linear downshift in the resonant frequency of this device, wherein the measured sensitivity is found to be 175 Hz cm2/μg. The silicon resonator is embedded in an oscillator feedback loop, which has a short-term frequency stability of 3 mHz (approximately 1.5 ppb) at an operating pressure of 3.2 mtorr, corresponding to an equivalent mass noise floor of 17 pg/cm2. Possible applications of this device include thin film monitoring and gas sensing, with the potential added benefits of scalability and integration with CMOS technology.

I.

INTRODUCTION

Resonant sensors offer the combined advantages of high resolution, large dynamic range, frequency output and extended bandwidth. The quartz crystal microbalance (QCM) is an excellent example of a resonant sensor that has been successfully commercialized for thickness film monitors and other mass sensing applications [1]. The QCM is however limited by integration with CMOS as well as in the scaling of the technology for multi-arrayed massively parallel detection. Micro- and nano- fabricated resonant structures have been employed as resonant mass sensors due to their miniscule sizes resulting in high mass sensitivities. Single crystal silicon resonators also typically display characteristically high quality factors due to the superior mechanical properties and low intrinsic loss of silicon. Nano-mechanical resonators benefiting from very high mass sensitivity have been shown to be capable of achieving zepto-gram resolution in vacuum [2]. The primary drawback in the implementation of nanomechanical platforms for mass sensing is in developing effective electrical interfaces to the sensors in addition to achieving good device-to-device performance repeatability for real-world applications. Most nano-mechanical mass sensors are operated in flexural mode resonance [3-4]. In comparison to flexural mode resonators, bulk mode resonators typically exhibit higher Q, an

In this paper, we report on the implementation of a single crystal silicon square-plate resonator operated in the wine glass mode as a mass sensor with an ultra-high Q of 4 million. The resonator is embedded in the feedback loop of an oscillator whose output frequency is modulated by mass deposited on the resonant structure. The quantity of mass accreted on the structure is estimated through a detectable shift in its resonant frequency. The mass sensor has a measured frequency-to-mass sensitivity of 175 Hz cm2/μg and a mass equivalent noise of 17 pg/cm2. This corresponds to an order of magnitude improvement over the previous result using a square resonator vibrating in the extensional mode. This result suggests that it is possible to realize an array of silicon mass balances for parallel mass detection each with a resolution comparable or better than a QCM. While nano-mechanical resonators present a better choice for high mass sensitivity, the reported device benefits from enhanced electrical interfacing, lower sensitivity to manufacturing tolerances and larger capture area, enabling the high-throughput measurement of mass flux.

This work has been supported by the US Army Soldier Systems Centre. Travel support has been provided by the UK Royal Academy of Engineering through the Research Student Development Fellowship award.

1-4244-2581-5/08/$20.00 ©2008 IEEE

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II.

DEVICE DESCRIPTION

A.

Micromechanical Resonator Sensing Platform The resonant frequency (f0) of a structure for a given mode of vibration is determined by its effective spring constant (kR) and dynamic mass (MR)

f0 =

1 2π

kR MR

(1)

The square wine glass resonant mode (SWG) may be described as a square plate that contracts along one axis in the plane of fabrication, while also simultaneously extending along an orthogonal axis in the same plane. The corners are stationary points, while displacement is maximum midway along the edges which bend either inwards or outwards as shown in Fig. 1. The mechanical resonant frequency of the resonator vibrating in the wine glass mode is given by:

f 0 = G 2 ρL2

Figure 3. Optical micrograph of the silicon mass sensor platform

Accretion of an infinitesimal quantity of mass (δm) on the resonant structure results in an associated shift in the frequency by Δf, linearly proportional to the added mass in the limit where δm « MR:

(2)

Δf = −

The resonators have been fabricated in the MEMSCAP SOI MEMS foundry process. Fig. 2 provides a crosssectional illustration of a fabricated device. An optical micrograph of the device is shown in Fig. 3.

f0 δm 2M R

(3)

B. Oscillator Circuit The schematic of the oscillator circuit together with the embedded micromechanical resonator is shown in Fig. 4. The first stage in the circuit is a transimpedance amplifier for converting the resonator motional current to a voltage. The band-pass filter then removes unwanted oscillation modes. The comparator allows for excellent control over the actuation signal amplitude in addition to the use of a voltage divider, effectively removing the amplitude noise of the loop signal. Finally, the comparator output is applied to the input of a single-ended-to-differential drive amplifier, which produces two complementary binary signals at its output. These two signals are applied to the input of the resonator and a tunable compensation capacitor.

Figure 1. Square wine glass mode shape simulated in ANSYS

Figure 4. Circuit schematic of bulk mode micromechanical oscillator

Figure 2. Illustrated cross section of the micromechanical resonator

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The compensation capacitor is tuned to closely match the parallel feedthrough capacitor. The output currents from the compensation capacitor and feedthrough capacitor are out of phase and hence effective cancellation of the parasitic feedthrough is achieved when these currents are added at the input of the transimpedance amplifier. This increases the ratio of the sensed motional current to that from the feedthrough capacitor, thus satisfying the condition for oscillation. III.

The Allan deviation measurements for a commercial quartz crystal oscillator (Agilent 33220A) have also been included on the same plot for reference. The best Allan deviation for the SWG oscillator is 0.5 ppb at an integration time of 0.3 s, which is twice that of the quartz crystal. Fig. 7 shows the frequency drift over the period when samples were taken (at a rate of -1.55 ppb/s). The cumulative change in the output frequency of the oscillator over the entire duration when samples were collected is about 4.6 ppm. The observed constant drift in the output frequency is most likely due to changes in the temperature of the ambient. The temperature coefficient of frequency sensitivity for a bulk mode single crystal silicon resonator like the one reported in this paper is typically around -25 ppm/0C. A frequency drift of up to 4.6 ppm would correspond to an approximate steady change in the ambient temperature by just under 0.2 0C over an hour. The drift in frequency due to changes in the ambient temperature would well account for the increasing deviation with larger integration times.

OSCILLATOR RESULTS

The resonator was placed in a vacuum chamber and connected to the rest of oscillator circuit as shown in Fig. 4. The resonator was excited into the wine glass mode by applying a bias voltage of 50 V to the drive electrodes. The open loop electrical transmission response of the resonator has been measured, and a Q of about 4 million is estimated. Further details on device characterization are reported elsewhere in [7]. Fig. 5 shows the output spectrum of the implemented oscillator. Successive samples of the oscillator output frequency were collected over a period of about 55 minutes using a frequency counter at fixed time intervals of 0.3 s, from which the overlapping Allan deviation was calculated as shown in Fig. 6.

IV.

SENSOR CALIBRATION

To demonstrate functionality of the device for mass sensing, successive layers of chromium (Cr) were evaporated over the front side of a second resonator of the same dimensions in fixed incremental steps of 5 nm. The electrical transmission characteristics were measured in air using an Agilent 4396B network analyzer upon completion of each deposition step. A corresponding shift in the resonant frequency is observed after each deposition step and shown in Fig. 8, which shows the resonator transmission measured in air after equal thicknesses of Cr are successively deposited on the resonator surface. The transmission response curves shown in Fig. 8 have been extracted from the measured raw data, which contains the resonant peak heavily buried in feedthrough, using the general procedure described in [8]. A calibration curve fit relating this frequency shift to the corresponding mass accreted on the resonator was obtained as shown in Fig. 8. The slope of the best-fit line defines the responsivity of the mass sensor, and has a measured value of 126 Hz/nm of Cr, equivalent to 4.37 Hz/ng (175 Hz cm2/μg), which agrees well with the predicted estimate calculated from (3).

Figure 5. Frequency spectrum of the bulk mode resonator oscillator

Figure 6. Measured Allan deviation of the resonator oscillator (red) including a commercial quartz crystal oscillator (blue) for comparison

Figure 7. Frequency output of oscillator measured over 55 minutes

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micromechanical device shows that it is possible to realize microfabricated mass sensor platforms based on bulk mode resonators that have a mass resolution comparable to a larger scale QCM. This could be extended to implement an array of microresonators for high throughput parallel detection, in applications ranging from thin-film deposition process monitoring to functionalized gas sensors. V.

CONCLUSIONS

We have described the incorporation of a bulk mode microresonator as the timing element of a micro-mechanical oscillator. The short-term frequency stability of the oscillator, measured by the Allan deviation, has been found to be 0.5 ppb, which is about twice that of a commercial quartz crystal oscillator. The best observed measurement of the standard deviation of the oscillator frequency is about 3 mHz (1.5 ppb) for an averaging time of 50 ms. The resonator functions as a platform for mass sensing, whose mechanical resonant frequency is modulated by the adsorption of mass on the structure. Since the frequency of the oscillator output is set by the frequency of resonator, the output of the oscillator shifts in response to deposited mass. The responsivity of the mass sensor was found to 175 Hz cm2/μg and the mass equivalent noise is 17 pg/cm2.

Figure 8. Corresponding shift in resonant frequency as successive layers of chromium are deposited on the resonant structure

ACKNOWLEDGMENT J. E-Y. Lee would like to thank J. Yan for providing the ANSYS diagrams for illustrations on the wine glass mode shape described in this paper. REFERENCES

Figure 9. Measured calibration curve relating shifts in the resonant frequency of the mass sensor to the thickness of chromium deposited

[1]

The standard deviation of the output frequency was measured using the frequency counter, and the minimum short-term frequency fluctuations observed was approximately 3 mHz using an averaging time of 50 ms over 20 samples. This corresponds to a fluctuation in output frequency of about 1.5 ppb. The mass equivalent noise floor of the device may be determined using (4):

⎛ f mn = ⎜⎜ 0 ⎝ 2M R

[2]

[3]

[4]

[5]

−1

⎞ ⎟⎟ f n ⎠

(4) [6]

where fn is the measured output frequency noise of the oscillator, and (f0/2MR) corresponds to the responsivity of the mass sensor which is defined by the slope of the calibration curve shown in Fig. 9. From (4), using the measured values of the responsivity (175 Hz cm2/μg) and standard deviation of the frequency noise (3 mHz), we obtain a mass equivalent noise of 17 pg/cm2. In comparison to a QCM reported at the same frequency operating in air [9], this is an improvement by about 2 orders of magnitude. The result from this silicon

[7]

[8]

[9]

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