Integrated Optical and Electronic Pressure Sensor

IEEE SENSORS JOURNAL, VOL. 11, NO. 2, FEBRUARY 2011

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Integrated Optical and Electronic Pressure Sensor Ivan Padron, Member, IEEE, Anthony T. Fiory, and Nuggehalli M. Ravindra

Abstract—A pressure sensor that combines two principles of measurement into one integrated unit with optical and electronic parts is fabricated and tested. The sensing element for both integrated parts is an embossed silicon diaphragm that deflects under differential pressure. The optical part of the sensor is based on Fabry–Perot interferometry; the electronic part of the sensor is based on the piezoresistive effect in silicon. In the application of Fabry–Perot interferometry, the sensing element utilizes an optical cavity, where interference of multiple reflections changes with movement of the diaphragm caused by pressure. In the application of the piezoresistive effect, a change in the electrical resistivity of a sensor material is induced by mechanical stress in the diaphragm and detected by a Wheatstone bridge circuit. The advantages of introducing the embossed diaphragm in sensor fabrication and its benefits for integration are discussed. The existence of a nearly ideal Fabry–Perot interferometer in the optical part of the sensor is demonstrated experimentally. Noise characteristics of the Fabry–Perot part of the sensor are presented. The independently produced electronic output serves to establish the quiescence point (Q-point) of the output from the optical part of the sensor. Index Terms—Diaphragm pressure sensor, embossed diaphragm, integrated sensor, Fabry-Perot interferometry, piezoresistors. [DOCUMENT FOR NJIT EDUCATIONAL USE.]

I. INTRODUCTION HE ability to use microelectromechanical systems (MEMS) fabrication methods in mass production of high performance sensors at low cost has opened a wide range of applications for pressure sensors, which include automotive, aerospace, marine, instrumentation and industrial process control, hydraulic systems, microphones, bioscience and medical applications [1], [2]. Since the introduction of MEMS, piezoresistive pressure transducers have become the dominant types, owing to their high performance, stability and repeatability. Recent industrial trends indicate increased need for pressure sensors that are suitable for hazardous environments, high temperatures and biomedical applications. Advanced applications involve requirements of small volume, high performance characteristics, environmental restrictions and materials compatibility. Of the various sensing mechanisms used for pressure measurements, optical techniques provide capabilities for small sizes, immunity to harsh environments, remote operation and ease of integration with other devices. Of particular importance

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Manuscript received June 03, 2010; revised July 06, 2010; accepted July 21, 2010. Date of publication September 23, 2010; date of current version November 17, 2010. This work was supported in part by the National Science Foundation Alliances for Graduate Education and the Professoriate (AGEP) Program. NSF/CUNY AGEP. The associate editor coordinating the review of this paper and approving it for publication was Prof. Istvan Barsony. The authors are with New Jersey Institute of Technology, Newark, NJ 07102 USA (e-mail: [email protected]; [email protected]; nmravindra@ gmail.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSEN.2010.2062175

Fig. 1. Configuration of the integrated optical and electronic pressure sensor.

is the immunity of optical sensors to electromagnetic wave interference, chemical attack, and high temperatures. The optical technique of Fabry–Perot interferometry [3], [4] is selected for investigation in this work, owing to its high sensitivity and accuracy. II. SENSOR DESIGN PRINCIPLES A schematic illustration of the integrated optical and electronic pressure sensor (IOEPS) studied in the work is shown in Fig. 1. A pressure source is applied through a sealed port in the sensor head. The sensing elements comprise a diaphragm with an embossed structure formed in single-crystal silicon, an optical fiber, and piezoresistors embedded in the diaphragm. The diaphragm elastically deflects in response to differential pressure applied across its two sides. The piezoresistors are sensitive to the strains induced by diaphragm deflection. The end face of a single-mode glass optical fiber is positioned opposite to the center of the diaphragm, where a small gap between the two surfaces (glass and silicon) forms an optical interference (Fabry-Perot) cavity. This design structure thus provides the means for combining two principles of measurement into one integrated unit, using its optical (Fabry-Perot) and electronic (piezoresistive) capabilities for simultaneously sensing the movement of the diaphragm under applied external pressure. Changes in the Fabry–Perot gap are detected with an optical fiber-optic system interconnecting a laser source and a photodetector which produces the optical output signal. Changes in the resistances of the piezoresistors are detected by a Wheatstone bridge circuit which yields the electronic output signal. The optical and electronic signals are analyzed in a signal processor to

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Fig. 3. Fabry–Perot cavity.

Fig. 2. Advantages of the embossed diaphragm in the fabrication of Fabry–Perot sensors. (a) Parallelism between the two surfaces under applied external load. (b) Avoidance of diaphragm-fiber misalignment during the fabrication process. (c) Reduction in the back pressure effects.

produce a measured quantity for detecting acoustical vibration, mechanical vibration, and pressure. The embossed diaphragm, Fabry–Perot cavity, piezoresistors, and the integrated system are described in the following subsections.

from the first glass/air interface and the second air/silicon interface. The net reflected beam entering the fiber tip comprises the optical interference signal, which is routed by fiber-optics to a photo-detector. Movement of the diaphragm modulates the interference signal [16], [17]. Denoting the intensity of the incident light beam as , the intensity of the reflected beam for planar interfaces is given by [18] (1) where and are the coefficients associated with reflections at the first and second interface, respectively. The phase delay between the two partial waves is given by [19] (2)

A. Embossed Diaphragm Introduction of a diaphragm with a rigid center body (referred to as an embossed diaphragm) in the present design offers considerable advantages, when compared to prior work on Fabry–Perot diaphragm-based sensors [5]–[15]. As illustrated in cross section in Fig. 2(a), the thicker center of the diaphragm (the central embossment or boss) remains rigid and undeformed upon deflection of diaphragm under differential pressure. The thick peripheral embossment clamps the perimeter of the diaphragm. Under applied differential pressure load, mechanical deformation concentrates in the thin region of the silicon crystal, as indicated in Fig. 2(a), right panel. Non-parallelism between the two cavity surfaces is virtually eliminated, because the central embossed surface remains flat. This property also avoids degradation of the optical interference signals that could otherwise be associated with surface bending. As illustrated in Fig. 2(b), parallelism and flatness of the embossed surface allows wide lateral alignment tolerance of the fiber tip relative to the center of the boss during the fabrication process. The embossed structure creates an adjacent pressure-relief volume that considerably reduces back-pressure effects, as indicated in Fig. 2(c). B. Fabry-Perot Cavity The Fabry–Perot part of the sensor utilizes an optical cavity (Fabry-Perot cavity) formed between the center rigid body surface of the diaphragm and the tip of a single-mode silica optical fiber (Fig. 3), where the length of the cavity is the distance between the surfaces of the fiber tip and the diaphragm embossment. A coherent beam of light from an external laser source is launched via the optical fiber into the cavity (containing air at atmospheric pressure in the present study). Multiple reflections within the cavity produce interference between waves reflected

where is the refractive index of the medium in the cavity formed between the two surfaces, is the incident angle, and is the wavelength. Application of (1) and (2) is discussed in Section III. C. Piezoresistors The electronic part of the sensor utilizes the large piezoresistive effect in p-type doped silicon [20], [21]. Four piezoresistors are formed over an oxide barrier on the silicon diaphragm near regions of maximum bending strains (elongation or compression) induced by diaphragm deflection [22], as illustrated in cross section and plan views in Fig. 4(a). The piezoresistors are interconnected in a fully active Wheatstone bridge configuration, as shown in Fig. 4(b). Pairs of resistors, e.g., and and , increase (decrease) in value in response to the from induced strains, yielding a change in output voltage held constant) that scales with the the Wheatstone bridge ( externally applied pressure [22]. D. Integration Fig. 5 illustrates the integrated optical and electronic pressure sensor (IOEPS) system. The optical fiber in the sensor head is connected via an optical fiber cable to a port in a 3-D optical coupler (directional circulator). The optical system was adapted from 1.55 m telecom components. A semiconductor laser source operating at 1.55 m is routed to the optical fiber in the sensor head. The reflected signal from the sensor is routed to a cooled photo-diode, which forms part of a transimpedance amplifier that produces a DC-coupled output. Four wires connect the Wheatstone bridge circuit on the diaphragm to a DC voltage source and a DC-coupled multimeter. Electrical signals representing the optical and electronic outputs of the sensor

PADRON et al.: INTEGRATED OPTICAL AND ELECTRONIC PRESSURE SENSOR

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Fig. 6. Photograph of IOEPS device.

III. THEORY

Fig. 4. (a) Piezoresistive sensor. (b) Piezoresistors in a Wheatstone bridge.

Theoretical analyses of the response of diaphragm structures to external pressures have been reported for corrugated structures of various types [24], [25]. While the embossed diaphragm in the pressure sensor is square in shape, the theory for the corresponding cylindrical symmetric structure has been obtained in an analytically closed form and thus provides a practical approximation. In this case, the deflection for an applied pressure is given by (3) and [Fig. 4(a)] are the outer and where inner radii of the thin annular region of the diaphragm (which in our sensor corresponds to one-half the side of the square boss and diaphragm, respectively); is the diaphragm thickness; and are Poisson’s ratio and Young’s modulus of silicon, respectively. Validity of (3) requires that the thickness of the embossments be a least six times greater than . Bending stresses induced in the thin part of the diaphragm are given by (4)

Fig. 5. Integrated Fabry–Perot and piezoresistive sensor system.

where the radius. are recorded and processed to generate the pressure measurement value. Application of differential pressure (e.g., through the pressure port of the sensor head) induces deflection of the silicon diaphragm that is detected optically as modulation of the Fabry–Perot interference signal and electronically as the off-balance voltage of the Wheatstone bridge. Piezoresistive pressure sensors with embossed diaphragms that are commercially available parts (e.g., [23]) were adapted to produce the pressure sensor head. These devices are fabricated using standard MEMS processing techniques. The center embossment in the diaphragm was utilized to serve as one of the reflective surfaces of the Fabry–Perot cavity. The other surface is prepared by forming a clean break in a single-mode optical fiber, using a technique of tapping a scribe mark on the fiber with a beveled diamond tool. This produces an optically reflective glass surface of diameter 9 m, which is the diameter of the optical fiber (core plus cladding). Fig. 6 is a photograph showing the sensor head (housed in metal cylinder), fiber optic cable (with coupler), electrical leads (four-wire pigtail), and pressure port (tube opposite fiber cable).

sign applies to the region near the inner (outer)

A. Optical Output into (2), where Substituting the expression is the Fabry–Perot gap at zero pressure, one obtains from (1) a theoretical expression for the Fabry–Perot interference signal. By design, the distance is made small compared to the width of the core of the optical fiber, so that beam spreading effects may in (2) may be applied. be neglected and the approximation , the applicable Further, since the cavity is an air gap expression for the phase shift in (1) is (5) with

given by (3).

B. Electronic Output The basic structure of a piezoresistive pressure sensor consists of four resistor sensing elements in a Wheatstone bridge configuration that respond to stresses induced in the thin crystalline silicon membrane. For small deflections, the stress can

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be taken as a linear function of the applied pressure differential across the two sides of the membrane. The output from the Wheatstone bridge circuit shown in Fig. 4(b) is given by the expression (6) , where the For a balanced system, one has applies for and the result is . Since the fractional change in resistance is propor, where the factor c is detional to the stress, termined by the coefficient of piezoresistivity. The electronic output signal can be written as (7) where the offset is introduced to take into account zero offsets in the Wheatstone bridge (imperfect resistor matching). The coefficient

Fig. 7. Optical output as function of pressure for two test setups. TABLE I FITTING PARAMETERS FOR CURVES IN FIGS. 7 AND 8

(8) in (7) represents the slope of the linear relation between the output and the pressure, and corresponds to the sensitivity of the electronic part of the sensor device. IV. SENSITIVITY MEASUREMENTS The sensors fabricated for this study were designed to operate in the pressure range of 0 to 35 kPa and have overpressure tolerance of 69 kPa. In reference to the dimensional parameters in the model function of (3), the inner and outer half-widths of the m and m, respecdiaphragm are m. The tively, and the diaphragm thickness is thickness of the center embossment is 100 to 105 m, which satisfies the criterion that it be at least six times larger than , and thus does not enter into the theory for the diaphragm dem was used flection, . A laser source operating at in connection with a 3-D coupler and a photodiode as shown in Fig. 5. Two digital multimeters were used to monitor the voltage outputs from the optical (diode amplifier) and electronic (Wheatstone bridge) parts of the sensor. A static weight-tester was used to apply precise and discrete increments of pressure up to 41.37 kPa. Output voltages were recorded at constant applied pressure. For the test measurements described below, the optical fiber tip was held in position within the sensor (Fig. 1) but the fiber itself was not permanently mounted. This approach allows testing various configurations of the Fabry–Perot part of the sensor. The tests included varying (1) the cavity length at zero pressure , (2) termination of the optical fiber tip, and (3) laser output power. All of these variants were held constant for a given experimental test set up. A. Optical Output In the first experimental test (denoted as Setup 1), the optical fiber tip was prepared by the diamond cutting method and inserted into the fiber access port to position the tip in proximity to the diaphragm; next, the fiber was clamped into position to

fix the Fabry–Perot cavity gap at a given length . The optical output signal was then recorded as a function of applied pressure. For Setup 2, the fiber was moved to establish a different cavity gap. The results of the two test setups are shown in Fig. 7, where the photodetector amplifier output voltage is plotted against applied pressure. The model function for the Fabry–Perot output, (1), with phase determined by (3) and (5) was fitted to the data using a multi-parameter non-linear least squares method. The parameters varied are the cavity gap , the diaphragm radius , the fiber-air reflectance , the air-silicon reflectance , and the incident beam intensity (expressed as a voltage). Diaphragm radius was also treated as an adjustable parameter, since it is an effective radius that models a square diaphragm. Owing to correlation between parameters and , parameter was held fixed at one-half the edge length of the boss in the diaphragm. This fitting method allows one to determine values for the cavity length parameter . The fitted functions are shown as curves in Fig. 7. Results for the fitted parameters are given in Table I. Note that the fitted values of parameter are within 4% of the design value (533.4 m), thereby validating the deflection model of (3). The values of reflectances and are found to differ from their theoretical values (0.2 , respectively). One possibility is that the fiber tip and


Fig. 8. Optical output as function of pressure for Setup 3.

surface is not perfectly smooth and flat (see below). The main difference between the two setups is that the cavity length is m, which results in a “phase shift” changed by 0.106 between the two curves in Fig. 7. While the fitted values of are close to the expected setup value (1 m), the results are determined modulo (0.775 m), owing to the periodicity of . The results also the Fabry–Perot interference function indicate that is small compared to the diameter of the optical fiber (9 m), which implicitly validates the parallel plate model for the Fabry–Perot cavity (1). In a third experimental test (Setup 3), the tip of the fiber was reformed (re-cut) and then repositioned within the sensor. Compared to the previous setups, laser power was reduced and data were taken with a finer mesh of pressure points. The data and the corresponding fitted curve are plotted in Fig. 8; the fitted parameters are given in Table I. Note that in Setup 3, the results for and , 0.19 and , respectively, bear close correspondence to theoretical reflectances of glass/air and air/silicon interfaces, , respectively. This shows that in principle the 0.20 and cutting method can produce a tip surface with sufficient planarity for an ideal Fabry–Perot interferometer. On comparing the data in Figs. 7 and 8, one also observes that while the signal voltage is lower (see also smaller in Table I), Setup 3 produces a greater depth of modulation in the optical signal, e.g., the ratio of maximum to minimum in optical output voltage is 1.3 for Setups 1 and 2, whereas it is 4.2 in Setup 3 (higher ratio can yield greater sensitivity). From the data and fit in Fig. 8, one concludes that there is no observable degradation or attenuation in the optical response with increasing pressure, i.e., there is no evidence of signal-averaging effects that could otherwise reduce the interference signal [11]. To quantitatively test for possible deviation from the plane wave approximation [basis of (1)], the Gaussian beam spreading model [26], [27] was applied to the data. In this model, (1) is , where the dimensionmultiplied by the factor less attenuation parameter is treated as a fitting constant. The result, , shows that Gaussian beam spreading is insignificant, and verifies that (1) the boss surface and fiber tip surface are parallel and closely spaced, and (2) the embossment of the diaphragm remains flat under applied pressure.

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Fig. 9. Sensor sensitivity as function of pressure for Setup 3.

Fig. 10. Electronic output as function of pressure.

Sensitivity of the optical sensor to pressure is obtained by taking the derivative of the optical output versus pressure. This is shown in Fig. 9, which corresponds to the derivative of the data and theoretical curve in Fig. 8. The optical sensor operates most usefully at pressures corresponding to maxima or minima in the derivative (steep slope in optical signal), where the absolute value of the sensitivity is determined to be 0.058 V/kPa. The sensor can be tailored for quiescent operation in a region of maximum sensitivity, e.g., through cavity design (selection of ). Sensitivity considerations are further discussed in connection with the noise test study in Section V. B. Electronic Output The electronic reading was collected with 5-volt input on the Wheatstone bridge. Fig. 10 shows that the relation between the applied pressure and the electronic output is highly linear, in agreement with the theoretical model of (7). The slope of the line represents the sensor sensitivity, which corresponds to 2.6 mV/kPa and yields a in (6). The determination of sensitivity coefficient offset at zero pressure corresponds to built-in resistor imbalance, as modeled by the parameter in (7).

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Fig. 11. Optical detector voltage noise as function of frequency.

Fig. 12. Optical detector noise versus sensitivity at four lowest frequencies.

V. NOISE TEST The experimental setup for noise measurement of the optical part of the sensor used the system shown in Fig. 5, except that, in this case, the output of the photo diode was connected to a lock-in amplifier (EG&G model 124A, with a model 118 input preamplifier) through a low-noise silver-mica coupling capacitor (4896 pF). The lock-in detector was operated as an AC rms volt meter with a 10% equivalent noise band width. Noise voltages were measured using a data matrix corresponding to various fixed applied pressures (0–36.2 kPa) and various fixed frequencies (3.2–32 kHz). The input channel of the lock-in was tuned to the frequencies 3.2, 10, 32, 100, 320, 1000, 3200, 10000, and 32000 Hz. The applied pressures were selected to correspond to a range of sensitivities, as determined from the derivative data shown in Fig. 9. The rms noise voltages are plotted as functions of frequency in Fig. 11. The legend indicates the symbols corresponding to the given applied pressures. One notes a similarity in the form of the frequency dependence among the data for the various pressures. Data denoted “diode” were obtained with the laser turned off, and indicate dark current noise in the photodetector and amplifier noise. For the most part, the noise in the optical detector appears to be uncorrelated with detector sensitivity. This is illustrated in Fig. 12, which shows the variation of rms voltage noise with sensitivity (from Fig. 9) at the four lowest frequencies. Only at 3.2 Hz is there a statistically significant dependence of the noise on sensitivity. Noise at this ultra sub-sonic frequency is likely to be an environmental pick up (e.g., building vibration). Environmental influence at low frequency would be negated by permanently bonding the fiber to the detector head (it was demountable for the test configurations in this work). Using a similar analysis, the noise in the optical signal is found to be also uncorrelated with the magnitude of the optical signal, as it is modulated by pressure (Fig. 8), which indicates an essentially null finding for detector shot noise. Since the noise data is largely independent of applied pressure, the noise data at each frequency in Fig. 11 were averaged over pressure and divided by the square root of the lock-in bandwidth to provide the conventional measure of spectral noise. The

Fig. 13. Average optical detector noise versus frequency.

results are shown in Fig. 13. The optical noise exhibits a 1/f behavior in the frequency range of 32 Hz to 1 kHz (dashed line in Fig. 13), and tendency for saturation at the highest and lowest frequencies. Representing these results in terms of pressure sensitivity (taking 0.058 V/kPa, see Fig. 9), one obtains noise sensikPa/Hz or better at frequencies below 32 tivity of kPa/Hz for frequencies above Hz, dropping to 1 kHz. From the results of this noise analysis, it appears that the system noise originates with the external instruments (laser, photodiode) and the noise from Fabry–Perot interferometer itself is below the test threshold of noise sensitivity. Quasi-static noise in the optical part of the sensor was estimated from the repeatability of the optical output voltage, estimated at 0.01 V for the data of Fig. 8. Dividing by the optical sensitivity of 0.058 V/kPa, one obtains 0.17 kPa, which represents an estimate of the combined accuracy and resolution of the optical part of the sensor. Noise in piezoresistive sensors is determined mainly by Johnson and Nyquist noise (thermal voltage noise as arising from the random motion of mobile carries in resistive electrical materials and shot noise induced by current flow), flicker noise (1/f, caused by fluctuation in the electrical conductivity,


transformed in this case into voltage fluctuation) and Brownian noise (introduced by mechanical fluctuations of the membrane from a Brownian force), as discussed in [29]. For the electronic part of the sensor, the resistor-based noise in Wheatstone is dominated by shot noise, given bridge output voltage nV/Hz for V and by k , where q is the elementary charge. From the electronic sensitivity of 2.6 mV/kPa, the corresponding noise in terms kPa/Hz . While this of pressure sensitivity is calculation omits amplifier noise, the estimated AC noise in the electronic part of the sensor is at least comparable to the observed high-frequency noise in the optical part of the sensor. Quasi-static noise in the electronic part of the sensor was determined by comparing the data for Wheatstone bridge output voltage shown in Fig. 10 with the linear fit, which yields a standard deviation of 0.31 mV. Dividing by the electronic sensitivity of 2.6 mV/kPa, one obtains 0.12 kPa, which represents an estimate of the combined accuracy and resolution of the electronic part of the sensor. The accuracies and noise sensitivities of the two parts of sensor are thus determined to have comparable magnitudes. VI. CONCLUSION The work reported in the above study has confirmed the advantages to be gained from introducing an embossed diaphragm in the design and fabrication of integrated Fabry–Perot and piezoresistive diaphragm-based sensors. Experimental test data were obtained that have (1) validated the theoretical models for the optical and electronic outputs as functions of applied pressure, (2) determined the sensitivities to pressure for the electronic and optical parts of the sensor, and (3) obtained the spectral noise behavior (noise equivalent pressure sensitivity) of the optical part of the sensor system, In particular, quantitative agreement with theory validates the presence of a true Fabry–Perot interferometer in the optical part of the sensor. The physical characteristics and behavior of the embossed diaphragm makes the electronic sensor especially linear, and for the optical part of the sensor, it eliminates any fundamental deficiency related to non-parallelism between the two surfaces (diaphragm and fiber), after applied pressure. The embossment also permits the sensor to be insensitive to lateral misalignment of the optical fiber and reduces considerably the back pressure, which could otherwise reduce the sensitivity of the sensor. The design presented in this work allows fabricating very small Fabry–Perot cavities, thereby eliminating parasitic degradation from signal averaging and beam spreading effects. The integration of optical and electronic sensors in a single device provides additional advantages, such as having two independent outputs from one sensor. Each output has the capability of measuring static and dynamic pressures simultaneously, thereby providing some measure of redundancy. Such a system is also capable of being adapted to measure two different physical quantities, such as temperature and pressure. The output signals from both parts of the sensor can be used independently of each other, such as for verification of the measured magnitude, or as a mechanism for back-up in continuous monitoring systems.

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ACKNOWLEDGMENT Dr. Padron thanks Dean Dr. R. Kane, Associate Dean C. Gonzalez, Office of Graduate Studies at NJIT, and Dr. G. Smith, Acting Assistant Provost CUNY, for their constant support. Also, the authors owe special gratitude for the technical support of Dr. G. Georgiou, Dr. H. Grebel, and L. Geras. REFERENCES [1] V. Kaajakari, Practical MEMS: Design of Microsystems, Accelerometers, Gyroscopes, RF MEMS, Optical MEMS, and Microfluidic Systems. New York: Small Gear Publishing, 2009. [2] J. Korvink and O. Haber, MEMS: A Practical Guide to Design, Analysis and Applications. Norwich, NY: William Andrew, 2006. [3] E. Pinet, “Fabry-Pérot fiber-optic sensors for physical parameters measurement in challenging conditions,” J. Sens., vol. 2009, Article ID 720980. [4] S. Yin, P. B. Ruffin, and F. T. S. Yu, Fiber Optic Sensors. Boca Raton, FL: CRC Press, 2008. [5] S. Watson, M. J. Gander, W. N. MacPherson, J. S. Barton, and J. D. C. Jones, “Laser-machined fibers as Fabry–Perot pressure sensors,” Appl. Opt., vol. 45, no. 22, pp. 5590–5596, 2006. [6] M. Li, M. Wang, and H. Li, “Optical MEMS pressure sensor based on Fabry–Perot interferometry,” Opt. Exp., vol. 14, no. 4, pp. 1497–1504, 2006. [7] S. Prasanna, S. M. Nagaraja, P. Pandojirao-Sunkojirao, and J. C. Chiao, “Modeling and design of a fiber optic pressure sensor,” in Proc. 2005 TexMEMS, VII Int. Conf. Micro Electro Mech. Sys., El Paso, TX [Online]. Available: http://www.uta.edu/faculty/jcchiao/paper_download/ 2005_Texmems_Shruthika.pdf [8] Wang, B. Li, O. L. Russo, H. T. Roman, K. K. Chin, and K. R. Farmer, “Diaphragm design guidelines and an optical pressure sensor based on MEMS technique,” Microelectron. J., vol. 37, no. 1, pp. 50–56, 2006. [9] M. Han, X. Wang, J. Xu, K. L. Cooper, and A. Wang, “Diaphragm-based extrinsic Fabry–Perot interferometric optical fiber sensor for acoustic wave detection under high background pressure,” Opt. Eng., vol. 44, no. 6, 2005, 060507. [10] W. J. Wang, R. M. Lin, T. T. Sun, D. G. Guo, and Y. Ren, “Performance-enhanced Fabry–Perot microcavity structure with a novel nonplanar diaphragm,” Microelectron. Eng., vol. 70, pp. 102–108, 2003. [11] W. J. Wang, R. M. Lin, Y. Ren, T. T. Sun, and D. G. Guo, “FabryPerot microcavity pressure sensor with a novel single deeply corrugated diaphragm,” Microw. Opt. Technol. Lett., vol. 39, no. 3, pp. 240–243, 2003. [12] W. J. Wang, D. G. Guo, R. M. Lin, and X. W. Wang, “A single-chip diaphragm-type miniature Fabry–Perot pressure sensor with improved cross-sensitivity to temperature,” Meas. Sci. Technol., vol. 15, pp. 905–910, 2004. [13] B. Yu, D. W. Kin, J. Deng, H. Xiao, and A. Wang, “Fiber Fabry–Perot sensor for detection of partial discharges in power transformers,” Appl. Opt., vol. 42, no. 16, pp. 3241–3250, 2003. [14] J. Han, D. P. Neikirk, M. Clevenger, and J. T. McDevitt, “Fabrication and characterization of a Fabry–Perot based chemical sensor,” in Proc. SPIE Microelectron. Structures MEMS for Optical Process. II, M. E. Motamedi and W. Bailey, Eds., Austin, Texas, USA, Oct. 14–15, 1996, vol. 2881, pp. 171–178. [15] Y. Kim and D. P. Neikirk, “Micromachined Fabry–Perot cavity pressure transducer,” IEEE Photon. Technol. Lett., vol. 7, no. 12, pp. 1471–1473, Dec. 1995. [16] I. Padron, A. T. Fiory, and N. M. Ravindra, “Novel MEMS Fabry–Perot interferometric pressure sensors,” in Materials Science Forum. Switzerland: Trans. Tech. Publications, 2010, vol. 638–642, pp. 1009–1014. [17] I. Padron, A. T. Fiory, and N. M. Ravindra, “Modeling and design of an embossed diaphragm Fabry–Perot pressure sensor,” in Proc. Mater. Sci. Technol. Conf., Pittsburgh, PA, 2008, pp. 992–997. [18] M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. New York: Cambridge Univ. Press, 1999. [19] Yariv, Optical Electronics, 4th ed. Fort Worth, TX: Saunders College Publishing, 1991. [20] P. Kleimann, B. Semmache, M. L. Berre, and D. Barbier, “Stress-dependent hole effective masses and piezoresistive properties of p-type monocrystalline and polycrystalline silicon,” Phys. Rev. B, vol. 57, no. 15, pp. 8966–8971, 1998.

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Ivan Padron (M’10) received the B.S. degree in physics from the University of Havana, Havana, Cuba, in 1993 and the Ph.D. degree in applied physics from NJIT-Rutgers, Newark, NJ, in 2010. He is with the Physics Department at The New Jersey Institute of Technology, Newark. Dr. Padron is a member of the American Physical Society, American Ceramics Society and TMS—The Minerals, Metals, Materials Society.

Anthony T. Fiory received the Ph.D. in physics from Rutgers University, New Brunswick, NJ, in 1970. He is Research Professor in the Physics Department at The New Jersey Institute of Technology, Newark. Dr. Fiory is a member of the American Physical Society.

Nuggehalli M. Ravindra received the Ph.D. degree in physics from the Indian Institute of Technology, Roorkee, India, in 1982. He is Professor and Chairman of the Physics Department at NJIT. Dr. Ravindra is a member of the American Physical Society, The American Association for the Advancement of Science and TMS—The Minerals, Metals, Materials Society.