MEMS force microactuator with displacement sensing for mechanobiology experiments

Transcription

1 MEMS force microactuator with displacement sensing for mechanobiolog eperiments F. Cerini, M. Ferrari, V. Ferrari Department of Information Engineering Universit of Brescia Brescia, Ital A. Russo, M. Apeitia Urquia STMicroelectronics Ital R. Ardito, B. De Masi Department of Civil and Environmental Engineering Politecnico di Milano Milano, Ital M. Seranti, P. Dell Era Department of Molecular and Translational Medicine Universit of Brescia Brescia, Ital Abstract This paper presents a Micro Electro-Mechanical Sstem (MEMS) that performs electrostatic force actuation and capacitive microdisplacement sensing in the same chip. B driving the actuator with a given voltage, a known force can be applied to a microsample under test b using a silicon probe tip, while the obtained displacement is measured. This allows to etract the mechanical properties of the microsample entirel on chip, and to derive its force-displacement curve without eternal equipment. The proposed device is intended for mechanobiolog eperiments, where the microsample is made of biological tissues or cells. The device generates a force in the order of few micronewtons and a maimum displacement of 1.8 µm can be measured. Kewords MEMS, electrostatic force actuator, capacitive displacement sensing, mechanobiolog. I. INTRODUCTION The use of micro electro-mechanical sstems (MEMS) to test mechanical properties of materials at the microscale is especiall promising for probing microbiological samples in in-vitro mechanobiolog eperiments [1]. Mechanical properties of cells are important factors to define their functionalit, to differentiate them, and pla a role in tissue formation. Moreover, changes in elasticit of the cells can be used as a marker to identif cell abnormalities that can be possibl correlated with various human diseases [2]. In order to measure the mechanical properties of microbiological samples, MEMS force actuators and sensors have been proposed in the last ears, emploing different actuation methods such as the electrothermal [3, 4] and electrostatic [5] principles. Fleible-beam optical [6-8] and capacitive [9, 10] force sensors have been also reported for cellular force measurement and for mechanical characteriation of biomembranes [11]. Tpicall, the reported configurations require eternal equipment to appl either the force or displacement, while the complementar quantit is measured b the microsstem. In this contet, the approach of this work is to integrate both force actuation and displacement sensing on the same chip that onl has a pair of electrical input and output ports, therefore enabling the measurement of the microsample mechanical properties entirel on chip. Quantitative biomechanics studies on single molecules or cells are epected to be possible. The paper presents earl results that validate the principle. The device description, operating principle and proposed electro-mechanical model are illustrated in Section II, eperimental results are presented in Section III, and conclusions are given in Section IV. II. DEVICE DESCRIPTION, OPERATING PRINCIPLE AND MODELLING Fig. 1 shows the laout, relevant measured dimensions and SEM images of the MEMS device. The device has been designed and fabricated b using the ThELMA process (Thick Epipol Laer for Microactuators and Accelerometers), developed b STMicroelectronics for inertial sensors and actuators based on heavil doped pol-silicon [12]. The mechanical microstructure consists of a central rigid movable shuttle (denoted as R), which is supported and anchored to the substrate b four folded-beam springs, as shown in Fig. 1. Interleaved comb structures etending laterall from the shuttle form variable-gap parallel-plate comb-finger capacitors with similar structures on the stator (denoted as S) solidl linked to the fied frame.the resulting configuration denoted as transverse combs has a capacitance. The device also contains four variable-area comb-finger capacitors between driver armatures (denoted as D) on the frame and corresponding armatures on the shuttle R. The resulting configuration denoted as lateral combs has a capacitance.

2 4.2 µm 1.3 mm 9.3 µm movement Drivers D [comb fingers] Sensor S [parallel plates] shuttle R Drivers D [comb fingers] probe tip Device part # D1a # D2a # D3a # D4a Length (µm) Width (µm) springs Gap (µm) # D1b # D2b # D3b # D4b Number/note Comb-fingers 13.5 a Parallel-plates Fleural springs b Folded Central shuttle Holes µm 2 Probe tip Out-of-plane thickness a. Initial overlapping length b. Measures for each beam driver # 1 driver # 2 sensor combs 370 µm driver # 3 driver # 4 springs shuttle R springs # 1 # 2 sensor combs # 3 # 4 ThELMA process highl doped pol-silicon drivers spring 0 µm R S R # 1 # 2 sensor combs probe tip a) b) c) Figure 1: Laout, measured geometrical dimensions and SEM images of the investigated MEMS device with enlarged views of drivers and spring (a), a set of parallel-plate combs of the displacement sensor (b) and the probe tip (c). The presence of both lateral combs (D-R) and transverse combs (S-R) configurations offers a double possibilit of actuation of the movable shuttle together with the fleibilit to set different values of electrostatic force between fied and movable parts, independentl of the parallel-plate distance. In displacement sensing, transverse combs offer higher sensitivit compared to the lateral combs configuration, though the response is nonlinear [5]. For these reasons, in this work, we use the D-R part for electrostatic force actuation and the S-R part for capacitive displacement sensing, respectivel. Due to the device geometr, the movement direction of the shuttle is along the longitudinal ais. Fig. 2 illustrates the device operating principle b the use of equivalent models based on the direct electromechanical analog (Voltage-Force; Current-Velocit). The probe tip, visible in the inset of Fig. 1c connected to the shuttle R, is used to press the microsample under test, represented b its mechanical impedance, b appling a known force, which can be set b imposing a proper driving voltage to the driver capacitor. The sensing capacitor is used to measure the probe tip displacement. In the simplified monodimensional lumped-element model of Fig. 2a, the shuttle is represented b a mass supported b a spring with mechanical stiffness, accounting for the a) b) D R L a) b) d D d D D driver, R C DR driver, k m FC DR mm k m F DR mm shuttle shuttle MEMS substrate MEMS substrate microsample sensor, CSR Z L probe microsample tipe Z L probe tipe d s sensor, 0 CSR w d ' 0 s w l ' S l S L V SR (t) Data acquisition V SR (t) and Data control S acquisition H and control S GPIB PC LCR meter H HP 4274A GPIB PC LCR meter HP 4274A F DR + - 1/k m F L ẋ Z L Figure 2: Monodimensional equivalent mechanical model of the device with the electrical setup (a) and equivalent electro-mechanical lumped-element circuit (b).

3 DR [nn/v 2 ] DR [nn/v 2 DR [nn/v ] 2 ] behavior Figure 3: Measured capacitance as a function of the tilt angle for a driven voltage kept constant to 25 V. In the insets, pictures of device tilted to -90, 0 and +120 respect to the ais. total elasticit of the four folder beams. The parameters and represent the spacing between two S-lamellae and the width of an R-lamella, respectivel. The position represents the initial mechanical equilibrium point of the shuttle without eternal electrical sources applied to the electrodes. The equilibrium point can be influenced b an initial asmmetr due, for eample, to a pre-stress of the folded beams, or the initial offset due to contact of the microsample with the probe tip before measurement. Consequentl, can be epressed as: The quantit, representing the shorter distance between an R-lamella and the neighboring lamella, and can be defined as: The voltage applied between the terminals D and R as shown in Fig. 2, results in the electrostatic force acting on the shuttle given b: The coefficient, representing the electro-mechanical transduction factor between the force and the squared voltage, can be epressed as: Angle [ ] +120 (1) (2) (3) [ ( )] (4) Figure 4: Eperimental values of measured at different levels of. For each level, tilting angles of, and were applied, while was kept constant to its no-tilting value ( case) b adjusting. The blue line is the eperimental behavior of as a function of when no-tilting occurs. where and are the dielectric permittivit of vacuum and the relative dielectric constant of the gaseous medium, respectivel, the total number of R-lamellae faced to D-lamellae, the gap between D- and R-lamellae, the out-of-plane thickness lamella, and a parameter which properl tunes the Palmer s fringing field effect, as reported in [13] Eperimental Eperimental Theoretical Theoretical V DR Figure 5: Theoretical and measured electro-mechanical transduction factor DR as a function of the applied voltage.

4 3-ais micro-manipulator with micropipet MEMS chip sstem for cell suction MEMS probe tip Ø = 1 µm glass microtip MEMS probe tip fied cell TEST A TEST B 10 µm Figure 6: Eperimental setup for positioning of the microsample with enlarged views of mechanical characteriation of a glass bending microtip (Test A) and a fied fibroblast cell (Test B). The total capacitance between the S and the R terminals, can be epressed as: ( ) (5) where is the sum of the parasitic capacitances, the total number of R-lamellae faced to S-lamellae, and the overlapping length. If a microsample as the load is present, under the simplifing assumption that it behaves as a spring with mechanical stiffness, Eq. (7) becomes: with microsample as the load and the total stiffness, which increases up to determined. B subtracting the known value of estimation of can be obtained. (8), can be, the From the epression of in Eq. (5), the following close-form epression of the distance can be derived: III. EXPERIMENTAL RESULTS { } (6) B inserting Eq. (6) into Eq. (2), the value of the displacement, for a given force caused b an applied voltage, is obtained. Assuming that the chip plane is held horiontall and no microsample is initiall present (free conditions), than the mechanical stiffness, can be derived b: without microsample (free conditions) (7) The characteriation tests described in this section were performed using the eperimental setup shown in Fig. 2a. In order to measure, the LCR meter was set to provide a sinusoidal signal with amplitude of and frequenc of, i.e. far from the resonant frequenc of the movable part that is around. The results presented in this work were obtained b using the driver D2 onl. The terminals R, substrate SUB, and the unused driver terminals D1, D3 and D4 are connected to the low terminal of the LCR meter in order to avoid parasitic electrostatic phenomena [14]. Given the geometrical laout, b tilting the device around the ais, it becomes sensitive to the in-plane component of

5 F [ N] FDR ' = 45 nm ' = 134 nm TEST A glass microtip eq. F DR = k m + k L free conditions (ero load) eq. F DR = [ m] k m F L TEST B in free conditions (ero load) with fied cell residual position and orientation changes of the fied cell with respect to the probe tip contact loss between the fied cell and the probe tip Figure 7: Force-displacement characteristics measured in free conditions (ero load) and with the glass bending microtip as the load. The mechanical stiffness k m of the spring and of the load k L results 3.62 N/m and 1.39 N/m, respectivel. The inset shows the measured capacitance versus. Figure 8: Measured capacitance as a function of the voltage in free conditions and with a fied fibroblast cell on a micropipette as the load. the weight force acting onto the shuttle. Under tilting around the ais of an angle between the ais and the vertical direction, Eq. (7) can rewritten as: where with is the gravitational acceleration. Fig. 3 shows the measured capacitance (in free conditions) as a function of the tilt angle for an applied kept constant to. As epected, the behaviour is sinusoidal. In accordance with Eq. (9), the minimum and maimum values of are reached for and, respectivel. In particular, when the sign of is the same of the spring force and it is opposite to, and vice-versa when. To calibrate the applied force as a function of the voltage, an eperimental calibration procedure b using as reference has been adopted. During the tilting of the device to and -, the displacement has been kept unaltered b adjusting the voltage to the required level in order to maintain constant. In this wa, the mechanical stiffness of the spring has no effect on the calibration. Fig. 4 shows as the eperimental values of measured at different levels of. For each level, tilting angles of, and were applied, while was kept constant to its no-tilting value ( case) b adjusting. Each value represented b a circle is the average of consecutive acquisitions with the error bars representing the interval (9) where is the standard deviation. The blue line shows the eperimental behavior of (in free conditions) versus for. Under the condition of unaltered displacement, Eq. (9) can be evaluated for and, and combined with Eq. (3) to obtain the close-form epression of given b: (10) where and are the values for and, respectivel. Fig. 5 shows the eperimental values of derived b using Eq. (10) for different applied voltages. The mass, estimated from a SEM geometr analsis with a pol-silicon densit of, results to be of 24 µg. The value of constant with is in agreement with the theoretical value of Eq. (4) within few percents. When reaches the minimum value of for, the shuttle is at the distance (i.e. in condition of geometrical smmetr), and the total parasitic capacitances estimated from Eq. (5) results to be. Fig. 6 shows the eperimental setup adopted for testing the microsstem and for the positioning of the microsample into the device. The enlarged views show the glass bending microtip and a fied fibroblast cell used during the eperiment as two tpes of load under test.

6 Fig. 7 shows the results of test A in which the force-displacement characteristics of the device have been measured in free conditions (ero load) and with a glass bending microtip as the load. In free conditions, the stiffness of results, constant throughout the displacement range since no electrostatic effect on stiffness is produced due to the variable-area configuration of the comb actuator. With the bending microtip as the load, the stiffness increases to and a change in the slope of the force-displacement characteristic occurs. From the intercept at, it is possible to etract the estimation of the initial asmmetr of and in free conditions and with the glass bending microtip as the load, respectivel. Fig. 8 shows the results of test B in which a single cell (fibroblast) fied for min in PFA (paraformaldehde) on a rigid micropipette has been used as the load. It can be observed that the plot of versus clearl evidences a specific behaviour when the cell is present. During the measurement, some residual position and orientation changes of the fied cell with respect to the probe tip are visible, and for higher than the contact between the cell and the probe tip it is lost. IV. CONCLUSIONS A MEMS that performs electrostatic force actuation and capacitive microdisplacement sensing on the same chip is presented. A monodimensional equivalent mechanical model of the device and an equivalent electro-mechanical lumped-element circuit based on the direct electromechanical analog have been proposed and validated in order to illustrate the device operating principle. An eperimental calibration procedure b using the weight force as reference has been adopted to estimate the value of the electro-mechanical transduction factor. In this wa, a known force can be applied to a microsample under test b using a silicon probe tip, while the obtained displacement is measured from the measured capacitance. The device has been used to measure the force-displacement characteristics in free conditions (ero load) and with a glass bending microtip as the load, resulting in mechanical stiffness of and, respectivel. Measurements of the capacitance as a function of the voltage have been performed with a single fibroblast fied for min in PFA (paraformaldehde), evidencing a specific behaviour when the cell is present. This allows to etract the mechanical properties of the microsample entirel on chip, and to derive its force-displacement curve without eternal equipment. The proposed device allows to measure in both static and dnamic regimes, therefore it can derive the complete viscoelastic behavior of the microsample in mechanobiolog eperiments. REFERENCES [1] Norman J., Mukundan V., Bernstein D., Pruitt B. L., Microsstems for Biomechanical Measurements, IPRF, vol. 65, pp , Ma [2] Gu N., D. 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