Cell Alignment in Aqueous Solution Employing a Flexural Plate Wave Piezoelectric MEMS Transducer

The possibility to steer floating cells dispersed in water by means of flexural plate waves (FPWs) generated by a 9 mm <inline-formula> <tex-math notation="LaTeX">$\times9$ </tex-math></inline-formula> mm piezoelectric MEMS transducer has been explored. The MEMS transducer has a squared cavity etched out in a silicon substrate formed by a 6 mm <inline-formula> <tex-math notation="LaTeX">$\times6$ </tex-math></inline-formula> mm composite diaphragm made of a piezoelectric aluminum nitride (AlN) layer on top of a doped silicon plate. The piezoelectric layer can be electrically actuated by means of metal interdigital transducers (IDTs) placed over the AlN film at the diaphragm edges. Cell alignment has been sought for by inducing standing FPWs in the diaphragm and in the contacting water layer in the cavity by the one-dimensional (1D) acoustic field pattern obtained by exciting two IDTs located symmetrically with respect to the diaphragm centre. The working principle has been validated by means of 2D finite element modelling and simulations. The MEMS transducer has been fabricated using the PiezoMUMPs process and experimentally tested by exploiting a tailored front-end electronic circuit. Inactive fibroblast cells with an approximate diameter of <inline-formula> <tex-math notation="LaTeX">$15~\mu \text{m}$ </tex-math></inline-formula> have been dispersed in demineralized water within the cavity at a concentration in the order of 105 cells/ml. By applying sinusoidal excitation signals to faced IDTs with zero phase shift and peak amplitude of 10 V, lines of cells spaced by half wavelength <inline-formula> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula>/2 = <inline-formula> <tex-math notation="LaTeX">$56~\mu \text{m}$ </tex-math></inline-formula> have been achieved at 12.5 MHz, in good agreement with theoretical predictions and simulation results.


I. INTRODUCTION
The alignment of cells plays a crucial role in fundamental biological analyses and medical applications.Advances in tissue engineering have significantly improved cell alignment to restore, analyse, or even replace different types of biological tissues.In biofabrication of blood vessels, the achievement of aligned and functional endothelial cells is of utmost importance as they form the inner lining of all blood vessel walls [1].The alignment of collagen fibers has been The associate editor coordinating the review of this manuscript and approving it for publication was Shuo Sun.correlated to breast cancer cell invasion and identified as one of the key factors to determine in advance cell abnormalities related to human diseases [2].Numerous studies have demonstrated that oriented biomaterials can accelerate and promote directional regrowth of damaged axons for brain injuries repair [3], [4].The field of tissue engineering relies on the development of alignment supports or techniques that can act as templates for tissue formation employable in vitro, as guidance for cellular regeneration, or in vivo, as founding structures for tissue growth [5].For in vivo cell alignment, hydrodynamic materials [6] or scaffolds are typically employed as structural components.Electrically conductive collagen scaffolds for skeletal muscle tissue engineering have been developed to align and differentiate myoblast cells [7].Whereas, in vitro cell alignment approaches are normally based on the exploitation of external stimuli and fields.For instance, optical tweezers rely on forces exerted by a focused beam of light to trap and pattern cells [8], [9].Magnetic tweezers exploit a magnetic field gradient in which particles are placed and are subjected to forces related to fluid magnetization [10].Electrokinetic-based approaches use electrosurface phenomena with embedded microelectrodes to pattern cells [11], [12].In general, the main issue while dealing with alignment supports or techniques is their biocompatibility, i.e., the ability to obtain the desired function without causing any local or systemic adverse response in the cells [13].To this extent, acoustophoresis has attracted attention to manipulate cells through acoustic waves, due to its intrinsic label-free, non-contact, and non-invasive properties [14].Acoustophoresis is commonly achieved by inducing in piezoelectric materials acoustic waves due to the applied electrical excitation signals [15].Acoustic waves are then employed as a coupling mean to exchange energy and to induce forces into the liquid where cells are typically dispersed [16].Specifically, in a standing wave field the acoustic radiation force (ARF) drives the particles dispersed in liquid into acoustic pressure nodes, thus allowing their manipulation and alignment [17], [18].Bulk acoustic waves (BAW) [19], surface acoustic waves (SAW) [20], and flexural plate waves (FPW) [21], are typical acoustic modes exploited in piezoelectric transducers.The adoption of FPWs has the advantage of exhibiting a wave velocity that decreases with decreasing plate thickness and may become lower than the wave velocity in liquids.Therefore, for a given wavelength, the corresponding frequency is relatively low, i.e. typically in the range of 5-20 MHz, which alleviates the requirements on the associated driving electronics compared to typical SAW devices.Furthermore, FPW sensors are suitable for the measurement of fluid properties, such as liquid viscosity, and gravimetric (bio)chemical analysis in solutions [22].
In this context, the present work proposes a piezoelectric MEMS transducer able to generate an acoustic field pattern based on standing FPWs for the alignment of cells in aqueous solution.The working principle has been investigated through a 2D finite element modelling and confirmed by comparing the obtained simulations with experimental results.A tailored front-end circuit based on a direct digital synthesizer has been designed to drive the device.With inactive fibroblast cells dispersed in demineralized water placed in the MEMS cavity, the applied excitation signals have allowed to align cells along a regular pattern with a spacing equal to half the acoustic wavelength.The present work extends the early contents reported in the conference paper [23] providing details of the working principle of the MEMS transducer related to the acoustic-fluidic coupling, including a 2D FEM model, adding the comparison of the electrical measurements with the simulation results of the single IDT admittance and describing the tailored front-end electronics employed for cell alignment.The paper is organized as follows: Working principle (Section II), MEMS description (Section III), Finite element analysis (Section IV), Experimental results (Section V) and Conclusions (Section VI).

II. WORKING PRINCIPLE
Top and bottom schematic views of the proposed MEMS transducer are shown in Figure 1a,b, respectively.The device embeds a squared cavity etched out in a silicon substrate and a composite piezoelectric-silicon diaphragm for steering and confining floating cells in liquid.The diaphragm can be electrically actuated by means of metal interdigital transducers (IDTs) deposited on the piezoelectric film.Each IDT is formed by two interleaved comb-shaped electrodes of equally spaced fingers with pitch p larger than the diaphragm thickness.By applying a sinusoidal excitation voltage between the IDT fingers, the converse piezoelectric effect is exploited to induce a dynamic deformation of the piezoelectric layer thickness and of the diaphragm in turn.As a consequence, Lamb waves are generated in the diaphragm which are coupled to the liquid in the cavity.In this work, by applying sinusoidal excitation voltages to two IDTs located symmetrically with respect to the cavity centre, the first antisymmetric vibrational mode (A0) of the diaphragm is exploited to achieve standing flexural plate waves (FPWs) with wavelength λ , as shown in Figure 1c.In turn, compressional acoustic waves are coupled into the liquid generating a one-dimensional (1D) acoustic field pattern in which pressure nodes are located at half the acoustic wavelength λ /2 [24].The cells dispersed in the liquid are thus steered and trapped in distinct positions by the developed forces.Specifically, along the vertical y-axis the equilibrium position of each cell is determined by the force balance between gravity and buoyancy [25].On the other hand, along the horizontal x-axis crossing the IDTs, each cell is subjected to the acoustic radiation force (ARF) and the viscous force [26].For floating cells with diameter larger than 3 µm the ARF typically exceeds the viscous force and pushes each cell toward the nearest standing-wave node thus forming a regular pattern with a gap of half the acoustic wavelength [20].

III. MEMS DESCRIPTION
More generally than the scope of the present study, the employed piezoelectric MEMS transducer has been designed as a versatile platform that can be exploited to investigate different applications [27], [28].The PiezoMUMPs process by MEMSCAP [29] has been used for fabrication.
Figure 2a shows the bottom view of the 9 mm × 9 mm device taken from the graphic design system (GDS) file.The 6 mm × 6 mm diaphragm is a stack of a highly doped silicon layer (Si) and an aluminum nitride (AlN) piezoelectric layer.The MEMS design has been accomplished by considering the acoustic-fluidic coupling between water and the composite Si-AlN diaphragm.Specifically, the condition in which the wavelength of the A0 flexural mode in the diaphragm and the wavelength of the longitudinal waves in water are equal has been estimated taking into account the frequency-towavelength relationships described by [30] and [31]: and  in the liquid are expected to be trapped and aligned along a regularly spaced pattern with a gap of λ /2 = 56 µm.
For the actuation of the AlN layer, eight IDTs are made available, each composed of two interleaved comb-shaped electrodes of twenty equally spaced fingers.As visible in Figure 2b, to ensure the generation of standing acoustic waves with wavelength λ =112 µm, the pitch p has been set equal to λ and the distance d between two opposite IDTs has been set to 34λ [32], while the finger width w is 28 µm.The IDT rectangular pads are made by a metal stack of 20 nm of chrome (Cr) and 1 µm of aluminum (Al).The four squared metal pads at the corners electrically connect the doped silicon layer of the diaphragm.Figure 2c shows the X-X' cross section view where the silicon dioxide (SiO 2 ) layer and the silicon (Si) substrate layer are visible with a thickness of 1 ± 0.05 µm and 400 ± 5 µm, respectively.The thicknesses of the AlN and doped silicon diaphragm layers are 0.5 µm and 10 ± 1 µm, respectively.Top-and bottom-view images of the fabricated device are shown in Figure 3a,b, respectively.The cavity employed to confine the cells dispersed in liquid can be noticed.

IV. FINITE ELEMENT ANALYSIS
A 2D finite element model in COMSOL Multiphysics ® has been developed to investigate the electro-mechanical behaviour and working principle of the piezoelectric MEMS described in Section II.
The cross-section of the simulated device and the structural layers that have been included in the 2D model are shown in Figure 4a,b, respectively.The metal layer has been considered as made by Al only, since its thickness is 50 times higher than the Cr thickness.The metal pads of the doped silicon layer have not been included in the model.<100> Si has been adopted for both the substrate and the silicon layer, while SiO 2 has been used as the oxide layer material.
For the AlN layer the piezoelectric coefficients have been specified as d 31 = −2.78pC/N and d 33 = 6.5 pC/N [33].
The piezoelectric multiphysics has been used to simulate the piezoelectric effect, combining the physics of solid mechanics and electrostatics.
Strain-charge constitutive relations and dielectric losses have been specified considering the AlN material properties, and a charge conservation boundary condition has been  applied to the AlN layer in the electrostatics physics.As a simplifying assumption, an isotropic damping constraint has been applied to the whole structure with a loss factor of 0.004.Electrical domain conditions have been set to the IDTs fingers located on the diaphragm by alternating voltage and ground constraints.To simulate the high doping concentration, a floating potential group has been applied to the surface of the silicon layer in contact with AlN, thus modelling a conductive electrode.The mesh has been carefully adjusted to obtain a convergent solution while containing the computational workload as shown in Figure 5a.Horizontally, a mapped mesh distribution size of 1 µm has been adopted, as visible in Figure 5b.A mapped distribution mesh size of 0.5 µm, 0.1 µm, 1 µm, 1 µm and 200 µm has been set for the thicknesses of metal, piezoelectric, doped silicon, oxide, and substrate silicon layers, respectively.
A frequency domain study has been performed to evaluate the electrical admittance Y (f ) of a single IDT seen as a one-port element, defined as the ratio between the current collected at the IDT fingers i c (t) and the applied sinusoidal excitation voltage v exc (t), with rms amplitude A exc set to 1 V,  both converted in the frequency domain.Specifically, the IDT3 located on the inner side of the diaphragm has been analysed while leaving all other IDTs floating, as shown in Figure 6.In accordance with the frequency range derived in Section III, the excitation frequency f exc has been varied from 10 to 15 MHz with a step size of 12.5 kHz. Figure 7 plots the obtained real and imaginary parts of the electrical admittance Y (f ) of IDT3 as a function of the excitation frequency f exc .
The obtained admittance pattern is mainly determined by the IDT3 location on the diaphragm.Acoustic waves are generated and propagated towards both the proximate and far boundaries of the diaphragm which behave as wave reflectors.Since IDT3 is not located in the centre of the diaphragm, the distance travelled by the acoustic waves to reach the reflectors differs [34], [35], [36].This leads to the generation  of distinct sets of peaks in the real part of Y (f ) between 10.8 and 12.8 MHz and between 12.8 and 14.8 MHz.The obtained peaks are consistent with the estimated frequency range f exc = 13 ± 1.4 MHz obtained from the acoustic-fluidic coupling for an unbounded plate described in Section II.

V. EXPERIMENTAL RESULTS
To validate the simulated results described in Section V, the electrical admittance versus frequency of the single IDT3 has been experimentally measured by means of a HP4194A analyzer while the other IDTs have been left floating.A sinusoidal excitation with rms amplitude A exc of 1 V has been used with the frequency f exc swept between 10 and 15 MHz with a step size of 12.5 kHz.The measured real and imaginary parts of the admittance Y (f ) are plotted in Figure 8a,b and compared with the corresponding results obtained from simulations.
The agreement between simulated and experimental results within the explored frequency range is remarkable.The residual discrepancies can be possibly due to the fabrication process tolerances and the simplifying assumptions adopted for the 2D model described in Section IV.The cell alignment with 1D acoustic field pattern generated through standing FPWs has been experimentally verified at room temperature by exciting both IDT1 and IDT3, which are located on the inner opposite sides of the diaphragm as shown in the  The excitation voltages v exc0 (t) and v exc1 (t) both with peak amplitude of 10 V have been applied to IDT1 and IDT3, respectively.The same excitation frequency f exc of both signals has been finely tuned until cell alignment was clearly observed.This approach allows to accurately adjust to the target condition.As shown in Figure 11b, ordered alignment has been reached at f exc =12.5 MHz, in agreement with the expected range predicted in Section III.From the enlarged image of Figure 11c the nominal spacing between two adjacent lines of cells in the alignment pattern can be estimated as 56 µm corresponding to half the acoustic wavelength, in accordance with theoretical expectations.The obtained experimental results confirm that the proposed piezoelectric MEMS transducer can be successfully employed to align cells dispersed in water by means of flexural plate waves.

VI. CONCLUSION
This work has presented a piezoelectric MEMS transducer to generate a 1D acoustic field pattern for cell alignment in aqueous solution by means of standing flexural plate waves (FPWs).The 9 mm × 9 mm MEMS includes a squared cavity formed by a 6 mm × 6 mm composite diaphragm of doped silicon (Si) and aluminum nitride (AlN) layers to steer cells dispersed in water.By properly setting the metal interdigital transducers (IDTs) pitch over the AlN film, the A0 flexural mode in the composite diaphragm and the longitudinal waves in water can be excited at the same frequency.Therefore, cell alignment in water can be achieved by vibrating the diaphragm.The expected excitation frequency range at around 12.5 MHz has been confirmed by analysing the electrical impedance of a single IDT through a 2D finite element modelling in COMSOL Multiphysics ® and by comparing the simulation and experimental results.A tailored front-end electronic circuit, based on a two-channel direct digital synthesizer (DDS), has been developed to generate two inusoidal excitation signals with peak amplitude of 10 V, zero relative phase shift at up to 15 MHz.Inactive fibroblast cells with an approximate diameter of 15 µm dispersed in demineralized water with a concentration in the order of 10 5 cells/ml have been placed in the MEMS cavity.The generated excitation signals have been fed to two IDTs located at the opposite inner sides of the diaphragm allowing to successfully achieve cell alignment at the excitation frequency of 12.5 MHz.The spacing between two adjacent cell lines in the alignment pattern has been optically estimated as 56 µm corresponding to half the acoustic wavelength.This validates the proposed MEMS transducer as a microdevice to generate a 1D acoustic field pattern in aqueous solution for cell alignment.Future activities will include the exploitation of 2D acoustic field pattern by driving four IDTs and the embodiment of the MEMS into a dedicated lab-on-chip system to further expand the application possibilities.

FIGURE 1 .
FIGURE 1. Top (a), bottom (b) and cross-section schematic views (c) of the proposed piezoelectric MEMS transducer.
where E = 167 GPa, η = 0.268, ρ = 2373 kg/m 3 and t = 10.5 µm are the overall, i.e. effective, Young's modulus, Poisson's ratio, mass density and thickness of the composite Si-AlN diaphragm, respectively, while c w = 1460 m/s is the sound speed in water.By employing (1), (2) and considering tolerances in layer thicknesses due to the manufacturing process, λ is estimated as 112 ± 11 µm which corresponds to an excitation frequency range of f exc = 13 ± 1.4 MHz to match f A0 .Considering the nominal case, cells dispersed

FIGURE 2 .
FIGURE 2. Bottom-view image of the designed piezoelectric MEMS (a), enlarged view of the IDTs (b) taken from the graphic design system (GDS) file, and cross-section view at X-X' (c).

FIGURE 3 .
FIGURE 3. Top (a) and bottom (b) images of the fabricated piezoelectric MEMS.

FIGURE 4 .
FIGURE 4. 2D model view of the proposed piezoelectric MEMS transducer (a).Enlarged image of the layers considered in the simulation model (b).

FIGURE 5 .
FIGURE 5. Mesh domain of the proposed piezoelectric MEMS transducer (a).Enlarged image of the mesh for metal, piezoelectric and silicon layers (b).

FIGURE 6 .
FIGURE 6.Schematic view of the proposed piezoelectric MEMS configured for the simulation of the electrical admittance of IDT3.

FIGURE 7 .
FIGURE 7. Simulated real (blue, left y-axis) and imaginary (green, right y-axis) parts of the admittance Y(f ) of a single IDT as a function of the excitation frequency f exc .

FIGURE 8 .
FIGURE 8. Comparison between simulated (blue) and measured (orange) real (a) and imaginary (b) part of the admittance Y(f ) of a single IDT as a function of the excitation frequency f exc .

FIGURE 9 .
FIGURE 9. Block diagram of the circuit employed to excite two IDTs for generating 1D acoustic field pattern.

FIGURE 10 .
FIGURE 10.Experimental setup employed to align cells in water (a).Top (b) and bottom (c) views of the dedicated PCB hosting the piezoelectric MEMS transducer.

FIGURE 11 .
FIGURE 11.Images of fibroblast cells dispersed in demineralized water placed in the MEMS cavity without (a) and with (b) voltage excitation applied.Enlarged view of the cells aligned at a nominal spacing of 56 µm (c).