Experimental Comparison of Piezoresistive MEMS and Fiber Bragg Grating Strain Sensors Jacqueline Rausch, Patrick Heinickel, Roland Werthschuetzky
Benjamin Koegel, Karolina Zogal, Peter Meissner
Institute of Electromechanical Design Darmstadt University of Technology Darmstadt, Germany Email:
[email protected]
Optical Communications Group Darmstadt University of Technology Darmstadt, Germany
Abstract—We report on the experimental comparison of piezoresistive MEMS sensors and optical fiber B RAGG grating sensors (FBGS) for strain measurements in force sensors. To our knowledge, this is the first direct comparison of piezoresistive and FBG transducers as force sensors. Cantilevers are used as deformation elements. The sensors are bonded on top and bottom side of the cantilever using a heat-curing epoxy adhesive. The piezoresistive ones are micro machined silicon chips with decoupled adhesive areas, and four ion implanted piezoresistive areas (Rsq = 125 Ω·cm, (1 × 2) mm2 ×350 µm). The FBGS are draw-tower-gratings (0.78 mm2 × 9 mm). The measured values are compared by analyzing nominal strain, sensitivity, resolution, measurement uncertainty and thermal behavior. The MEMS sensor is more sensitive than the FBGS (0.28 %, / N > 0.004 %/ N), its measurement uncertainty is lower (2 % < 5 %) and the resolution ∆ = 10−3 µm / m is 100 times higher than in case of FBGS ∆ = 1.38 µm / m.
I. I NTRODUCTION A novel instrument with a force feedback system for minimally invasive abdominal surgery is being developed [1]. Driven by integrated piezoelectric actuators an operation platform with four additional degrees of freedom carries manipulators (e.g. high frequency dissector) and positions them inside the abdominal area. To assist the surgeon during the operation, the relating forces between soft tissue and manipulation tool are measured with a force sensor. Typically the force vector consists of three force components Fi , each one with an absolute value of |Fi | ≤ 5 N [2]. An active control element is feeding back the haptic information to the surgeons’ hand. In order to measure forces at the tool tip a miniaturized multi component force sensor is designed [2]. It consists of a deformation element and several strain sensing elements to calculate the interaction force. Table I lists the main requirements on the sensor which serves as a rule for evaluating several sensor principles of the strain sensing elements. In view of this application different sensor principles have been compared. In this paper two principles for strain measurement in transducers are discussed: fiber B RAGG grating sensors and piezoresistive MEMS sensors which are bonded onto top and bottom side of a deformation element. FBGS are widely used for structural health monitoring, detection of temperature and mechanical measurands like pressure and strain. They have no electromagnetic interference (usage in a computer
978-1-4244-5335-1/09/$26.00 ©2009 IEEE
TABLE I M AIN R EQUIREMENTS ON AN I NTRACORPORAL F ORCE S ENSOR
Parameter
Specification
Nominal force
≥ 5N
Overload protection
≥ 20 N
Sensitivity @ 1 N
≤ 0.4 %
Resolution ∆F
≤ 0.01 N
Hysteresis error fH
≤ 10 %
Nonlinearity fL
≤ 10 %
tomography scanner), a high overload-protection (max. strain 10, 000 µm / m) and allow multipoint measurement. Their drawbacks are the high temperature sensitivity, which requires compensation measurements [3], and the lower gage factor. Piezoresistive MEMS sensors are state-of-the-art in pressure and force transducers, miniaturized, have a high gage factor and minor measurement uncertainty, but need a complex packaging of integrated circuits. Finally, the overload-protection is lower (max. strain 3, 000 µm / m). To weigh up disadvantages and advantages of the sensor principles used for transducers, several measurements are done. The organization of the paper is as follows: The operating mode of the two sensor principles are described in paragraph two. Afterwards the experimental setup will be introduced in paragraph three and the measurement results are discussed in paragraph four. Paragraph five summarizes and gives an outlook. II. S ENSOR P RINCIPLES A. FBGS 1) Operating Mode: A fiber B RAGG grating is a periodic, sinusoidal refraction index modulation (∆n = 0.01 % ... 0.1 %, period Λ ≈ 500 nm) in the core of a Ge-doped single mode fiber. The index modulation is achieved by irradiating the photosensitive fiber with UV light during the manufacturing process before coating or afterwards. The resulting B RAGG grating causes partial reflections which are constructively interfering for a certain wavelength, the B RAGG wavelength λB = 2 · n · Λ (Fig. 1), where n is the effective refractive
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+
p -type doped area (piezoresistor)
intensity
input
L
l
1250nm
i
1400nm
l intensity
reflexion
n
}
-3
Dn = 10 ...10
(a) longitudinal
z
index and Λ the grating period. The B RAGG wavelength λB is shifting by the effect of strain and temperature T . Monitoring the resulting wavelength shift is the basic operation principle of fiber B RAGG grating sensors (FBGS). Both reflected and transmitted spectrum can be evaluated. The measurand strain provokes a change of the refractive index due to a physical elongation of the grating itself and the photoelastic effect. The measurand temperature causes a thermal expansion of the fiber and the refractive index varies due to its inherent temperature dependence [4]. The following equation describes the interrelationship of measurands and resulting wavelength shift (1)
where C0 is the photoelastic coefficient, αD the thermal expansion coefficient of the deformation element1 . The factor (1 − C0 ) can be interpreted as the gage factor k and takes a value of about 0.78. The refractive index change ∂n/∂T · n−1 is in the range of 5 ... 8 · 10−6 / K. According to equation (1) the measurement effects of both mechanical and thermal measurand are in the same range. For a sole measurement of strain the temperature compensation is essential. 2) Temperature Compensation: The first possibility is to integrate a second unstrained FBG2 for detecting the temperature response ∆λT /λ0T . The resulting strain D 3 of the deformation element can be calculated using the following equation: ∆λD ∆λT k · αD + δn 1 − · (2) D = · k λ0D λ0T k · αF + δn The second possibility is to compensate the thermal dependence using two FBGS at top and bottom side of a bending element comparable to the well-known Wheatstone full-bridge configuration of conventional strain gages. Both FBGS are exposed to the same temperature, while the acting strain is opposing. The resulting strain D can be calculated as follows: k ∆λ1 ∆λ2 1 D = · − = (D1 − D2 ) , (3) 2 λ01 λ02 2 case of aluminium αD = 23 · 10−6 / K. expansion coefficient of the fiber αF = 0.55 · 10−6 / K. 3 Index D marks parameters influenced by the deformation element, index T marks parameters effected by the temperature. 1 In
2 Thermal
R4
1
VCC R3
s1 (b) transversal
(c) data acquisition
Fig. 2. Principle assembly of silicon piezoresistors and typical data acquisition.
Principle assembly of a fiber B RAGG grating.
∆λ ∂n/∂T = (1 − C0 ) · ( + αD · ∆T ) + · ∆T λ0 n
R1
R2
32
s1 -4
i
Dv
lw
l
Fig. 1.
n-type
bw
ncore(z)
1304nm 1305nm
h
n-type
cladding core
where index 1 marks the top side and 2 the bottom side of the bender. Provided that both fibers are similarly bonded, parameters influenced by temperature δn · ∆T and αD · ∆T of top and bottom side are canceling each other. B. MEMS Sensor 1) Operating Mode: A piezoresistive silicon sensor consists of a n-type doped, (100)-orientated silicon substrate. Four p+ type doped areas are orientated in [110]-direction, forming piezoresistors with a resistance of R0 = ρ0 · lw / (bw · hw ). The depth hw and resistivity ρ0 of the piezoresistors depend on dopant concentration NR and the doping process itself. The mechanical strain results a stress distribution in the silicon element and thus a change of the resistivity ρ. The change of the resistance ∆R is evaluated measuring the output voltage ∆v. Due to the piezoresistive effect the resistance change ∆R is depending on the position and orientation of resistive areas and hence the direction and orientation of the current density J in relation to the stress distribution in the silicon element. Neglecting the shear components two effects occur: If the current density and the acting stress are parallel to each other the longitudinal effect (index l) is occurring, if current density and stress are acting perpendicularly the transversal effect (index t) is appearing. The interrelationship of resistance change and the described effects are combined in the following equation. ∆ρ ∆R ≈ = πl · σl + πt · σt (4) R0 ρ0 The π-coefficients are the so called piezoresistive coefficients, which depend on the material and its crystalline structure. To obtain the values for calculating the resulting resistance change and hence the sensitivity of the sensing element the manufacturing process has to be considered too. The manufacturing of the sensing elements is the topic of the Institute for Micro Sensors (CIS) in Erfurt, Germany. In an established ion implanting process a boron concentration maximum of NR = 3 · 1018 / cm3 is adjusted to realize the piezoresistive areas. Thus a sheet resistivity of Rsq = 125 Ω·cm results from the ion implanting [5]. The longitudinal coefficient takes the value πl = 71.8 · 10−5 MPa−1 and transversal coefficient πt = −65.2 · 10−5 MPa−1 . Taking H OOKE’s law into account the measurand strain can be evaluated. Evaluating e.g. the longitudinal strain 2 the Young’s Modulus ESi = 169 GPa of
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y e1
e2
b
h
TABLE II S PECIFICATIONS OF THE C ANTILEVER
y
x
s(z) z z
l
F bending moment: MB = F(l-z) deflection line w(z)
Fig. 3. Principle beam bender and realizations. The sensing elements are bonded near to the restraint.
Parameter
MEMS
FBGS
Material
steel
aluminum
Young’s Modulus E
193.6 GPa
70 GPa
Dimensions (l × b × h)
(1.4 × 2) × 9 mm3
(14.5 × 3) × 30 mm3
Nominal load F
5N
20 N
Nominal strain
250 µm / m
160 µm / m
silicon can be used to calculate the strain within the sensing element. ∆R ≈ πl · σ2 = ESi · πl · 1 (5) R0 2) Temperature Compensation: Piezoresistive silicon sensors are also sensitive to temperature changes due to the thermal drift of sensitivity (TCπ) and the resistance itself (TCR), which lead to a measuring error. For a precise strain measurement, temperature compensation can be done using a currentfed Wheatstone full-bridge configuration of the piezoresistors (see Fig. 2). The output signal ∆v is proportional to the supply Vcc = I0 · R0 (see equation (6)) and it is assumed that the resistance of the four piezoresistors is equal in unloading case. A self-compensation occurs due to the counteracting thermal drifts of sensitivity and resistance [5]. ∆v 1 ∆R1 ∆R2 ∆R3 ∆R4 = · − + − (6) I0 · R0 4 R01 R02 R03 R04 To compensate the thermal expansion of the deformation element itself two silicon elements are bonded on top and bottom side of the deformation element, using similar effects described with the FBGS. III. E XPERIMENTAL S ETUP A. Assembly of the Cantilever To compare the two sensing principles a beam bender is used as a deformation element due to its well known mechanical behavior. By applying a load at the tip the bender deforms and a strain distribution occurs on its surface. Using B ERNOULLI’s bending theory the dimensions of the bender have been calculated and thus the transversal strain component 1 can be neglected. The longitudinal strain can be derived using the following equation 2 (y, z) ≈ w00 (z) · y =
6 · (l − z) , E · b · h2
(7)
where E is the Young’s modulus of the bender and l, b, h are the benders dimensions (see fig. 3). Two test setups have been realized. Table II lists the related specifications. The sensing elements are bonded on the cantilevers using a two component epoxy adhesive UHU plus endfest 300 and cured at a temperature of 70 ◦ C in a vacuum chamber.
Fig. 4.
Realization of the force sensor with two FBGS.
B. Sensing Element In case of the FBGS assembly a draw-tower fiber distributed by HBM GmbH, Germany is used. The fiber has a diameter of about 500 µm and contains three B RAGG gratings with B RAGG wavelengths of λB1 ≈ 1554 nm, λB2 ≈ 1559 nm and λB3 ≈ 1565 nm. Each grating has a length of about 9 mm. Two of the gratings are mounted onto the cantilever measuring the strain, the third one for tracking the temperature inside the climate chamber. The data acquisition is done by an optical spectrum analyzer with a resolution of ∆λ ≈ 1 pm [4]. The resulting wavelength shift is tracked. In case of the MEMS assembly two silicon chips manufactured by EPCOS AG are used.4 Each sensing element has been modified for being sensitive to bending strain and to obtain four separate piezoresistive areas for being able to interconnect them in the appropriate way. To decouple the adhesive area from the measuring position and hence the position of the resistors the bridge-like geometry is chosen for the silicon element (see Fig. 5). One silicon element has a height of 390 µm (membrane thickness nearly 40 µm), a length of 2 mm and a width of nearly 1 mm. The data acquisition is done using a current-fed Wheatstone full-bridge configuration with a supply current of I0 ≈ 1 mA. The analog output voltage is detected using an AD converter (USB Basic BNC opto, Goldammer) at a sample rate of 250 Hz. 4 Looking forward to the preparation of the silicon elements at the CIS, chips of EPCOS AG with comparable properties like resistance and dimensions are used.
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detail: R
Ry1
Ry2 R
Rx2
F contacting
MEMS 1 MEMS 2 5 mm
Fig. 5. Realization of the force sensor with two silicon strain sensing elements. Fig. 6.
C. Experimental Investigation Different experiments have been performed. First the static characteristic curve of each assembly has been measured at constant room temperature (Fig. 6 and Fig. 7). Load weights up to 2 kg are used in case of the FBGS and 0.5 kg in case of the MEMS, respectively. Sensitivity, linearity and hysteresis error of each assembly are determined. Due to its inherent temperature dependency (about 9.8 pm / K), the thermal behavior of the FBGS assembly has been analyzed in detail. The cantilever has been placed into a climate chamber and the temperature has been increased from 10 ◦ C up to 60 ◦ C. At each temperature level four loading cases have been analyzed: 0 N, 2.5 N, 5 N and 10 N. Both compensation configurations as outlined above have been tested.
Fig. 7.
Static characteristic curve of the piezoresistive sensor.
Static characteristic curve of the fiberoptic sensor.
IV. R ESULTS B. Thermal Behaviour A. Static Characteristic Curve The resultant characteristics of both assemblies are shown in Figure 6. All parameters like resolution, nonlinearity and hysteresis error are referred to the nominal value and calculated according to terminal-based conformity. The MEMS assembly shows a nonlinearity of fL < 1 % at maximum and a hysteresis error of about 2 %. The resolution of depends on the noise level of the silicon elements. The maximal noise amplitude takes a value of 20 mV and thus forces down to ∆F = 0.02 N and thus strain ∆ = 10−3 µm / m is detectable. The sensitivity takes a value of 0.288 % / N. The FBGS assembly shows an apparent hysteresis of more than 7 % which is repeatable. A possible explanation is the creep of the epoxy layer between deformation element and fiber. The nonlinearity is similar to the MEMS assembly. As the resolution of the data acquisition (optical spectrum analyzer) system is limited to ∆λ ≈ 1 pm forces down to ∆F = 0.07 N are detectable. This corresponds a strain resolution of ∆ = 1.38 µm / m, which is about ten times lower than in case of the MEMS assembly. Also the sensitivity is worse and takes a value of 0.004 % / N.
The resultant characteristics of the two compensation configurations are shown in Fig. 8 and Fig. 9. In case of the unstrained FBGS for temperature measurement the thermal compensation failed. The challenge is the similar mounting of both fibers, which did not work in the first assembly. The thermal behavior of the different epoxy layers has not been taken into account in the modeling. In the second configuration both fibers are simultaneously mounted on top and bottom of the cantilever using a special clamping to realize a defined epoxy layer for both FBGS. The temperature compensation shows a better characteristic than in the first assembly but the influence of the epoxy layer is still not satisfactorily compensated. V. C ONCLUSION We have shown an experimental comparison of FBGS and piezoresistive strain sensors for miniaturized force transducers. The piezoresistive strain sensor shows a higher sensitivity, a better resolution, and a lower nonlinearity and hysteresis error. The mounting conditions of the fibers are hard to repeat. For
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strain e / mm/m
In case of the MEMS sensor well-known bonding techniques of conventional strain gauges are used, which guarantees repeatable bonding conditions and leads to a high repeatability of the measuring results. For strain measurement on miniaturized deformation elements with a low nominal strain of about 250 µm / m piezoresistive strain sensors are more suitable than FBGS. Using other topologies of the deformation element [7] which guarantee higher nominal strain, the performance of the FBGS will be better. ACKNOWLEDGMENT temperature T / °C
Fig. 8. Thermal behavior of the sensor using an unstrained FBGS for temperature measurement.
The authors would like to thank P. Thiele, EPCOS AG, and T. Kleckers, HBM GmbH, providing the silicon chips and the FBGS. Financial support was provided by federal state Hessen, Ministry of Science and Art. R EFERENCES
Fig. 9. Thermal behavior of the sensor using the improved compensation method.
[1] H. F. Schlaak et al, A Novel Laparoscopic Instrument with Multiple Degrees of Freedom and Intuitive Control, Proceedings of EMBEC, Antwerp, 2008. [2] J. Rausch et. al, Development of a Piezoresistive Strain Gauge for Multi-Component Force Measurement in Minimally Invasive Surgery, Proceedings of Euro Sensors 2008, Dresden, 2008. [3] Y. S. Hsu et al., Temperature Compensation of Optical Fiber B RAGG Grating Pressure Sensor, IEEE Photonics Technology Letters, vol. 8, no. 7, 2006. [4] A. Kersey et al, Fiber Grating Sensors, Journal of Lightwave Technology, vol. 15, no. 8, 1997. [5] T. Meiss, T. A. Kern et al., Fertigung eines Miniaturkraftsensors mit asymmetrischem Grundkoerper zur Anwendung bei Katheterisierungen, Mikrosystemtechnik Kongress, Dresden, 2007. [6] M.-H Bao and S. Middelhoek, Handbook of Sensors and Actuators. Bd. 8: Micro mechanical transducers: pressure sensors, accelerometers and gyroscopes, 1. Auflage, Elsevier, 2000. [7] M. Mueller, L. Hoffmann, T. Buck and A. Koch, Realization of a fiberoptic force-torque sensor with six degrees of freedom, Proceedings of SPIE Vol. 7266, 2008.
successful temperature compensation an adequate assembly jig has to be developed.
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