Patricia Nieva - Academia.edu (original) (raw)
Papers by Patricia Nieva
2018 IEEE 68th Electronic Components and Technology Conference (ECTC), 2018
Several applications require Micro electro mechanical systems MEMS devices to operate under high ... more Several applications require Micro electro mechanical systems MEMS devices to operate under high temperatures. Previous efforts to study the properties of MEMS materials have shown that an increase in temperature leads to a decrease in the fracture strength. In this paper, three different thin film silicon nitride dog-bone shaped structures suspended on a silicon substrate are used to determine their fracture strength as a function of temperature using tensile strength testing. Analytical modeling is used to determine the elastic resistance of the thin film dog-bones to stresses caused by the forces originated by the difference in coefficient of thermal expansion between the dog-bones and their substrate. The calculated forces incorporate the effect of temperature in these interactions and the mechanical properties of the two materials by considering the temperature dependence of elastic modulus and coefficient of thermal expansion. Analytical results show that the fracture strength...
Optical Components and Materials XI, 2014
ABSTRACT This study aims to expand the body of knowledge about the optical properties of battery ... more ABSTRACT This study aims to expand the body of knowledge about the optical properties of battery cathode materials. Although some studies have been conducted on the optical properties of Lithium Iron Phosphate (LiFePO4), to the authors' knowledge, this is the first study of its kind on electrodes extracted from commercially available LiFePO4 batteries. The use of Vis/NIR and FTIR spectroscopy provides for a methodology to study the optical properties of LiFePO4 and may allow for the characterization of other properties such as particle size and the proportions of LiFePO4 versus FePO4 material. Knowledge of these properties is important for the development of a mechanism to measure the state-of charge (SOC) in lithium ion batteries. These properties are also important in a host of other applications including battery modeling and materials characterization. Cylindrical LiFePO4 batteries (from A123 Systems Inc.) were acquired from the commercial market and charged to 10 different states between 30% and 80% of their nominal capacity using a constant-current, constant-voltage (CCCV) cycling method. Visual inspection of the extracted electrodes shows that the LiFePO4/C-cathodes display subtle changes in color (shades of grey) with respect to SOC. Vis/NIR measurements support the visual observation of uniform intensity variations versus SOC. FTIR measurements show an absorbance signature that varies with SOC and is distinct from results found in the literature for similar LiFePO4-based material systems, supporting the uniqueness of the absorbance fingerprint.
Sadhana Acad Proc Eng Sci, Aug 1, 2009
Reliability, Packaging, Testing, and Characterization of MOEMS/MEMS and Nanodevices XII, 2013
ABSTRACT In this paper, a new MEMS capacitive temperature sensor is presented which is based on a... more ABSTRACT In this paper, a new MEMS capacitive temperature sensor is presented which is based on a circular silicon plate with a gold annulus deposited on top forming a novel bimaterial structure. The bimaterial structure is anchored to a substrate on its edge and forms the top electrode of a capacitor. A stationary silicon electrode beneath the bimaterial structure forms the second electrode. The PolyMUMPs® foundry process has been used to fabricate the device. Experiments show that for an effective area of about 0.1 mm2 this MEMS capacitive temperature sensor achieves a sensitivity of 0.75+/-0.25 fF/°C over the temperature range of 25 to 225 °C, which shows an improvement of more than 25% over equivalent microcantilever devices with the same effective area. Numerical modeling is used to show that the new design exhibits high flexibility in tailoring its thermomechanical response over the desired temperature range. The simplicity of its design and flexibility of the materials from which it can be constructed also makes this new MEMS sensor a good onchip temperature measurement device for MEMS characterization.
Volume 12: Micro and Nano Systems, Parts A and B, 2009
Axial Force Regulation in MEMS Resonant Sensors. [ASME Conference Proceedings 2009, 321 (2009)]. ... more Axial Force Regulation in MEMS Resonant Sensors. [ASME Conference Proceedings 2009, 321 (2009)]. Pezhman A. Hassanpour, Chris T. Wong, Patricia M. Nieva, Amir Khajepour. Abstract. In this paper, a passive mechanism ...
2008 1st Microsystems and Nanoelectronics Research Conference, 2008
Abstract A new multifunctional sensor for simultaneous mea-surement of pressure and temperature ... more Abstract A new multifunctional sensor for simultaneous mea-surement of pressure and temperature is proposed and modeled. The design includes elastic membranes and bi-layer beams as pressure and temperature sensing bodies, respectively, and capa-citance readout for transduction. ...
Volume 12: Micro and Nano Systems, Parts A and B, 2009
ABSTRACT A capacitive temperature sensor with separate thermal actuation and capacitive readout i... more ABSTRACT A capacitive temperature sensor with separate thermal actuation and capacitive readout is introduced. A bi-layer plate with fixed-free boundary condition is used for the thermal actuation to change the gap between two parallel electrodes used for capacitance measurement. Different coefficients of thermal expansion (CTE) of the two layers in actuator cause out-of-plane deformations in the plate when the temperature changes. The proposed design has the capability to control the response of the sensor by increasing its sensitivity in a given temperature range. To obtain the desired characteristic C-T curve, the design utilizes asymmetric geometries. Different design parameters such as the size of the bi-layer plate and the sense electrodes are considered as design variables. ANSYS® FEM simulations are used to extract the C-T responses of different geometries. The results of the FEM simulations show that for a given fabrication process and material properties, the design can be modified to provide the highest sensitivity and linearity in the C-T response for a given temperature range. This temperature sensor can be used for remote and on-chip temperature measurement or temperature compensation.
Proceedings of Spie the International Society For Optical Engineering, 2006
This paper presents the design, fabrication and testing results of a Fabry-Perot Micro-Opto-Mecha... more This paper presents the design, fabrication and testing results of a Fabry-Perot Micro-Opto-Mechanical Device (FPMOD) used as a vibration sensor. The un-cooled high-temperature operational capability of the FPMOD provides a viable low-cost alternative to sensors that require environmentally controlled packages to operate at high temperature. The FPMOD is a passive MEMS device that consists of a micromachined cavity formed between a substrate and a top thin film structure in the form of a cantilever beam. When affixed to a vibrating surface, the amplitude and frequency of vibration are determined by illuminating the FPMOD with a monochromatic light source and analyzing the back reflected light to determine the deflection of the beam with respect to the substrate. Given the Fabry-Perot geometry, a mechanical transfer function is calculated to permit the substrate motion to be determined from the relative motion of the beam with respect to the substrate. Because the thin film cantilever beam and the substrate are approximately parallel, this convenient two-mirror cavity arrangement needs no alignment, no reference arm, and no sophisticated stabilization techniques. The small size of the FPMOD (85-175μm), the choice of materials in which it can be manufactured (Silicon Nitride and Silicon Carbide), and its simple construction make it ideal for harsh high-temperature applications. Relative displacements in the sub-nanometer range have been measured and close agreement was found between the measured sensor frequency response and the theoretical predictions based on analytical models.
ACS applied materials & interfaces, Jan 27, 2016
Optical characterization of graphite anodes in lithium ion batteries (LIB) is presented here for ... more Optical characterization of graphite anodes in lithium ion batteries (LIB) is presented here for potential use in estimating their state of charge (SOC). The characterization is based on reflectance spectroscopy of the anode of commercial LIB cells and in situ optical measurements using an embedded optical fiber sensor. The optical characterization of the anode using wavelengths ranging from 500 to 900 nm supports the dominance of graphite over the solid electrolyte interface in governing the anode's reflectance properties. It is demonstrated that lithiated graphite's reflectance has a significant change in the near-infrared band, 750-900 nm, compared with the visible spectrum as a function of SOC. An embedded optical sensor is used to measure the transmittance of graphite anode in the near-infrared band, and the results suggest that a unique inexpensive method may be developed to estimate the SOC of a LIB.
Microelectronic Engineering, Nov 1, 2010
Particulate Science and Technology, 2015
Biomicrofluidics, 2015
This research reports an improved conjugation process for immobilization of antibodies on carboxy... more This research reports an improved conjugation process for immobilization of antibodies on carboxyl ended self-assembled monolayers (SAMs). The kinetics of antibody/SAM binding in microfluidic heterogeneous immunoassays has been studied through numerical simulation and experiments. Through numerical simulations, the mass transport of reacting species, namely, antibodies and crosslinking reagent, is related to the available surface concentration of carboxyl ended SAMs in a microchannel. In the bulk flow, the mass transport equation (diffusion and convection) is coupled to the surface reaction between the antibodies and SAM. The model developed is employed to study the effect of the flow rate, conjugating reagents concentration, and height of the microchannel. Dimensionless groups, such as the Damköhler number, are used to compare the reaction and fluidic phenomena present and justify the kinetic trends observed. Based on the model predictions, the conventional conjugation protocol is ...
Proceedings of SPIE - The International Society for Optical Engineering
ABSTRACT
Proceedings of the IEEE International Conference on Micro Electro Mechanical Systems (MEMS)
We report the theory, design methodology and experiment of an electrostatically actuated silicon-... more We report the theory, design methodology and experiment of an electrostatically actuated silicon-plate Phononic Bandgap (P n BG) crystal architecture. This architecture is a high-order distributed mechanical system comprised of a two-dimensional P n BG crystal which is truncated to finite periodicity and suspended from the substrate utilizing tethers. Electrostatic actuation mitigates the use of piezoelectric transducers and provides action at a distance type forces so crystal edges may be free standing for reduced anchor loss. A finite element method model of the P n BG crystal is developed. A P n BG crystal is fabricated in a SOI process. Preliminary verification of the architecture is obtained utilizing a laser-Doppler vibrometer. INTRODUCTION Phononic Bandgap (P n BG) crystals, for classical elastic wave localization, are composite structures created through the N-dimensional (N = 1, 2, 3, 4, for up to three physical dimensions and one time dimension) periodic or aperiodic arran...
Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2007, 2007
ABSTRACT A multifunctional optical MEMS sensor system that can be used for the simultaneous measu... more ABSTRACT A multifunctional optical MEMS sensor system that can be used for the simultaneous measurement of displacement, temperature, and pressure has been fabricated. The system is based on an array of micromachined Fabry-Perot devices suitable for high temperature and pressure operations. The central concept of the sensor system is that airflow force around the moving structure (air viscous damping) strongly affects the oscillating height of the microcavity and hence, the mechanical performance of the device. The major effect that the viscosity and the density of the air have on the damping provides the mechanism for the simultaneous detection of pressure and temperature in addition to displacement. Since the air is trapped by the viscous damping effects there is no need for a sealed cavity. In addition, the very simple configuration in the optical interferometric system can be considered for the integration in the sensor system package. A model to accurately predict the frequency response of the Fabry-Perot structure subjected to a mechanical excitation on the substrate at different pressures and temperatures is presented. The model shows that shifts of the order of 10.5°C and 7.46psi can be detected for temperatures and pressures around 536°C and 446psi respectively using 90mum long microcantilever beams vibrating at a frequency of 97.4 kHz. To the best of our knowledge, this sensor array is one of the few, if not the only MOEMS device in the literature capable of simultaneous measurement of displacement, temperature, and pressure in high temperature environments.
Smart Structures and Materials 2006: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, 2006
ABSTRACT This paper presents the design, fabrication and testing results of a Fabry-Perot Micro-O... more ABSTRACT This paper presents the design, fabrication and testing results of a Fabry-Perot Micro-Opto-Mechanical Device (FPMOD) used as a vibration sensor. The un-cooled high-temperature operational capability of the FPMOD provides a viable low-cost alternative to sensors that require environmentally controlled packages to operate at high temperature. The FPMOD is a passive MEMS device that consists of a micromachined cavity formed between a substrate and a top thin film structure in the form of a cantilever beam. When affixed to a vibrating surface, the amplitude and frequency of vibration are determined by illuminating the FPMOD with a monochromatic light source and analyzing the back reflected light to determine the deflection of the beam with respect to the substrate. Given the Fabry-Perot geometry, a mechanical transfer function is calculated to permit the substrate motion to be determined from the relative motion of the beam with respect to the substrate. Because the thin film cantilever beam and the substrate are approximately parallel, this convenient two-mirror cavity arrangement needs no alignment, no reference arm, and no sophisticated stabilization techniques. The small size of the FPMOD (85-175mum), the choice of materials in which it can be manufactured (Silicon Nitride and Silicon Carbide), and its simple construction make it ideal for harsh high-temperature applications. Relative displacements in the sub-nanometer range have been measured and close agreement was found between the measured sensor frequency response and the theoretical predictions based on analytical models.
2018 IEEE 68th Electronic Components and Technology Conference (ECTC), 2018
Several applications require Micro electro mechanical systems MEMS devices to operate under high ... more Several applications require Micro electro mechanical systems MEMS devices to operate under high temperatures. Previous efforts to study the properties of MEMS materials have shown that an increase in temperature leads to a decrease in the fracture strength. In this paper, three different thin film silicon nitride dog-bone shaped structures suspended on a silicon substrate are used to determine their fracture strength as a function of temperature using tensile strength testing. Analytical modeling is used to determine the elastic resistance of the thin film dog-bones to stresses caused by the forces originated by the difference in coefficient of thermal expansion between the dog-bones and their substrate. The calculated forces incorporate the effect of temperature in these interactions and the mechanical properties of the two materials by considering the temperature dependence of elastic modulus and coefficient of thermal expansion. Analytical results show that the fracture strength...
Optical Components and Materials XI, 2014
ABSTRACT This study aims to expand the body of knowledge about the optical properties of battery ... more ABSTRACT This study aims to expand the body of knowledge about the optical properties of battery cathode materials. Although some studies have been conducted on the optical properties of Lithium Iron Phosphate (LiFePO4), to the authors' knowledge, this is the first study of its kind on electrodes extracted from commercially available LiFePO4 batteries. The use of Vis/NIR and FTIR spectroscopy provides for a methodology to study the optical properties of LiFePO4 and may allow for the characterization of other properties such as particle size and the proportions of LiFePO4 versus FePO4 material. Knowledge of these properties is important for the development of a mechanism to measure the state-of charge (SOC) in lithium ion batteries. These properties are also important in a host of other applications including battery modeling and materials characterization. Cylindrical LiFePO4 batteries (from A123 Systems Inc.) were acquired from the commercial market and charged to 10 different states between 30% and 80% of their nominal capacity using a constant-current, constant-voltage (CCCV) cycling method. Visual inspection of the extracted electrodes shows that the LiFePO4/C-cathodes display subtle changes in color (shades of grey) with respect to SOC. Vis/NIR measurements support the visual observation of uniform intensity variations versus SOC. FTIR measurements show an absorbance signature that varies with SOC and is distinct from results found in the literature for similar LiFePO4-based material systems, supporting the uniqueness of the absorbance fingerprint.
Sadhana Acad Proc Eng Sci, Aug 1, 2009
Reliability, Packaging, Testing, and Characterization of MOEMS/MEMS and Nanodevices XII, 2013
ABSTRACT In this paper, a new MEMS capacitive temperature sensor is presented which is based on a... more ABSTRACT In this paper, a new MEMS capacitive temperature sensor is presented which is based on a circular silicon plate with a gold annulus deposited on top forming a novel bimaterial structure. The bimaterial structure is anchored to a substrate on its edge and forms the top electrode of a capacitor. A stationary silicon electrode beneath the bimaterial structure forms the second electrode. The PolyMUMPs® foundry process has been used to fabricate the device. Experiments show that for an effective area of about 0.1 mm2 this MEMS capacitive temperature sensor achieves a sensitivity of 0.75+/-0.25 fF/°C over the temperature range of 25 to 225 °C, which shows an improvement of more than 25% over equivalent microcantilever devices with the same effective area. Numerical modeling is used to show that the new design exhibits high flexibility in tailoring its thermomechanical response over the desired temperature range. The simplicity of its design and flexibility of the materials from which it can be constructed also makes this new MEMS sensor a good onchip temperature measurement device for MEMS characterization.
Volume 12: Micro and Nano Systems, Parts A and B, 2009
Axial Force Regulation in MEMS Resonant Sensors. [ASME Conference Proceedings 2009, 321 (2009)]. ... more Axial Force Regulation in MEMS Resonant Sensors. [ASME Conference Proceedings 2009, 321 (2009)]. Pezhman A. Hassanpour, Chris T. Wong, Patricia M. Nieva, Amir Khajepour. Abstract. In this paper, a passive mechanism ...
2008 1st Microsystems and Nanoelectronics Research Conference, 2008
Abstract A new multifunctional sensor for simultaneous mea-surement of pressure and temperature ... more Abstract A new multifunctional sensor for simultaneous mea-surement of pressure and temperature is proposed and modeled. The design includes elastic membranes and bi-layer beams as pressure and temperature sensing bodies, respectively, and capa-citance readout for transduction. ...
Volume 12: Micro and Nano Systems, Parts A and B, 2009
ABSTRACT A capacitive temperature sensor with separate thermal actuation and capacitive readout i... more ABSTRACT A capacitive temperature sensor with separate thermal actuation and capacitive readout is introduced. A bi-layer plate with fixed-free boundary condition is used for the thermal actuation to change the gap between two parallel electrodes used for capacitance measurement. Different coefficients of thermal expansion (CTE) of the two layers in actuator cause out-of-plane deformations in the plate when the temperature changes. The proposed design has the capability to control the response of the sensor by increasing its sensitivity in a given temperature range. To obtain the desired characteristic C-T curve, the design utilizes asymmetric geometries. Different design parameters such as the size of the bi-layer plate and the sense electrodes are considered as design variables. ANSYS® FEM simulations are used to extract the C-T responses of different geometries. The results of the FEM simulations show that for a given fabrication process and material properties, the design can be modified to provide the highest sensitivity and linearity in the C-T response for a given temperature range. This temperature sensor can be used for remote and on-chip temperature measurement or temperature compensation.
Proceedings of Spie the International Society For Optical Engineering, 2006
This paper presents the design, fabrication and testing results of a Fabry-Perot Micro-Opto-Mecha... more This paper presents the design, fabrication and testing results of a Fabry-Perot Micro-Opto-Mechanical Device (FPMOD) used as a vibration sensor. The un-cooled high-temperature operational capability of the FPMOD provides a viable low-cost alternative to sensors that require environmentally controlled packages to operate at high temperature. The FPMOD is a passive MEMS device that consists of a micromachined cavity formed between a substrate and a top thin film structure in the form of a cantilever beam. When affixed to a vibrating surface, the amplitude and frequency of vibration are determined by illuminating the FPMOD with a monochromatic light source and analyzing the back reflected light to determine the deflection of the beam with respect to the substrate. Given the Fabry-Perot geometry, a mechanical transfer function is calculated to permit the substrate motion to be determined from the relative motion of the beam with respect to the substrate. Because the thin film cantilever beam and the substrate are approximately parallel, this convenient two-mirror cavity arrangement needs no alignment, no reference arm, and no sophisticated stabilization techniques. The small size of the FPMOD (85-175μm), the choice of materials in which it can be manufactured (Silicon Nitride and Silicon Carbide), and its simple construction make it ideal for harsh high-temperature applications. Relative displacements in the sub-nanometer range have been measured and close agreement was found between the measured sensor frequency response and the theoretical predictions based on analytical models.
ACS applied materials & interfaces, Jan 27, 2016
Optical characterization of graphite anodes in lithium ion batteries (LIB) is presented here for ... more Optical characterization of graphite anodes in lithium ion batteries (LIB) is presented here for potential use in estimating their state of charge (SOC). The characterization is based on reflectance spectroscopy of the anode of commercial LIB cells and in situ optical measurements using an embedded optical fiber sensor. The optical characterization of the anode using wavelengths ranging from 500 to 900 nm supports the dominance of graphite over the solid electrolyte interface in governing the anode's reflectance properties. It is demonstrated that lithiated graphite's reflectance has a significant change in the near-infrared band, 750-900 nm, compared with the visible spectrum as a function of SOC. An embedded optical sensor is used to measure the transmittance of graphite anode in the near-infrared band, and the results suggest that a unique inexpensive method may be developed to estimate the SOC of a LIB.
Microelectronic Engineering, Nov 1, 2010
Particulate Science and Technology, 2015
Biomicrofluidics, 2015
This research reports an improved conjugation process for immobilization of antibodies on carboxy... more This research reports an improved conjugation process for immobilization of antibodies on carboxyl ended self-assembled monolayers (SAMs). The kinetics of antibody/SAM binding in microfluidic heterogeneous immunoassays has been studied through numerical simulation and experiments. Through numerical simulations, the mass transport of reacting species, namely, antibodies and crosslinking reagent, is related to the available surface concentration of carboxyl ended SAMs in a microchannel. In the bulk flow, the mass transport equation (diffusion and convection) is coupled to the surface reaction between the antibodies and SAM. The model developed is employed to study the effect of the flow rate, conjugating reagents concentration, and height of the microchannel. Dimensionless groups, such as the Damköhler number, are used to compare the reaction and fluidic phenomena present and justify the kinetic trends observed. Based on the model predictions, the conventional conjugation protocol is ...
Proceedings of SPIE - The International Society for Optical Engineering
ABSTRACT
Proceedings of the IEEE International Conference on Micro Electro Mechanical Systems (MEMS)
We report the theory, design methodology and experiment of an electrostatically actuated silicon-... more We report the theory, design methodology and experiment of an electrostatically actuated silicon-plate Phononic Bandgap (P n BG) crystal architecture. This architecture is a high-order distributed mechanical system comprised of a two-dimensional P n BG crystal which is truncated to finite periodicity and suspended from the substrate utilizing tethers. Electrostatic actuation mitigates the use of piezoelectric transducers and provides action at a distance type forces so crystal edges may be free standing for reduced anchor loss. A finite element method model of the P n BG crystal is developed. A P n BG crystal is fabricated in a SOI process. Preliminary verification of the architecture is obtained utilizing a laser-Doppler vibrometer. INTRODUCTION Phononic Bandgap (P n BG) crystals, for classical elastic wave localization, are composite structures created through the N-dimensional (N = 1, 2, 3, 4, for up to three physical dimensions and one time dimension) periodic or aperiodic arran...
Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2007, 2007
ABSTRACT A multifunctional optical MEMS sensor system that can be used for the simultaneous measu... more ABSTRACT A multifunctional optical MEMS sensor system that can be used for the simultaneous measurement of displacement, temperature, and pressure has been fabricated. The system is based on an array of micromachined Fabry-Perot devices suitable for high temperature and pressure operations. The central concept of the sensor system is that airflow force around the moving structure (air viscous damping) strongly affects the oscillating height of the microcavity and hence, the mechanical performance of the device. The major effect that the viscosity and the density of the air have on the damping provides the mechanism for the simultaneous detection of pressure and temperature in addition to displacement. Since the air is trapped by the viscous damping effects there is no need for a sealed cavity. In addition, the very simple configuration in the optical interferometric system can be considered for the integration in the sensor system package. A model to accurately predict the frequency response of the Fabry-Perot structure subjected to a mechanical excitation on the substrate at different pressures and temperatures is presented. The model shows that shifts of the order of 10.5°C and 7.46psi can be detected for temperatures and pressures around 536°C and 446psi respectively using 90mum long microcantilever beams vibrating at a frequency of 97.4 kHz. To the best of our knowledge, this sensor array is one of the few, if not the only MOEMS device in the literature capable of simultaneous measurement of displacement, temperature, and pressure in high temperature environments.
Smart Structures and Materials 2006: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, 2006
ABSTRACT This paper presents the design, fabrication and testing results of a Fabry-Perot Micro-O... more ABSTRACT This paper presents the design, fabrication and testing results of a Fabry-Perot Micro-Opto-Mechanical Device (FPMOD) used as a vibration sensor. The un-cooled high-temperature operational capability of the FPMOD provides a viable low-cost alternative to sensors that require environmentally controlled packages to operate at high temperature. The FPMOD is a passive MEMS device that consists of a micromachined cavity formed between a substrate and a top thin film structure in the form of a cantilever beam. When affixed to a vibrating surface, the amplitude and frequency of vibration are determined by illuminating the FPMOD with a monochromatic light source and analyzing the back reflected light to determine the deflection of the beam with respect to the substrate. Given the Fabry-Perot geometry, a mechanical transfer function is calculated to permit the substrate motion to be determined from the relative motion of the beam with respect to the substrate. Because the thin film cantilever beam and the substrate are approximately parallel, this convenient two-mirror cavity arrangement needs no alignment, no reference arm, and no sophisticated stabilization techniques. The small size of the FPMOD (85-175mum), the choice of materials in which it can be manufactured (Silicon Nitride and Silicon Carbide), and its simple construction make it ideal for harsh high-temperature applications. Relative displacements in the sub-nanometer range have been measured and close agreement was found between the measured sensor frequency response and the theoretical predictions based on analytical models.