River Rapids Conference Proceedings of the Society for Experimental Mechanics Series MEMS and Nanotechnology, Volume 8 Barton C. Prorok LaVern Starman Jennifer Hay Gordon Shaw, III Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics River Publishers
Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Tom Proulx Society for Experimental Mechanics, Inc. Bethel, CT, USA
River Publishers Barton C. Prorok • LaVern Starman • Jennifer Hay • Gordon Shaw, III Editors MEMS and Nanotechnology, Volume 8 Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics
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Preface MEMS and Nanotechnology, Volume 8: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics represents one of the eight volumes of technical papers presented at the 2013 SEM Annual Conference & Exposition on Experimental and Applied Mechanics organized by the Society for Experimental Mechanics and held in Greenville, SC, June 2–5, 2014. The complete proceedings also includes volumes on: Dynamic Behavior of Materials; Challenges in Mechanics of Time-Dependent Materials; Advancement of Optical Methods in Experimental Mechanics; Mechanics of Biological Systems and Materials; Composite, Hybrid, and Multifunctional Materials; Fracture, Fatigue, Failure and Damage Evolution; Experimental and Applied Mechanics. Each collection presents early findings from experimental and computational investigations on an important area within Experimental Mechanics, MEMS and Nanotechnology being one of these areas. The MEMS and Nanotechnology fields are specialized scientific areas that involve miniaturizing conventional scale components and systems to take advantage of reduced size and weight and/or enhanced performance or novel functionality. These fields also encompass the application of principles ranging from the micron scale down to individual atoms. Sometimes these principles borrow from conventional scale laws but often involve new physical and/or chemical phenomena that require new behavioral laws and impart new properties to exploit. Studying how mechanical loads interact with components of these scales is important in developing new applications as well as assessing their reliability and functionality. Establishing this symposium at the Annual Meeting of the Society for Experimental Mechanics provides a venue where state-of-the-art experimental methods can be leveraged in these endeavors. The 2013 symposium is the fourteenth in the series and addresses pertinent issues relating to design, analysis, fabrication, testing, optimization, and applications of MEMS and Nanotechnology, especially as these issues relate to Experimental Mechanics of microscale and nanoscale structures. It is with deep gratitude that we thank the Organizing Committee, Session Chairs, Authors and Keynote Speakers, Participants, and SEM Staff for making the 15th-ISMANa valuable and unforgettable experience. Auburn, AL, USA Barton C. Prorok Wright-Patterson AFB, OH, USA LaVern Starman Knoxville, TN, USA Jennifer Hay Gaithersburg, MD, USA Gordon Shaw, III v
Contents 1 Newly Discovered Pile Up Effects During Nanoindentation.................................... 1 MariAnne Sullivan and Barton C. Prorok 2 Spring Constant Characterization of a Thermally Tunable MEMS Regressive Spring............... 7 Kyle K. Ziegler, Robert A. Lake, and Ronald A. Coutu Jr. 3 Shape Optimization of Cantilevered Devices for Piezoelectric Energy Harvesting................... 17 Naved A. Siddiqui, Dong-Joo Kim, Ruel A. Overfelt, and Barton C. Prorok 4 Bonded Hemishell Approach to Encapsulate Microdevices in Spheroidal Packages ................. 25 Ryan M. Dowden, Derrick Langley, Ronald A. Coutu Jr., and LaVern A. Starman 5 Development of an Infrared Direct Viewer Based on a MEMS Focal Plane Array.................. 35 Garth M. Blocher, Morteza Khaleghi, Ivo Dobrev, and Cosme Furlong 6 Modeling and Testing RF Meta-Atom Designs for Rapid Metamaterial Prototyping................. 45 Russell P. Krones, Derrick Langley, Peter J. Collins, and Ronald A. Coutu Jr. 7 Pyroelectric AlN Thin Films Used as a MEMS IR Sensing Material ............................. 55 LaVern A. Starman, Vladimir S. Vasilyev, Chad M. Holbrook, and John H. Goldsmith 8 In Situ Energy Loss and Internal Friction Measurement of Nanocrystalline Copper Thin Films Under Different Temperature........................................... 67 Yu-Ting Wang, Yun-Fu Shieh, Chien-hua Chen, Cheng-hua Lu, Ya-Chi Cheng, Chung-Lin Wu, and Ming-Tzer Lin 9 Effect of Current Density and Magnetic Field on the Growth and Morphology of Nickel Nanowires .................................................................. 75 Mahendran Samykano, Ram Mohan, and Shyam Aravamudhan vii
Chapter 1 Newly Discovered Pile Up Effects During Nanoindentation MariAnne Sullivan and Barton C. Prorok Abstract This work focuses on clearly defining the effects of pile up during nanoindentation of thin films deposited on substrates. Thin film behavior is important to understand in order to prevent failure in nano- and microscale mechanical devices utilized in computers or cell phones. During nanoindentation tests, phenomena such as sink-in or pile-up can occur depending on the mismatch of elastic moduli and Poisson’s ratios. This, in turn, alters the projection of the indent on the sample. While others have tried to measure and account for the pile up through changes in contact area, we have found that the pile up area does not affect the extracted elastic mechanical properties of the film or substrate materials. By depositing different thicknesses of gold on various plastically deforming substrates, pile up trends are visualized. Accounting for pile up is not necessary, as demonstrated through experimental data matched with models and images from scanning electron microscopy. These findings will help future experiments to correctly calculate elastic mechanical properties that have pile up issues. Keywords Nanoindentation • Thin films • Pile up • Nanoscale mechanics • Multilayers 1.1 Introduction Thin films are vital in today’s society with the ubiquitous use of electronics and the necessity for thin coatings for protective applications. When choosing these materials, the properties need to be well known, and this can be done through extracting film properties. Elastic modulus can be measured from these films with nanoindentation tools [1, 2]. However, when indenting a film on substrate, there can be unique interactions. Figure 1.1 demonstrates a normal indent from a three sided pyramid (center), sink in (left), and pile up (right). With a hard film on a soft substrate, the image on the left is formed because the indenter tip is pushed through while the substrate seems to collapse underneath. Pile up happens with a soft film on a hard substrate, and the fight between film and substrate is responsible for these variations in the projected image [3]. When using nanoindentation as a tool, the projected area is greatly important to calculate the elastic modulus [2]. In the images from Fig. 1.1, however, it is clear there are changes in the triangle that is typically seen after an indent with a Berkovich tip. Other researchers have tried to account for these differences by changing the area, but with this research, some interesting discoveries were made that show elastic properties are not affected by the pile up issue. In our lab, a model has been created that improves on the Doerner and Nix [4] and Gao [5] models because there is a weighting factor for both the film and the substrate. The equation is stated below: 1 E¼ 1 Ef 1 Φs ð Þ Ef Es 0:1 þ 1 Es Φf ð1:1Þ Where E is composite modulus; Ef is film modulus; Es is substrate modulus; Φf ¼e αf t=h ð Þ and Φs ¼e αs t=h ð ð ÞÞ where αs and αf are substrate and film Poisson’s ratios, respectively; t is film thickness; h is displacement into the sample [6, 7]. M. Sullivan (*) • B.C. Prorok Department of Mechanical Engineering, 275 Wilmore Laboratories, Auburn University, Auburn, AL 36849, USA e-mail: mzs0050@auburn.edu; prorok@auburn.edu B.C. Prorok et al. (eds.), MEMS and Nanotechnology, Volume 8: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-07004-9_1, #The Society for Experimental Mechanics, Inc. 2015 1
The values are all elastic properties of the film or substrate. The (Ef/Es)0.1 is added for correcting for the beginning of indentation, and was added through empirical data. This equation is used in this study because it was discovered that the model fits regardless of the pile up, which will be further explained. 1.2 Experimental Procedure In order to test thin films on substrates, first material combinations were carefully chosen. This paper focuses on gold deposited on silicon. A Denton sputtering system with DC power and a rotating sample holder was used to create the films. Conditions were chosen from previous work [6]. A 10 nm layer of titanium was sputtered initially in order to improve adhesion. Times were chosen to coat gold of 250, 500, 750, and 1,000 nm onto plastically deforming substrates. These were silicon, magnesium oxide (MgO), aluminum oxide (Al2O3), and aluminum nitride (AlN). The substrates were all ceramics because plasticity issues wanted to be minimized. In this research, solely the elastic components are desired because we are using the continuous stiffness measurements (CSM), where data is taken from every unload. Next, nanoindentation tests were run on an MTS Nanoindenter XP. CSM was used, and indents reported were always an average of 25 indents in a five by five matrix. Scanning electron microscopy (SEM) with a JEOL 7000F machine was used to image the surfaces after indentation. A novel method was used to measure the pile up and compare between thicknesses or substrates, described further in the results section. 1.3 Results and Discussion The nanoindentation data shows that the Zhou-Prorok model fits well for all gold on silicon data, no matter the thickness. This model correctly predicts the elastic modulus as a function of displacement into surface, seen in Fig. 1.2. Error bars show that data as an average of 25 indents. Each dotted line is indicative of the model with the proper values for elastic moduli and Poisson’s ratios of gold and silicon, and the only change is the thickness. The trend is as expected, and the behavior is described by the model. Also on the plot in Fig. 1.2 is the substrate modulus for silicon and the film modulus for gold. This gives a better understanding of how the modulus is changing with depth compared to the film and substrate when the thickness is changed. Data is only plotted up to film thickness, before the indenter punches through to the substrate. What is then shown in Fig. 1.3 is the same data with thickness dependence removed. The x-axis is now plotted as normalized displacement, or h/t. All of the lines collapse onto the same trend, which follows the model as the dotted line, as well. This is shown to prove that the thickness does not affect the model’s predictions of the elastic modulus. Next, a novel method of measuring pile up was completed. Other researchers have tried using geometries to estimate the pile up [8, 9], but a method of counting pixels was used in this study. ImageJ software was utilized by scaling the image based on the micron bar, and then measuring areas of the indents. Visually, this is seen in Fig. 1.4. In Fig. 1.4a, the normal Fig. 1.1 Sink in, normal, and pile up projections after nanoindentation using a Berkovich tip 2 M. Sullivan and B.C. Prorok
Fig. 1.2 Composite modulus vs. displacement into surface for four thicknesses of gold film on silicon substrate Fig. 1.3 Composite Modulus vs. Normalized Displacement for four thicknesses of gold film on silicon substrate 1 Newly Discovered Pile Up Effects During Nanoindentation 3
indent is seen in the SEM with a large amount of pile up. In Fig. 1.4b, the projected area is measured, which matches the geometry given for a Berkovich tip indenter. Finally, Fig. 1.4c visualizes the pile up area that is measured. These areas were measured at increasing indent depths, from 200 to 1,200 nm. Figure 1.5 demonstrates the trend of increasing pile up vs. indent depth for all four thicknesses of gold on silicon. The very interesting trend is that despite the change in thickness, the pile up falls on the same line. The dotted line plotted is Fig. 1.4 Schematic of measured areas used software to count pixels: (a) normal indent, (b) projected area, and (c) pile up area Fig. 1.5 Measured pile up area vs. displacement into surface 4 M. Sullivan and B.C. Prorok
calculated projected pile up. This is taken from the equations from the nanoindenter [1], and is plotted as a reference. The pile up area is less than this projected area, and if the two were to be added, it would be the total area. Although others have tried to use this total area values, the plot clearly shows that pile up is not affected by film thickness. No matter the depth of the indent, the pile up will be the same in all cases. 1.4 Conclusions Overall, this work first concludes that SEM images and the software ImageJ can be used to measure the pile up of the indents. This replaces tedious methods such as atomic force microscopy. The next conclusion is that there is no effect on pile up with changing the thickness of gold films on silicon substrates. Other substrates and films are being studied (MgO, Al2O3, AlN), and the same trend is appearing across combinations that provide pile up. Instead of having to worry about accounting for pile up, elastic properties can be considered the same as if there were no pile up. The model seemed to account for the pile up, but when measuring and calculating the trends, the pile up instead has no effect on the elastic properties of the material. These findings will help shape the way that the elastic modulus is measured for soft films on hard substrates where pile up occurs. It is greatly important to extract the film properties correctly so that material selection during thin film applications can happen without errors. References 1. Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–1583 2. Oliver WC, Pharr GM (2004) Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology. J Mater Res 19:3–20 3. Chen X, Vlassak JJ (2001) Numerical study of the measurement of thin film mechanical properties by means of nanoindentation. J Mater Res 16:2974–2982 4. Doerner MF, Nix WD (1986) A method for interpreting the data from depth-sensing indentation instruments. J Mater Res 1:601–609 5. Gao H, Chiu C-H, Lee J (1992) Elastic contact versus indentation modelling of multi-layered materials. Int J Solid Struct 29:2471–2492 6. Zhou B, Prorok B (2010) A discontinuous elastic interface transfer model of thin film nanoindentation. Exp Mech 50:793–801 7. Zhou B, Prorok BC (2010) A new paradigm in thin film nanoindentation. J Mater Res 25:1671–1678 8. Kese K, Li ZC (2006) Semi-ellipse method for accounting for the pile-up contact area during nanoindentation with the Berkovich indenter. Scr Mater 55:699–702 9. Kese K, Rowcliffe DJ (2003) Nanoindentation method for measuring residual stress in brittle materials. J Am Ceram Soc 86:811–816 1 Newly Discovered Pile Up Effects During Nanoindentation 5
Chapter 2 Spring Constant Characterization of a Thermally Tunable MEMS Regressive Spring Kyle K. Ziegler, Robert A. Lake, and Ronald A. Coutu Jr. Abstract Springs are a widely utilized component in the Microelectromechanical systems (MEMS) industry, especially in inertial devices. Many of these devices rely on the restoring forces of springs to return the device to equilibrium, such as in an accelerometer. By adding external springs with negative spring constant behavior, the total spring constant can be modified. Previous work at AFIT investigated the spring characteristics of a buckled MEMS Si/SiO2 membrane. This research followed on previous work and attempted to modify the spring behavior. A Ti/Au meander resistor was deposited atop the membrane in an effort to actuate the membrane and change the spring constant. Membrane buckling was investigated through analytical equations and Finite Element analysis (FEA) to predict device behavior. Membrane deflections and thermal effects were measured using an interferometric microscope (IFM) and showed a deflection change of 13.3–22.2 μm in the square style of resistor and 15.1–23.5 μm in the spiral type of resistor. The results concluded that by introducing a thermal stress, the membrane could be actuated with a subsequent change in spring constant. From the initial position to the fully thermally actuated position, we expect the spring to undergo a threefold increase in spring stiffness in the linear region. Keywords MEMS • Buckling • Springs • Thermal actuation 2.1 Introduction Buckling is commonly identified as a type of failure method in a structural member, and it has been studied as far back as the eighteenth century when Euler studied and developed equations describing beam buckling [1]. Buckling occurs within a long but thin structure loaded in compression, which, instead of fracturing, the member drastically bows in one direction. Buckling in macro-scale structures is typically avoided, while buckling in MEMS devices has been utilized in numerous applications. It can be used in devices to maintain a specific position without input power, such as in memory [2]. It has been used in the domain of microfluidics for valve mechanisms [3, 4], and it can be used for actuators [5]. Recently, buckling in MEMS has been used for its ability to display linear regressive spring constant behavior [6], which can be explained by the following. Suppose that a buckled membrane is loaded normal to the planar surface. The membrane deflects in the direction opposite of the buckling. This deflection causes the spring constant of the structure to change. Initially, the membrane resists deflection, similar to a normal compressive spring with linear behavior [7]. Upon reaching a certain deflected distance, the membrane will begin to require a linearly decreasing load i.e. less force required for further deflection. The goal of this research is to demonstrate that by thermally increasing the post-buckled deflection, the spring constant of the structure will increase. K.K. Ziegler • R.A. Lake • R.A. Coutu Jr. (*) Air Force Institute of Technology, 2950 Hobson Way, Bldg 641, Wright-Patterson AFB, OH 45433, USA e-mail: Ronald.Coutu@afit.edu Disclaimer: The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the U.S. Government. B.C. Prorok et al. (eds.), MEMS and Nanotechnology, Volume 8: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-07004-9_2, #The Society for Experimental Mechanics, Inc. 2015 7
2.2 Design At the root of the design is the buckled membrane, for which Silicon on Insulator (SOI) is used. The joint silicon (Si) and silicon dioxide (SiO2) buckles when the supporting handle wafer is etched away. The compressive stresses required for buckling are characteristic to SOI and formed during fabrication. In this process, the device layer is bonded at high temperatures, and once cooled; the difference in coefficients of thermal expansion generates large internal planar stresses [8]. As a result, SiO2 contains high compressive stress (>200 MPa), but the surrounding silicon is lightly stressed due in part to the high modulus of elasticity and low coefficient of thermal expansion. When transversely displaced, the buckled membrane displays linear regressive spring constant behavior. Shown in Fig. 2.1a, b, the buckled membrane’s spring characteristics are shown with the corresponding location during actuation. By thermally stressing, and subsequently, straining the membrane, this research seeks to increase the displacement of the membrane from the initial buckled position. With the increased deflection, the membrane will display modified spring characteristics, shown in Fig. 2.1c. In order to introduce thermal stress to the membrane, current was passed through a deposited resistor which transfers heat energy to the membrane in the form of joule heating. Two styles of resistor were used in this research. The first resistor design (Fig. 2.2a) consisted of straight edges and sharp corners. The purpose of this resistor was to quickly fabricate and test a design, to provide a high heater surface area, and to reach a maximum temperature with under 25 V applied. Additionally, the total resistance from pad to pad is calculated to be 1.07 10 5 Ω. Also shown in Fig. 2.2a are a series of four bars that surround the filament area, these did not affect the resistor performance, and they were used only to align the resistor mask when designing. The second resistor style (Fig. 2.2b) was designed in a spiral shape to reduce current concentration around corners, a concern with the first style of resistor [9]. The design included a thinner filament with increased filament spacing and a total resistance of 1.05 10 4 Ω. These two styles enabled us to determine if a difference in filament thickness or spacing could be a factor in heater performance. Additionally, this research focused solely on testing the capabilities of joule heating on a buckled membrane, and minimizing power consumption for packaging and incorporating into MEMS devices will be left to future research. The resistors were fabricated atop the membrane prior to buckling. In the following section, the fabrication procedures are outlined. Fig. 2.1 (a) Schematic of the measured force response from a incrementally displaced membrane. (b) Cross-sectional view of buckled membrane actuation. (c) Predicted effect to force response from thermal actuation 8 K.K. Ziegler et al.
2.3 Fabrication A two mask process is required for the device fabrication. One masks is required for the topside resistors, and another is needed for backside etch holes. The resistors are deposited atop an SOI wafer with a 5 μm device layer and a 2 μmoxide layer for optimal buckling characteristics, namely the degree of internal residual stress. 2.3.1 Resistor Fabrication The process begins with the application a single layer of SF11 photoresist followed by a single layer of 1818 photoresist, both of which mask the resistor shape (Fig. 2.3a). 1818 is exposed using an MJB3 mask aligner to define the resistor locations. 1818 is further used to mask the SF11 layer below which is exposed in a deep ultra violet (DUV) flood exposure system. SF11 undercuts the 1818 layer (Fig. 2.3b) preventing connection of the sacrificial gold and resistor gold, and ensuring the success of the lift-off technique for unwanted gold removal. Once SF11 has been exposed, and following a brief develop procedure, bare silicon is exposed in locations where the resistors will be deposited. To do this, gold is evaporated over the surface of the sample, depicted in Fig. 2.3c. The samples are now ready for the backside etching process. 2.3.2 Backside Etch Process The thick side (handle) portion of the sample is patterned using SU-8 photoresist to protect areas where etching is undesired. This design consists of a series of one millimeter squares and circles patterned using manufacturer specified photoresist deposition, exposure, and develop times and temperatures. After the photoresist processing step, the bulk silicon is rapidly and anisotropically etched using the deep reactive ion etching (DRIE) method. Etching selectivity permits using the oxide layer as a natural etch stop. The resultant structure contains a thin layer of both Si and SiO2 which buckles out of plane upon etch completion. The complete process is shown in Fig. 2.4. a Probe Pad Heating Filament Heating Filament Probe Pad b Fig. 2.2 (a) Square meander resistor design. (b) Spiral resistor design 2 Spring Constant Characterization of a Thermally Tunable MEMS Regressive Spring 9
2.4 Modeling and Simulation Timoshenko and Gere established equations for modeling multiple geometric buckling scenarios [10]. Here the strain energy method is utilized for estimating buckling. Through this method, the outward deflection of the membrane is found by minimizing the strain energy of the system. These equations consider the energy generated by both the strain energy of bending and the work done by the compressive forces during buckling. Popescu et al. simplified the mathematical expressions provided by Timoshenko and Gere and formed equations used to estimate the deflection in a buckled structure [11]. Adding the two energy equations, solving the integrals, and simplifying these equations results in the total strain energy of the membrane which is represented by Eq. 2.1. Equation 2.1 Total Strain Energy U¼33 Dh2 a2 Wo h 4 þ100 Dh2 a2 Wo h 2 1 σ σcr ð 2:1Þ Fig. 2.4 Backside etch process. (a) Initial sample, (b) SU-8 photoresist deposition and patterning, (c) DRIE process, (d) instantaneous membrane buckling upon etch completion Fig. 2.3 Resistive heating element deposition process. (a) Initial photoresist spin-on, (b) ultraviolet (UV) light exposure and develop, (c) gold deposition through electron beam evaporation, (d) excess gold and photoresist removal 10 K.K. Ziegler et al.
Where Wo is the center deflection, his the thickness, aandbare the length and width, σx andσy are the compressive stresses, and Dis the flexural rigidity represented by Eq. 2.2 Equation 2.2 Flexural rigidity D¼ Eh3 12 1 ν2 ð Þ ð 2:2Þ This equation can be plotted to visually show the expected amount of deflection in the membrane. Figure 2.5a graphically illustrates Eq. 2.1 with the appropriate material properties used in the equation. Thermal behavior is studied in this thesis, and Eq. 2.1 can be modified to include thermal stresses. By adding thermal stress (Eq. 2.3) to the total stress (σ), Eq. 2.1 accommodates for the addition of heat to the buckled membrane. Equation 2.3 Thermal stress σtherm ¼ Eeff αeff T T 1 ð Þ ð2:3Þ This effect is shown in Fig. 2.5b, with each energy curve representing a 100 K increase in temperature. Using Fig. 2.5a we predict the membrane will initially buckle with 18μm of deflection, and with Fig. 2.5b we can predict the membrane will actuate upward with a decreasing change in deflection to 30 μm predicted at the maximum temperature reached by resistive heating. While analytical equations can determine the profile and the degree of deflection in the membrane, advanced modeling is necessary to understand transverse loading, heat transfer, and the electro-thermal behavior. Through finite element analysis (FEA) techniques, stress, strain, temperature, fluid flow, deflection, electrical characteristics, and other analyses can be performed for unusually shaped or loaded objects. Fig. 2.5 (a) Initial energy curve for the buckled Si/SiO2 membrane. The local minima indicate locations of buckled equilibrium. (b) Successive energy curves corresponding to increased temperature in the membrane 2 Spring Constant Characterization of a Thermally Tunable MEMS Regressive Spring 11
2.4.1 Finite Element Analysis (FEA) CoventorWare ® is a finite element analysis (FEA) software tool which assists MEMS researchers by using familiar processes to create models for FE analysis. Users specify material properties, create a design layout, and develop a process as if the device were to be fabricated. The system compiles this information and provides the user with a three-dimensional rendition (solid model) of the device. It is at this step where the user decides the type and style of the finite elements (mesh). After generating a mesh, the user can select from a comprehensive suite of solvers, each focused on a specific area of MEMS. Within these, boundary and loading conditions are specified to closely approximate device behavior. For this research, a flat plate with rigid edges is used to model the membrane. Initial membrane buckling was modeled first with thermal effects added in later simulations. Next, resistor heating with applied voltage values was used in conjunction with the temperature model to determine the thermal effects. Visual depictions of the initial buckling, thermal profile, and the expected membrane actuation with applied voltages are shown in Fig. 2.6. Figure 2.6a shows the result of the compressive stress in the membrane at room temperature. Figure 2.6b shows the membrane with only an applied voltage to the probe pads. This illustrates the maximum temperature expected in the membrane at 6 V (1,200 K) and the temperature gradient from the center to the edges. Figure 2.6 is not color coded to show different materials, but the gold resistor is included and can be seen overhanging the membrane corner. Finally, in Fig 2.6c the temperature is applied to the original membrane model to simulate the effects of thermal stress. FEA predicts the deflection of the membrane to range from 12.4 μm of initial deflection to 31.6 μm with 6 V of applied voltage. 2.5 Experimental Results and Testing In order to determine the vertical displacement from the thermal effects, the devices were measured under a white light interferometric microscope (IFM). The Zygo ® IFM is equipped with movable probes which can be connected to a power supply in order to supply the necessary input voltages and measure micro scale devices. The IFM user interface screen (shown in Fig. 2.7a) provides the user with an optical image to aid with microscope focusing, a top view contour image showing the vertical displacements, a three-dimensional model generated from the microscope image, and a cross-sectional image showing the surface profile. In this research, the probes were connected to a 25 V power supply, in which 0–6 V were used, and carefully lowered to the contact pads, after which power was applied to the probes. Prior to making contact with the probe tips, the Zygo ® table was first positioned for optimal focus. Measurements were then taken by manually adjusting the applied voltage and measuring the deflection in the membrane. The deflections were recorded for 0–6 V across twenty samples. Fig. 2.6 (a) Initial buckling shape and deflected distance. (b) Heating profile with an applied voltage across the resistor. (c) Membrane buckling deflection distance with thermal influence 12 K.K. Ziegler et al.
Once tested, the displacements at each voltage were plotted, and the average of 20 separate devices was recorded. The square meander resistor increased from an initial deflection of 13.3–22.2 μm (Fig. 2.7b), and the spiral resistor deflected from an initial displacement of 15.1–23.5 μm. Each resistor maintained a different respective voltage limit before resistor failure as well as a different deflected distance. The average square meander resistor failed at 6 V and the spiral resistor failed at 8 V. The resistor failure was caused by the gold melting and failing to provide an electrical connection, and the voltage at which it failed was defined by the individual resistance of the resistor. Furthermore, the major focus of this research was to have the resistor heat the membrane and cause further deflection, and the resistor was only driven to failure to observe the maximum heating potential. Referring back to the models, analytical modeling consistently overestimated membrane deflection by 30 % and FEA underestimated initial buckling by 6 % and overestimated maximum actuation by 35 %. The cause of the discrepancy stems from the assumptions made in the models. Analytical models do not take into consideration the bending effect of the gold film, which reduce the overall buckling distance. Furthermore, FEA assumes a perfectly fixed edge, and idealizes the probeprobe pad contact. Using this information in conjunction with the derivative of Eq. 2.3, the force/deflection characteristics of the membrane were estimated. The stress value in the equation was modified to reflect the actual membrane deflection at each voltage. The result, illustrated in Fig. 2.8, shows the characteristics of the force/deflection curve, and in particular, the change in stiffness of the different membranes. The membrane initial equilibrium position is indicated by the “membrane displacement” label on the figure, and through transverse actuation, the membrane will follow the curve traveling from right to left. Each curve corresponds to a different voltage applied to the resistor, and within each curve, the returning force from the membrane at each deflected position is indicated by the vertical axis. Because of this, the slope of this line is indicative of the stiffness of the membrane. In this plot, the equation predicts a threefold increase of membrane stiffness. This change in membrane stiffness could be useful in a wide array of MEMS devices, in particular for tuning the characteristics of inertial devices. Additionally, the linear regressive characteristics, in particular the negative stiffness region could be used as stiffness offset. Further research should investigate scaling this device to useful sizes, and implementing this structure in a current MEMS device. Fig. 2.7 (a)Zygo ® user interface screen. (b) Average measured deflection data for the square resistor mounted on the membrane at 0–6 V applied 2 Spring Constant Characterization of a Thermally Tunable MEMS Regressive Spring 13
2.6 Conclusion A buckled membrane formed from Si and SiO2 was thermally actuated in order to test its capabilities as a tunable spring. Two types of deposited resistors were used to provide the thermal energy to the membrane, a square meander and a spiral resistor. Both analytical and finite element methods were used to model the behavior of the membrane under applied thermal effects. The membrane was fabricated using conventional cleanroom processes, and tested under an IFM to measure the degree of deflection. Experimental deflection values were determined to be different from the model’s prediction because of the assumptions made in the modeling process. Finally, the measured deflection values were used with the analytical model to estimate the change in spring constant with thermal effects. Acknowledgments The authors would like to thank the Air Force Research Laboratory (AFRL) Sensors and Propulsion Directorates for their assistance, use of their resources, and facilities. The authors also thank the technical support and dedicated work of AFIT’s own cleanroom staff, Rich Johnston and Thomas Stephenson. References 1. Brush DO, Almroth BO (1975) Buckling of bars, plates, and shells. McGraw-Hill, New York 2. H€alg B (1990) On a micro-electro-mechanical nonvolatile memory cell. IEEE Trans Electron Devices 37(10):2230–2236 3. Wagner B, Quenzer HJ, Hoerschelmann T, Lisec T, Juerss M (1996) Bistable microvalve with pneumatically coupled membranes. In: Micro electro mechanical systems, San Diego 4. Jerman H (1994) Electrically-activated, normally-closed diaphragm valves. J Micromech Miroeng 4:210–216 5. Lin L, Lin S-H (1998) Vertically driven microactuators by electrothermal buckling effects. Sens Actuators A 71:35–39 6. Starman LA, Coutu RA (2012) Using micro-Raman spectroscopy to assess MEMS Si/SiO2 membranes exhibiting negative spring constant behavior. J Exp Mech 53:593–604 7. Almen JO, Laszlo A (1936) The uniform-section disk spring. Am Soc Mech Eng 58:305–314 Fig. 2.8 Analytically determined force/deflection behavior. The original membrane displacement is indicated on the x-axis, and the slope of the curves is directly correlated to the stiffness of the membrane 14 K.K. Ziegler et al.
8. Kaltsas G, Nassiopoulou A, Siakavellas M, Anastassakis E (1998) Stress effect on suspended polycrystalline silicon membranes fabricated by micromachining of porous silicon. Sens Actuators 68(1–3):429–434 9. Coutu RA, Ostrow SA (2013) Microelectromechanical systems resistive heaters as circuit protection devices. IEEE Trans Compon Packaging Manuf Technol 3(12):2174–2179 10. Timoshenko SP, Gere JM (1961) Theory of elastic stability. McGraw-Hill, New York 11. Popescu DS, Lammerink SJ, Elwenspoek M (1994) Buckled membranes for microstructures. In: IEEE workshop on micro electro mechanical systems, Oiso 2 Spring Constant Characterization of a Thermally Tunable MEMS Regressive Spring 15
Chapter 3 Shape Optimization of Cantilevered Devices for Piezoelectric Energy Harvesting Naved A. Siddiqui, Dong-Joo Kim, Ruel A. Overfelt, and Barton C. Prorok Abstract Cantilevered piezoelectric devices under transverse base excitations, for generating usable power from ambient vibrations is a highly researched topic over the past decade. The commonly used rectangular shaped bimorphs require a large proof mass to drive sufficient power, and suffer from having a large stress concentration near the fixed end of the device. Tapering geometry provides a constant axial strain through the length of a triangular cantilever, and therefore provides the opportunity for more reliable operation due to enhanced efficiency. However, in order to make fair comparisons for power output, it is important to compare devices with matching resonance frequency, device volume, and inertial loads to study the effect of geometry. This study takes an experimental approach for designing such devices, and evaluates the effects of shape change with and without the presence of proof masses. While a mass-less triangular device does not outperform a rectangular counterpart for power output generation, tapering the geometry does increases the k31 electromechanical coupling coefficient, while the damping ratios are nearly the same. The addition of a nominal 2 g proof mass increases the output power by an order of magnitude, and the triangular device outperforms its rectangular counterpart by 40 %; and a subsequent 30 % with 4 g of proof mass. With the addition of proof masses, the electromechanical coupling and damping ratio also increase, which are always greater in the case of the cantilevered triangular bimorphs, and these important parameters may be used as design parameters for better device design. Keywords Shape-optimization • Energy harvesting • Piezoelectric • Cantilever • Coupling • Damping ratio 3.1 Introduction Harvesting energy from ambient sources such as vibrations, present in air ducts, machine noise, or even human sources such as walking or heartbeats is an extremely attractive precedence which can offer the possibility of replacing finite sources of energy such as batteries. This would be especially attractive for the powering of sensors or devices that are placed in inaccessible locations where batteries are difficult to replace. Researchers have been heavily investigating energy harvesting using piezoelectric devices for such applications for the past decade [1–3]. Piezoelectric energy harvesting in such an atmosphere is typically realized using piezoelectric bimorphs, commonly made out of PZT materials which are cantilevered and affixed on a vibrating host structure. The transversal vibrations from the host, that provide transverse displacements, resulting in axial stresses and strains in the piezoelectric bimorphs are what are directly related to producing charge in a bimorph, known as the d31 mode of operation. The most commonly used cantilevered piezoelectric are rectangular in shape, and in order to drive sufficient power from the device, a large mass affixed at the free end of the beam is required [4]. This causes a large stress concentration near the fixed end of the cantilever, which decreases linearly towards the free end. N.A. Siddiqui • D.-J. Kim • R.A. Overfelt • B.C. Prorok (*) Materials Research and Education Center, 275 Wilmore Laboratories, Auburn University, Auburn, AL 36849, USA e-mail: nas0006@auburn.edu; prorok@auburn.edu B.C. Prorok et al. (eds.), MEMS and Nanotechnology, Volume 8: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-07004-9_3, #The Society for Experimental Mechanics, Inc. 2015 17
Hence, inefficiency occurs in the device as a function of length, and the maximum power being generated is limited by the maximum stress in the device, covered by a fraction of the area in the cantilever. This issue can be addressed by optimizing geometry for a cantilevered device. Researchers have reported that tapering the geometry of a cantilevered device into a triangle [5, 6], hence changing the moment of inertia can lead to a constant axial stress/strain in the device, as shown in Fig. 3.2 [7]. This could lead to greater average strains as a result of a constant radius of curvature [8]. In addition, a triangular shaped beam is aided with a larger possible inertial loading capacity [9, 10]. Researchers have explored this concept, and have in fact even reported optimized geometries, and there have been indications that tapered geometries do provide a greater power output [10–12]. However, in most cases, the resonance frequencies of the devices tend to vary due to changing geometry, and sometimes not explicitly reported in literature. Moreover, the controlling parameters behind the enhanced power outputs are not well understood. This paper attempts at comparing rectangular and triangular shaped cantilevered devices of similar resonance frequencies and volume, which are then loaded with varying degrees of proof masses. The effect of these shape change parameters are observed, and their effects on electromechanical coupling coefficient and damping are reported. 3.2 Methodology A reference rectangular geometry and its triangular counterpart with matching resonance frequency and volume were evaluated using the commercial numerical package ANSYS Mechanical APDL 14.0. The structures were designed using the 20 node structural element SOLID186, and a modal analysis was performed. The material properties were based on the commercially available PZT-5H bimorph from Piezo Inc. The PZT-5H bimorph that was selected for experimental investigations was the series-poled T220-H4-203X for the reference geometry, which has an individual piezoelectric layer 0.19 mm thick, and a brass layer 0.13 mm thick. Corresponding triangular samples with matching natural frequency and volume were cut out of larger 503X series PZT5H bimorphs, using an abrasive slurry wire saw, Model 850—South Bay Technology. The piezoelectric bimorphs were mounted on a vibration shaker—Labworks Inc. ET 132-203 that was driven using a function generator, Agilent 33220A. The signal was amplified to a desired acceleration level using a power amplifier, Labworks Inc. PA-119. The acceleration signal was measured using a low mass accelerometer, PCB Piezotronics Model 352C65 that was conditioned using PCB Piezotronics Model 480C02 Signal Conditioner. The signal from the accelerometer and the output voltage from the piezoelectric bimorphs under excitation were measured using a digital oscilloscope, Tetronix TDS 3014B. The piezoelectric bimorph was also connected in series with a resistor switch board, which provides the various load resistances. A schematic of the experimental setup is provided in Fig. 3.1. Function Generator Amplifier Shaker Conditioner Prototype Accelerometer Oscilloscope RL Fig. 3.1 Vibration energy harvesting test setup schematic [13] 18 N.A. Siddiqui et al.
The voltage response from the piezoelectric bimorph into each individual load resistance value was obtained at resonance. The power at each point was calculated using Eq. 3.1 [4]: P¼ V2 rms 2Rl ð 3:1Þ where, Vrms is the root mean squared voltage generated by the piezoelectric bimorph into a load resistor Rl. The electromechanical coupling coefficient was determined based on the open circuit and closed circuit resonance frequencies of each individual device, and calculated using Eq. 3.2 [4]: k2 ¼ ω2 oc ω2 sc ω2 oc ð 3:2Þ where, ωoc is the resonance frequency measured under open circuit conditions, andωsc is the resonance frequency measured under short circuit conditions. 3.3 Results and Discussion The reference rectangular geometry was chosen based on the T220-H4-203X piezoelectric bimorph that had a clamped length of 21.5 mm, and has a manufacturer pre-defined width of 6.35 mm, and total thickness of 0.51 mm. This results in a device volume of 70 mm3. A modal analysis of this device results in a fundamental resonance frequency of 513 Hz. An isosceles triangular device of 70 mm3 with fixed thickness of 0.51 mm was evaluated by conducting a parametric study in ANSYS 14.0 that resulted in a device 30.5 mm in altitude and width of 8.95 mm, with a fundamental frequency of 513 Hz. In the static mode, an arbitrary point load of 0.5 N on the free end of these devices provides an identical maximum axial stress. However, this stress linearly decreases in the rectangular device, while remains constant for over 90 % of overhang length on the triangular device. Therefore, this device has the possibility of being better engaged in producing charge, and this possibility is investigated in the dynamic situation for piezoelectric energy harvesting, and reported below. The devices described in Fig. 3.2 were prepared for the shaker table setup, and evaluated on the shaker table setup under a base excitation load of 2.45 ms 2 (0.25 g). The devices were connected into various load resistors in order to evaluate the power generated, based on the voltage response. Results for the two devices without a proof mass, designated as Rect-0M and Tri-0M for the rectangular and triangular devices respectively are presented in Fig. 3.3. As shown in Table 3.1, these two devices of the same volume have fairly comparable open circuit resonance frequencies of 532 and 522 Hz respectively. It is observed that the voltage being generated from the two devices expectedly increase with increasing values of load resistance. The rise is quite sharp at low values of load resistance, and tends to settle down at higher values. The power dissipated into the load resistances also increase very sharply at low values of load resistances, up to about 10,000 Ω. However, after these values, a decrease in the rise is observed, where there is actually a dip in the case of the triangular device. In fact, an inflection point at about 25,000Ωload resistance can be observed in both cases, after which the peak power is found at around 100,000Ωfor both structures. The maximum power generated by the rectangular device is 4.2 μW, and 3.9 μW for the triangular device. Therefore, there is an indication that in the absence of proof masses, the devices are performing well below their capacity, and therefore, the most noticeable result is that the triangular device fails to outperform the rectangular device. This is likely due to a lower maximum stress in the triangular device, and more even strain distribution, as indicated in literature [9]. The triangular device only slightly outperforms the rectangular device at high values of load resistance, but this increase is not significant. It is however worth noticing the data presented in Table 3.1, in order to understand the characteristics in the two shapes operating in the absence of a proof mass. It is seen that these devices have a large difference between their open circuit and short circuit resonance frequencies, which is 17 Hz for the rectangular device, and even larger at 24 Hz for the triangular device. This difference is depicted in the calculation for the k31 electromechanical coupling coefficient, which is found to be 3 Shape Optimization of Cantilevered Devices for Piezoelectric Energy Harvesting 19
0.25 for the rectangle, and increased to 0.30 for the triangular device, roughly a 25 % increase. This increase in coupling coefficient is a direct result of the change in shape between the two devices of identical volume and similar resonance frequency. Also, it is important to take into consideration the value of the damping ratio as well, which is measured for the samples under open circuit conditions. Table 3.1 shows a slightly higher average damping coefficient of 0.0066 in the case of rectangular bimorphs as compared to 0.0065 in the case of triangular bimorphs, which is nearly identical. This may be related to the similarity between the powers generated by the two devices. The rectangular and triangular cantilevered bimorphs were then loaded with a proof mass of 2 g, which is 6.35 mm 6.35 mm 6.35 mm in size. This tunes the resonance frequency of the devices to 120 Hz or lower. The proof mass samples are designated as Rect-1M and Tri-1M where 1M represents the addition of mass on a single layer. The short circuit resonance frequency for the rectangle loaded with the mass is about 114 Hz, and the triangular sample is about 93 Hz. These are levels of vibrations easily found in surroundings from microwaves, HVAC systems. . .etc [14], hence making them more usable. It can be observed in Fig. 3.4 that the addition of the nominal 2 g proof mass on the two samples creates an order of magnitude difference in the power output from the cantilevered bimorphs. The voltage generated from the triangular bimorph is always greater than the rectangular counterpart, and the difference keeps increasing with increasing load resistances. Hence, this is deemed a necessary addition to the devices. Figure 3.4 shows that the maximum power generated from the rectangular cantilever is about 56μW into a 75,000Ωload resistor. The performance from the triangular cantilever here is appreciably increased, with an output of 78μW, an improvement of nearly 40 % from a device with the same volume and comparable resonance frequency. This is stark contrast from the previous case, and is indeed a reflection of enhanced power output due to geometry. It is also seen in Fig. 3.4 that the power curves are much more flat, and the presence of the dual peaks and the inflection point at 25,000 Ω is diminished. In terms of the electromechanical coupling coefficient, Table 3.2 shows that the value increases 0.31 and 0.36 for the rectangular and triangular case, which in an increase in both cases from the no-proof-mass case. This is an indication of enhanced efficiency in the device. This also suggests that the dual peak nature in Fig. 3.2 is not entirely related to the coupling coefficients. Also, the coupling coefficients are larger not with a large overall difference between 0.00E+00 1.00E+07 2.00E+07 3.00E+07 4.00E+07 5.00E+07 6.00E+07 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Stress (Pa) Length (m) Rectangle Triangle Fig. 3.2 Quasi-static analysis with 0.5 N load at the tip for rectangular and triangular cantilevers of 70 mm3 Table 3.1 Results from the rectangular and triangular cantilevered bimorphs without a proof mass Sample fr-sc (Hz) fr-oc (Hz) Δfr (Hz) % Difference k31 ζ Rect-0M 515 532 17 3.20 0.2508 0.0066 Tri-0M 498 522 24 4.60 0.2997 0.0065 20 N.A. Siddiqui et al.
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