A SUBMERSIBLE PIEZORESISTIVE MEMS LATERAL

W3P.059

A SUBMERSIBLE PIEZORESISTIVE MEMS LATERAL FORCE SENSOR FOR CELLULAR BIOMECHANICS APPLICATIONS M. Gnerlich, S.F. Perry, S. Tatic-Lucic Lehigh University, Bethlehem, PA, USA ABSTRACT A submersible lateral force sensor has been developed as part of an integrated MEMS chip for cell biomechanics experiments with forces below 100 nN. The piezoresistive elements in the sensor are defined by a single mask on an SOI wafer without the need for a doping or annealing step, and are easily integrated into other SOI MEMS. We examine the optimal design of this force sensor, as well as characterization results from fabricated devices.

KEYWORDS force sensor, MEMS, piezoresistor, cell mechanics

INTRODUCTION

with the rest of our system, we use a design that is defined by the silicon geometry rather than doping [1]. By design, it operates in conductive cell culture medium without suffering a significant loss of sensitivity. Finally, the force sensor developed here operates at less than one volt, causing minimal self-heating.

METHODS Principle of Operation When a fixed cantilever beam is subjected to force at the tip, compressive and tensile stresses are created at the base of the beam. Piezoresistive elements at the base then convert this stress to a change in resistance (see Figure 2) and a set of metal traces connect the resistors in a full bridge.

A novel lateral force sensor with high sensitivity and low minimum detectable force has been developed for cellular biomechanics applications. This force sensor is part of an integrated system for measuring the mechanical properties of single cells, and it includes an actuator, dielectrophoresis trapping electrodes, a temperature sensor and an on-chip heater (see Figure 1).

Force Sensor

Actuator Array

Cell Location DEP

RTD Heater Ring

Figure 1: Overview of a fabricated BioMEMS chip (4 mm by 4 mm) showing the location of the force sensor, actuator array and shuttle, DEP electrodes, temperature sensor (RTD), and heater ring. The force sensor is the focus of this paper.

By compressing an individual cell while simultaneously measuring the force applied, the overall stiffness of a cell can be measured. This application requires a submersible and highly sensitive lateral force sensor. The force sensor developed for this purpose is based on silicon piezoresistive (PZR) transducers arranged in a full bridge configuration (see Figure 2). In order to simplify the integration of the PZR transducer

978-1-4577-0156-6/11/$26.00 ©2011 IEEE

Figure 2: Force applied to the center of the force sensor creates compressive and tensile stress in the piezoresistor regions (top). The electrical equipotentials and equivalent resistors are color coded and labeled (middle). Resistor pairs act in parallel (e.g. R1 = R1A || R1B), and each pair forms one quarter of a full bridge; VS - V0 drives the bridge and the output voltage is taken across V1 - V2 (bottom).

Sensitivity and Noise Modeling In order to model the expected sensitivity of the lateral force sensor, we apply linear beam bending theory to a cantilever beam with two regions (see Figure 3) of different area moment of inertia.

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Transducers’11, Beijing, China, June 5-9, 2011

Transducer Length

highly doped single crystal silicon and low voltages, thermal noise dominates. 4 (4)

Beam Length

ln

Region 2

Region 1

Force

Figure 3: The transducer length and beam length of the force sensor are varied to find the best geometry for maximum sensitivity. The dashed line shows plane of symmetry, and the hatched blocks show anchor points.

Starting with a point force at the end of cantilever beam under fixed-free bending, where F is force, E is elastic modulus, and Ix is the moment of inertia around so that is at the end of the x-axis, let the beam, 0 is at the base, and is at the edge between the two different cross sections. , , (1) (2) (3) The stress can be evaluated directly from Equation 1, using the moment of inertia for the region of interest (see Figure 4) which has been derived in Equations 2 and 3.

2 (6) where kb is Boltzmann’s constant, R is the resistance of the element, T is temperature, α is a dimensionless processing parameter (approximately 5x10-6 for single crystal silicon) [2], Vb is the bias voltage across the element, q is electronic charge, and I is current through the element. In addition, thermal-mechanical noise was considered using the transducer sensitivity to convert to an equivalent electronic noise. (7) where kb is Boltzmann’s constant, km is the mechanical stiffness, T is temperature, f0 is resonant frequency and Q is quality factor. The resonant frequency and quality factor were extracted from CoventorWare’s MemMech modal-harmonic analysis and used in equation 7, but the equivalent noise was found to be insignificant compared to the thermal noise. The combined governing equations for mechanical and electronic behavior were programmed into MATLAB, where the resulting sensitivity and signal to noise ratio (SNR) for the transducer was plotted as a function of various parameters (see Figure 5). Since the piezoresistive coefficient varies as a function of doping concentration, a lookup table was included in the calculation which relates doping concentration, resistivity and peizoresistivity factor [3]. -1

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After the stress in the piezoresistive transducer region for a given applied force has been estimated, the nominal resistance at zero stress and the resistance change due to applied force are calculated to derive the overall sensitivity. The intrinsic noise is also calculated in Equations 4 (thermal), 5 (1/f), and 6 (shot) to derive the expected signal to noise ratio for a given applied force, but for

Beam Length (μm)

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Figure 4: Cross-sectional diagrams for the two regions of the force sensor cantilever beam where the layout of the long cantilever beam with etch-holes (region 1) is shown left, and the layout of the transducer region (region 2) is shown right. The mechanical effects of the side beams in region 2 have been neglected.

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Figure 5: Sensitivity (left side) and SNR (right side) of the force sensor as a function of silicon resistivity and bias voltage (top), and piezoresistive element length and cantilever beam length (bottom).

For the top row of Figure 5, the beam length was fixed at 450 μm, the piezoresistive element length was 32 μm, and the parasitic bridge resistance was 4.7 Ω. For

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the bottom row of Figure 5, the piezoresistive element width was 1 μm, the silicon resistivity was 1.8 mΩ-cm, and the parasitic bridge resistance was 4.7 Ω. The best SNR occurs at high doping levels of approximately 2 mΩ-cm; this finding is in line with previous studies of optimal SNR for piezoresistive silicon [4]. Sensitivity decreases at high doping levels due to the decrease in the piezoresistivity coefficient, and it also decreases as parasitic resistances in the bridge become comparable to the resistance of the sensing elements, themselves. The SNR is best when the resistance of the sensing elements is low and the bias voltage is high (due to thermal noise dominance). The signal to noise ratio (estimated between 15 and 22 dB for a 1 nN force) makes this sensor design suitable for cell biomechanics experiments where measurements of e [5]. forces from 10 nN to 100 nN are expected Model Verification The beam stresses and the resulting resistivity changes have been verified in CoventorWare 2010 using the MemMech and MemPZR solvers. Since there is very limited movement at the base of the cantilever, the side beams needed for electrical connection to the piezoresistive elements do not cause significant stress non-uniformity (see Figure 6), which would reduce overall sensitivity.

buried oxide layer. Next, the wafer is stripped and prepared for metal lift-off using AZ nLOF 2070. A chrome/gold (50nm/200nm) layer was deposited using ebeam metal evaporation to define the bonding pads and metal interconnects. All areas that do not need to be freely moving are encapsulated using AZ n4035, and the structures are released in a 5:1 buffered HF wet etch. SOI wafer with photoresist mask for DRIE (DEVICE mask)

DRIE of device layer to stop at buuried oxide layer Photoresist mask (METAL mask)

for

lift-off

E-beam metal deposition (50 nm chrome / 200 nm gold) Lift-off using stripper followed by negative tone resist spin-on Exposure and development to form electrical isolation (ISOLATION mask) Wet etch of oxide to release free standing silicon device structures

Figure 7: Fabrication process with cross sections

Figure 6: Representative x-direction stress at 1 μN (beam length is 450 μm and the piezoresistive element length is 32 μm). The figure on the right has been exaggerated in the ydirection to show the stresses in the piezoresistive element.

MemPZR can compute the change in current for a fixed voltage and applied stress, and the overall sensitivity of various configurations is compared to both the linear beam model predictions and actual results (see Results section). In addition to the mechanical stress and resulting piezoresistive change, the temperature in the piezoresistive elements for various bridge voltages due to self-heating was also simulated in air and water and used as part of the SNR calculations above. Fabrication The fabrication uses a simple 3-mask process starting with a highly doped n-type silicon device layer (1.8 mΩcm ) on an SOI wafer with 10 μm device layer and 2 μm buried oxide layer (see Figure 7). This produces a low intrinsic signal to noise ratio and also prevents conductive cell medium from shorting out the sensor. A photoresist mask for dry etching of silicon is made from OCG 825 (850 nm thickness), and the silicon is removed from the unprotected areas using an Adixen AMS-100 ISpeeder DRIE machine where the etch stops at the

Characterization In order to calibrate the force sensors after wirebonding and packaging, a 25 μm diameter pure gold wire was used as a reference spring that is attached to a tungsten probe tip. The spring constant of the gold cantilever with circular cross section was calculated and used as a reference for all sensitivity measurements. In turn, the probe tip is connected to a calibrated closedloop piezo-driver to precisely load and unload the force sensor using the reference spring. During the calibration procedure, the on-chip temperature is maintained at 37 °C using the on-chip heater and temperature sensor. The bridge is driven by a 400mV, 800 Hz sinusoidal signal and the differential bridge output is amplified 1000X by a differential amplifier based on the Linear Technologies LT1007 low noise operational amplifier before being digitized by a National Instruments PCI-6225 DAQ and filtered in National Instruments LabView 8.5 software. The AC bridge voltage is simultaneously monitored and a ratiometric (V/V) value is recorded. The force sensor sensitivity ((V/V)/N) is derived from the resulting forcevoltage plot using linear fit.

RESULTS The typical force sensor has a sensitivity of 225 (V/V)/N for a cantilever beam 450 μm in length with a 32 µm long piezoresistor element at the base. Measured sensitivities range from of 110 to 276 (V/V)/N depending on the device geometries (beam length and

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piezoresistor element length) and the averages are shown in Table 1. The sensitivity changed by only a few percent when cell medium was added to the chip and the calibration repeated, which is below the standard deviation for a measure of sensitivity. Table 1: Measured sensitivities of fabricated force sensors Piezoresistive Element Length 16 μm 32 μm 64 μm

Beam Length 300 μm

110 (N=1)

152 (N=1)

190 (N=1)

450 μm

163 (N=4)

225 (N=6)

238 (N=1)

200 (N=3) 254 (N=2) 600 μm * not included in fabrication 600

225

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200

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225 200

225

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64

Figure 8: Actual measured sensitivity ((V/V)/N) of fabricated devices (see Table 1).

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600

CONCLUSION

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225

32 PZR Length (μm)

64

Figure 9: Predicted sensitivity ((V/V)/N) from the linear beam bending model stress and piezoresistive coefficient.

Beam Length (μm)

600

325 300 275

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We would like to thank Prof. Richard Vinci (Lehigh University) and Raymond Filozof (S.F.C. L.U.).

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A novel lateral force sensor based on a piezoresistive transducer has been designed, fabricated and tested for use in cell biomechanics experiments. Not only is the force sensor sensitive and has a high signal to noise ratio, but it also can be submerged directly in cell medium and operate at low voltage. This force sensor relies on a simple fabrication method and can be integrated into many platforms based on SOI wafers. Measurements of cell mechanical behavior during compression using this new force sensor are underway.

ACKNOWLEDGEMENTS

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transducers, the preamplifier and ADC noise, environmental interference, and the averaging period. The overall sensitivity of the fabricated devices (Figure 8) is somewhat lower than the predicted sensitivities of the linear beam bending model (Figure 9). We expect this is due to variations in the piezoresistive element width since the 1 to 2 μm geometry is at the limit of our contact photolithography fabrication capabilities. At this scale, small variations in size can have a big effect on the stress of the ribbon-like pieozoresistor, and this stress is directly proportional to the sensitivity. The sensitivities predicted by the FEA model (Figure 10) likely overestimate the sensitivity compared to the beam bending model and measured results, but the trend of decreasing sensitivity as the piezoresistive element length increases agrees with our data (compare to Figure 8, left side). This trend is possibly due to non-ideal bending of the piezoresistive element. Each end of the piezoresistive beam is fixed, but it is otherwise free to move. As the overall transducer length (region 2 in Figure 3) increases and the position of one end becomes farther from the base, there is more lateral movement in addition to pure compression and tension. This kind of behavior can be seen in the stress distribution in the right side of Figure 6, but is completely neglected by the linear beam bending model.

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REFERENCES

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Figure 10: Predicted sensitivity ((V/V)/N) from CoventorWare mechanical-piezoresistive FEA simulations.

These measurements were made using a 50 Hz measurement bandwidth for the AC bridge and a 500 ms averaging period, which produced a minimum detectable force of 10 nN. This detection limit is set by the combination of the intrinsic noise of the piezoresistive

[1] E. J. Eklund, A.M. Shkel, J. of Micromechanics and Microengineering, Vol. 17, pp. 730–736, 2007. [2] X. Yu, J. Thaysen, O. Hansen, A. Boisen. J. of App. Physics, Vol. 92, No. 10, pp. 6296-6301, 2002. [3] O.N. Tufte, E.L. Stelzer, Physical Review, Vol. 133, No. 6A, pp. A1705-A1716, 1964. [4] A. Mohammed, W. Moussa, E. Lou, Sensors, Vol. 8, pp. 2642-2661, 2008. [5] O. Thoumine, A. Ott, J. of Cell Science, Vol. 110, pp. 2109-2116, 1997.

CONTACT S. Tatic-Lucic, Tel: +1-610-758-4552; [email protected]

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