Micro-Electro-Mechanical-Systems for Sensor Applications · 2012-08-03 · Defence R&D Canada –...

Defence R&D Canada – Atlantic

DEFENCE DÉFENSE&

Micro-Electro-Mechanical-Systems for

Sensor Applications

Gino RinaldiNSERC Research Fellow

Technical Memorandum

DRDC Atlantic TM 2009-081

April 2009

Copy No. _____

Defence Research andDevelopment Canada

Recherche et développementpour la défense Canada

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Micro-Electro-Mechanical-Systems for Sensor Applications

Gino Rinaldi NSERC Research Fellow

Defence R&D Canada – Atlantic Technical Memorandum DRDC Atlantic TM 2009-081 April 2009

Principal Author

Gino Rinaldi

NSERC Research Fellow

Approved by

Ken McRae

Head / Air Vehicles Research Section

Approved for release by

Calvin Hyatt

Chair

© Her Majesty the Queen as represented by the Minister of National Defence, 2009

© Sa Majesté la Reine, représentée par le ministre de la Défense nationale, 2009

Original signed by Gino Rinaldi

Original signed by Ken McRae

Original signed by Ron Kuwahara for

Abstract

In today’s world, microengineering is on the threshold of new technological breakthroughs in many applications, such as microfluidics, bio-medical imaging, microscopy, and microphotonics. However, sensors are not being fabricated for the demands imposed by current and future applications. In this regard, sensors need to be engineered and optimized for a given application. Harsh environments, size requirements, data transfer, and sensor packaging are a few of the issues needing to be addressed. For aerospace applications, size and weight considerations are very important, as are the limitations imposed by the harsh operating environment of a gas turbine engine. The advent of micro-electro-mechanical-systems technology, advanced microfabrication and modeling capabilities has brought about interest in the development of intelligent sensor systems. Micro-sensor technologies are expected to play a significant role in such development. Using silicon microfabrication processes, it has been suggested that common sensors could be replaced or complemented with miniaturized, high reliability, low-cost, low-power and batch manufactured micro-sensors. A silicon-on-insulator transducer is introduced for possible pressure sensing applications in high temperature engine components and compartments. A case study is presented in which the effects of mass and surface stress are investigated for microcantilever sensor applications. A theoretical formulation based on the Rayleigh-Ritz energy approach is developed for the dynamic analysis of the microcantilevers, and an optical non-contact experimental method is employed to validate the theoretical model.

Résumé

Dans le monde d’aujourd’hui, la microingénierie est sur le point de réaliser de nouvelles percées technologiques dans de nombreuses applications, comme la microfluidique, l’imagerie biomédicale, la microscopie et la microphotonique. Cependant, les capteurs ne sont pas fabriqués en fonction des besoins des applications actuelles et futures. À cet égard, les capteurs doivent être réalisés et optimisés en fonction d’une application donnée. De plus, il faudra tenir compte, entre autres, des milieux hostiles, des critères de dimension, des transferts de données et des boîtiers de capteurs. Pour les applications aérospatiales, les dimensions et le poids sont des éléments très importants à prendre en considération, tout comme les limites imposées par l’environnement opérationnel hostile d’un moteur à turbine à gaz. L’avènement de la technologie des systèmes microélectromécaniques, la microfabrication de pointe et des capacités de modélisation a éveillé un intérêt pour le développement de systèmes de capteurs intelligents. Les technologies de microdétection devraient jouer un rôle important dans ce développement. Grâce aux procédés de microfabrication au silicium, on a suggéré de remplacer ou de compléter des capteurs courants par des microcapteurs miniaturisés, très fiables, peu coûteux, de faible puissance et fabriqués en lots. On a fait appel à un transducteur silicium sur isolant pour les applications possibles de détection de la pression dans les composants et les compartiments moteurs à haute température. Le présent document décrit une étude de cas dans le cadre de laquelle les effets d’une masse et des contraintes de surface sont étudiés pour les applications de capteurs à micropoutre. Une formule théorique axée sur la méthode énergétique de Rayleigh-Ritz est développée pour l’analyse dynamique des micropoutres, et une méthode optique sans contact expérimentale est utilisée pour valider le modèle théorique.

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Executive summary

Micro-Electro-Mechanical-Systems for Sensor Applications Rinaldi, G.; DRDC Atlantic TM 2009-081; Defence R&D Canada – Atlantic; April 2009.

Introduction or background

The advent of micro-electro-mechanical-systems (MEMS) technology, advanced microfabrication and modeling capabilities has brought about interest in the development of intelligent micro-sensor systems. Microengineering is on the threshold of new technological breakthroughs in many micro-sensor applications such as microfluidics, bio-medical imaging, microscopy, and microphotonics. However, harsh environments, size requirements, data transfer, and sensor packaging are a few of the issues needing to be addressed. For aerospace applications, size and weight considerations are very important, as are the limitations imposed by the harsh operating environment, for example, of a gas turbine engine. In this report, MEMS technology in general is discussed and a silicon-on-insulator (SOI) transducer is introduced for possible pressure/temperature sensing applications in high temperature engine components and compartments. Also, a case study is presented in which the effects of mass and surface stress on the frequency response of the micro-sensor in order to determine the most suitable sensing domain for a given application. A theoretical formulation based on the Rayleigh-Ritz energy approach is developed for the dynamic analysis of the microcantilevers, and an optical non-contact experimental method is employed to validate the theoretical model.

Results

The experimental results obtained for the SOI micro-sensors showed that while the sensors were sensitive to both pressure and temperature the tests also revealed a flaw in the electronics of the sensor platform. Due to the type of packaging selected for the micro-sensor, one of the electrical connections for the transistor of the SOI MEMS device was left floating as opposed to electrically grounded. Hence, it was not possible to calibrate the micro-sensor for a given pressure/temperature due to drifting of the output signal between measurements.

For the work presented on the microcantilever sensor, a plot of the 2nd natural frequency with added mass demonstrates the variability of the frequency with mass position on the microcantilever. Of particular interest is the nodal point at which mass independence is revealed. This nodal point was exploited to investigate purely stress related influences on the dynamic characteristics of the microcantilever sensor. In this regard, the nodal point of the 2nd natural frequency response was used to decouple mass-stress influences. The theoretical results were in good agreement with experiment.

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Significance

The SOI material shows excellent potential for micro-sensor applications such as in hot sections of gas turbine engines for both military and civilian applications.

Silicon can be easily shaped and sensitized to a variety of influences. These qualities are highly regarded for micro-sensor applications. The case study work presented herein, contributes to the optimization of the microcantilever sensor’s dynamic response as a function of mass and surface stress influences. The main criterion, for choosing one or the other is based on the time for the surface reaction to take place between the sensing material and the target material. The results presented contribute to the performance optimization of micro-cantilever based medical and bio-sensors.

Future plans

A MEMS based pressure sensor will be implemented for gas turbine engine health monitoring applications. A proof-of-concept experiment using a DC-fan will be carried out on a laboratory test bench. From the bench top experiments a test matrix will be established and the sensor will then be implemented on an actual gas turbine engine (J85 or CF700). It is also the aim of this research, in general, to extend the field of application of MEMS sensors to include other applications such as corrosion and fatigue crack detection.

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Sommaire

Micro-Electro-Mechanical-Systems for Sensor Applications Rinaldi, G.; DRDC Atlantic TM 2009-081; R & D pour la défense Canada – Atlantique; April 2009.

Introduction ou contexte

L’avènement de la technologie des systèmes microélectromécaniques (MEMS), de la microfabrication de pointe et des capacités de modélisation a éveillé un intérêt pour le développement de systèmes de microcapteurs intelligents. La microingénierie est sur le point de réaliser de nouvelles percées technologiques dans de nombreuses applications de microcapteurs, comme la microfluidique, l’imagerie biomédicale, la microscopie et la microphotonique. Il faudra toutefois tenir compte entre autres des milieux hostiles, des critères de dimension, des transferts de données et des boîtiers de capteurs. Pour les applications aérospatiales, les dimensions et le poids sont des éléments très importants à prendre en considération, tout comme les limites imposées par l’environnement opérationnel hostile, par exemple, d’un moteur à turbine à gaz. Dans le présent rapport, la technologie MEMS en général est examinée, et on a fait appel à un transducteur silicium sur isolant (SOI) pour les applications possibles de détection de la pression et de la température dans les composants et les compartiments moteurs à haute température. De plus, le présent document décrit une étude de cas dans le cadre de laquelle les effets d’une masse et des contraintes de surface sur la réponse en fréquence du microcapteur ont été mesurés pour déterminer le domaine de détection le plus approprié pour une application donnée. Une formule théorique axée sur la méthode énergétique de Rayleigh-Ritz est développée pour l’analyse dynamique des micropoutres, et une méthode optique sans contact expérimentale est utilisée pour valider le modèle théorique.

Résultats

Les résultats expérimentaux obtenus pour les microcapteurs SOI ont montré que bien que les capteurs fussent sensibles à la pression et à la température, le système électronique de leur plate-forme présentait une lacune. En raison du type de boîtier choisi pour le microcapteur, l’une des connexions électriques du transistor du dispositif MEMS SOI était flottante, au lieu d’être mise à la masse. Par conséquent, l’étalonnage du microcapteur à une pression ou à une température donnée était impossible en raison de la dérive du signal de sortie entre les mesures.

Pour le travail présenté sur le capteur à micropoutre, un tracé de la deuxième fréquence propre en fonction d’une masse ajoutée a montré la variabilité de la fréquence en fonction de la position de la masse sur la micropoutre. Le point nodal où une variation de la masse ne produit aucun changement de la réponse en fréquence est particulièrement intéressant. Ce point nodal a été utilisé pour étudier les influences liées uniquement aux contraintes sur les caractéristiques dynamiques du capteur à micropoutre. À cet égard, le point nodal de la réponse en deuxième fréquence propre a été utilisé pour dissocier l’influence de la masse et l’influence des contraintes. Les résultats théoriques concordaient bien avec les résultats expérimentaux.

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Portée

Le produit SOI présente un excellent potentiel pour les applications de microcapteurs, comme les sections chaudes des moteurs à turbine à gaz pour les applications militaires et civiles.

Le silicium est facile à façonner et à sensibiliser à diverses influences. Ces qualités sont très recherchées dans les applications de microcapteurs. Le travail présenté ici contribue à l’optimisation de la réponse en régime dynamique des capteurs à micropoutre en fonction de l’influence de la masse et des contraintes de surface. Le principal critère pour sélectionner l’un des deux types d’influence repose sur le temps nécessaire pour que se produise une réaction de surface entre le produit sensible et la substance à détecter. Les résultats présentés contribuent à l’optimisation du rendement des capteurs à micropoutre dans les domaines médical et biologique.

Recherches futures

Un capteur de pression axé sur les MEMS sera mis en place pour les applications de contrôle de l’état du moteur à turbine à gaz. Une expérience de validation de principe au moyen d’un ventilateur à courant continu sera réalisée sur un banc d’essai de laboratoire. À partir des expériences réalisées à la surface du banc d’essai, un plan d’essai sera conçu, puis le capteur sera installé sur un vrai moteur à turbine à gaz (J85 ou CF700). En général, la présente recherche vise en outre à étendre le champ d’application des capteurs MEMS, par exemple, à la détection de la corrosion et des fissures de fatigue.

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Table of contents

Abstract ............................................................................................................................................ i Résumé ............................................................................................................................................. i Executive summary ........................................................................................................................ iii Sommaire......................................................................................................................................... v Table of contents ........................................................................................................................... vii List of figures ................................................................................................................................. ix List of tables .................................................................................................................................. xii Acknowledgements ...................................................................................................................... xiii 1. Introduction............................................................................................................................... 1

1.1 Background ................................................................................................................... 1 1.2 Applications................................................................................................................... 1

2. Microfabrication ....................................................................................................................... 2 2.1 Clean room requirements .............................................................................................. 2 2.2 Photolithography ........................................................................................................... 3

2.2.1 Spin coating..................................................................................................... 3 2.3 Limitations..................................................................................................................... 4

3. Silicon-on-Insulator Technology .............................................................................................. 7 3.1 Details of the MicraGeM process.................................................................................. 8 3.2 Silicon-on-insulator pressure sensors: Catholic University of Louvain ...................... 10 3.3 Sensor packaging......................................................................................................... 11 3.4 Sensor operation .......................................................................................................... 13 3.5 Transistor characterization and experimental setup .................................................... 16

3.5.1 Experimental results...................................................................................... 18 3.5.1.1 Static pressure measurements ..................................................... 19 3.5.1.2 Dynamic pressure measurements ............................................... 21

4. Case Study: MEMS Microcantilever Sensor .......................................................................... 24 4.1 Microcantilever sensors............................................................................................... 25 4.2 Microcantilever applications ....................................................................................... 26 4.3 Microfabrication limitations at the boundary support ................................................. 27 4.4 Lumped mass model formulation................................................................................ 28

4.4.1 Rayleigh-Ritz energy method ....................................................................... 29 4.4.1.1 Dynamic Analysis....................................................................... 30 4.4.1.2 Analytical results ........................................................................ 33

4.5 Experimental section ................................................................................................... 37 4.5.1 Effect of added mass ..................................................................................... 38 4.5.2 Water droplet evaporation............................................................................. 42

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4.5.3 Surface stress................................................................................................. 45 5. Conclusions............................................................................................................................. 47 References ..................................................................................................................................... 49 List of symbols/abbreviations/acronyms/initialisms ..................................................................... 56 Distribution list.............................................................................................................................. 60

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List of figures

Figure 1: (a) Light-field mask pattern. (b) Dark-field mask pattern................................................ 3 Figure 2: Schematic illustration of a typical spin-coating apparatus............................................... 4 Figure 3: (a) A generalized overview of the photolithography process. (b) Etch profile for

positive photoresist. (c) Etch profile for negative photoresist....................................... 5 Figure 4: Scanning-electron-microscope (SEM) images of the effects of non-uniform etching

at corners. (a) Image of a microcantilever with a cutout (vent hole). The rounded corners at the boundary support and cutout are visible. (b) A close-up image of the rounded corner at the boundary support........................................................................ 6

Figure 5: A schematic overview of the MicraGeM process layers and the undercutting of the silicon structure. ............................................................................................................ 6

Figure 6: (a) Etching of pyrex and deposition of Metal_1 layer. (b) Silicon layer is anodically bonded to pyrex. (c) Patterning and release of silicon structures and deposition of Metal_2 layer. ............................................................................................................... 7

Figure 7: An overview of a MicraGeM chip design with SCSi structures. ..................................... 9 Figure 8: (a) Pyrex etch layer with Metal_1; (b) SCSi layer with Metal_2 contact pads and

wiring scheme. .............................................................................................................. 9 Figure 9: MicraGeM SOI technology microcantilevers. .............................................................. 10 Figure 10: Schematic illustration of the cross-section of the multilayered membrane. ................ 11 Figure 11: Top: overview of the SOI based pressure membrane and electrical connections.

Bottom: Close up view of the center mounted edgeless-transistor on the membrane.................................................................................................................... 12

Figure 12: Details of the edgeless, center-mounted transistor....................................................... 12 Figure 13: (a) 24-pin ceramic package. The hole is required to create a differential pressure

environment. (b) Wire bonded devices. Left: Edge mounted. Right: Center mounted....................................................................................................................... 14

Figure 14: Edge mounted transistors on the SOI membrane. The drains are shown in either a parallel (//) or perpendicular (⊥) configuration with respect to the applied stress (σ)................................................................................................................................ 15

Figure 15: Left: Center mounted devices. Right: Edge mounted devices. ................................... 15 Figure 16: Standard Faraday box used for transistor characterization. ......................................... 16 Figure 17: Semiconductor parameter analyzer used the characterization of the transistors.......... 17 Figure 18: Tube furnace to be used for thermal environment experiments of the SOI devices. ... 17 Figure 19: An overview of the test equipment used for the thermo-baric measurements. ........... 18 Figure 20: Top: Typical ID-VD curves for various gate voltages VG. Bottom: ID-VG curve

plot. VTh ~0.5V........................................................................................................... 19

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Figure 21: The drain current ID as a function of the drain voltage VD and the applied static pressure. The increased static pressure induced an increase in the electron mobility across the drain characterized by the increase in ID...................................... 20

Figure 22: Transistor ID-VD characteristics as a function of the applied thermal load for VG = 2V and VD = 2V. ......................................................................................................... 21

Figure 23: ID-VD curve traces required to obtain the equivalent resistance of the transistor......... 22 Figure 24: A voltage divider circuit with an equivalent resistance REq inserted into the circuit. .. 22 Figure 25: The voltage across an equivalent resistance REq is monitored with an oscilloscope.

The voltage is a function of the varying drain current ID due to dynamic pressure conditions. ................................................................................................................... 23

Figure 26: Time domain output observed on an oscilloscope of the dynamic pressure generated using a pneumatic switch attached to an air hose. ...................................... 23

Figure 27: (a) Macro-scale diving board. (b) Microcantilever sensor........................................... 25 Figure 28: Microscope images of (a) MUMPS technology microcantilevers. (b) MicraGeM

technology microcantilevers. ...................................................................................... 26 Figure 29: Atomic force microscope probes. ................................................................................ 27 Figure 30: Schematic representation of a microcantilever with artificial boundary support

springs. ........................................................................................................................ 28 Figure 31: Lumped parameter model of an elastic system. ........................................................... 28 Figure 32: Analytical results for the effect of added mass and added mass position along the

normalized length of a microcantilever on the (a) 1st natural frequency. (b) 2nd natural frequency. (c) 3rd natural frequency. ............................................................... 34

Figure 33: 3D analytical results for the effect of mass and mass position along the length of a microcantilever on the (a) 1st natural frequency. (b) 2nd natural frequency. (c) 3rd natural frequency......................................................................................................... 35

Figure 34: A comparison of the changes to the 1st, 2nd and 3rd natural frequencies of a microcantilever as a function of the position of the added test-mass along the normalized length of the microcantilever.................................................................... 36

Figure 35: Experimental set-up and equipment. (a) Helium-Neon (HeNe) laser with diverging-converging lens train. (b) MEMS support post. ......................................... 37

Figure 36: Schematic top view of the microcantilever array configuration used in this work. The microcantilevers are sandwiched between two microscope slides....................... 38

Figure 37: HeNe laser LDV based surface velocity detection mechanism and signal processing.................................................................................................................... 38

Figure 38: The variation of the 1st natural frequency as a function of the position of the added mass............................................................................................................................. 39

Figure 39: The variation of the 2nd natural frequency as a function of the position of the added mass............................................................................................................................. 39

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Figure 40: The variation of the 3rd natural frequency as a function of the position of the added mass............................................................................................................................. 40

Figure 41: A comparison of the experimental center frequency responses as a function of the position of the added 5 x 10-6kg mass on the normalized microcantilever length and the theoretical curve for the 1st natural frequency. ............................................... 40

Figure 42: A comparison of the experimental center frequency responses as a function of the position of the added 5 x 10-6kg mass on the normalized microcantilever length and the theoretical curve for the 2nd natural frequency. .............................................. 41

Figure 43: A comparison of the experimental center frequency responses as a function of the position of the added 5 x 10-6kg mass on the normalized microcantilever length and the theoretical curve for the 3rd natural frequency................................................ 41

Figure 44: Time lapse (3 minutes between each) microscope side images of the evaporation of a water droplet on a microcantilever surface. ......................................................... 43

Figure 45: Top view of a microscope image of a water droplet on a microcantilever surface...... 43 Figure 46: Evaporation of a water drop modeled as a spheroid. The contact area remains

constant between the droplet and microcantilever surface. Arrows show the reduction in droplet height due to evaporation............................................................ 44

Figure 47: The variation of the 1st natural frequency of a microcantilever as a function of the evaporation of a water droplet on its surface. ............................................................. 44

Figure 48: Schematic side-view of the distributed mass of a water droplet at x = 0.8 along the normalized length of a cantilever. ............................................................................... 45

Figure 49: The shift of the 1st natural frequency as a function of the applied stress σd................. 46 Figure 50: The shift of the 2nd natural frequency as a function of the applied stress σd................ 46

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List of tables

Table 1: Variation of the natural frequency (center frequency values) for the first three resonance modes as a function of the load position on the microcantilever (NL = no load). ...................................................................................................................... 42

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Acknowledgements

The author would like to acknowledge the assistance of Mr. Vahé Nerguizian from École de Technologie Supérieur in Montreal, Canada, in the testing and characterization of the MEMS transistors. The author also wishes to thank Dr. Jean-Pierre Raskin from the Catholic University of Louvain in Louvain-la-Neuve, Belgium for graciously supplying him with the MEMS transistor devices.

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1. Introduction

1.1 Background

In the course of human technological advancement there has been no material more versatile and effectively exploited than silicon. Its versatility is due to a combination of three factors:

i) It has good mechanical properties as its Young’s modulus of elasticity is comparable to that of steel.

ii) It can be shaped to a high degree of precision.

iii) It can be sensitized to many physical properties.

The intrinsic mechanical properties, high strength and high reliability of silicon can be integrated with electronic components, and the low thermal expansion, high heat conductivity and high elasticity of silicon can be exploited to fabricate miniaturized electro-mechanical sensors and actuators [1-3]. It is these multidisciplinary properties that are exploited to develop the field of micro-electro-mechanical-systems (MEMS) for a vast number of applications.

By using similar micromachining tools initially developed for the silicon integrated circuits (IC) and semiconductor industry, MEMS engineers are microfabricating miniature structures from silicon and other materials. In this regard, MEMS could help to realize the integration of mechanical, electronics, optical and other elements on a common silicon substrate through the utilization of a specific microfabrication technology. Since MEMS devices are manufactured using batch fabrication techniques, high levels of functionality, reliability, and sophistication can be placed on a small silicon chip at a relatively low cost. The IC component along with the software can be thought of, in general, as the decision-making module of microsystems, and MEMS enhances this control capability with electro-mechanical or optical-electro-mechanical sensing. MEMS microfabrication technology has enabled electrically actuated micromotors, capable of rotating at more than 10000 revolutions-per-minute (RPM), the size of a human hair for fans, pumps, and turbo generators [4-8]. However, although MEMS devices are micro-small, MEMS technology is not only about size and making things out of silicon, instead, MEMS should be thought of as a new enabling-microfabrication methodology in which complex electro-mechanical microsystems are developed using batch microfabrication techniques in which a high volume of microdevices are fabricated in one process similar to the way integrated-circuits (IC) are manufactured [9-11].

1.2 Applications MEMS are used in many applications ranging from blood pressure and blood glucose monitoring, to active suspension systems and airbag deployment sensors for automobiles. Within the next few years MEMS accelerometers are expected to completely replace conventional devices in all

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foreign and domestic model cars [12-18]. Recently, micromachining methodologies have also been extended to optical microsystems, consisting, in general, of a combination of mirrors, fiber-optics, and/or electro-optical waveguides for light steering, optical alignment or sensing applications [19-25].

From an engineering point of view there are several advantages to having smaller components. Smaller systems have fast response times due to small mass and inertia and have high natural frequencies making them relatively impervious to external vibrations as might be expected in harsh environments. Response times of 3μs for a fiber optic attenuator based on an electrostatically actuated suspended microdevice have been reported [26]. MEMS are having an impact on many different areas including basic science, aerospace, environmental condition monitoring, consumer goods, and medicine. MEMS are a significant step forward toward the ultimate miniaturization of current macro-scale machines and devices.

2. Microfabrication

Microfabrication is a term that generally implies the micromachining of crystalline silicon at the microscale through an appropriate photo-lithography mask design and etch process [27-30]. There are many different silicon foundry processes available today. Three such silicon foundry processes are: MUMPs [31] technology which is based on a 7 layer polysilicon-oxide-metal additive surface micromachining process, MikroMasch (μMasch) [32] that employs a bulk micromachining of silicon process, and the Micralyne generalized MEMS (MicraGeM) [33] process using a silicon-on-insulator (SOI) bulk micromachining process. The advantage of this particular process is that it allows MEMS designers to develop fully suspended structures with metal electrical contacts. Each of the above mentioned processes employ sets of microfabrication steps that enable the realization of microstructures based on the original designs produced by any number of multiple designers. All micromachining and microsystem fabrication involves a lithography step in which the pattern of the microsystem design is transferred onto the silicon chip for processing and shaping.

2.1 Clean room requirements The handling of silicon wafers for microfabrication purposes requires special attention to both the manner in which they are handled as well as to the environment in which they will be handled [34]. These two issues are critical because dust and other contaminants will interfere with every microfabrication process step. Typical contaminants include dust, stains associated with handling, residue from surface adhesion of acetone and alcohol, and smoke particles, for example. Silicon wafers must be cleaned prior to processing. A combination of baking at high temperatures and rinsing in de-ionized water is a suitable method. For environmental contaminant control, the silicon wafer processing should be carried out in a clean room of at least 1000 rating. This rating specifies the maximum number of dust particles per cubic meter. State of the art clean rooms have ratings of at least 100 and in most cases less than this. The rule of thumb regarding clean room functionality and suitability is that in order to obtain a rating of 100, the clean room itself should be enclosed in a clean room with a rating of 1000.

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2.2 Photolithography Micromachining consists of several process steps that are dependent upon the choice of silicon microfabrication technology. All micromachining and microsystem fabrication involves a lithography step in which the pattern of the microsystem design is transferred onto the silicon chip for processing and shaping. For microscale applications, the most widely used form of lithography is photolithography. Successive patterns can be transferred onto the silicon thereby enabling complex multi-layered devices. The microfabrication tolerances can be attributable, in part, to current photolithographic resolution limitations.

The design pattern transfer is done through the transmission of ultra-violet (UV) light through a photolithography mask which is then placed in direct contact with a photoresist spine-coated surface. In this manner the mask pattern describing the geometry of the microstructure is transferred onto the silicon wafer which can then be micromachined, through etching, into the desired shapes. Shown in Figure 1 are two different yet similar mask patterns, light field and dark field that can be employed in the photolithography step [35].

Figure 1: (a) Light-field mask pattern. (b) Dark-field mask pattern

2.2.1 Spin coating The main component in the photolithography step is the organic photoresist polymer that is sensitive to UV light. The polymer undergoes changes in structure when exposed to the UV radiation. The photoresist material is spin-coated onto the silicon wafer at rotational speeds of up to 10000 RPM after a preliminary soft-baking process used, in general, to prepare the wafer surface for application of the photoresist material through the growth of a thin oxide layer which may serve as a mask for the next etch step and is removed by dipping in acetone solution. The soft baking step is usually a short process at temperatures typically ranging from 75-100°C. The application steps of photoresist to the silicon wafer in themselves are a somewhat guarded


process due to the inherent irregularities that can result in photoresist thickness across the wafer surface. These irregularities will then cause difficulties in the mask pattern transfer by UV light. The photoresist polymer is applied in some cases manually to the silicon chip by an eye drop applicator. This is a process that requires some intuition and acquired expertise on the part of the technician for the amount of polymer to be dropped on to the silicon surface. Typical photoresist thicknesses after spin coating are of the order of ~2μm. Shown in Figure 2 is a standard photoresist spin coating assembly. The silicon wafer is held in place by a vacuum mechanism at the base of the wafer support disk. The spinning causes the photoresist polymer to flow to the edges of the wafer and the uniformity is more or less controlled by the rotational spin velocity and the duration of the spin cycle.

Spinner

Silicon wafer support disk

Silicon wafer

Figure 2: Schematic illustration of a typical spin-coating apparatus.

After the spin step the silicon wafers are again soft baked for several minutes to remove any built in stresses and also to augment the adhesion between the wafer surface and the photoresist polymer. The type of photoresist chosen, either positive or negative will determine which portions of the silicon structure to be etched away, where for positive photoresist all sections not enclosed by the mask are removed, and for negative photoresist all sections enclosed by the mask are removed. This is illustrated in Figure 3. The choice of what type of mask, light-field or dark-field, and photo-resist combination to employ is ultimately left to the microsystem designers and the particular process material and steps they will employ [36-40].

2.3 Limitations One of the main challenges in the microfabrication process is to control in a quantifiable manner the end support boundaries. These boundaries are the intersections of the crystalline planes of silicon, for example, the 111 and 100 planes. Each set of these planes is inclined at an angle of 54.74 degrees with respect to the surface [41,42]. Unfortunately, with the currently available microfabrication technology (etching processes), it is not possible to fully control these parameters, hence, an (unwanted) undercutting of the structure occurs [35]. When attempting to microfabricate suspended microstructures, such as cantilevers or plates, where symmetry and 90 degree intersections at the corners are required, deformations occur due to the undercutting effect resulting from (slightly) preferential etch directions. This is due to the


greater available number of dangling bonds (free electrons for bonding with the etchant and hence removal from the structure). This effect is shown in Figure 4. Figure 5 illustrates the under-etching phenomenon for suspended structures [44].

UV light

Non-contact mask

Photoresist layer

Oxide layer

Silicon wafer

Positive photoresist

Negative photoresist

(b) (c)

(a)

Figure 3: (a) A generalized overview of the photolithography process. (b) Etch profile for positive photoresist. (c) Etch profile for negative photoresist.


Cantilever support

Cutout

(a) (b)

Figure 4: Scanning-electron-microscope (SEM) images of the effects of non-uniform etching at corners. (a) Image of a microcantilever with a cutout (vent hole). The rounded corners at the boundary support and cutout are visible. (b) A close-up image of the rounded corner at the boundary

support.

Pyrex layer

Limit of undercut

Pyrex etch

SOI Silicon layer

Microcantilevers

Figure 5: A schematic overview of the MicraGeM process layers and the undercutting of the silicon structure.

These intrinsic limitations are an important consideration for the microfabrication of suspended microcantilever beams used for a variety of sensor/actuator applications such as atomic force microscope (AFM) probes [44-46] and micro-optics [47,48]. The static and dynamic mechanical behaviour of these types of devices are closely tied to the material used in the fabrication process, the geometry of the device, the environment in which they are to be employed, thermal and electrostatic influences and the microfabrication limitations resulting in non-classical support boundary conditions. In this regard, boundary conditioning is used in order to quantify the influence of non-classical support conditions and operating conditions on both static and dynamic behavior of microcantilever beams [48-52].


3. Silicon-on-Insulator Technology

MicraGeM (Micralyne Generalized MEMS) is a SOI MEMS prototyping process under development at Micralyne Inc. [33] in conjunction with the Canadian Microelectronics Corporation (CMC) [53]. It is a microsystem design and production facility that enables university researchers in Canada to develop MEMS devices based on the SOI platform. In this particular microfabrication technology the SOI wafer consists of a single-crystal-silicon (SCSi) handle and a SCSi device layer (material density ρ = 2320kgm-3, Young’s modulus of elasticity E = 129.5 x 109Pa) with a sufficiently thick, buried oxide layer separating them. The SCSi handle and buried oxide portions of the wafer are removed in a wet-etch process, leaving the single crystal silicon membrane over the cavities/gaps. A chrome-gold layer is deposited on the silicon surface and then is lithographically patterned and etched to expose the silicon using a wet etch process. Final structures are patterned with a photoresist mask and released in a plasma etch. An overview of the process is given in Figure 6.

(a)

(b)

Pyrex Wafer

Metal_1 on Pyrex

Silicon Handle

Buried Oxide Layer

Single Crystal Silicon

Metal_2 on Silicon

(c)

Figure 6: (a) Etching of pyrex and deposition of Metal_1 layer. (b) Silicon layer is anodically bonded to pyrex. (c) Patterning and release of silicon structures and deposition of Metal_2 layer.

This particular MEMS microfabrication technology is different from traditional MEMS processes by the materials used in the process, and by its variable geometry. This microfabrication process allows users to develop fully-suspended MEMS devices with metal electrodes (rather than silicon). Users of the process can select two fabrication options during each production run. This makes the MicraGeM process more versatile and flexible than other MEMS prototyping


technologies, enabling designers to develop MEMS devices with varying thickness of layers and gap sizes between layers. Silicon-on-insulator MEMS are found in many microphotonic waveguide [54-57].

3.1 Details of the MicraGeM process For each fabrication run MEMS designers are given the following process choices regarding the thickness of the silicon layer and etch depth.

i) Option A: A 10µm thick SCSi membrane over a 10µm gap.

ii) Option B: A 2µm thick, SCSi over a 2µm gap, or a 10µm thick SCSi layer over a 12µm gap.

Each design is allocated a run space of 10mm x 5mm for each option and designers receive 10 MicraGeM chips for their submitted designs. In the first step, a 525µm thick pyrex wafer is patterned with Mask_1, or Mask_2 for etch depths of 2µm or 10µm, respectively. Both masks can be applied concurrently if an etch depth of 12µm is required by the designer. Through a lift-off method using the Mask_3 step, Metal_1 (50nm titanium, 50nm platinum, 200nm gold) is applied to the etched pyrex surface. In step two, an SOI wafer consisting of a 525µm thick silicon handle, oxide layer, and SCSi is anodically bonded, SCSi side down, to the pyrex layer. Anodic bonding is an electrostatic process in which a high voltage (1000V) is applied. The applied potential induces a migration of ions across the pyrex-silicon interface and creates an irreversible chemical bond at the boundary [58-60]. The next process step completely removes the silicon handle and oxide layer leaving only 10µm thick SCSi layer on pyrex. Metal_2 consisting of a 100Å chrome and 750Å gold layer is then deposited onto the SCSi layer. Mask_4 is used to pattern the Metal_2 layer. The Metal_2 layer is used mainly for its light reflection properties for applications in micromirrors, for example. In the final process step, Mask_5 is used to pattern the structures on the SCSi as specified by the designers and a plasma etch process is used to release the final structures.

The finished wafers are then diced and packaged and sent out to the respective designers. Although not discussed in detail here, there are other design parameters such as minimum separation and sizing of structures that will require careful consideration during the design process. Shown in Figure 7 is an overview of a typical MicraGeM layout (the highlighted features are shown in Figure 8). The electrification is provided through the Metal_1 contact pads. All pyrex etch surfaces must be connected by a channel for passage of the etchant.


Limit of pyrex wafer

Figure 7: An overview of a MicraGeM chip design with SCSi structures.

Metal_1 on pyrex

Metal_1 wire and contact pads

Channel in pyrex layer for etchant

SCSi Metal_2 on silicon

Metal_2 on silicon wires

Metal_2 contact pads

(b)

(a)

Figure 8: (a) Pyrex etch layer with Metal_1; (b) SCSi layer with Metal_2 contact pads and wiring scheme.


An SEM image of several microcantilever structures fabricated employing this technology is shown in Figure 9.

Figure 9: MicraGeM SOI technology microcantilevers.

3.2 Silicon-on-insulator pressure sensors: Catholic University of Louvain

The SOI technology devices designed and fabricated at the Catholic University of Louvain (UCL) in Belgium [61] incorporate innovative design architectures. They consist of single devices and circuits implanted directly on a 1.5µm thick multilayered membrane as illustrated in Figure 10 [62,63]. The membrane is made of a weakly stressed quadruple stack consisting of the following:

i) A 400nm buried oxide of the SOI substrate. ii) A 300nm LPCVD silicon nitride layer which brings the main part of the

membrane mechanical robustness. iii) A 250nm densified PECVD oxide (LOCal oxidation of silicon (LOCOS))

film of interconnection. iv) A 500nm thick APCVD oxide layer for the passivation of the electronics.

The passivation layer is particularly useful to protect the devices during the tetramethylammonium hydroxide (TMAH) release, and against the operational environment. The membrane structure has to fulfill two main requirements [62]:

i) The micromachining technique used for the release of the membrane must be compatible with the standard SOI CMOS process [64,65].

ii) The membrane has to be strong, flat, and ripple free in order to have a highly sensitive system.


Figure 10: Schematic illustration of the cross-section of the multilayered membrane.

The main advantages of this approach are the inherent co-integration process capability allowing fabrication of sensors and their associated electronics on the same die [62,63], the low power consumption (MEMS characteristic) and high temperature abilities of SOI technology. In this regard, there are published reports of employing SOI technology for temperature applications >200°C [64-66].

3.3 Sensor packaging A standard SOI complemetary metal-oxide semiconductor (CMOS) process [67,68] supplemented by two main steps was used for all the UCL pressure sensors shown below. The first supplemental step is a nitride-layer deposition and patterning for the membrane formation, while the second step is constituted by a TMAH back-etching to expose the underside of the membrane. Edgeless transistors are placed at the center of a 250 x 250μm2 membrane as shown in Figures 11 and 12.


membrane

edgeless transistor

membrane

Figure 11: Top: overview of the SOI based pressure membrane and electrical connections. Bottom: Close

up view of the center mounted edgeless-transistor on the membrane.

Figure 12: Details of the edgeless, center-mounted transistor.

Membrane

Drain

Gate

Source


The transistors received from UCL are in a loose-die format. Hence, they will be mounted onto a 24-pin dual-inline-package (DIP) as seen in Figure 13a. In order to create a differential pressure environment a hole is drilled into the package in order to allow exposure of the backside of the membrane to the local (reference) pressure environment as shown in Figure 13a. This step is necessary due to the over-damping effect created within the cavity due to air being trapped between the backside of the membrane and the base of the DIP after bonding. Without this step the motion of the membrane is greatly restricted and no pressure changes may be detected. The wire bonding of electrical connections were carried out in-house as shown in Figure 13b.

3.4 Sensor operation The effect of the applied pressure induces stress/strain across the SOI membrane. For center mounted devices the strain is maximal, while for edge mounted devices the stress is maximum at that location. In this regard, the deflection of the membrane causes changes to the drain geometry (defined as: width-over-length) as a function of its orientation (parallel or perpendicular) to the stress gradient as illustrated in Figure 14 [62,63]. The transistor drain current (ID) variation is related to the pressure induced stress applied on the membrane by the relationship:

( )⊥⊥+=Δ− σπσπ ////DD II , where π// and π⊥ are the piezoresistive coefficients of the material, σ// and σ⊥ are the applied stresses parallel and perpendicular, respectively, to the drain geometry [62]. Hence, static and dynamic pressures can be measured directly as a function of a change in the drain current ID. Dynamic pressures can be applied with a rotor, such as a DC fan, for example. Other membrane/transistor configurations that will be tested consist of center mounted and edge mounted transistors as shown in Figure 15. In these devices the drain channels are oriented either parallel or perpendicular to the surface stress (as shown in Figure 14). The only differences between various transistors, other than the drain channel orientation, are the dimensions of the drain channel themselves.


(a)

(b)

24 pin ceramic DIP

hole

Figure 13: (a) 24-pin ceramic package. The hole is required to create a differential pressure environment.

(b) Wire bonded devices. Left: Edge mounted. Right: Center mounted.


membrane

Drain channels

Figure 14: Edge mounted transistors on the SOI membrane. The drains are shown in either a parallel (//)

or perpendicular (⊥) configuration with respect to the applied stress (σ).

membrane membrane

Figure 15: Left: Center mounted devices. Right: Edge mounted devices.


3.5 Transistor characterization and experimental setup The packaged transistors may be characterized using a standard Faraday box as shown in Figure 16 and semiconductor parameter analyzer shown in Figure 17. In this regard, threshold voltages can be obtained for the various devices prior to testing them in the tube furnace shown in Figure 18. For the high-temperature testing, the package device will be placed into the furnace and wires run from the device to the Faraday box or oscilloscope, as the case may be. An infrared heating lamp may also be used. An overview of the experimental setup is shown in Figure 19.

packaged device source, gate and drain

Figure 16: Standard Faraday box used for transistor characterization.


Figure 17: Semiconductor parameter analyzer used the characterization of the transistors.

Figure 18: Tube furnace to be used for thermal environment experiments of the SOI devices.


1

2 4

3 5

6

1. Parameter analyzer 2. Faraday box 3. Signal generator 4. Power supply 5. Oscilloscope 6. Frequency analyzer

3

Figure 19: An overview of the test equipment used for the thermo-baric measurements.

3.5.1 Experimental results The experimentation carried out consisted of first determining standard drain-current (ID) and drain-voltage (VD), (ID-VD), and ID gate-voltage (VG), (ID-VG) characteristics for each transistor. A sample is shown in Figure 20 for the center mounted transistor shown in Figures 11 and 12. These tests serve the dual purpose of making sure that the particular transistor is functioning properly, and to establish the threshold-voltage (VTh) for that particular device (from the ID-VG curve trace).


0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

1.40E-03

1.60E-03

1.80E-03

0 0.5 1 1.5 2

VD (V)

ID (A

)

VG = 2

VG = 1.5

VG = 1

VG = 0.5

0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

1.40E-03

1.60E-03

1.80E-03

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

VG (V)

ID (A

)

ID saturation domain

Figure 20: Top: Typical ID-VD curves for various gate voltages VG. Bottom: ID-VG curve plot. VTh ~0.5V.

3.5.1.1 Static pressure measurements

Static pressure measurements were carried by applying a constant air flow, using a laboratory air supply, over the SOI membrane. A VG value of 2V and a VD value of 2V were used in the experiments. In this saturation domain the transistor drain current is saturated, as seen in Figure 20, and the transistor behaves effectively as a constant current source. The current saturation is an intrinsic characteristic of the transistor. Hence, changes to the drain current, for particular values of VG-VD within the saturation domain, can be monitored more readily. The drain current ID is a function of the applied stress and quantified through an increase in the electron mobility


(related to π//, π⊥ as discussed above) across the drain as can be seen in the increase of ID as shown in Figure 21.

1.75E-04

1.76E-04

1.77E-04

1.78E-04

1.79E-04

1.80E-04

1.81E-04

1.75 1.8 1.85 1.9 1.95 2VD (V)

ID (A

)

Without air flowWith air flow

Figure 21: The drain current ID as a function of the drain voltage VD and the applied static pressure. The

increased static pressure induced an increase in the electron mobility across the drain characterized by the increase in ID.

Similarly, the effect of thermal loading alone will change the drain geometry of the transistor due to the thermal characteristics of silicon [69] and thereby also affect the mobility of the electrons across the drain as shown in Figure 22.


0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

6.00E-04

7.00E-04

0 0.5 1 1.5

VD (V)

ID (A

)

2

VG = 2V

25 oC

60 oC

Figure 22: Transistor ID-VD characteristics as a function of the applied thermal load for VG = 2V and VD = 2V.

3.5.1.2 Dynamic pressure measurements

Dynamic pressure was created using a laboratory wall mounted air supply and air tube (pressure was adjustable) with an electrically operated switch that was toggled between open/close conditions. Pressure variations were obtained as a function of air flowing over the exposed membrane. In this regard, the signal conditioning required that the varying drain current (pressure) be monitored using an oscilloscope. In order to employ this method the drain current was converted to a voltage by inserting an equivalent resistance REq into the circuit, and then measuring the change in voltage across REq with the oscilloscope. This is explained here:

i) The I -V characteristics of the device are traced for several values of V as

illustrated in Figure 23. D D G

ii) Define the saturation domain where the drain current remains steady (saturated). In this area, the effect of pressure is easily seen.

iii) A biasing point is chosen within the saturation domain. In this example, VG at bias is 2V, VD at bias is 1.5V and ID at bias is 690μA


iv) At the biasing point, the equivalent resistance of the device is obtained from: REq = VD/ID (at bias). Hence, in this example REq = 2.174kΩ.

v) The final circuit is basically a voltage divider as shown in Figure 24.

vi) As the circuit divides the voltage ~equally between the transistor and REq, in order to have 1.5V at the drain and 1.5V across REq it is necessary to have a source voltage VS = 3V (VS = 2VD) as shown in Figure 25.

Saturation domain

VG = 2V

VD = 1.5V

ID = 690μA

Figure 23: ID-VD curve traces required to obtain the equivalent resistance of the transistor.

VS

VG = 2V

REq

VD = 1.5V

3V

2.174kΩ

ID = 690µA

= 2VD

Figure 24: A voltage divider circuit with an equivalent resistance REq inserted into the circuit.


As mentioned above, the voltage across REq is monitored, with an oscilloscope, as a function of the varying (dynamic) pressure as shown in Figure 26.

VS

VG = 2V

REq

VD = 1.5V

3V

2.174kΩ

ID = 690µA

= 2VD

Oscilloscope -0.0006

-0.0004

-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0.00 0.05 0.10 0.15 0.20Time (s)

Ampli

tude (

AU)

Figure 25: The voltage across an equivalent resistance REq is monitored with an oscilloscope. The voltage

is a function of the varying drain current ID due to dynamic pressure conditions.

-0.0006

-0.0004

-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0.00 0.05 0.10 0.15 0.20Time (s)

Ampli

tude (

AU)

Figure 26: Time domain output observed on an oscilloscope of the dynamic pressure generated using a

pneumatic switch attached to an air hose.


4. Case Study: MEMS Microcantilever Sensor

A method to characterize the dynamic response of microcantilever sensors as a function of added mass and surface stress influences is presented. Stress effects are, generally, of much smaller magnitude than mass influences, hence it would be of value to eliminate the mass influence, and to operate the sensor in a purely stress-domain. In this regard, the analytical and experimental data can provide information into the performance optimization of microelectromechanical sensors through the frequency responses obtained for a given sensing domain (mass or stress influenced). This has important implications for bio-medical and health monitoring applications in which changes to the applied mass or surface stress on a microcantilever, due to the interaction between the sensor reactant material and the target material, may be readily observed through changes to the frequency response of the microcantilever.

Silicon microcantilevers can be easily shaped and sensitized to a variety of influences. They are resistant to low level vibrations due their small mass and the elasto-mechanical properties of the silicon material. These particular qualities are highly regarded and sought after for sensor applications. The work presented herein, will contribute to the optimization of microcantilever sensors’ dynamic response as a function of mass and surface stress influences on the microcantilever. This will enable one to determine the most suitable sensing method for a given application. Such influences as reactant evaporation will cause a reduction of the reactant mass and hence, an unwanted change in the natural frequency of the microcantilever sensor. In order to avoid this effect, the nodal point of the 2nd natural frequency can be used for stress sensing. If a change in the reactant mass is desirable, for a given application, then the sensor can be made to function in a purely mass domain. The main criterion, for choosing one or the other, is based on the time for the surface reaction to take place between the sensing material and the target material. The work presented herein will contribute to the performance optimization of microcantilever based medical and bio-sensors.

The main objective of this case study is to demonstrate the simplicity and versatility of MEMS based microcantilever sensors, and to investigate the influence of added mass and stress effects on the frequency response of the sensors in order to determine the most suitable sensing domain for a given application. In this regard, the frequency response of microcantilevers depends not only on the applied mass and surface stress, but also on the position of the load. A graphical plot of the 2nd and 3rd natural frequencies of microcantilevers demonstrate variable frequencies in which they rise and fall as a function of the load position on the microcantilever. An interpretation of the analytical frequency results of the 1st, 2nd and 3rd natural frequencies, for the effects of added mass, identifies nodal points for the 2nd and 3rd natural frequencies that demonstrate mass invariance. Hence, at these nodal points, the frequency response remains constant regardless of mass and may be used for identifying purely induced surface stress influences on the microcantilever’s dynamic response. The Rayleigh-Ritz energy method is used for the theoretical analysis.


4.1 Microcantilever sensors Generally, microcantilevers are very similar in design to macro-scale diving boards. Figure 27 illustrates and compares the macro-scale diving-board with a micro-scale cantilever sensor. The static and dynamic transverse deflections are a function of the applied loads, the material’s mechanical properties and the geometry of the microcantilever [70]. For sensor applications, the position and distribution of the applied load will influence the response of the microcantilever. These are important considerations particularly where optimized sensitivity is required. Figure 27b shows the static deflection, under an applied load, of a microcantilever sensor. The deflection is measured optically using a laser and position-sensitive-detector (PSD).

(a)

(b)

Figure 27: (a) Macro-scale diving board. (b) Microcantilever sensor.

From a design point of view, microcantilevers are the most humble and uncomplicated microstructures and are generally fabricated using silicon based materials. This is due to the fact that silicon has some interesting mechanical properties that can easily be exploited. Firstly, silicon displays high strength, a high resistance to stress cycling, and high purity with a low defect density. These properties ensure that silicon-based micro-devices have uniform and stable characteristics, resulting in a long service life and high reliability [3,71]. Also, the crystalline orientation of the atomic structure of silicon allows it to be shaped to a high degree of precision, and it has electro-thermal characteristics that enable the implementation of actuation mechanisms where the amount of deflection can be controlled in a quantifiable manner either electrically or


thermally, or with a combination of both [72]. Figure 28 provides examples of microcantilevers of various geometries.

(a) (b)

Figure 28: Microscope images of (a) MUMPS technology microcantilevers. (b) MicraGeM technology microcantilevers.

In this work, an analytical and experimental investigation into the effects of mass and surface stress on the dynamic response of microcantilevers is presented.

4.2 Microcantilever applications Microcantilevers are found in a variety of applications ranging from micro-biological analysis to integrated micro-optical systems [48,73-78]. For microcantilever sensor applications, changes in the operational environment can be quantified through changes in static or dynamic deflections (e.g. modal response) of the microcantilever [2,3,79]. A great deal of research has been devoted to developing micro-biosensors that could provide real-time results [80]. Microcantilevers have been termed as ideal structures for analyzing and sensing bio-reactions at the micro-level [81]. By applying a load onto the microcantilever, a change in its resonance frequency and surface stress can be monitored. In this regard, bio-molecular interactions between target (what is to be detected) and probe (reactant on cantilever) materials, produces a beam deflection that can be easily detected optically as illustrated in Figure 27b. Additionally, microcantilevers have been identified to be important in AFM probes. Atomic force microscopes are used to view the surface topography of materials in the micrometer to the sub-nanometer scale. The high-resolution imaging made possible by AFM is particularly useful in applications such as sub-angstrom surface roughness measurements and DNA profiling [82]. Figure 29 shows a scanning-electron microscope (SEM) image of three AFM cantilevers [32].


Micro-electro-mechanical-systems, have in general, been manufactured using methods initially developed for the integrated circuits and semiconductor industry using silicon and employing batch fabrication techniques [9,10,83]. MEMS based sensors, such as microcantilevers can be placed within a very small area at relatively low cost.

Figure 29: Atomic force microscope probes.

4.3 Microfabrication limitations at the boundary support The mechanical behaviour of microcantilevers must also take into account the influences of microfabrication limitations at the support. In general, the corner support at the boundary is not a perfect right-angle due to the intrinsic shortcomings of MEMS manufacturing processes resulting in non-classical support boundary conditions [11,52,84]. Figure 30 represents a schematic of a microcantilever with artificial boundary support springs used to model the non-classical boundary support conditions due to microfabrication limitations. In this schematic, L is the length of the microcantilever, h is the thickness, Λ is the position along the length of the microcantilever, KT and KR the translational and rotational spring constants, respectively, at the boundary support.

In this work, the boundary support condition of the microcantilever used in the experiments (length, thickness and width were measured under microscope, Young’s modulus and density are manufacturers values) was estimated by measuring the natural frequency of the unloaded microcantilever, and then tuning, through the rotational stiffness (KT = ∞ as there is no translational motion), the analytical results to match those obtained experimentally [51,72]. In this way, a rotational stiffness KR per unit length value of 120 N/rad was obtained for the microcantilever sensor employed in this work.


Microcantilever

KT

KR

L Λ

h

Figure 30: Schematic representation of a microcantilever with artificial boundary support springs.

4.4 Lumped mass model formulation In the analytical model development, the microcantilever is represented by a lumped mass model, as shown in Figure 31, where K represents the natural stiffness of the elastic system, M its mass, Mapp the applied mass and y is the absolute displacement. In this formulation, damping effects are neglected, and the resulting equation of motion of the system is given by,

( ) 0=++ KyyMM app && (1)

K

y M

Mapp

Figure 31: Lumped parameter model of an elastic system.


4.4.1 Rayleigh-Ritz energy method This analytical approach is an energy based method in which the dynamic properties, eigenvalues and mode shapes, are estimated and are a function of the potential, U, and kinetic, T, energies of the system. In general, the Rayleigh-Ritz energy approach is a simple way to analyze the flexural response of a variety of microstructures such as plates and cantilever beams [85-87]. The assumed deflections, y(x), at position x (x is a non-dimensional quantity equal to L/Λ and varies from 0 to 1) along the length of the cantilever beam are given by,

)()(1

xxy i

n

iiφα∑

=

= (2)

where αi, are the deflection coefficients of the beam, and )(xiφ , are the set of orthogonal polynomials [85] satisfying the geometric boundary conditions, and n are the total number of these polynomials. In order to incorporate the influence of microfabrication limitations at the support boundary of the microcantilever, the first or parent polynomial )(0 xφ of the set is constructed so as to satisfy the geometric boundary conditions for a microcantilever with free-free support boundary conditions defined by,

0)0(' =X , , ,0)0('' =X 0)0(''' =X 0)1(' =X , 0)1('' =X , 0)1(''' =X (3) where represent the slope, moment and shear at the ends x = 0,1 of the microcantilever, respectively. Hence, the deflection shape function is given by,

''','',' XXX

5

54

43

32

210)( xaxaxaxaxaaxX +++++= (3a) where a0, a1, a2, a3, a4 and a5 are arbitrary constants. By applying the boundary conditions given in Equation (3), the deflection shape function (for rigid-body motion) reduces to,

0)( axX = (3b) and the parent polynomial of the set is obtained,

2/11

0

2

0

)(

)()(

⎟⎟⎠

⎞⎜⎜⎝

⎛=

∫ dxxX

xXxφ (3c)

For the case of free-free boundary conditions, the first member of the set of orthogonal polynomials has the value 1. Subsequent members of the set are generated using the Gram-Schmidt orthogonalization process [88]. For the analytical work presented herein, 6th order polynomials were employed.


The natural frequencies of the system can be obtained from the Rayleigh quotient defined as,

*2

TU

energykineticMaximumenergypotentialMaximum

==ω (4)

where,

2*ωTT = (4a)

obtained from,

222

22

21

21

21 yAL

syMMvT ωρ=== (4b)

where v is the velocity, ω is the natural frequency in radians-per-second, ρ is the material density and A is the cross-sectional area of the microcantilever.

4.4.1.1 Dynamic Analysis In the static and dynamic regimes, several contributing factors will determine the deflections y(x) and natural frequencies ω of the microcantilever, consisting principally of mechanical and material properties. In this work only the dynamic properties will be investigated. The mechanical properties include boundary support conditions for a suspended structure such as a microcantilever and its geometry, whereas the material properties include Young’s modulus of elasticity and the density of silicon. In addition to these intrinsic properties, it is possible to influence the elastic qualities of the microcantilever through the addition of mass, electrostatic, thermal or surface stress influences. Herein the analysis involves the addition of mass and surface stress influences on a microcantilever structure, from which changes to the natural frequencies are investigated. The maximum potential energy U of the system is calculated employing a two step iterative process and includes the beam energy UB, boundary support spring energy UB SS and surface stress energy UStr, and is given by,

U = UB + USS + UStr (5)

In the theoretical formulation, the surface stress energy UStr is calculated as a function of the applied mass’ influence on the flexural properties of the microcantilever (iteration step one). Therefore, the stress energy associated with the kth flexural mode of a vibrating microcantilever with added mass is given by [89],

dxxYxYLwh

kU k

x

xk

dStr )()(")(

2

1

∫=σ

(6)


where σd is the surface stress, w is the width of the microcantilever, x1 and x2 are the integration limits for the distributed stress, Yk(x) is the kth (k ≤ i) mode given by,

k

n

iiik xxY ⎟

⎠

⎞⎜⎝

⎛= ∑

=1)()( φα (6a)

and where Yk′′(x) is the second derivative with respect to x. The total potential energy U is recalculated with the value obtained for the stress energy UStr (iteration step two) and is given by, U* = UB + USS (7)

where U* includes the contribution of UStr for a given added mass and for a particular flexural mode. The same approach may be applied for the surface stress energy associated with higher modes. With respect to Equation (7) the following definitions apply,

( )∫=1

0

23

3

)("24

dxxyLwEhU B (8a)

where E is Young’s modulus of elasticity and 0 and 1 represent the fixed and free ends (non-dimensionalized) of the microcantilever, respectively. The potential energy associated with the boundary support springs is given by,

22

2 ))0('(21))0((

21 y

LK

yKU RTSS += (8b)

Similarly, the maximum kinetic energy of the microcantilever system includes the microcantilever beam kinetic energy TB and the kinetic energy due to the added mass TB M, and is given by,

T = TB + TB M (9) With respect to Equation (9) the following definitions apply,

( )∫=1

0

22 )(21 dxxyALTB ρω (10a)

The kinetic energy associated with the added mass is given by,

( )∫=2

1

22 )(21 x

xM dxxymT ω (10b)

where m is the added mass. Minimizing the Rayleigh quotient of Equation (4) with respect to all the deflection coefficients,


[ ] 0* 2 =−∂∂ TU

i

ωα

(11)

yields the following eigensystem,

[ ]∑=

=+−+n

jjijMijBiijSSijB TTUU

1

0)( αλ (12)

ni ...1=∀

With respect to Equation (12) the following definitions apply,

∫=1

0

"" )()( dxxxU jiijB φφ (13a)

)0()0(*)0()0(* ''

jiRjiTijSS KKU φφφφ += (13b)

33

3 12*,12*Eh

LKKEh

LKK RR

TT == (13c)

∫=1

0

)()( dxxxT jiijB φφ (13d)

∫=2

1

)()(x

xjiijM dxxxT φφ (13e)

Solution of Equation (12) yields the eigenvalues, λk, and modes shapes Yk of the microcantilever where k = 1, 2…l ≤ n. The kth eigenvalue is given by,

3

322 )(12

EwhLmALk

k+

=ρωλ (14)

from which the kth natural frequency πω2

kkf = is obtained in Hertz (Hz). The first three

eigenvalues for a microcantilever without added mass (m = 0), obtained using this approach are: 3,2,1=kλ = 1.875, 4.693, 7.85, which are in good agreement with published values such as

found in Theory of Vibrations with Applications [90].


4.4.1.2 Analytical results In this section, the theoretical results of the variation of the normalized 1st, 2nd and 3rd natural frequencies of a microcantilever are presented where a test mass was placed at various locations along the normalized length of the microcantilever. Several different test masses are used in order to extract and show the nodal points for the 2nd and 3rd natural frequencies. The analytical normalized natural frequencies obtained are shown in Figure 32 and Figure 33. A direct comparison of the variation of the first three natural frequencies, for a given sample mass, as a function of its placement along the normalized microcantilever length is shown in Figure 34.


(a)

(b)

(c)

0.5

0.6

0.7

0.8

0.9

1

1.1

0 0.2 0.4 0.6 0.8 1Normalized Length

Norm

alize

d 3rd

Natur

al Fr

eque

ncy

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1


Norm

alize

d 2nd

Natu

ral F

reque

ncy

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1


Norm

alize

d 1st

Natur

al Fr

eque

ncy

Increasing mass

Increasing mass

Node

Increasing mass

Node Node

Position of Added Mass



Figure 32: Analytical results for the effect of added mass and added mass position along the normalized length of a microcantilever on the (a) 1st natural frequency. (b) 2nd natural frequency. (c) 3rd

natural frequency.


(a)

(b)

(c)

Figure 33: 3D analytical results for the effect of mass and mass position along the length of a microcantilever on the (a) 1st natural frequency. (b) 2nd natural frequency. (c) 3rd natural

frequency.


0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 0.2 0.4 0.6 0.8 1Position of Added Mass

Norm

alize

d Natu

ral F

reque

ncy

1st Natural Frequency2nd Natural Frequency3rd Natural Frequency

Figure 34: A comparison of the changes to the 1st, 2nd and 3rd natural frequencies of a microcantilever as a

function of the position of the added test-mass along the normalized length of the microcantilever.

From Figures 32a, 33a and 34 it can be seen that for the 1st natural frequency there is only a reduction in the microcantilever resonance frequency as the added mass is moved away from the fixed end of the microcantilever, whereas contrarily, for the 2nd and 3rd natural frequency curves there exist nodal points at which the natural frequency returns to the value of the microcantilever without the added mass. Hence, if the sensing mechanism is to be based on a change in mass, the reactant should not be placed at the nodal points of the 2nd and higher natural frequencies. The 1st flexural mode is the one in which a change in reactant mass is detected quite readily. However, consideration must be given to evaporation effects in which the reactant mass is reduced due to evaporation to the surrounding environment. This is an important issue because the reduced mass due to evaporation will change the reference or base-line natural frequency of the sensor. If, for example, a target material is introduced into the sensing environment, the presence of the target material will be detected by a change in the natural frequency of the sensor due to the interaction between the target and probe materials. However, evaporation of the sensor’s reactant material will offset the base-line output reading of the sensor, and consequently the target material may not be detected. Hence, it becomes critical to distinguish between evaporation and reaction effects. At the nodal points of the 2nd and higher natural frequencies, evaporation or mass effects can be neglected (as long as there is sufficient material to produce a reaction) and the sensor output may be characterized solely as a function of the stress induced by the chemical-reaction of the sensor reactant in the presence of some target material.


4.5 Experimental section In order to measure dynamic surface deflections (single point sampling) of microcantilevers, an optical laser-Doppler-velocimetry (LDV) based non-contact method was used for the testing [72]. This method allows one to integrate and quantify the effect(s) of electrostatic, thermal, and geometrical influences, for example, on the dynamic properties of microstructures, in general, in a minimally intrusive way. The experimental set-up used for the testing of various microcantilevers is shown in Figure 35. A schematic of the surface velocity detection mechanism is shown in Figure 37.

(b)

Microscope

XYZ platform and support post

Mirror

(a)

Laser

Diverging lens

Converging lens

Figure 35: Experimental set-up and equipment. (a) Helium-Neon (HeNe) laser with diverging-converging

lens train. (b) MEMS support post.

The microcantilevers used in this work were fabricated using a polyvinylidenefluoride (PVDF) metalized film [91]. The metal coating provides very good reflective properties that are required for the data acquisition module of the LDV system. The measured length L, width w and thickness h of the microcantilever are 9mm, 900μm and 110μm, respectively. The PVDF material has a density and Young’s modulus of 1760kgm-3 and 2GPa, respectively. They were mounted between two microscope slides that were glued together as illustrated in Figure 36. The rigidity of the boundary support was then determined as described in Section 4.2 above.


Microscope slide

Microcantilevers

Figure 36: Schematic top view of the microcantilever array configuration used in this work. The

microcantilevers are sandwiched between two microscope slides.

HeNe laser

Cantilever deflection at resonance

Signal processing

Figure 37: HeNe laser LDV based surface velocity detection mechanism and signal processing.

4.5.1 Effect of added mass

The test results presented herein were obtained by measuring the dynamic response of a microcantilever with a small added mass (5 x 10-6kg) placed at positions x = 0.3, x = 0.6 and x = 0.75, respectively, of the normalized length of the microcantilever. For all the experimentation, a piezoelectric-shaker was employed for the swept sinusoidal base excitation [92]. The 1st, 2nd and 3rd experimental natural frequencies were thus obtained and are shown in Figures 38-40. The center frequency (of the response bandwidth) obtained for each case is plotted and compared to the theoretical values as illustrated in Figures 41-43 and given in Table 1.


0

0.2

0.4

0.6

0.8

1

50 70 90 110 130 150 170 190 210 230 250 270 290Frequency (Hz)

Norm

alize

d Amp

litude

Microcantilever with no added mass

Added mass at x = 0.3



Figure 38: The variation of the 1st natural frequency as a function of the position of the added mass.

0

0.2

0.4

0.6

0.8

1

500 700 900 1100 1300 1500 1700 1900Frequency (Hz)

Norm

alize

d Amp

litude





Figure 39: The variation of the 2nd natural frequency as a function of the position of the added mass.


0

0.2

0.4

0.6

0.8

1

2000 2500 3000 3500 4000 4500 5000Frequency (Hz)

Norm

alize

d Amp

litude





Figure 40: The variation of the 3rd natural frequency as a function of the position of the added mass.

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8Normalized Length

1st Natu

ral F

reque

ncy (

Hz)

1

TheoryExperiment


Figure 41: A comparison of the experimental center frequency responses as a function of the position of the added 5 x 10-6kg mass on the normalized microcantilever length and the theoretical curve for

the 1st natural frequency.


600

800

1000

1200

1400

1600


2nd N

atural

Freq

uenc

y (Hz

)

TheoryExperiment


Figure 42: A comparison of the experimental center frequency responses as a function of the position of the

added 5 x 10-6kg mass on the normalized microcantilever length and the theoretical curve for the 2nd natural frequency.

Figure 43: A comparison of the experimental center frequency responses as a function of the position of the

added 5 x 10-6kg mass on the normalized microcantilever length and the theoretical curve for the 3rd natural frequency.

2200

2700

3200

3700

4200

4700


3rd N

atural

Freq

uenc

y (Hz

)

TheoryExperimental



Table 1: Variation of the natural frequency (center frequency values) for the first three resonance modes as a function of the load position on the microcantilever (NL = no load).

Position of load Resonance mode

(NL) x1 (0.3) x2 (0.6) x3 (0.75)

Mode 1 (Hz) 252 220 128 90 Mode 2 (Hz) 1555 700 1080 1548 Mode 3 (Hz) 4340 2800 3708 3240

The results for the experimental center frequencies presented in Figures 41-43 above are in good agreement with the theoretical model and clearly show the trends for the variation of frequency response for each given flexural mode as a function of the 5 x 10-6kg test mass’ position on the microcantilever.

4.5.2 Water droplet evaporation

For sensor applications in which the microcantilever surface is employed and on which the sensor reactant is deposited, it is important to understand and quantify the effects of mass and surface stress individually. As an example, the evaporation of a given sensor reactant over time will reduce its mass and hence change the frequency response of the microcantilever sensor accordingly. Hence, it may not be possible to distinguish between frequency response changes due to interactions between the sensor reactant and the target material, or reactant mass reduction due to evaporation. To illustrate this point a series of time lapse microscope side images of the evaporation of a 1μL (1 x 10-6kg) de-ionized water droplet on a microcantilever surface are shown in Figure 44, and a top view of the water droplet on the microcantilever surface is shown in Figure 45. Within 15 minutes the water drop has completely evaporated (room temperature ~22°C). Shown in Figure 47 is the effect of mass reduction on a microcantilever’s 1st natural frequency as a function of the evaporation of a droplet of water on its surface. The water droplet was placed at x = 0.3. It is assumed that the contact area between the water droplet and the microcantilever surface remains constant, as shown in Figure 46, due to the surface tension between the water and microcantilever surface [93].


t = 0

Microcantilever

t = 15min

Figure 44: Time lapse (3 minutes between each) microscope side images of the evaporation of a water droplet on a microcantilever surface.

Water droplet

Figure 45: Top view of a microscope image of a water droplet on a microcantilever surface.


Constant contact area

Figure 46: Evaporation of a water drop modeled as a spheroid. The contact area remains constant between

the droplet and microcantilever surface. Arrows show the reduction in droplet height due to evaporation.

239

240

241

242

243

244

245

246

247

248

-2 0 2 4 6 8 10 12 14 16Time (min)

1st Natu

ral F

reque

ncy (

Hz)

Microcantilever without water droplet

Figure 47: The variation of the 1st natural frequency of a microcantilever as a function of the evaporation

of a water droplet on its surface.


From Figure 47 the evaporation effect on the 1st natural frequency can be clearly seen. The overall shift in frequency due to the evaporation is 2.83% with a 0.47Hz/min rate of change. For enzymatic reactions such as between hydrogen-peroxide (H2O2) and horse-radish-peroxidase (HRP) several hundred seconds are required for the reactants to fully engage [77]. Hence, the effects of evaporation must be considered when measuring either the static (using PSD) or dynamic (measuring resonance) characteristics of the sensor in which the presence of some target material is to be detected.

4.5.3 Surface stress

Although no experiments were carried out, the effect of surface stress is now presented (analytically) with experimental σd values previously published (enzymatic reaction stress values σd of ~50MPa have been reported [81]). The surface stress σd is varied between 10MPa and 100MPa and the surface stress energy as given in Equation (6) is calculated and normalized (UStr(i)/UStr(max)). In order to eliminate the mass influence, the nodal position at x = 0.8 for the 2nd natural frequency is exploited to quantify frequency response changes due to surface stress alone. The shift in frequency, for the 1st and 2nd natural frequencies, with the added mass alone and mass with stress effect included are calculated. A virtual 5 x 10-6kg mass (reactant and target material) is distributed between x1 and x2 (mass radius ~ 0.8mm) and centered symmetrically about x = 0.8 as shown in Figure 48.

x = 0.8

x1 x2

Figure 48: Schematic side-view of the distributed mass of a water droplet at x = 0.8 along the normalized length of a cantilever.

The results for the shift in 1st and 2nd natural frequencies due to the stress are given in Figure 49 and Figure 50, respectively.


0

1

2

3

4

5

6

7

8

0 0.2 0.4 0.6 0.8Normalized Stress Energy

1st Natu

ral F

reque

ncy S

hift (

Hz)

1

Figure 49: The shift of the 1st natural frequency as a function of the applied stress σd.

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8Normalized Stress Energy

2nd N

atural

Freq

uenc

y Shif

t (Hz

)

1

Figure 50: The shift of the 2nd natural frequency as a function of the applied stress σd.


From Figures 49-50 the shift of the 1st and 2nd natural frequencies as a function of the surface stress can be seen. For a typical 50MPa surface stress value, a shift in frequency of ~3.6Hz is obtained for the 1st natural frequency. This shift in frequency is due to the stress resulting from the reaction between the sensor reactant material and the target material on the microcantilever surface. This shift can be monitored for sensor applications. However, if the reaction time is slow (water drop evaporation after 6 min resulted in ~3Hz shift), the evaporation of the reactant and target material can cause a greater shift in frequency than the reaction itself and the target material may not be detected using the 1st natural frequency response. Hence, reaction time constraints and distinguishing between evaporation or mass effects and surface reaction events should considered before employing the 1st natural frequency response.

Conversely for the 2nd natural frequency, with the reactants placed at the nodal point x = 0.8, the effects of mass and evaporation can be eliminated and any observed changes in frequency are solely due to the surface stress resulting from bio- or chemical interactions. The nodal phenomenon for 2nd and higher natural frequencies can be used to monitor or detect target materials solely based on surface interactions between the sensor reactant material and the target material when a significant amount of time is required for the reaction to take place. Even though the mass effect can be eliminated at the 2nd and higher natural frequency nodal points as shown herein, consideration should be given to the fact that there may not be any reactant material left on the sensor after a given amount of time, and hence, no reaction can take place in the presence of the target material.

For microcantilever based sensor applications, due to the micro-scale level, it is important to establish the correct sensing mechanism, mass or stress based, for a given application. Changes to mass can be readily monitored by employing the 1st natural frequency if the reaction time is fast and evaporation is not critical. The nodal points of the 2nd natural frequency can be used to monitor surface stress effects when the reaction time is relatively long in comparison to mass effects. Therefore, two sensing domains can be defined for microcantilever sensors: the mass domain and the stress domain. The most suitable approach for a given application has to be carefully contemplated.

It is these particular qualities of microcantilevers, combined with ease of design and fabrication, which makes them very versatile when it comes to micro-sensor applications.

5. Conclusions

An investigation into MEMS-based sensors has been presented. These types of devices find many applications in which the static and dynamic behaviour can be exploited for sensor applications. Silicon-on-insulator pressure sensors were tested in both the static and dynamic regimes for possible integration into hot areas of gas turbine engines. Also, the effects of added mass and surface stress on microcantilever sensors were presented. It was shown that both mass and surface stress influences the natural frequency response of the microcantilever. Also, the effect of the added mass position on the microcantilever was presented from which the nodal points for 2nd and 3rd natural frequencies were identified. For sensor reactant material and target material stress influenced measurements, the nodal point for the 2nd natural frequency was


identified as suited for these investigations. Two sensing domains were defined for the microcantilever sensor, mass and stress related, respectively. The experimental results presented were in good agreement with the Rayleigh-Ritz energy formulation based on a lumped parameter model.


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List of symbols/abbreviations/acronyms/initialisms

a0 arbitrary constant





a5 arbitrary constant A ampère

A cross sectional area AFM atomic force microscope APCVD atmospheric-pressure-chemical-vapour-deposition AU arbitrary units CMC Canadian Microelectronics Corporation CMOS complemetary metal-oxide semiconductorD drain (transistor) DC direct-current (voltage) DIP dual-inline-package

E Young’s modulus of elasticity G gate (transistor)

h thickness HeNe helium-neon (laser) HRP horse-radish-peroxidase Hz Hertz H2O2 hydrogen-peroxide IC integrated-circuit

ID transistor drain current kg kilogram (1000 grams) kV kilo-volt (1000 volts)

kΩ. kilo-ohms (1000 ohms (unit of resistance))

K system stiffness

KR rotational spring constant


KT translational spring constant

KR* normalized rotational spring constant

KT* normalized translational spring constant

L length LDV laser-Doppler-velocimetry LOCOS LOCal oxidation of silicon LPCVD low-pressure-chemical-vapour-deposition m meter min minute mm millimeter (1/1000 of a meter)

M mass

Mapp applied mass MEMS micro-electro-mechanical-systems MicraGeM Micralyne Generalized MEMS MUMPs multi-user-MEMS-process MPa mega-Pascal (1 million Pascal) nm nano-meter (1/1000000000 of a meter) N Newton NL no load Pa Pascal PECVD plasma-enhanced-chemical-vapour-deposition PSD position-sensitive-detector rad radian

REq equivalent resistance RPM revolutions-per-minute s second S source (transistor) SCSi single-crystal-silicon SEM scanning-electron-microscope SOI silicon-on-insulator t time

T kinetic energy

T* maximum kinetic energy

TBB beam kinetic energy


TM kinetic energy of added mass TMAH tetramethylammonium hydroxide

U maximum potential energy

U* iterative maximum potential energy

UBB beam energy

UStr surface stress energy

USS boundary support spring energy UCL Catholic University of Louvain UV ultra-violet

v velocity V volt

VD transistor drain-voltage

VG transistor gate-voltage

VS transistor source-voltage

VTh transistor threshold-voltage

w width

x non-dimensional length X laser beam deflection (static)

X(x) deflection shape function

X′(0) cantilever slope at x = 0 (boundary condition)

X′′(0) cantilever moment at x = 0 (boundary condition)

X′′′(0) cantilever shear at x = 0 (boundary condition)

X′(1) cantilever slope at x = 1 (boundary condition)

X′′(1) cantilever moment at x = 1 (boundary condition)

X′′′(1) cantilever shear at x = 1 (boundary condition)

y absolute deflection

y(x) assumed cantilever deflection at position x

Yk(x) mode shapes

αi deflection coefficients

)(0 xφ parent polynomial

)(xiφ orthogonal polynomials

λk eigenvalues

Λ positional length coordinate

μA micro-ampere (1/1000000 of an ampere (unit of current))


μ micro (1/1000000)

μL micro-liter (1/1000000 of a liter)

μm micro-meter (1/1000000 of a meter)

μMasch MikroMasch

μs micro-second (1/1000000 of a second)

π// piezoresistive coefficient (parallel to the transistor drain)

π⊥ piezoresistive coefficient (perpendicular to the transistor drain)

ρ material density

σd surface stress

σ// applied stress (parallel to the transistor drain)

σ⊥ applied stress (perpendicular to the transistor drain)

ω rotational frequency ~ approximately Å Angstrom (1/10000000000 of a meter)

∀ for all

°C degrees centigrade > greater than

∞ infinity




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DOCUMENT CONTROL DATA (Security classification of title, body of abstract and indexing annotation must be entered when the overall document is classified)

1. ORIGINATOR (The name and address of the organization preparing the document. Organizations for whom the document was prepared, e.g. Centre sponsoring a contractor's report, or tasking agency, are entered in section 8.)

DRDC Atlantic 9 Grove St. Dartmouth, NS

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Unclassified

3. TITLE (The complete document title as indicated on the title page. Its classification should be indicated by the appropriate abbreviation (S, C, R or U) in parentheses after the title.) Micro-Electro-Mechanical-Systems for Sensor Applications

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April 2009

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In today’s world, microengineering is on the threshold of new technological breakthroughs inmany applications, such as microfluidics, bio-medical imaging, microscopy, andmicrophotonics. However, sensors are not being fabricated for the demands imposed by currentand future applications. In this regard, sensors need to be engineered and optimized for a givenapplication. Harsh environments, size requirements, data transfer, and sensor packaging are afew of the issues needing to be addressed. For aerospace applications, size and weightconsiderations are very important, as are the limitations imposed by the harsh operatingenvironment of a gas turbine engine. The advent of micro-electro-mechanical-systemstechnology, advanced microfabrication and modeling capabilities has brought about interest inthe development of intelligent sensor systems. Micro-sensor technologies are expected to play asignificant role in such development. Using silicon microfabrication processes, it has beensuggested that common sensors could be replaced or complemented with miniaturized, highreliability, low-cost, low-power and batch manufactured micro-sensors. A silicon-on-insulatortransducer is introduced for possible pressure sensing applications in high temperature enginecomponents and compartments. A case study is presented in which the effects of mass andsurface stress are investigated for microcantilever sensor applications. A theoretical formulationbased on the Rayleigh-Ritz energy approach is developed for the dynamic analysis of themicrocantilevers, and an optical non-contact experimental method is employed to validate thetheoretical model.

14. KEYWORDS, DESCRIPTORS or IDENTIFIERS (Technically meaningful terms or short phrases that characterize a document and could be helpful in cataloguing the document. They should be selected so that no security classification is required. Identifiers, such as equipment model designation, trade name, military project code name, geographic location may also be included. If possible keywords should be selected from a published thesaurus, e.g. Thesaurus of Engineering and Scientific Terms (TEST) and that thesaurus identified. If it is not possible to select indexing terms which are Unclassified, the classification of each should be indicated as with the title.)

Micro-sensors, microcantilevers, MEMS, silicon-on-insulator, microfabrication, mass loading, surface stress, frequency response, laser-Doppler-velocimetry, nodal points, Rayleigh-Ritz energy method


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