1 Introduction

Micro electromechanical systems (MEMS) based resonator sensors are utilized in a wide variety of fields to detect both physical and chemical quantities. This includes the sensing of density and viscosity in liquids [1,2,3], pressure sensing in gases [4, 5] and the sensing of mass changes when used as micro balance for the detection of chemical and biological agents [6,7,8,9,10,11]. Of the various types of resonator geometries (strings, membranes, etc.), cantilever based devices have attracted much attention due to the low impact of residual stress on key device parameters like the resonance frequency. Cantilever modes are into different basic types of mode shapes: transversal, torsional, extensional and lateral.

Transversal or out-of-plane modes are primarily used for atomic force microscopy and micro balance applications [9, 12]. When comparing the performance of these modes in liquids, it was found, that the quality factor, which is in liquids primarily linked to viscous damping, does not exceed 35 [9]. This is a limitation when going into liquids with higher viscosity, as the increased damping will not allow any oscillation of the resonator to occur. To overcome this drawback to at least some degree, lateral or in-plane modes can be used, which can reach quality factors between 65 and 100 in water [9, 13, 14].

This paper will give an overview over a MEMS based piezoelectric sensor platform developed at ISAS, TU Wien.Footnote 1 This sensor platform utilizes a novel type of resonator mode, which features unprecedented quality factors in water of up to 366 for higher mode orders. As a consequence, measurements not just in water, but also in highly viscous liquids like lubrication oil, or even bitumen are enabled. The devices presented in this paper are all based on this sensor platform, the design however varies depending on the application.

2 Methods

2.1 Sensor design and fabrication

The sensor fabrication process starts with a 4 inch silicon on insulator (SOI) wafer with a typical device layer thickness of 20 μm. The wafer is covered by a bi-layer of 250 nm thermal oxide and 80 nm LPCVD silicon nitride to ensure electrical isolation of the bottom electrodes. These electrodes are deposited using evaporation and patterned via a lift-off procedure. Subsequently, the piezoelectric layer of aluminum nitride (AlN) is deposited using reactive magnetron sputtering and the top electrode is realized in the same way as the bottom electrodes. The device is defined by a top side deep reactive ion etch (DRIE) step and released by a backside DRIE step followed by the removal of the buried oxide by hydrofluoric acid.

A typical device geometry with two electrode stripes is shown in Fig. 1. The finished devices are placed in dual inline packages and wire bonded. More details can be found in [15, 16].

Fig. 1.
figure 1

Schematics of the typical cantilever architecture. (\(a\)) Top view (\(b\)) cross-sectional view, including a visualization of the electrical field. Reprinted from [15], ©2014 with permission from Elsevier

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2.2 Sensor characterization and measurement

A Butterworth-van Dyke equivalent circuit consisting of a parallel connection of a resistor (\(R_{\mathrm{p}}\)), a capacitor (\(C_{\mathrm{p}}\)) and a LCR circuit (\(R_{\mathrm{m}}\), \(C_{\mathrm{m}}\) and \(L_{\mathrm{m}}\)) is used to describe the electrical characteristics of the MEMS resonator. \(R_{\mathrm{p}}\) and \(C_{\mathrm{p}}\) represent the static AlN capacitor, whereas \(R_{\mathrm{m}}\), \(C_{\mathrm{m}}\) and \(L_{\mathrm{m}}\) model the electrical signal of the mechanical resonance. Figure 2 shows the typical spectra of the conductance \(G\) and the susceptance \(B\) of the MEMS resonator. The static conductance is given by 1/\(R_{\mathrm{p}}\) and is increased by \(\Delta G = 1/R_{\mathrm{m}}\) in resonance. The quality factor \(Q\) is calculated from the circuit parameters by the well-known equation \(Q= {1} / {R_{\mathrm{m}}} \sqrt{{L_{\mathrm{m}}} / {C_{\mathrm{m}}}}\) or by fitting the susceptance minimum and maximum.

Fig. 2.
figure 2

Visualization of the real (\(G\)) and imaginary (\(B\)) part of the admittance Y including parasitic effects (\(R_{p}\), \(C_{p}\)). Reprinted from [15], ©2014 with permission from Elsevier

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In order to obtain a high measurement signal, it is important to maximize \(\Delta G\) and to minimize 1/\(R_{\mathrm{p}}\). This can be challenging especially in liquids, as the high damping will reduce the quality factor and hence, \(\Delta G\). A more detailed description of the mathematical modelling approach of the resonator can be found in [15].

Electrical measurements of the MEMS resonators both in air and in liquids are done with an Agilent 4294A impedance analyzer under controlled temperature conditions. Optical measurements of the out-of-plane movement are performed with a Polytec MSA 400 laser Doppler vibrometry system. Density \(\rho \) and dynamic viscosity \(\mu \) of the investigated liquids are measured with a Stabinger SVM 3000 viscometer at defined temperatures. The test liquids included deionized water, ethanol, isopropanol, D5, N10, N35, N100, S200 and D500. Doing so, dynamic viscosity at room temperature were varied up to 615 mPa s [17]. Vibrational modes are specified using the notation by LeissaFootnote 2 [18].

3 Results

The following sections will present a short overview of the most important results achieved with the AlN MEMS resonator sensor platform developed at ISAS.

3.1 Roof-tile shaped modes

Figure 3 shows both optical and electrical spectra of a 2017 μm × 1272 μm cantilever resonator in both air and isopropanol with the corresponding mode shapes for each resonance. The high damping of most resonance modes is clearly visible; however, one mode shape features high quality factors independent of the environmental conditions, labeled as 13 mode. This mode shape is representative for a new class of torsional type modes: the roof-tile shaped modes. Subsequent studies using the same sensor design approach confirmed this result and demonstrated high quality factors for the 12 mode of 10 in highly viscous liquids like D500. Furthermore, a direct correlation between the quality factor and \({1} / {\sqrt{\rho \mu }}\) was found, which shows the potential for this sensor to measure both the density and dynamic viscosity of liquids [17].

Fig. 3.
figure 3

Frequency spectra of the MEMS resonator in air and in iso-propanol. The plots show the out-of-plane (left axis, lower curve) as well as the conductance spectrum (right axis, upper curve). [15], ©2014 with permission from Elsevier

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By increasing the drive frequency, higher orders of the 12 mode can be excited. The impact on the quality factor in deionized water is shown up to the 10th order in Fig. 4. Hexadecimal numbering is used for the Leissa nomenclature. The insets show the corresponding mode shape and the dashed line represents viscous damping deduced from theoretical considerations where the cantilever is approximated by a sphere to enable an analytically solution of the Navier-Stokes equations [19]. The corresponding results for the resonance frequency \(f\)res, \(Q\) and \(\Delta G\) are given in Table 1. A quality factor of 366 was measured for the 1B mode in water at a frequency of 3.5 MHz, which was the highest value measured up to that time for cantilever type resonators in liquid media. While \(Q\) continuously increases with increasing \(f\)res, \(\Delta G\) does not feature a clear trend. This is due to the fact, that the electrode design can act as a filter for higher modes due to partial or complete cancelation of charges, if the electrode covers areas with both positive and negative volume strains [20]. It is therefore necessary to tailor the electrode design.

Fig. 4.
figure 4

Q-factors of different multi roof tile-shaped modes as a function of resonance frequency in deionized water. The small insets represent the mode shapes under study derived from FEM simulations. Reprinted with permission from [19], ©2015 AIP Publishing LLC

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Table 1. Performance of the higher orders of the roof tile-shaped modes in deionized water. Due to its high order, hexadecimal numbers are used for the labelling. Reprinted with permission from [19], ©2015 AIP Publishing LLC
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3.2 Electrode and anchor optimization

The roof-tile shaped modes in cantilever type resonators generally feature only a single nodal line along the x-axis (the anchor) and multiple nodal lines along the y-axis. This enables an optimized electrode design (OED) by using multiple electrode stripes perpendicular to the anchor nodal line, which simplifies the electrical feed lines significantly.

To increase device performance, effort was invested in a tailored mode specific anchor design by moving from a single side clamped cantilever type resonator to a double side clamped bridge type resonator. Compared to a typical bridge design, the resonating plate is only fixed at the nodal lines, which minimizes the anchor strain and basically results in a design mimicking the mathematical free-free boundary condition best. The results for these resonators in liquids with respect to \(Q\) are shown in Fig. 5 and for \(\Delta G \) in Fig. 6, respectively. The quality factor increases as expected with increasing mode order and decreases with increasing \({1} / {\sqrt{\rho \mu }}\). An impact of OED on \(Q\) was not observed. \(\Delta G\) on the other hand was significantly improved by OED. The highest value \(\Delta G = 379\) μS was measured for the 05 mode in isopropanol. Compared to the result without OED, this corresponds to an improvement by a factor of 77 and demonstrates the importance of OED.

Fig. 5.
figure 5

Q-factors of the 0X-modes with and without OED in different liquids. Reprinted from [21], ©2016 with permission from Elsevier

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Fig. 6.
figure 6

Electrical characterization of the 0X-modes with and without OED in different liquids represented by the conductance peak \(\Delta \) G as a function of the resonance frequency. Reprinted from [21], ©2016 with permission from Elsevier

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3.3 Applications

The fermentation of grape must into wine involves yeasts, which convert sugars in the must into ethanol. During this process, it is possible for the yeasts to stop growing and not produce ethanol any longer. This is referred to as stuck fermentation and poses a serious problem in wine making, if not detected at an early stage. The different ethanol concentrations in normal and stuck states of fermentation results in a slight variation of the density of the grape must and can thus be detected by the presented MEMS resonator sensor, shown in Fig. 7.

Fig. 7.
figure 7

Optical micrograph of the silicon die (\(6~\mathrm{mm} \times 6~\mathrm{mm}\)) fabricated at ISAS, TU Wien. The electrode patterning is matched to the modal shape of the resonator. Reprinted from [22] under CC BY 4.0

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For this application, the sensor in the package is fully coated by a 4 μm thick amorphous silicon dioxide film to eliminate any parasitic leakage currents through the grape must, which would result in a lower \(R_{\mathrm{p}}\) value. The sensor is operated in the 15-mode and tested in model solutions \(N_{1-9}\) and \(S_{1-9}\), which represent both normal and stuck fermentation stages [22]. The resonance frequency and quality factor are measured and used to calculate the density of the liquid according to [22, 23].

Figure 8 shows both the ethanol concentration and the resonance frequency for normal as well as stuck fermentation. It is clearly visible, that the ethanol concentration deviates from the normal fermentation characteristics already at an early stage of the process. In addition, an excellent correlation between \(f\)res and the ethanol concentration is observed.

Fig. 8.
figure 8

15-mode frequency response analysis of ordinary (\(N_{1-9}\)) and stuck (\(S_{1-9}\)) fermentation process in comparison to the nominal ethanol concentration of the investigated model solutions. Reprinted from [22] under CC BY 4.0

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Figure 9 shows the density variation with continuous fermentation, measured with both the MEMS sensor and a Stabinger viscometer. The results of the bulky, table-top sized Stabinger lab equipment are in excellent agreement with those from the MEMS sensor. This also demonstrates, that it is possible to distinguish between the normal and stuck fermentation branch at a very early stage during the fermentation process with an integrated MEMS sensor approach.

Fig. 9.
figure 9

Density values for ordinary (\(N_{1-9}\)) and stuck (\(S_{1-9}\)) fermentation model solutions determined with the MEMS resonator and a Stabinger SVM3000 viscometer. Reprinted from [22] under CC BY 4.0

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Similar measurements were performed on Airen grape must after a filtering process to remove large grape skin particles. The monitoring is done ex-situ on samples taken every 5 hours after centrifugation. A shift in the resonance frequency comparable to Fig. 8 is observed, demonstrating that this sensor system has the potential to monitor even this complex biological process precisely compared to state of the art equipment.

In the above mentioned lab experiment, any particles are removed to avoid contamination of the sensor. In technical liquids like lubrication oils on the other hand, the detection of particles is of high interest as the amount of such particles gives a direct indication with respect to the wear in the mechanical components such as pumps, of a hydraulic system. Since most machine parts are made of steel, the most prominent type of wear particle is ferrous debris.

In order to detect such particles efficiently with the MEMS resonator sensor developed at ISAS, it is necessary to actively attract those ferrous particles to the sensor surface. This is done by a planar coil, which is placed close to the tip of the cantilever type resonator and loaded with a current of 150 mA. Note, that this coil is realized as part of the microfabrication process of the sensor. The final sensor is shown in Fig. 10.

Fig. 10.
figure 10

Optical micrograph of the MEMS sensor, consisting of two identical micro cantilevers with planar coils integrated close to the free ends. Reprinted from [24], ©2019 with permission from Elsevier

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The added mass of the ferrous particles \(\Delta m\) will shift the resonance frequency according to

$$ \Delta f=- \frac{1}{2} \frac{\Delta m}{M} f_{\mathrm{res}} \phi ^{2} \left ( x_{\Delta m}, y_{\Delta m} \right ). $$
(1)

\(M\) is the total oscillation mass and \(\phi \left ( x_{\Delta m}, y_{\Delta m} \right )\) is the value of the mode shape function at the position of the mass [24]. The mode shape function describes the position dependence of the shift in \(f\)res due to particle-related mass loading. Regions with high displacement amplitudes will be significantly more responsive compared to those with low amplitude (\(i\).\(e\). the nodal lines). The coil is designed to mainly attract particles in regions with high responsivity to maximize the overall performance of the sensor.

The MEMS device is tested in a model solution of deionized water and dispersed iron oxide (Fe3O4) nanoparticles with a hydrodynamic diameter of 250 nm and a final concentration of 350 μg/ml. To compensate for any parasitic sensor drift due to temperature or unintended sedimentation, a pair of cantilever sensors is used with only one coil active, enabling a differential measurement approach (see Fig. 10). The resonance spectrum is fitted by the phase function, which allowed an accuracy in the determination of \(f\)res of 50 Hz. The results of this study are shown in Fig. 11.

Fig. 11.
figure 11

(\(a\)) Resonance frequency of the active and reference cantilever in water. The accumulation of ferrous particles starts at \(t_{1}\). At \(t_{2}\) the accumulation stops and the sensor is rinsed with fresh deionized water. (\(b\)) Accumulated particle mass during the experiment. Reprinted from [24], ©2019 with permission from Elsevier

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The coil is current loaded at the time \(t_{1}\). The instant increase in \(f\)res can be attributed to current induced heating. A steady decrease of \(f\)res is then observed over a period of 100 min., as ferrous particles are collected and the sensor mass is increased. Note, that the reference sensor provides a stable output characteristic as a function of time.

Using Eq. (1) and integrating over the cantilever surface yields the total accumulated mass as shown in Fig. 11b). After 100 min., the total mass is about 0.49 μg, which corresponds to a mass responsivity of 82.85 pg/Hz. Given the accuracy of \(f\)res with 50 Hz, this results in a limit of detection for this sensor of 4 ng. The high responsivity is impressive for a sensor design of this size, since approaches with similar responsivities typically utilize much smaller sensor geometries [24, 26, 27].

Finally, the outstanding performance in terms of quality factors can be utilized to even measure the viscosity of extremely viscous materials like bitumen. For this purpose, bitumen is heated up to 100°C, placed on the MEMS sensor and annealed for 10 min. to ensure complete sensor coverage as shown in Fig. 12. The bitumen covered sensor is then placed into a Vötsch VCL4006 climate chamber to perform impedance spectroscopy in a temperature range between 75 and 150°C. A Lorentzian is fitted to the conductance spectrum shown in Fig. 13 to measure both \(f\)res and \(Q\), which is then used to determine the dynamic viscosity of the investigated bitumen derivatives as described in [22, 25].

Fig. 12.
figure 12

Schematic illustration of the measurement procedure, represented by cross-sectional views of the resonator. In (\(a\)), the bare resonator is depicted. About 100 μl bitumen is placed on top of the resonator as shown in (\(b\)). In the following annealing process (\(c\)), the bitumen penetrates into the cavity and the resonator is then excited as shown in (\(d\)). ©2019 IEEE. Reprinted, with permission, from [25]

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Fig. 13.
figure 13

Frequency response characteristics of the electrical conductance G of the piezoelectric MEMS resonator, when immersed in the bitumen derivative B3 at different temperatures (\(T = 75\), 100, 125 and 150 °C). ©2019 IEEE. Reprinted, with permission, from [25]

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The results are shown in Fig. 14 for three types of bitumen derivative at various temperatures. The reference values are measured with a Brookfield DV3T viscometer. Basically, the results of both the MEMS sensor and the viscometer are in good agreement. With this cantilever based resonator, the viscosity can be measured up to a dynamic viscosity of 64000 mPa s with a moderate quality factor of 4 at 75°C.

Fig. 14.
figure 14

Comparison of the measured dynamic viscosity values for the bitumen derivatives B1-B3 and the corresponding reference values at \(T=75\), 100, 125 and 150°C. ©2019 IEEE. Reprinted, with permission, from [25]

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4 Conclusions

A promising class of mechanical modes is introduced, labeled as roof-tile shaped modes, and their benefit and potential for cantilever-type MEMS devices were presented. This class of 2-dimensional mode features extremely high quality factors in liquid media. While high quality factors are often not necessary in applications in vacuum or air, they are of utmost importance for applications in liquids, especially when the latter are highly viscous. Due to the high damping in such environments, a low quality factor in air would result in no measureable signal after immersion. Besides the careful selection of the mode class, a high output sensor signal is achieved by matching the electrode design to the specific resonance mode shape.

These roof-tile shape resonator based sensors have been successfully operated and evaluated in three application scenarios: wine fermentation, detection of ferrous particles in liquids and viscosity measurements of bitumen. All in all, this broad range demonstrates the versatility and the potential of this technology platform for in-situ real-time monitoring of physical quantities in liquids, while there are still interesting open questions such as energy loss by acoustic radiation and a theoretical model for the fluid structure interaction of 2D mode shapes immersed in liquids. These topics are the subject of ongoing and future investigations.