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  • 1. CHAPTER-1 INTRODUCTION Arrays of micro cantilevers are increasingly being used as physical, biological, and chemical sensors in various MEMS applications. In this work, the overall sensitivity of the micro cantilevers that are used in MEMS applications by increasing their deflection and frequency characteristics due to shape are changed are studied. To improve the sensitivity investigated the basic and modified design C-section micro cantilevers are studied. A micro cantilever is a device that can act as a physical, chemical or biological sensor by detecting changes in cantilever bending or vibrational frequency. It is the miniaturized counterpart of a diving board that moves up and down at a regular interval. This movement changes when a specific mass of analyte is specifically adsorbed on its surface similar to the change when a person steps onto the diving board. But microcantilevers are a million times smaller than the diving board having dimensions in microns. The ability of label-free detection, scalability to allow massive parallelization, and sensitivity of the detection range applicable to, in vivo problems are some of the important requirements for a future generation of biosensors. Although generally used in the topological investigations of surfaces such as in atomic force microscopy, arrays of micro cantilevers are attracting much interest as sensors in a wide variety of applications. Micro cantilever sensors have emerged as a universal, very powerful and highly sensitive tool to study various physical, chemical, and biological phenomena. As biosensors, they are found to display label-free, real-time and rapid assaying features. This project proposes the stoney equation first used to calculate the surface stress induced moment and then applied to the microcantilever free end to produce deflection. The stress analysis of the proposed design, We found that the stoney equation is predicting cantilever deflections, and that for increasing the sensitivity of a microcantilevers biosensors increasing the cantilever thickness is more practical. 1
  • 2. The cantilevers transduce changes in temperature, mass, or surface stress into a (nano) mechanical response. Antibody immobilization, followed by specific antigen binding or DNA hybridization, induces surface stresses in the cantilever; due to Vander Waal, electrostatic, or steric interactions. These surface stresses bend the cantilever. Bending of the cantilever can be detected optically. A piezoresistor strain gauge embedded in the cantilever experiences a change in strain due to the bending and responds with a change in resistance (electrical detection). Surface stresses produced due to DNA hybridization, antibody immobilization are small (5 N/m to 0.5 N/m). These stresses should be effectively translated to strain in the piezoresistive layer so as to cause a detectable change in resistance, i.e., for the electrical detection of surface stresses observed in bio sensing applications, composite piezoresistive cantilever structures are used as the sensing elements. In such a cantilever structure, it is necessary to understand how the variations in material type, thickness and piezo layer placement with in the cantilever stack. Micro cantilever biosensors generally use optical deflection readout technique to measure the absorption at induced deflections, and hence in assaying the unknown species present in a media. In micro cantilever biosensors, the accuracy of measurement strongly depends on the accurate determination of the surface stress induced deflections. The deflections usually range a few tens to a few hundred of a micrometer. Measuring deflections of this order requires extremely sophisticated readout arrangements. Therefore, increasing the sensitivity of a micro cantilever without increasing the complexity in the deflection detection is a major challenge. The overall sensitivity of a micro cantilever biosensor depends on the design sensitivity of the cantilever and the measurement sensitivity of the deflection measurement system. A sensitive cantilever design should efficiently convert the bimolecular stimulus into a large cantilever deflection, whereas the measurement sensitivity should ensure that the deflections measured are only induced because of the bimolecular stimulus and not due to some ambient disturbance source. The design sensitivity of the cantilever can be improved by changing the cantilever design in such a way that for a given surface stress larger deflections can occur. This scheme can be realized by reducing the bending stiffness of the cantilever or by using softer cantilever materials. To improve the measurement sensitivity, the fundamental 2
  • 3. resonant frequency of the cantilevers should be made as large as possible, because the accuracy in deflection measurement depends not only on the deflection occurred, but also on the signal-to-noise ratio. Most of the noise in the deflection signal can be attributed to flow and thermal induced excitations. To improve the signal-to-noise ratio, and hence the measurement sensitivity, the resonant frequency of the cantilever should be made as high as possible. Thus, to increase the overall cantilever sensitivity, one should select a design that exhibits both higher deflection and higher resonant frequency. To improve the design sensitivity of cantilevers various designs and schemes have been reported. Silicon micro cantilevers are commonly used in biosensors. However, due to high elastic modulus, silicon cantilevers exhibit extremely low deflections for a given surface stress change. Therefore to increase the deflections, polymer cantilevers can be used. Since the elastic modulus of polymers is generally much lower than silicon, the deflections induced are magnified many folds. Polymer cantilevers, however, have a major drawback in being very temperature sensitive, because of the thermal bimetallic effects. Thermal induced deflections exceeding the surface-stress induced deflections are not uncommon. Hence, polymer cantilevers require a fine control of the surrounding. The other way to improve design sensitivity is to increase the cantilever deflection by changing the shape of the cantilever. By reducing the moment of inertia of a cantilever its bending stiffness can be reduced, which results in higher deflection. For calculation of deflection analytically the Stoney’s equation is being used. The stoney equation is the main basis for the cantilever deflection for thin films. The deflection of cantilever main depends on the material to be used, surface stress, bending moment etc., The C-section micro cantilever is being used for the analysis of deflection. For various surface stress values the deflection is being used and the graphs are being drawn. With the objective of increasing the deflection and resonant frequency at the same time, the project investigates the deflection and stress analysis of C-Section profile micro cantilevers. The surface-stress induced deflection in the micro cantilever is modeled by an equivalent in-plane tensile force acting on the top surface of the cantilever, in the length direction. Commercial finite element method (FEM) software 3
  • 4. ANSYS Multi-physics is used in this analysis. All the cantilevers are investigated for deflection and stress by using ANSYS. 1.1 Mass Sensitive Detection by Microcantilevers A micro-cantilever is a device that can act as a physical, chemical or biological sensor by detecting changes in cantilever bending or vibrational frequency. It is the miniaturized counterpart of a diving board that moves up and down at a regular interval. This movement changes when a specific mass of analyte is specifically adsorbed on its surface similar to the change when a person steps onto the diving board. But microcantilevers are a million times smaller than the diving board having dimensions in microns and different shapes as shown in figure 1. Fig.1: Meshed cantilever showing fix and load ends. Molecules adsorbed on a microcantilever cause vibrational frequency changes and deflection of the microcantilever. Viscosity, density, and flow rate can be measured by detecting changes in the vibrational frequency. Another way of detecting molecular adsorption is by measuring deflection of the cantilever due to adsorption stress on just one side of the cantilever. Depending on the nature of chemical bonding of the molecule, the deflection may be up or down. Biochips with mechanical detection systems commonly use microcantilever bi-material (e.g. Au–Si) beams as sensing elements. The Au side is usually coated with a certain receptor. Upon the binding of the analyte (e.g. biological molecules, such as proteins or biological agents) with the receptor, the receptor surface is either tensioned or relieved. This causes the microcantilever to deflect, usually in nanometers, which can be measured using optical techniques. The deflection is proportional to the analyte concentration. The 4
  • 5. concept has been employed in screening certain diseases such as cancer and detecting specific chemical and biological warfare agents. 1.2 Microcantilever Deflection Detection Methods 1.2.1Deflection in Biosensors: Biosensors are electronic devices that convert bio molecular interactions into measurable signal. The purpose of a bio-sensor is to detect and analyses the unknown biological elements present in a medium. Biosensors have two main elements, a bio- receptor and transducer. Bio-receptors are target specific and known bio-molecules that combined with the target analytic molecules, and generate a unique signal during the reaction for sensing purpose one surface of the bio sensor is functionalized by depositing a sensing layer of known bio receptor molecules on to it. This bio-sensitive layer either contains the bio receptors or the bio receptors are covalently bonded to it. The most common types of bio-receptors used in bio-sensing are based on proteins, antibody/antigen or nucleic acid interactions. The traducer element of the biosensor converts the bio-molecular reactions between the target and bio-receptor molecules into a measurable signal. The signals can be measured using appropriate detection technics like electro chemical, optical or mechanical. In bio-sensing applications sample preparation and molecular labeling of the target analytic is a basic requirement therefore, label-free detection technique is critical in developing rapid, economic and user-friendly biosensors and bio analytical kits. Figure 2.Working principle of micro cantilever bio sensor. Functionalization of bio sensor by depositing bio receptors (left). Surface stress induces deflection (right). Symbols ◊ and Y represent target analytes and bio receptor molecules. 5
  • 6. With the ability of label-free detection and scalability to allow massive parallelization already realized by microcantilevers biosensors, the next challenge in cantilever biosensor development lies is achieving the sensitivity in detection range applicable to in vivo analysis. The sensitivity of a cantilever biosensor strongly depends on it ability to convert biochemical interaction into micromechanical motion of the cantilever. The deflections of a cantilever biosensor are usually of the order of few tens to few hundreds of a nanometer. Such extremely low deflections necessitate use of advanced instruments for accurately measuring the deflections. As a consequence, most of the applications of cantilever biosensors are done in laboratories equipped with sophisticated deflection detection and readout techniques. The authors believe that if the deflections of a cantilever biosensor be increased, its advantages will be two fold. First, if the deflections are high a less sensitive readout technique can be used to accurately measure the deflection, which will help in reducing the cost of a cantilever-based biosensor kit. Second, it will help us in detecting analytes in in vivo solution concentrations range. The concentrations of some clinically important analytes vary between 10-4 to 10-15 mol/L. The detection of analytes in such large dynamic range requires an extremely sensitive cantilever. This study proposes and analyses a new high sensitive cantilever design that can assay analytes in extremely low concentrations. Commercial finite element analysis software ANSYS is used to analyze and compare the conventional and the proposed microcantilevers designs. 1.2.2 The Piezoresistive Deflection Detection Method The piezoresistive method involves the embedding of a piezoresistive material near the top surface of the cantilever to record the stress change occurring at the surface of the cantilever. As the microcantilever deflects, it undergoes a stress change that will apply strain to the piezoresistor, thereby causing a change in resistance that can be measured by electronic means. The advantage of the piezoresistive method is that the readout system can be integrated on the chip. The disadvantage is that the deflection resolution for the piezoresistive readout system is only one nanometer compared with one Angstrom by optical detection method. Another disadvantage with the method is that a piezoresistor has to be embedded in the cantilever. The fabrication of such a cantilever with a composite structure is more complicated. 6
  • 7. The piezoresistor material in the beam must be localized as close to one surface of the cantilever as possible for maximum sensitivity. The type of doping being used for fabrication of the piezoresistive material is an important factor. The piezoresistive coefficient of N-type silicon is greater than that for P-type. The resistance of a piezoresistive material changes when strain is applied to it. The relative change in resistance as function of applied strain. The sensitivity of a piezoresistor varies proportionally to the thickness t and the radius of curvature. The Gage Factor is proportional to Young’s Modulus, E, which is the intrinsic characteristic of material. The Gage Factor can also be calculated directly by straining the cantilevers and measuring the resistance change. 1.3Bending Behavior of Cantilever Beams Uniform surface stress acting on an isotropic material increases (in the case of compressive stress) or decreases (in case of tensile stress) the surface area. If this stress is not compensated at the opposite side of a thin plate or beam, the whole structure will bend. Between the areas of compressive stress and tensile stress, there is a neutral plane which is not deformed. Due to bending, a force F is acting at a distance of x in the neutral plane results in a bending moment M=F.x. Therefore, the radius of curvature R is given by: (1) Where E is the apparent Young’s modulus and I is the moment of inertia given by the following equation for rectangular beams (2) The change in the surface stress at one side of the beam will cause static bending, and the bending moment can be calculated as: 7
  • 8. 1.4 Objective of project • To calculate the deflection, stress concentration of C- section micro cantilever beams • Calculating the deflection of microcantilevers using the stoney equation. • To analyze the deflection and stress concentration of same beam in the finite element software ansys • The mathematical and simulated values have been found and compared and errors are determined in this project 1.5 PREFACE: CHAPTER 1: This chapter deals with the introduction of the project about micro cantilevers their deflection, surface stress and the stoney equation which is used for the theoretical calculation and about ansys. CHAPTER 2: In this chapter the literature review and the data collection required for the project is being written CHAPTER 3: This chapter deals with description and derivation of the stoney equation required for the calculation of deflection and about ansys which is used for the simulation is being described in this chapter CHAPTER 4: In this chapter the results for deflection of the cantilever are being found analytically for different values of surface stress and same as in simulation CHAPTER 5: The errors have been determined and tabulated for different surface stress and graphs are being drawn between surface stress vs deflection and pressure vs deflection 8
  • 9. CHAPTER-2 LITERATURE REVIEW & DATA COLLECTION 2.1 CANTILEVERS Beams are mechanical structures deeply studied in Mechanical Engineering. One of the reasons for the study under certain approximations, e.g. small deformations, differential equations that determine their deformation are one-dimensional, what usually makes their behavior can be very simply explained and often obtain high accuracy in analytical results. In addition, when performing Finite Element Modelling (FEM) very complex structures can be simplified as consisting of many assembled beams, what increments the importance of these structures. There exists several kind of beams. Depending on the boundary conditions of both edges, the single-clamped or double-clamped beams can be found. In addition, depending on the shape of the beam and/or the cross section, infinite of types can be found. Fig 3: Cantilevers 2.2 MEMS (MICRO ELECTRO MECHANICAL SYSTEMS) Silicon is the most used material for the fabrication of microelectronic circuits. The development of microelectronics fabrication techniques has been allowing the definition of smaller devices. Since the beginning of the 80s, numerous groups have been working in the use of such fabrication techniques to define tri-dimensional structures and hence what is named Micro Electro Mechanical Systems (MEMS). The 9
  • 10. main characteristic of these systems is the presence of a mechanical part that is essential in the working principle of the system. The mechanical properties of the named part are of biggest importance inside the characteristics of the whole system. The materials used to compound the part are, for example: crystalline Silicon, polycrystalline Silicon, Silicon nitride, Silicon dioxide, aluminum, etc. But the preferred one is crystalline Silicon, due to its outstanding mechanical properties. (Electronic characteristics of Si are good, but worse than those of other semiconductors, as Gas. In most of the cases, MEMS are used as sensors where the mechanical part corresponds to the transducer element of the sensor. The fabrication of the transducer element by means of silicon processing technologies allow a reduction in size of the whole sensor and, with the reduction in size of the mechanical transducer, the sensitivity is also improved. Even more, if the transduction principle was electro- mechanical, the variations in the mechanical properties of the transducer (changes in deflection, stresses, etc.) would provide an electronic signal which could be electronically processed by some circuitry located nearby the transducer. And this was the origin of Micro Electro Mechanical Systems (MEMS). Fig.4 A simple micro cantilever Talking about MEMS, it refers to devices whose mechanical parts have dimensions ranging from 1mm to 1m, that combine both electric and mechanic components and are fabricated using integrated circuits processing technologies Inside the MEMS there are several types of sensors and they can be arranged in different ways depending on the mechanical structure of the transducer (cantilever, membrane, etc.), on the transduction principle that is being used on the circuitry to process the signal. 10
  • 11. A particular type of beam is the cantilever beam. A cantilever is a beam anchored at one end and other projecting into space. It is a well known mechanical structure that has been widely used in constructions during the last two centuries, mainly for bridges and balconies. In addition, they have also been used as mechanical transducers in some sensors, e.g. with strain gauges for force or thermal gradient measurements, as fundamental part of some devices like phonograph, etc. 2.3 MICRO CANTILEVERS IN MEMS On the other hand, the development of microelectronics fabrication techniques has been allowing the definition of smaller devices. In addition to transistors, diodes and other circuit elements, since the beginning of the 80s, numerous groups have been working in the use of such fabrication techniques to accomplish what is named Micro Electro Mechanical Systems (MEMS), what implies the fabrication of micrometric mechanical structures. Examples of MEMS devices are accelerometers (used for example in airbag control systems), pressure sensors, biochemical sensors (used for medical applications, environment analysis, etc.), etc. The mechanical part of these MEMS devices can be made of any materials that are used in microelectronics fabrication, e.g. aluminum, silicon dioxide, silicon nitride, polycrystalline silicon and crystalline silicon. The latter is the most used because it is a crystalline material, hence its mechanical properties are well determined, and also because of it outstanding mechanical properties. This fact is one of the main advantages of silicon-based MEMS. In addition, as it has been advanced, when decreasing dimensions, sensitivity increases (this happens not only in cantilevers but in almost every mechanical device). Hence, if dimensions are reduced until the micrometer range, a much deformations in cantilever profile (static mode) can be produced by acceleration, mechanical surface stress and punctual forces, while changes in resonant frequency can be produced by mass addition and punctual forces. All these physical magnitudes are what directly affect the cantilever, but they can be originated by several different phenomena, that will be commented below. In addition, transducer sensitivity is greater with decrease in their dimensions. Hence, the smaller the cantilever, the more sensitive it is (to any of the possible applied loads commented before). 11
  • 12. Fig 5: Schematic diagram of a typical dynamic-mode operation. A functionalized cantilever is oscillating at its resonant frequency (a). When biomolecules bind to the surface, mass of the cantilever increases, causing the resonant frequency to decrease (b). On the other hand, the development of microelectronics fabrication techniques has been allowing the definition of smaller devices. In addition to transistors, diodes and other circuit elements, since the beginning of the 80s, numerous groups have been working in the use of such fabrication techniques to accomplish what is named Micro Electro Mechanical Systems (MEMS), what implies the fabrication of micrometric mechanical structures. Examples of MEMS devices are accelerometers (used for example in airbag control systems), pressure sensors, biochemical sensors (used for medical applications, environment analysis, etc.), etc. The mechanical part of these MEMS devices can be made of any of the materials that are used in microelectronics fabrication, e.g. aluminum, silicon dioxide, silicon nitride, polycrystalline silicon and crystalline silicon. The latter is the most used because it is a crystalline material, hence its mechanical properties are well determined, and also because of its outstanding mechanical properties. This fact is one of the main advantages of silicon-based MEMS. In addition, as it has been advanced, when decreasing dimensions, sensitivity increases (this happens not only in cantilevers but in almost every mechanical device). Hence, if dimensions are reduced until the micrometer range, a much bigger sensitivity is achieved compared to that of macro devices. Cantilevers are one of the most used mechanical structures in MEMS. One of the main reasons is that, their shape can easily defined and they can be fabricated on a wide variety of materials by using different fabrication processes. In addition, micron 12
  • 13. and sub-micron cantilevers, phenomena originating beam deflection or changes in resonant frequencies can be determined. • Surface stress: temperature changes, DNA hybridization, Prostate Specific Antigen (PSA) concentration, etc. • Mass change: particles flux, PSA detection, etc. • Force at the apex: properties of bimolecular, DNA strand separation, Vander Waals forces, etc. The detection of this plethora of magnitudes is often allowed because of the use of smart and specialized fabrication and post-processing of the cantilevers. For example, to measure temperature differences, a composite cantilever (fabricated using at least two materials) has to be used. Cantilever coated with different polymers has been proved satisfactory in order to detect different odorants, or in order to detect pH changes. On the other hand, a careful choice of the beam dimensions has to be made in order to fabricate devices with the required resolution and sensitivity for each individual application. 2.4 APPLICATIONS OF MICRO-CANTILEVERS BIOSENSORS However, it is as biosensing tools that micro and sub-micro cantilevers have been undergoing the furthest development in recent years and where they have been proved to be one of the best alternatives. As pointed out, a biosensor should allow specific and quantitative detection of analytics, label-free detection of the biological interaction, massive parallelization by the scalability of the sensors and high-enough sensitivity for in vivo applications. Three types of instruments are being developed to meet those requirements (Surface Plasmon Resonance, Quartz Crystal Microbalances and cantilever-based sensors) and the latter is thought to be the one which fits better in of them. First, size of mechanical part allows high sensitivity, short response times (high resonant frequencies), access to small volume samples and parallel integration. In addition, by means of functionalization of cantilevers surface(s) label -free and specific detection is achieved. This is based on the fact that some bimolecular can only bind to one or a few different molecules (see for example antigen-antibody 13
  • 14. binding). This can be understood as an ability to recognize those molecules and can be used in order to detect one of them, i.e. if a surface is functionalized with an antigen, only its own specific antibody will bind, and hence specific detection of that compound will be performed. Using these specific bindings, detection of molecules is allowed by means of forces at the apex, mass change or surface stress-induced bending, although the most extended technique is the latter. The intermolecular forces arising from adsorption of small molecules to a surface is known to induce surface stress and this transduction is used to cause cantilever bending which is using any deflection measurement, finally transduces bimolecular detection into an electronic signal. Hence, cantilever-based sensors offer a wide range of applications that are only limited by surface functionalization techniques. Many different compounds have been sensed up-to-date, as for example: Prostate Specific Antigen (PSA) , biotin-avidin, Acute Myocardial Infarction (AMI) markers, DNA (with single-base mismatch resolution) etc. Temperature Sensors / Heat Sensors Changes in temperature and heat bend a cantilever composed of materials with different thermal expansion coefficients by the bimetallic effect. Microcantilever based sensors can measure changes in temperature as small as 10-5 K and can be used for photo thermal measurement. They can be used as micro calorimeters to study the heat evolution in catalytic chemical reactions and enthalpy changes at phase transitions. Bimetallic microcantilevers can perform photo thermal spectroscopy with a sensitivity of 150 fJ and a sub-millisecond time resolution. They can detect heat changes with Joule sensitivity. Viscosity Sensors Changes in the medium viscoelasticity shift the cantilever resonance frequency. A highly viscous medium surrounding the cantilever as well as an added mass will damp the cantilever oscillation lowering its fundamental resonance frequency. Cantilevers can therefore be vibrated by piezoelectric actuators to resonate and used as viscosity meters. 14
  • 15. Micro-Cantilever-Based Sensors Cantilevers can be used as mechanical transducers. They are very commonly used because of their versatility, given that loads of different signals can affect their configuration, that is, can be sensed by means of a cantilever beam. Cantilevers can be used in two different modes of operation, i.e. static and dynamic. In the static mode of operation, cantilever deflection is monitored continuously in order to detect deformations produced by external measurands. On the other hand, in dynamic mode changes in the value of the resonant frequency are measured. Fig.6: Static-mode operation. Two cantilevers, one of them with a gold and functionalized layer on top and the other working as a reference cantilever (a), are exposed to the flux of some biomolecules, which will bind with the functionalization of measuring cantilever causing it to deflect (b). Many of the research groups are working with the cantilever sensors. The below said gives a detailed report on the cantilever sensors. 1) Christiane Ziegler, (2004) explains about the cantilevers based bio-sensors. He explains briefly about the theory of cantilevers biosensors, transduction principles in various materials. Further explains on liquid –phase sensing with particular emphasis on biological applications. The most common method to measure the deflection of a cantilever is the optical lever technique. Another optical detection method is based on the interference effect 2) T. Chu Duc et al, explains about the Piezoresistive Cantilever for Mechanical Force sensors. They describe about the piezoresistive cantilever force sensors that are used to evaluate the impact force between microhandling tools and micro particles in the nano-Newton range. This cantilever is based on conventional silicon wafers, the applied force on this sensor is parallel to wafer surface. The proposed structure and its electronic circuit suppress the effect of the vertical force with 19 dB in practice. 15
  • 16. 3) Michel Godin et al, (2003), reported on combined in situ micromechanical cantilever-based sensing and ellipsometry. Two cantilever-based chemical sensors are used. First, a differential cantilever-based chemical sensor, while the second is passivated cantilever is used as a reference. Both sensors, operated in static mode, achieve a cantilever deflection measurement sensitivity of 0.2 nm and a surface stress resolution of 5x10-5 N/m. Simultaneous surface stress and monolayer thickness measurements were performed during the formation of dodecanethiol SAMs on gold. 4) Mo Yang et al, (2003) describes about the High sensitivity piezoresistive cantilever design and optimization for analyte-receptor binding. The mechanical design and optimization of piezoresistive cantilevers for biosensing applications is studied using finite element analysis. The change of relative resistivity of piezoresistive microcantilevers is analyzed in the presence of the chemical reaction at the receptor surface under the condition of oscillating flow. Finally, the optimum SCR modified ‘C’ piezocantilever system for biosensing is designed and the optimal parameters are set for high sensitivity. They have developed a finite element computational model for simulating the chemo-mechanical binding of analytes to specific binding molecules on functionalized surfaces 5 Mohd. Zahid Ansari,(2009), reported on Comparison between deflection and vibration characteristics of rectangular and trapezoidal profile Microcantilevers. They concluded that Arrays of microcantilevers are increasingly being used as physical, biological, and chemical sensors in various applications. To improve the sensitivity of microcantilever sensors, this study analyses and compares the deflection and vibration characteristics of rectangular and trapezoidal profile microcantilevers. Three models of each profile are investigated. The cantilevers are analyzed for maximum deflection, fundamental resonant frequency and maximum stress. The surface stress is modelled as in-plane tensile force applied on the top edge of the microcantilevers. 6) Nitin S. Kale, (2009), explained about the Fabrication and Characterization of a Polymeric Micro cantilever With an Encapsulated Hotwire CVD Polysilicon Piezoresistor. In this they explained about the process to fabricate and characterize a novel polymeric cantilever with an embedded piezoresistor. This device exploits the low Young’s modulus of organic polymers and the high gauge factor of polysilicon. 16
  • 17. 7) Daniel Ramos, (2007), reported on the Study of the Origin of Bending Induced by Bimetallic Effect on Microcantilever. An analytical model is used for the deflection and force of a biomaterial cantilever. Axial load is implemented upon temperature changes.by using the stoney equation the bending in the cantilevers is being found. For different temperature changes the stoney model is used for stress calculation 8) Sumio Hosaka et al, (2006), reported on the possibility of a femtogram mass biosensor using a self-sensing cantilever. In the experiments, measured the change in the mass of adsorbed water molecules and the reaction between an antigen and an antibody on the cantilever from the resonance frequency shift. 9) Eric Finot et al, (2008), explained about the Measurement of Mechanical Properties of Cantilever Shaped Materials. Microcantilevers were first introduced as imaging probes in Atomic Force Microscopy (AFM) due to their extremely high sensitivity in measuring surface forces. As temperature gauges, double-layered microcantilevers operating in deflection mode, can reach extreme thermal sensitivities. 10) Ricardo C. Teixeira et al, reported on the Stress Analysis of Ultra Thin Ground Wafers. The influence of the backside induced stress in Si wafers thinned down to ~20μm by means of an IR time-of-flight like technique. Such aggressive thinning is a requirement for high density via interconnect, stacked die packaging and flexible electronics. 11) Ricardo C. Teixeira et al, reported on Stress Analysis on Ultra-Thin Ground Wafers. For the stress analysis the ground wafers of the size 100µm is used. The stress is being found by the help of stoney equation. They concluded that even applying several corrections for Stoney’s formula average stress on the thinned wafer is still below 10 MPa From the above literature survey many of the research groups are using stoney equation for finding the deflection of the cantilever; hence we also implement stoney equation for finding the deflection analytically. 17
  • 18. CHAPTER-3 Materials and Methods 3.1 Mathematical Theory of Cantilever Deflection: The stoney equation is a fundamental expression relating the residual surface stress (∆σ) per unit length in a film to the curvature (k) of a substrate the film is deposited onto. The curvature does not depend on the material or the geometric properties of the film. This equation is commonly used in determining the residual surface stress in thin films. In its original form, the equation is given as: (1) Where E and t are the elastic modulus and the thickness of the substrate. Since the cantilever plate is long and wide, in general practice E is replaced by the biaxial modulus E/ (1-v) to accommodate he poissions ratio(v) coupling. Surface stresses in solids are assumed analogous to the surface tension in liquids. The unit surface stress measurement is different from that of bulk stress. For the bulk stress it is N/m2 , where as for surface stress it is N/m. For modeling purpose the surface stress induced deflection in a substrate is often compared to a concentrated moment induced 1deflection in a thin plate. Figure shows the schematic for a cantilever plate subjected to a concentrated moment on its free end while the other end is fully constrained. Modeling the surface stress induced curvature in a micro cantilevers by equating to a concentrated moment induced curvature. The concentrated moment and the surface stress are related as M0=∆σt/2, where t is thickness of the microcantilevers. 18
  • 19. Fig 7: cantilever subjected to bendining moment Applying stoney equation, assumption that the surface stress bends the plate with uniform curvature, into the concentrated moment induced plate bending the following curvature relation for plate bending can be given as: (2) Where M0 is the applied concentrated moment, E is the elastic modulus of the plate, I is the moment of inertia of a beam. For beam of rectangular cross-section the moment of inertia is given as I=bt3 /12, where b and t are the thickness of the beam, respectively. Comparing the curvature relations the following relation between the surface stress and the moment per unit length can be established: (3) This relation shows that the moment is directly proportional to the surface stress and the geometric properties of the plate. Moreover, it does not depend on the 19
  • 20. material properties of the plate. The governing differential equation for an isotropic, tin plates expressing the bending and twisting moments in terms of the curvature and deflection is given as; (4) (5) (6) Where D=Et3 /12(1-v2 ) is the flexural rigidity of the plate. In these equations, the moment are expressed in moment per unit length. Assuming Mx=My=M0 and neglecting the shear component Mxy, the above equation can be solved to give: (7) If the cantilever is clamped in such a way that its y direction is restricted, the above equation can be further simplified as: (8) This is well known form of stoney equation commonly used in predicting the residual surface stress in thin films by measuring the induced deflection. (9) 20
  • 21. This is the modified form of stoney’s equation. Where k is a constant dependent on the material and geometric properties of the cantilever. For a cantilever of l/b <, 5 and ν ≤ 0.25, the value of K lies between 0.3 and 1.05. The above equation is used to calculate the deflection of the cantilever and the simulation is done with Ansys. A simple java program is also written to make the calculations very easy. INTRODUCTION TO ANSYS ANSYS is general-purpose finite element analysis (FEA) software package. Finite Element Analysis is a numerical method of deconstructing a complex system into very small pieces (of user-designated size) called elements. The software implements equations that govern the behavior of these elements and solves them all; creating a comprehensive explanation of how the system acts as a whole. These results can be presented in tabulated or graphical forms. This type of analysis is typically used for the design and optimization of a system for too complex to analyze by hand. Systems that may fit into this category are too complex due to their geometry, scale, or governing equations. ANSYS provides a cost-effective way to explore the performance of products or processes in a virtual environment. This type of product development is termed virtual prototyping. With virtual prototyping techniques, users can iterate various scenarios to optimize the product long before the manufacturing is started. This enables a reduction in the level of risk, and in the cost of ineffective designs. The multifaceted nature of ANSYS also provides a means to ensure that users are able to see the effect of a design on the whole behavior of the product, be it electromagnetic, thermal, mechanical etc. The ANSYS computer program is a large-scale multi purpose Finite Element program that may be used for solving several classes of engineering analysis. The analysis capabilities of ANSYS include the ability to solve static and dynamic structural analysis, steady state and transient heat transfer problems, more frequency and buckling Eigen value problems, static or time varying magnetic analysis, and various types of field and coupled field applications. 21
  • 22. The programming contains many special features which allow nonlinearities or secondary effects to be included in the solution, such as plasticity, large strain, hyper elasticity, creep, swelling, large deflections, contact, stress stiffening, temperature dependency, material anisotropy, and radiation. 3.2 Structural Modules in ANSYS Structural analysis is probably the most common application of the finite element method. The term structural (or structure) implies not only civil engineering structures such as bridges and buildings, but also naval, aeronautical, and mechanical structures such as ship hulls, aircraft bodies, and machine housings, as well as mechanical components such as pistons, machine parts, and tools. 3.2.1 Types of Structural Analysis The seven types of structural analyses available in the ANSYS family of products are explained below. The primary unknowns (nodal degrees of freedom) calculated in a structural analysis are displacements. Other quantities, such as strains, stresses, and reaction forces, are then derived from the nodal displacements. You can perform the following types of structural analysis. Each of these analysis types are discussed in detail in this manual. a. Static Analysis: Used to determine displacements, stresses, etc. under static loading conditions. Both linear and nonlinear static analysis. Nonlinearities can include plasticity, stress stiffening, large deflection, large strain, hyper elasticity, contact surfaces, and creep. b. Transient Dynamic Analysis: Used to determine the response of a structure to arbitrarily time-varying loads. All nonlinearities mentioned under Static Analysis above are allowed 22
  • 23. c. Buckling Analysis: Used to calculate the buckling loads and determine the buckling mode shape. Both linear (Eigen value) buckling and nonlinear buckling analysis are possible. 3.2.2 Thermal ANSYS is capable of both steady state and transient analysis of any solid with thermal boundary conditions Steady-state thermal analysis calculate the effects of steady thermal loads on a system or component. Users often perform a steady-state analysis before doing a transient thermal analysis, to help establish initial conditions. A steady-state analysis also can be the last step of a transient thermal analysis; performed after all transient effects have diminished. ANSYS can be used to determine temperatures, thermal gradients, heat flow rates, and heat fluxes in an object that are caused by thermal loads that do not vary over time. Such loads include the following: • Convection • Radiation • Heat flow rates • Heat fluxes (heat flow per unit area) • Heat generation rates (heat flow per unit volume) Constant temperature boundaries. A steady-state thermal analysis may be either linear, with constant material properties; or nonlinear, with material properties that depend on temperature. The thermal properties of most material vary with temperature. This temperature dependency being appreciable, the analysis becomes nonlinear. Radiation boundary conditions also make the analysis nonlinear. Transient calculations are time dependent and ANSYS can both solve distributions as well as create video for time incremental displays of models. 3.2.3 Fluid flow 23
  • 24. The ANSYS/FLOTRAN CFD (Computational Fluid Dynamics) offers comprehensive tools for 'analyzing two-dimensional and three-dimensional fluid flow fields. ANSYS is capable of modeling a vast range of analysis types such as: airfoils for pressure analysis of airplane wings (lift and drag), flow in supersonic nozzles, and complex, three-dimensional flow patterns in a pipe bend. In addition, ANSYS/FLOTRAN could be used to perform tasks including:  Calculating the gas pressure and temperature distributions in an engine exhaust manifold.  Studying the thermal stratification and breakup in piping systems.  Using flow mixing studies to evaluate potential for thermal shock.  Doing natural convection analysis to evaluate the thermal performance of chips in electronic enclosures.  Conducting heat exchanger studies involving different fluids separated by solid regions.  FLOTRAN analysis provides an accurate way to calculate the effects of fluid flows in complex solids without having to use the typical heat transfer analogy of heat flux as fluid flow. Types of FLOTRAN analysis that ANSYS is able to perform include: • Laminar or Turbulent Flows • Thermal Fluid Analysis • Adiabatic Conditions • Free surface Flow • Compressible or incompressible Flows 3.2.4 Magnetic Magnetic analyses, available in the ANSYS/Multiphysics and ANSYS/ Emag programs, calculate the magnetic field in devices such as: 24
  • 25. • Power generators • Magnetic tape/disk drive &Transformers • Electric motors • Video display device sensors. Magnetic fields may exist as a result of an electric current, a permanent magnet, or an applied external field 3.2.5 Acoustics / Vibration ANSYS is capable of modeling and analyzing vibrating systems. Acoustics is the study of the generation, propagation, absorption, and reflection of pressure waves in a fluid medium. Coupled acoustic analysis takes the fluid-structure interaction into account. An uncoupled acoustic analysis models only the fluid and ignores any fluid- structure interaction. The ANSYS program assumes that the fluid is compressible, but allows only relatively small pressure changes with respect to the mean pressure. Also, the fluid is assumed to be non-flowing and in viscid (that is, viscosity causes no dissipative effects). 3.2.6 Coupled Fields A coupled-field analysis is an analysis that takes into account the interaction (coupling) between two or more disciplines (fields) of engineering. A piezoelectric analysis for example, handles the interaction between the structural and electric fields: it Ives for the voltage distribution due to applied displacements, or vice versa. Other examples of coupled-field analysis are thermal-stress analysis, thermal-electric analysis, and fluid-structure analysis. Some of the applications in which coupled-field analysis may be required are pressure vessels (thermal-stress analysis), fluid flow constrictions (fluid-structure analysis), induction heating (magnetic-thermal analysis), ultrasonic transducers 25
  • 26. (piezoelectric analysis), magnetic forming (magneto-structural analysis), and micro electro mechanical systems (MEMS). 3.3 Communicating with ANSYS Program There are two methods to use ANSYS. The first is by means of the graphical user interface or GUI. This method follows the conventions of popular Windows and X-Windows based programs. The second is by means of command files. The command file approach has a steeper learning curve for many, but it has the advantage that an entire analysis can be described in a small text file, typically in less than 50 lines of commands. This approach enables easy model modifications and minimal file space requirements. 3.3.1 Communicating via GUI The easiest way to communicate with ANSYS is by using the ANSYS menu system called the Graphical User Interface (GUI). GUI consists of windows, menus, dialog boxes and other components that allow one to enter input data and execute the ANSYS functions by simply picking buttons with mouse or typing in response to prompts. 3.3.2 Communicating through Prompts Commands are the instructions that direct the ANSYS program. ANSYS has hundreds of commands, each designed for a specific function. Most commands are associated with specific (one or more) processors and to work only with that processor or those processors. Typing it in command window can access a command. Every ANSYS command has a specific format. 3.4 The ANSYS Environment 6 windows 3.4.1 Input Window Below the Utility Menu and to the left, their was an Input Window. The Input window shows program prompt messages and operator to type in commands directly. 3.4.2 Main Menu 26
  • 27. Directly below Input Window you will find a vertical list of menu items referred as the ANSYS Main Menu. The Main Menu contains the primary ANSYS functions, organized by preprocessor, solution, general postprocessor, design optimizer. It is from this menu that the vast majority of modeling commands are issued. 3.4.3 Output window The Output Window shows text output from the program, such as listing of data etc. It is usually positioned behind the other windows and can be put to the front if necessary. 3.4.4 Utility Menu The window at the top of the screen, displaying a long horizontal list of menu items, is referred to as the Utility menu. Utility Menu contains functions that are available throughout the ANSYS session, such as file controls, selections, graphic controls and parameters. 3.4.5 Toolbar To the right of the Input Window, there is a Toolbar. Contains abbreviations: Short-cuts to commonly used commands and functions. A few predefined abbreviations are available. Requires knowledge of ANSYS commands. A powerful feature which can use to create own "button menu" system. 3.4.6 Graphics window Displays graphics created in ANSYS or imported into ANSYS. 3.5. Performing a typical ANSYS Analysis A typical ANSYS analysis has three distinct steps: i. Build the model. ii. Apply loads and obtain the solution. iii. Review the results. 27
  • 28. 3.5.1 Building a Model Building a finite element model requires more of an ANSYS user's time than any other part of the analysis. First, by specify a job name and analysis title. Then, use the PREP7 preprocessor to define the element types, element real constants, material properties, and the model geometry. The basic steps to build the model for ANSYS analysis are: • Specify the job name and title. • Enter ANSYS preprocessor. • Specify the element type. • Specify the element real constants. • Specify the material properties. • Define the model geometry. • Exit preprocessor. Specifying the job name and Analysis title The job name is the name that identifies the ANSYS job. When the job is first fined, it becomes the first part of all the files that are created by the software during the analysis. By using a job name for analysis it can be ensured that no files are overwritten. This task is not required for an analysis, but is recommended. Defining Units The ANSYS program does not assume a system of units for your analysis. Except in magnetic field analyses, It may be use any system of units so long as you make sure that you use that system for all the data you enter. (Units must be consistent for all input data.) Using the /UNITS command, you can set a marker in the ANSYS database indicating the system of units that you are using. This command does not convert data 28
  • 29. from one system of units to another; it simply serves as a record for subsequent reviews if the analysis. Defining Element Types The ANSYS element library contains more than 100 different element types. Each element type has a unique number and a prefix that identifies the element category: BEAM4, PLANE77, SOLID96, etc. The element type determines, among other things: 1. The degree-of-freedom set (which in turn implies the discipline-structural, thermal, magnetic, electric, quadrilateral, brick, etc.) 2. Whether the element lies in two-dimensional or three-dimensional space. BEAM4, for example, has six structural degrees of freedom (UX, UY, U7-, ROTX. ROTY, ROTZ) is a line element, and can be modeled in 3-D space. PLANE has a thermal degree of freedom (TEMP), is an eight-node quadrilateral element, and can be modeled only in 2-D Space. Defining Real Element Constants Element real constants are properties that depend on the element type, such as cross-sectional properties of a beam element. For example, real constants for BEAM3, the 2-D beam element, are area (AREA), moment of inertia (1ZZ), height (HEIGHT), Shear deflection constant (SHEARZ), initial strain (ISTRN), and added mass per unit length (ADDMAS). Not all element types require real constants, and different elements E the same type may have different real constant values. Defining Material Properties Most element types require material properties. Depending on the application, material properties may be: • Linear or nonlinear • Isotropic, orthotropic. or anisotropic • Constant temperature or temperature-dependent. 29
  • 30. Creating the model geometry Once you have defined material properties, the next step in an analysis is generating a finite element model-nodes and elements-that adequately describes the model geometry. The graphic below shows some sample finite element model. There are two methods to create the finite element model: Solid modeling and direct generation. With solid modeling, you described the geometric shape of your model, and then instruct the ANSYS program to automatically mesh the geometry with nodes and elements. You can control the size and shape of the elements that the program creates. With direct generation, you “manually’ define the location of each node and the connectivity of each element. Several convenience operations, such as copying patterns of existing nodes and elements, symmetry reflection, etc. are available. 3.6 Apply loads and obtain the solution Loading Overview The main goal of a finite element analysis is to examine how a structure or rent responds to certain loading conditions. Loads: The word loads in ANSYS terminology includes boundary conditions and externally or internally applied forcing functions, Examples of different disciplines are; Structural: displacements, forces, pressures, temperatures (for thermal strain), gravity. Thermal: temperatures, heat flow rates, convections, internal heat generation, infinite surface. Magnetic: magnetic potentials, magnetic flux, magnetic current segments, source density, infinite surface. Electric: electric potentials (voltage), electric current, electric charges, charge vs. infinite surface. Loads are divided into six categories: 30
  • 31.  DOF constraints  Forces (concentrated loads)  Surface load 31
  • 32. CHAPTER-4 4.1 Mathematical calculation of C-section micro cantilevers: The following figure is considered for our project. The cantilever is made up of SU-8 polymer. The properties of the material are being used. The deflection is found using stoney equation. For different values of pressure the deflection is being found. Case-1: For pressure 0.01 N/mm2 Surface stress (�) = 0.8 N/m Elastic Modulus (E) = 5Gpa Poisson ratio (v) = 0.22 Length (l) = 200µm Width (w) = 120µm 32
  • 33. Thickness (t) = 2.8µm Area (a) = 17600µm From stoney equation the formulae for deflection is By substituting the values the equation is = 0.37µm Deflection (Z) =0.37µm Case 2: For pressure: 0.012 N/mm2 Surface stress (�) =1.05 N/m From stoney equation the formulae for deflection is = 0.56µm Deflection (Z) =0.56µm Case 3: For pressure: 0.013 N/mm2 Surface stress (�) =1.14 N/m 33
  • 34. From stoney equation the formulae for deflection is = 0.54µm Deflection (Z) =0.54µm Case 4: For pressure: 0.014 N/mm2 Surface stress (�) =1.2 N/m From stoney equation the formulae for deflection is = 0.57µm Deflection (Z) =0.57µm Case 5: For pressure: 0.015 N/mm2 Surface stress (�) =1.3 N/m From stoney equation the formulae for deflection is 34
  • 35. = 0.61µm Deflection (Z) =0.61µm Simple java program to find the deflection in the micro cantilevers: /* * To change this template, choose Tools | Templates * and open the template in the editor. */ package deflectiondetermine; import java.io.BufferedReader; import java.io.InputStreamReader; /** public class Main { /** * @param args the command line arguments */ public static void main(String[] args)throws Exception { BufferedReader br=new BufferedReader (new InputStreamReader(System.in)); 35
  • 36. float pasionRatio,surfaceStress,thickness; int area; double elasticLimit,deflection; System.out.println("Enter the value pasionRatio t"); pasionRatio=Float.parseFloat(br.readLine()); System.out.println("Enter the value of surface Stress t"); surfaceStress=Float.parseFloat(br.readLine()); System.out.println("Enter the value of thickness t"); thickness=Float.parseFloat(br.readLine()); System.out.println("Entere the value of elasticLimit t"); elasticLimit= Double.parseDouble(br.readLine()); System.out.println("Enter the value of area t"); area=Integer.parseInt(br.readLine()); deflection=((3*(1-pasionRatio)*surfaceStress)*area)/ (elasticLimit*thickness*thickness); System.out.println("The value of Deflection"+deflection); } } 36
  • 37. 4.2 MODELLING AND SIMULATION The surface-stress induced deflection in a microcantilever can be modelled by applying a lengthwise in-plane tensile force at the free end of the top surface of the cantilever. The simulations assume that the cantilevers are made of silicon, and have an Young’s modulus of 5GPa and a Poisson’s ratio of 0.22, respectively. The cantilevers are subject to a surface pressure (Δσ) of 0.8 N/m on their top surfaces. Since surface stress is expressed in unit of force per unit width, multiplying the surface stress by the cantilever width will give the total tensile force acting on the top surface. ANSYS PROCEDURE Data of Microcantilevers Sections : C-Section Required material : Polymer (su-8) Required element : Brick 8 node 45(isotropic, elastic) Poisson’s ratio : 0.22 Young’s modulus : 5 Gpa Pressure : 0.01N/mm2 37
  • 38. Edge length : 0.005 Element type : Static (steady state) Extrusion : 2.8e5 Software : Ansys10.0 PROCEDURE: 1. Define material Step1: Define element type 1. Main menu>preprocessor>element type>add/edit/delete 2. add 3. structural solid (left column) 4. Brick8nodesolid (right column) 5. [o.k.] Step 2: Define material properties 1. Main menu>preprocessor>material props>material modals 2. (double click “structural “ then “linear”, then “elastic”, then “isotropic” 3. “EX”= 5e9 4. “prxy”=0.22 5. [o.k.] 6. [close] 38
  • 39. Step3: nodes 1. Main menu>preprocessor>modeling>create >nodes>in active cs>creat nodes in active coordinate system. 2. Main menu>preprocessor>modeling>create >key points>on nodes> pick nodes on current plane. 3.mainmenu>preprocessor>modeling>create>Lines>lines>straight line>pick the key points on work plane. [ok] Fig.8: Creating key points 3. Main menu>create>line> st. line>pick plotted key points on working plane 4. Main menu>create>areas>arbitrary>by lines. A Plane is formed with plotted key points. 39
  • 40. Fig.9: Creating plane 2. Extrude the area Step4: 1. Main menu>modeling>operate>extrude>element opts>no. of .element divisions =10 2. Operate>extrude>areas>along normal Pick area Length of Extrusion=2.8e5 Given area is extruded 40
  • 41. Fig 10: Extrusion 3. Mesh the area Step5: 1. main menu>preprocessor>meshing>mesh tool 2. “size control GLOBAL”=[set] 3. Element edge length=0.05 4. [o.k.] 5. [mesh] 6. [Pick all] 7. [close] 41
  • 42. Fig. 11: Meshing of C-Section 4. Apply loads Step6: 1. Main menu>preprocessor>loads>applyloads>structural>displacements>onlines. Select the lines which are to be fixed. D.O.F . O.K. 2. Main menu>preprocessor>load>define load>apply>pressure>on areas Pick the area Pressure applied =0.01 N/mm2 [o.k.] 42
  • 43. Fig 12: Applying loads 5. Obtain solution step7: Specify static analysis type 1. Main menu>solution> analysis type> new analysis 2. Static 3. [o.k.] Step8: solve 1. Main menu>solution>solve>current LS 2. Review the information in the status window then choose file>close. 3. [o.k.] 4. [Close] to acknowledge that the solution is done. Step9: Results 1. Main menu>general post processor>plot results>contour plot> nodal solutions. 2. Close after observing the listing. Step10: animate the deflection 43
  • 44. 1. Utility menu>plot ctrls>animate>deformed shape. 2. [O.K.] 3. Step11: exit the ANSYS Programme. Fig 13: Deflection in z direction For pressure=0.013N/mm2 Fig 14:Deflection in Z direction 44
  • 45. For pressure=0.014N/mm2 Fig 15: Deflection in z direction For pressure =0.015N/mm2 Fig.16: Deflection in z direction 45
  • 46. Von mises stress: Fig: 17 von-mises stress Stress intensity: Fig: 18 stress intensity 46
  • 47. CHAPTER - 5 RESULTS AND DISCUSSIONS Basically the deflection of the cantilever beam should be high, when the sensing element senses the material to be detected. Similarly stress of the cantilever beam should be low so that the beam will be more resistant when any high load is applied on the surface of the beam. Since von mises stress is less than stress intensity the model is in safe zone. The deflection is calculated by using stoney equation and then it is analyzed in ansys. The errors are being determined below and are tabulated. COMPARISIONS OF THE C-SECTION MICROCANTILEVERS: Pressure (p)N/mm2 Surface Stress(∆σ) N/m Simulation deflection(µm) Analytical Deflection(µm) Error (µm) 0.01 0.8 0.42 0.37 0.05 0.012 1.05 0.57 0.5 0.07 0.013 1.14 0.62 0.54 0.08 0.014 1.2 0.67 0.59 0.08 0.015 1.3 0.70 0.61 0.09 Graph between surface stress vs Deflection: 47
  • 48. 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.42 0.57 0.62 0.67 0.71 Deflectionin µm 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0.37 0.5 0.54 0.57 0.61 Deflectionin µm Graph between pressure vs deflection CHAPTER - 6 48 SurfacestressinN/m PressureinN/mm2
  • 49. CONCLUSION Arrays of micro-cantilevers are increasingly being used as physical, biological, and chemical sensors in various applications. In this work, the overall sensitivity of the micro-cantilevers that are used in mems for increasing their deflection and stress characteristics of the cantilevers are investigated. To improve the sensitivity the basic and modified design of c- section profile micro-cantilevers are studied. The overall sensitivity of micro-cantilever depends on both the deflection and the stress of the cantilever. The deflection is found analytically by the stoney equation for various surface stress values. The same is simulated in fea software Ansys. The simulation results and the calculated values are compared. The results shows that the analysis with mathematical and simulated are within a minimum error of .1 (10%) at an approval. The surface stress was successfully modeled by an in-plane tensile force applied to the top surface of the cantilevers and the deflections ware studied. References 49
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  • 51. hydrationinduced tension in nucleic acid films. Nature Nanotechnol. 2008, 3, 301–307. 11. Suri, C.R.; Kaur, J.; Gandhi, S.; Shekhawat, G.S. Label-free ultra-sensitive detection of atrazine based on nanomechanics. Nanotechnology 2008, 19, 235502–235600. 12. Villanueva, G.; Plaza, J.A.; Montserrat, J.; Perez-Murano, F.; Bausells, J. Crystalline silicon cantilevers for piezoresistive detection of biomolecular forces. Microelectron. Eng. 2008, 85, 1120–1123. 13. Ansari, M.Z.; Cho, C.; Kim, J.; Bang, B. Comparison between deflection and vibration characteristics of rectangular and trapezoidal profile microcantilevers. Sensors 2009, 9, 2706–2718. 14. Daniel Ramos, Johann Mertens, Montserrat Calleja and Javier Tamayo* on Study of the Origin of Bending Induced by Bimetallic Effect on Microcantilever 15. Ricardo C. Teixeira1,2, Koen De Munck2, Piet De Moor2, Kris Baert2, Bart Swinnen, Chris Van Hoof1,2 and Alexsander Knüettel3 on Stress Analysis on Ultra-Thin Ground Wafers 51