MEMS and Nanotechnology, Volume 4

Conference Proceedings of the Society for Experimental Mechanics Series

For other titles published in this series, go to www.springer.com/series/8922

Tom Proulx Editor

MEMS and Nanotechnology, Volume 4 Proceedings of the 2011 Annual Conference on Experimental and Applied Mechanics

Editor Tom Proulx Society for Experimental Mechanics, Inc. 7 School Street Bethel, CT 06801-1405 USA [email protected]

ISSN 2191-5644 e-ISSN 2191-5652 ISBN 978-1-4614-0209-1 e-ISBN 978-1-4614-0210-7 DOI 10.1007/978-1-4614-0210-7 Springer New York Dordrecht Heidelberg London

©

Library of Congress Control Number: 2011923429 The Society for Experimental Mechanics, Inc. 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

MEMS and Nanotechnology—The 12th International Symposium on MEMS and Nanotechnology (ISMAN)—represents one of eight volumes of technical papers presented at the Society for Experimental Mechanics Annual Conference & Exposition on Experimental and Applied Mechanics, held at Uncasville, Connecticut, June 13-16, 2011. The full set of proceedings also includes volumes on Dynamic Behavior of Materials, Mechanics of Biological Systems and Materials, Mechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials; Optical Measurements, Modeling and, Metrology; Experimental and Applied Mechanics, Thermomechanics and Infra-Red Imaging, and Engineering Applications of Residual Stress. Each collection presents early findings from experimental and computational investigations on an important area within Experimental Mechanics. The 12th International Symposium on MEMS and Nanotechnology (ISMAN) was organized by: Cosme Furlong, Worcester Polytechnic Institute; Gordon A. Shaw, National Institute of Standards and Technology; Barton Prorok, Auburn University; Ryszard J. Pryputniewicz, Worcester Polytechnic Institute. Microelectromechanical systems (MEMS) and nanotechnology are revolutionary enabling technologies (ET). These technologies merge the functions of sensing, actuation, and controls with computation and communication to affect the way people and machines interact with the physical world. This is done by integrating advances in various multidisciplinary fields to produce very small devices that use very low power and operate in many different environments. Today, developments in MEMS and nanotechnology are being made at an unprecedented rate, driven by both technology and user requirements. These developments depend on micromechanical and nanomechanical analyses, and characterization of structures comprising nanophase materials.

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To provide a forum for an up-to-date account of the advances in the field of MEMS and nanotechnology and to promote an alliance of governmental, industrial, and academic practitioners of ET, SEM initiated a Symposium Series on MEMS and Nanotechnology. The 2011 Symposium is the twelfth 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. The symposium organizers thank the authors, presenters, organizers and session chairs for their participation and contribution to this track. We are grateful to the SEM TD chairs who cosponsored and organized sessions in this track. The opinions expressed herein are those of the individual authors and not necessarily those of the Society for Experimental Mechanics, Inc. Bethel, Connecticut

Dr. Thomas Proulx Society for Experimental Mechanics, Inc

Contents

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Integrated Process Feasibility of Hard-mask for Tight Pitch Interconnects Fabrication C.-J. Weng, National University of Tainan/University of Kang Ning

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Thermoelectric Effects in Current Induced Crystallization of Silicon Microstructures G. Bakan, N. Khan, H. Silva, A. Gokirmak, University of Connecticut

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3

Evaluation of Resistance Measurement Techniques in Carbon Black and Carbon Nano-tubes Reinforced Epoxy V.K. Vadlamani, V.B. Chalivendra, University of Massachusetts Dartmouth; A. Shukla, S. Yang, University of Rhode Island

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4

A Nano-tensile Tester for Creep Studies L.I.J.C. Bergers, Eindhoven University of Technology/ Foundation for Fundamental Research on Matter/Materials Innovation Institute; J.P.M. Hoefnagels, E.C.A. Dekkers, M.G.D. Geers, Eindhoven University of Technology

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The Measurement of Cyclic Creep Behavior in Copper Thin Film Using Microtensile Testing K.-S. Hsu, M.-T. Lin, C.-J. Tong, National Chung Hsing University

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New Insight Into Pile-Up in Thin Film Indentation B.C. Prorok, B. Frye, B. Zhou, K. Schwieker, Auburn University

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Measuring Substrate-independent Young’s Modulus of Thin Films J. Hay, Agilent Technologies, Inc.

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Analysis of Spherical Indentation of an Elastic Bilayer Using a Modified Perturbation Approach J.H. Kim, Stony Brook University; A. Gouldstone, Northeastern University; C.S. Korach, Stony Brook University

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Nano-indentation Studies of Polyglactin 910 Monofilament Sutures L. Sun, V.B. Chalivendra, P. Calvert, University of Massachusetts Dartmouth

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10 Analytical Approach for the Determination of Nanomechanical Properties for Metals K.K. Jha, N. Suksawang, A. Agarwal, Florida International University

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11 Advances in Thin Film Indentation B. Zhou, K. Schwieker, B. Frye, B.C. Prorok, Auburn University

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12 Cyclic Nanoindentation Shakedown of Muscovite and its Elastic Modulus Measurement H. Yin, G. Zhang, Louisiana State University

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viii 13 Assessment of Digital Holography for 3D-shape Measurement of Micro Deep Drawing Parts in Comparison to Confocal Microscopy N. Wang, C. Falldorf, C. von Kopylow, R.B. Bergmann, BIAS GmbH 14 Full-field Bulge Testing Using Global Digital Image Correlation J. Neggers, J. Hoefnagels, Eindhoven University of Technology; F. Hild, S. Roux, LMT Cachan; M. Geers, Eindhoven University of Technology

93 99

15 Experimental Investigation of Deformation Mechanisms Present in Ultrafine-grained Metals A. Kammers, S. Daly, The University of Michigan

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16 Characterization of a Variation on AFIT's Tunable MEMS Cantilever Array Metamaterial M.E. Jussaume, P.J. Collins, R.A. Coutu, Jr., Air Force Institute of Technology

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17 MEMS for Real-time Infrared Imaging I. Dobrev, M. Balboa, R. Fossett, C. Furlong, E.J. Harrington, Worcester Polytechnic Institute

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18 New Insights Into Enhancing Microcantilever MEMS Sensors S. Morshed, B.C. Prorok, Auburn University

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19 A Miniature MRI-compatible Fiber-optic Force Sensor Utilizing Fabry-Perot Interferometer H. Su, M. Zervas, C. Furlong, G.S. Fischer, Worcester Polytechnic Institute

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20 Micromechanical Structure With Stable Linear Positive and Negative Stiffness J.P. Baugher, Wright State University; R.A. Coutu, Jr., Air Force Institute of Technology

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21 Terahertz Metamaterial Structures Fabricated by PolyMUMPs E.A. Moore, D. Langley, R.A. Coutu, Jr., Air Force Institute of Technology

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22 Investigations Into 1D and 2D Metamaterials at Infrared Wavelengths J.P. Lombardi, III, R.A. Coutu, Jr., Air Force Institute of Technology

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23 MEMS Integrated Metamaterials With Variable Resonance Operating at RF Frequencies D. Langley, E.A. Moore, R.A. Coutu, Jr., P.J. Collins, Air Force Institute of Technology

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24 Creep Measurements in Free-standing Thin Metal Film Micro-cantilever Bending L.I.J.C. Bergers, Eindhoven University of Technology/Foundation for Fundamental Research on Matter/Materials Innovation Institute; J.P.M. Hoefnagels, M.G.D. Geers, Eindhoven University of Technology

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25 MEMS Reliability for Space Applications by Elimination of Potential Failure Modes Through Analysis R. Soni, Nagesh Karajagi Orchid College of Engineering and Technology, Solapur 26 Analysis and Evaluation Methods Associated With the Application of Compliant Thermal Interface Materials in Multi-chip Electronic Board Assemblies J. Torok, S. Canfield, D. Edwards, D. Olson, IBM Corporation; M. Gaynes, T. Chainer, IBM T.J. Watson Research Center

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27 Hierarchical Reliability Model for Life Prediction of Actively Cooled LED-based Luminaire B.-M. Song, B. Han, A. Bar-Cohen, University of Maryland; R. Sharma, M. Arik, GE Global Research Center

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28 Direct Determination of Interfacial Traction-separation Relations in Chip-package Systems S. Gowrishankar, H. Mei, K.M. Liechti, R. Huang, The University of Texas at Austin

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Integrated process feasibility of hard-mask for tight pitch interconnects fabrication

Chun-Jen Weng [email protected] Center for General Education, National University of Tainan Department of Logistic and Technology Management, University of Kang Ning, Tainan, Taiwan, R.O.C.

ABSTRACT As scaling continues beyond nano-technology, integrated circuit reliability is gaining increasing concerns in IC (Integrated Circuit) fabrication technology with decreasing transistor gate size, and the impact of trace interconnect failure mechanisms on device performance and reliability will demand much more from integration schemes, interconnect materials, and processes. An optimal low-k dielectric material and their related deposition, pattern lithography, etching and cleaning are required to form dual-damascene interconnect patterns fabrication processes. As technology nodes advance to nanotechnology, metal hard-mask such as TiN is used to gain better etching selectivity and profile controlling to the low-k materials during the pattern etching process. A hard-mask scheme approach of interconnects patterning of wafer fabrication is the ability to transfer patterns into under layers with tightest optimal dimension control. Employing a hard-mask scheme in the fabrication process, successfully achieved lithography patterning, dry etch selectivity in high aspect ratio interconnects comparison with a non hard-mask process were discussed. An optimal planarization treatment of photo-resist, good etch selectivity, a feasible manufacturing integrated process of hard mask dual damascene scheme, optimal profile controlling the critical interconnects and good electrical device performances were studied for tight pitch damascene interconnect architecture. KEYWORDS: Hard-mask, Wafer Fabrication, Interconnects processes integration.

1. INTRODUCTION The increase in integration on an IC leads to a high-density BEOL multi-level interconnection structure which communicates the transistors to the package. The back-end-of line (BEOL) RC delay has gradually become a critical limiting factor in semiconductor circuit performance as a result of the rapid shrinking of critical dimensions of trace width of the semiconductor electronics. Nanotechnology semiconductor wafer manufacturing process defects can often impact product yields, depending on the type, size, and location of the defect, as well as the design and yield sensitivity of the respective semiconductor product devices. The fabrication process defects occurring in a semiconductor device, which involves forming layer patterns on a semiconductor wafer by film patterns formation based on the result of manufacturing processes, thereby reducing the difference in critical dimension of patterns in the patterning process effect, the topology of the wafer, and the difference processing parameter and material. For the implementation of copper and low-k materials into a small pitch damascene interconnect architecture, it is important to understand use of etching and lithography technology to improve the wafer fabrication process technologies. As design rules continue to shrink, the demand increases for effective inspection tools to detect defects that affect device yields. During BEOL schematic formation, via hole etching, and trench etching are the dominant etching steps to form Cu interconnect layers; these steps are widely applied to manufacture the 90 nm node and beyond. Fabrication defects are one of the principle causes for yield reduction of wafers for IC manufacturers. Defects specification has been a highly problematic aspect of the wafer fabrication industry. The critical applications of anisotropic etching, plasma ashing and cleaning to form precisely controlled profiles of high-aspect-ratio form precise via holes and trenches used in advanced Cu/low-k interconnects in the back end of line (BEOL) are described in detail [1]. Moreover, the investigation of resist pattern collapse with top rounding resist profile was shown in [2]. They found that the pattern size is reduced as the device is more integrated. The resist deformation phenomenon has been a serious problem under 100 nm line width patterns. Because 65nm BEOL trenches etch is apt to suffer the marginal photo-resist issue, it is a T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_1, © The Society for Experimental Mechanics, Inc. 2011

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big challenge for trench etches process to simultaneously satisfy the requirements for both metal sheet resistance (Rs) and connecting resistance (Rc). The advanced process control based on lithographic defect inspection and reduction was proposed [3]. They proposed a methodology based on post lithographic defect inspection, and defective die count analysis was used, which provided effective process monitoring and yield maintenance. The reliability challenges for copper interconnects were discussed [4]. The three most critical process factors and elements affecting copper interconnect reliability are copper vias and interfaces and the liner coverage. Using a low-k dielectric with a copper interconnect introduces several new challenges to reliability, including dielectric breakdown, temperature cycle, and stability within packages. Effects of width scaling and layout variation on dual damascene copper interconnect electromigration were also demonstrated in [5-6]. By study and optimization of hard mask stacks and etching fabrication; [7] developed dry etch processes for the fabrication of EUV hard mask used for etching in CMOS technology. The controlling surface reactions during etching of SiOCH and organic material model were proposed [8]. With the wide application of low-k dielectric materials at the 90 nm technology node and beyond, the long-term reliability of such materials is rapidly becoming a critical challenge for technology qualification in most important reliability issues during Cu/low-k technology development [9,10]. A method of forming optimal dual damascene process for the BEOL process was proposed [11,12]. To overcome these challenges, accurate and repeatable depth assessment of damascene structures requires the ability to resolve high-aspect-ratio structures in both a high density and isolated structures in the manufacturing process by improving yield. 2. EXPERIMENTS As technology nodes advance to nanotechnology and beyond, IC companies are investigating the use of a metal hard mask in order to gain better etching selectivity to the low-k materials during the dry etching process. A hard mask mechanism approach of fabrication for the modification interconnects fabrication processes of low-k and copper interconnects is used for dual damascene process for critical dimension control to obtain tight profile. When scaling the critical dimensions into nanotechnology, the impact of layout and line edge becomes important. Implementation of Cu and low dielectric constant (low-k) materials in the manufacturing process requires a complete understanding of these process characteristics and the challenges that appear during the hard mask based dual damascene approach. The nanotechnology copper dual damascene architecture was fabricated according to the scheme shown in Fig. 1. Dual-damascene technology in the fabrication of advanced interconnects presents itself as an integration and reliability challenge. B ondi ng pad

(BEOL)

Metal interconnects

M6 Via 5 M5 Via 4

D ielec tr ic film s ta ck

Tr en ch

Trench

W id e D im ension

V ia

M4 V ia 3 M3 Via 2 M2

B EOL C riti cal Di mens ion

V ia 1 M1

(FEO L)

NMOS

P MOS

Si

Fig. 1. Semiconductor multilayer interconnects physical structure. As design rules continue to shrink, the demand increases for effective inspection tools to detect defects that affect device yields. Defect inspection metrology is an integral part of the yield ramp and process monitoring phases of semiconductor manufacturing. Systematic yield losses are process-related problems that can affect all die chips on a wafer. It is important to produce better die chip per wafer by minimizing the cycle time to detect and fix yield problems associated with the advanced process module technology. High aspect ratio structures have been identified as critical structures where there are no known manufacture solutions for defect detection. A serious problem in wafer fabrication is the defects issue during the pattern development process, because it decreases the yield of wafer production. Abnormal patterning phenomena lead to yield loss after the electrical device test and productivity yield losses. Pattern profiles strongly depend on many manufacturing module processes, and can be suppressed by optimization of lithography, cleaning and etch processes. The defects inspection

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map can be revealed the abnormal pattern profiles, which results in yield loss and abnormal electrical device. In Fig. 2, the defects inspection of the fabrication processes was investigated. Fabrication defects are one of the principle causes for yield reduction of wafers for IC manufacturers. Defects specification has been a highly problematic aspect of the wafer fabrication industry. Interconnect line shorts defects have a high potential of becoming fabrication yield killers for semiconductor manufacturing. It is important for in-line inspections for detecting, classifying and correcting yield limiting defects on all critical manufacturing processes steps.

(b) SEM images of wafer center (Normal)

(a) Defects inspection

(c) SEM images of wafer edge (Pattern collapse)

Fig. 2. Inspection images of comparisons of structure after trench pattern etching. 3. RESULTS AND DISCUSSION Wafer manufacturing variations can be classified as process systematic and random variations. Process systematic variations are predictable in nature and depending on deterministic factors such as layout structure and surrounding topological environment. A comprehensive evaluation and investigation of the physically relevant causes to develop feasible integrated processes are important for critical dimension interconnect trace. As Fig.3 demonstrated, the hard mask patterning scheme preserves minimizing damage caused by the plasma and strip processes, and reducing the thickness requirement for the underlying barrier film, and enables superior CD and profile control. The comparison of feasible hard mask lithography planarization scheme for dense pattern was also shown in Fig.4. As technology nodes advance to nanotechnology and beyond, IC companies are investigating the use of a metal hard mask such as TiN in order to gain better etching selectivity to the film materials during the dry etching process. Hard mask etching processes have been developed which allowed us to obtain tight profile and CD control. Small amounts of polymer are intentionally left on the sidewalls of trenches and vias during the dry etching process in order to achieve a vertical profile and to protect the low-k materials under the etching mask. As hard mask approach adopted for better CD controlling in manufacturing process, the deposition film stack thickness is also increased. Three steps photo-resist gap fill approach and etching back planarization techniques are the process of increasing the flatness or planarity of the surface of a semiconductor wafer. This treatment method for etching which can increase the metal-to-photo-resist etching selectivity of a metal layer aimed to be etched with respect to photo-resist layers overlaying the metal hard mask layer. Moreover, etching of hard mask presents a challenge, as etching process should find a balance between contradicting requirements of providing sufficient selectivity to photo-resist and avoiding formation of excessive sidewall polymer resulting in CD gain. Photoresist 3

Photoresist 1 Hard mask TiN/SiN

( a) Film stack

(b) Photoresist fill ing

Photoresist 2

(b) Photor esist filling (c) E tching back (Flatting)

(c) Patterning

Etching back

Fig. 3. Feasible hard mask planarization integrated processes approach of high aspect ration trench patterning.

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Photoresist 3

Hard mask Photoresist 2

Photoresist 1

Fig. 4. Comparison of feasible hard mask lithography planarization scheme for dense pattern. In the comparisons of top SEM view images and cross-section view of dense via chain pattern of Fig.5 illustrates the different critical via chain structure and critical pattern of the improvement for different locations of wafer. Because the extra added hard mask films, consequently the depth of the via is also increased in manufacturing patterning process. The impact of via etching performance of different via chain structure was investigated. Comparing the results from dense and isolation critical via chain schemes shows that this present optimal via profiles. After via etching process, the hard mask remain of dense pattern is enough for the buffer of follow-up processes as: trench etching and chemical mechanical polish. An improved resist etch-back technique using three resist layers also has been developed which offers enhanced planarity over the dielectric film layers process. A photo-resist gap-fill material is used to ensure that the lithography process produces the best profiles and enables critical dimension control. The impact of trench etching on the electrical and reliability performance of different via chain structure was investigated. Fig. 6 illustrates top view SEM image and cross-section of the critical dense via chain developed photo-resist structure. Comparing results of trench developed photo-resist profile, the optimal photo-resist can strongly effect on trench patterning. It was identified that the profile of photo-resist top was severely damaged due to via gap filling attack of the lithography process. To compare lithography photo-resist profile structure for different trench pattern density, the TEM cross section images of trench etching photo-resist profile are illustrated in Fig.7. In order to check the causes of this patterns collapse phenomenon, the profile of photo-resist profile of trench etching is important in process development. For the via-first dual damascene process, a good controlling of photo-resist and via gap filler photo-resist typically used to ensure a lithography process produces the best profiles and critical dimension control and integrates structures having small feature sizes. The via gap filler material treatment may include etching the dielectric layer and the gap-filling material layer to planarize the via gap filler material layer. Therefore, a planarizing bottom photo-resist film and via gap filler material are used to ensure a trench lithography process produces the best profiles and critical dimension control in follow-up etching process. Isolation via

Dense vias

Dense vias

Hard mask remain

300 nm

300 nm

100 nm

(a) Top view (b) Cross-section Fig. 5. Inspections of hard mask remain on different pattern density after via etching. Cross-section

Top view

Normal

100 nm

0.5 μm

100 nm

0.5 μm

Pattern Collapse

(a) After lithography

(b) After Etching

Fig. 6. Inspections of lithography photoresist profile effects on trench patterning.

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Developed trench Photoresist

(a) Wide trench

(b) Isolation via/dense trench

(c) Dense/dense trench

Fig. 7. Comparison of lithography photo-resist profile structure for different trench pattern density.

Edge

Center

Dry etching processes are commonly used to fabricate vertical sidewall trenches and vias for interconnect dual damascene fabrication processes. The important factor that causes the pattern profile in a dual damascene architecture is the locations and the design pattern density. In comparison the SEM pictures of Fig. 8 show trench etch results by optimal treatment planarization photo-resist gap filling for different dense pattern design. The optimal pattern profile controlling which makes no abnormal pattern even via chain, narrow and wide interconnect trace line for overall wafer. Different lines and via holes with feature sizes down to 100 nm have been realized by in-line process inspection and electrical device verification. The developed etch processes have been successfully applied for high aspect ratio hard mask fabrication. The impact of trench etching on the electrical and reliability performance of different via chain structure was investigated. Fig. 9 illustrates the cross-section of the critical dense via chain structure obtained that was after the trench etching. Comparing results from different critical dense via chain schemes shows that this present optimal integrated processes can also get effective pattern as demonstrated in post trench etch clean of via fist post trench dual damascene process.

Fig. 8. Feasible process inspections on different critical patterns after trench etching.

(a)

(b)

Fig. 9. Cross-section verification of different via chain pattern after trench etching. Fig. 10 shows the TEM micrographs of the cross-sectional profiles of Cu dual damascene structure along the silicon substrate / gate transistor / critical interconnects / wide metal interconnects, respectively. The damascene structure of the interconnect chain with the layers identified after copper processes. Consequently, the wafer fabrication integrated process provided the best electrical performance at both dense via chain and isolated via test structures by the present study. As demonstrated in Fig.11 (a) and (b), the electrical device test pattern is always used to check the semiconductor process in-line electrical device verification; The drain voltage (VD=1V), for source voltage (VS) and substrate voltage (VSUB); VS=VSUB=0V, and electrical current (Id). The electrical resistance is Rc= VD / Id. The distribution of electrical

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resistance is tight for optimal integrated process and there are no open electrical test data for optimal integration process. Figs. 11 (b) shows the representative cumulative resistance distribution of the dense via chains associated with the optimal treatment etch processes. The via contact resistance spread of dense via chains were also compared among the different wafer processes.

Fig. 10. TEM inspection of multilayer interconnect scheme. Rc (ohm/ Via) 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Electrical test cross-section

200 nm

wafer Resistance distribution

Fig. 11. Contact resistance of electrical device test of optimal integration process. Fig. 12 shows the distributions of sheet resistance measurements of the different interconnect trace width respectively. No significant deterioration of sheet resistance of good trench profiles after the etch process is shown in Fig. 12(b) for comparison. The resistance spread of dense trace lines were also compared among the different pattern width. It is obvious that the wafer fabrication process resulted in the tightest control of resistance spread even 70 nm width. Fig. 13 shows the cumulative distributions of leakage current measurements of the metal bridging-continuity. The line-to-line leakage current of both metal bridging-continuity structures were well controlled. No significant deterioration of line-to-line leakage current is demonstrated. The median leakage current of the trace / space combinations is located below 1.0E-9 A. That means the wafer process provided a better control of the pattern isolation even for 90 nm /90 nm (trace width/ space). Moreover, the integrated wafer fabrication processes resulted in tight distribution of leakage current compared different pattern designs. That means the integrated wafer processes provided a better control of the resistance spread and pattern isolated. R s (ohm/ sq) 0.250 0 .25 0 0.225 0 .22 5 0.200 0 .20 0 0.175 0 .17 5 RS (ohm/sq)

0.150 0 .15 0 0.125 0 .12 5 0.100 0 .10 0 W =0 .100

90

W =0.0 90

85

W =0. 080

80

W=0 .075

75

W = 0. 070

70

Interco nnect widt h (n m)

Fig. 12. Interconnect sheet resistance of different width by optimal integration processes.

7 B r id g e C u rr e n t ( A ) 1 .0E-0 5

1 .0E-0 7

1 .0E-0 9

1 .0E-1 1

1 .0E-1 3 9 0 /9 0

9 0 /1 0 0

9 0 /1 1 0

90 /12 0

9 0 / /1 3 0

T ra c e w id t h / s p a c e ( n m )

Fig. 13. Space effects of Interconnect bridge current of optimal integration processes. 4. CONCLUSIONS Hard mask etching processes have been developed which allowed us to obtain tight profile and CD control. The impact and improvement of high aspect ratio nanotechnology hard mask dual damascene by integrated manufacturing processes were studied. The effects of integrated fabrication processes on lithography, etching in dual damascene copper interconnects manufacturing processes have been investigated. With the understanding of the complexities involved in copper interconnects and the associated integration processes, a robust reliability is achievable for the new enhancement copper technology. ACKNOWLEDGMENT The author gratefully acknowledges the support and assistance of NSC 98-2221-E-426-002. REFERENCES [1]

Haruhiko A.B.E., Masahiro Y., Nobuo F. Developments of Plasma Etching Technology for Fabricating Semiconductor Devices. Jpn. J. Appl. Phys. 2008;47:1435–55.

[2]

Lee HJ, Park JT, Yoo JY, An I, Oh HK. Resist Pattern Collapse with Top Rounding Resist Profile. Jpn. J. Appl. Phys. 2003;42:3922.

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Leavey J, Boyle J, Skumanich A. Advanced process control based on lithographic defect inspection and reduction. In: Proc. IEEE Int. Symp. Semiconductor Manufacturing Conf; 2000, p. 33-40.

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Tatsumi T. Control of reactive plasmas for low-k/Cu integration, Applied Surface Science 2007;253:6716–37.

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Choi SJ, Oh CI, Uh DS. New materials of spin-on organic hardmask for sub-70 nm devices, Microelectron Eng 2007;84(12):2832–36.

[10] Aelst JV, Struyf H., Boullart W, Vanhaelemeersch S. High aspect ratio via etch development for Cu nails in 3-D-stacked ICs, Thin Solid Films. Thin Solid Films 2008;516:3502–06. [11] Weng CJ, Lin YS, Chen CY. Method of forming Damascene Structure, US Patent 2007: US 7,189,640 B2 [12] Weng CJ. Nanotechnology copper interconnect processes integrations for high aspect ratio without middle etching stop layer. Materials Science in Semicon. Proces. 2010; 13(1):56–63.

Thermoelectric Effects in Current Induced Crystallization of Silicon Microstructures

Gokhan Bakan, Niaz Khan, Helena Silva, Ali Gokirmak Department of Electrical and Computer Engineering, University of Connecticut 371 Fairfield Way, U-2157, Storrs, CT 06269 USA

Abstract We have observed melting of nanocrystalline silicon microwires self-heated through single high-amplitude microsecond voltage pulses which leads to growth from melt upon resolidification. The resolidified regions form two single-crystal domains for wires with sub-micrometer widths. The current densities (J) involved in this process are ~ 1-10 MA/cm2 for suspended wires, and ~ 10-100 MA/cm2 for wires on oxide. These extremely high current densities and the resulting high temperatures (~ 1700 K) and temperature gradients (~ 1 K/nm) along the microwires give rise to strong thermoelectric effects. The thermoelectric effects are characterized through capture and analysis of light emission from the self-heated wires biased with lower magnitude AC voltages (J < 5 MA/cm2). The hottest spot on the wires consistently appears closer to the lower potential end for n-type, and the higher potential end for p-type microwires. Experimental light emission profiles are used to verify the linear thermoelectric models and material parameters used for simulations. Good agreement between these experimental and simulated profiles indicates that the linear models can be used to predict the thermal profiles for current induced crystallization of microstructures. However, the linear models are expected to be insufficient to fully explain the thermoelectric processes for higher current densities and stronger thermal gradients that are generated by high-amplitude short duration pulses.

Introduction Polycrystalline (poly-Si), amorphous (a-Si) and nanocrystalline silicon (nc-Si) are commonly used for large area electronics such as flat panel displays [1], x-ray imaging arrays [2] and solar cells. Currently a-Si is used for silicon thin film transistors (TFTs) for large area electronics [1] due to its uniformity and low-temperature processing, despite its relatively low electrical carrier mobility [3]. There is a growing demand for displays and sensors on larger areas, using flexible and shatter-proof substrates like plastics, that can operate at higher speeds and sensitivities. Large areas require uniformity, flexible substrates require low temperature processing, and higher speed and sensitivity require use of crystalline material instead of amorphous. Cost effective techniques to achieve single-crystal Si on arbitrary substrates will also enable significant technological advancements, such as integration of high performance circuitry with displays or sensor arrays as complete systems. The interest in achieving high speed circuitry for large area electronics has motivated studies on crystal growth on glass and plastics [4], transfer of crystalline structures onto glass and plastic substrates, and crystallization of low temperature deposited silicon [1, 2, 5]. Crystallization of low temperature deposited a-Si films is a promising approach that has been studied in the past decades. This requires thermal processing of a-Si. High temperature annealing of a-Si films typically results in polycrystalline films. However, it has been reported that patterning the films to form microstructures with widths smaller than 250 nm can result in growth of single crystals along the length with preferred crystal orientation. Metal induced crystallization [6, 7] reduces the required temperature significantly, making it more compatible with low-temperature substrates but there are some concerns regarding the metal contamination in the crystallized films [8]. Local heating techniques, where the energy required for heating is directly delivered to the film or the patterned structures, allow the substrate to remain at room temperature. These techniques include sequential lateral solidification using an excimer laser [9, 10], rapid melting and growth from melt using self-heating [11] or microfabricated heaters atop the structures [12]. Some of the laser annealing techniques, such as sequential lateral crystallization, are currently in industrial use.

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_2, © The Society for Experimental Mechanics, Inc. 2011

9

10 The approach described in this paper is crystallization of nc-Si microwires through single microsecond voltage pulses (J < 10 MA/cm2) leading to self-heating, melting and growth from melt in a very short time (~ 1 μs). Larger current densities (J~20 MA/cm2) are required for further reduction in voltage pulse duration (d ~ 20 ns). The short duration local heating of the structures to be crystallized makes this approach compatible with low-temperature substrates. Real-time current-voltage measurements can be made on these structures during the crystallization process which can help understanding the mechanisms involved. The extreme thermal gradients (~1 K/nm) and the short time scales involved in these experiments are similar to those in pulse laser annealing. The main differences in this case are due to formation of molten filaments in the current path and thermoelectric effects which appear to be very strong under the extremely high electric current densities during the voltage pulse. Here, we give an overview of our experimental observations on melting, growth from melt and thermoelectric effects, and computational studies on heating and cooling of the wires including the role of thermoelectric effects.

Fabrication The microwires are patterned on n- and p-type nc-Si films deposited on oxidized single crystal Si wafers (~500 nm SiO2) in a low pressure chemical vapor deposition (LPCVD) system at 580 C or 600 C with phosphorous doping or at 560 C with boron doping ([P], [B] > 1020 cm-3). The room temperature resistivities of the n-type films deposited at 580 and 600 C are 30.4 ± 5.6 and 23.0 ± 0.3 PȍFPUHVSHFWLYHO\DQGUHVLVWLYLW\RIS-W\SHILOPLV“PȍFP Some of the microwires are suspended by etching the underlying oxide using buffered oxide etch. The ZLUHV¶ dimensions range from 0.5 to 5.5 ȝPin length and 100 nm to 1 ȝm in width. Metal extensions (Ti/Al stack) are deposited to form ohmic contacts to the Si pads.

Microsecond voltage pulse crystallization The experiments are conducted using a semiconductor probe station, a parameter analyzer, a pulse generator unit (PGU), and an oscilloscope. I-V characteristics of the microwires are measured before and after the voltage pulses using the parameter analyzer. The applied voltage and current through the microwire are measured by the oscilloscope during the pulse. Tungsten needles are used to probe the metal contacts or the silicon contact regions of microwires without metal extensions [13]. The melting of the wires is verified by extracting the wire resistivity during the pulse. This is achieved by calculating the resistance of a number of structures with different widths and lengths, yielding to resistivity of 73.3 “ȝȍFP [13, 14]. This value is in good agreement with previous reports on liquid Si resistivity of ȝȍFPE\*OD]RYHWDO[15], 75.2±0.6 ȝȍFPE\6FKQ\GHUVHWDO[16] DQGȝȍFPE\6DVDNLHWDO[17]. Liquid silicon at melting temperature is reported to be ~10% denser than silicon at solid phase at room temperature [15], which scales down the extracted liquid silicon resistivity value to 66.0 ± ȝȍFP. Melting of the wires requires less current and the mechanical stress induced by the substrate is eliminated if the wires are suspended by removing some of the underlying oxide. The heat loss from the suspended wires is predominantly to the contact regions at the two ends. The as-fabricated suspended microwires, wide and thin with uniform nanocrystalline texture, as seen in scanning electron microscope (SEM) images taken after the pulse (Fig. 1a), acquire a cylindrical shape with smooth surfaces (due to surface tension) and a lump in the middle (Fig. 1b) upon melting and resolidification. The as-fabricated structures have compressive stress, seen as sagging of the structures after the release (Fig. 1a). The recrystallized wires are stretched between the contact pads indicating a tensile stress. The resolidification process starts from the silicon pads and move towards the middle of the microwire. Some of the liquid silicon cannot fit in the middle as the two solid-liquid fronts meet, since silicon expands as it solidifies. Excess silicon is ejected and forms a lump after resolidification (Fig. 1b). The microwires which experience longer duration pulses show tapering and breaking (Fig. 1c) through silicon migration towards the silicon pads. Strong thermal gradient along the suspended microwires, due to low heat loss to the substrate, is expected to suppress nucleation along the wire and consequently limits the number of grains to two, one starting from each end. The conductance of the microwires is enhanced after the voltage pulse. Fig. 1EVKRZVDȝPORQJPLFURZLUHZLWKSUH-pulse WRWDOUHVLVWDQFHRINȍ7KHWRWDOUHVLVWDQFH5 Si FRQVLVWVRIWKHPLFURZLUHaNȍ DQG6LSDGUHVLVWDQFHVaNȍ  After the voltage pulse, the total resistance of the microwire in Fig. 1EZDVPHDVXUHGDVNȍZKLFKLVVPDOOHUWKDQWKH pre-pulse Si pad resistance. Low post-pulse resistance is attributed to conductance enhancement in both the microwires and the contact regions, even though the changes in the contact regions are not observable under SEM in this case. Resistivity of the pulsed, unbroken microwires is reduced by a factor of up to10x [18] indicating crystal growth rather than solidification in amorphous form.

11

(b)

nc-Si

(a)

(c)

lump SiO2

disconnected

Si accumulation L: 3.5 μm

1 μm

L: 2.5 μm

RInitial: 56.7 kȍ RFinal: 22.2 kȍ L: 3.5 μm

Fig. 1 (a) An as-fabricated, n-type, suspended microwire, and two microZLUHVDIWHUE 9ȝVDQGF 9ȝV pulse. Resistance of the wire in b) decreased significantly after the pulse [19]

Capture and analysis of light emission from the microwires under long duration biases The microsecond pulsing of the microwires results in very high current densities (1-100 MA/cm2). The peak temperature on the wire reaches the melting temperature of Si (1690 K) while the contact pads remain at room temperature, leading to thermal gradients on the order of ~1 K/nm. Thermoelectric effects are expected to be very significant at such current densities and thermal gradients [20, 21]. The transient effects in the short time scales involved in melting and crystallization in these experiments are difficult to probe. However, it is possible to gain some information about the steady-state temperature profile and the thermoelectric effects from the light emission from the wire as it is heated up to ~1000 K and beyond. This allows for verification of the high temperature materials parameters and models used for the computational studies. The first optical observation of thermoelectric effects in a single material system (Thomson effect) was reported by Mastrangelo et al. [22]. The authors observed that the peak light intensity (hottest spot) on p-type poly-Si micro-lamps was shifted from the center toward the higher potential end (V+). Englander et al. [23] observed a similar asymmetric light emission profile shifted towards the lower potential terminal in n-type poly-Si micro-heaters. Jungen et al. [24] also reported a shift towards the lower potential end for self-heated, n-type poly-Si, micro-bridges. Thermoelectric effects (thermoelectricity) is due to the coupling of electronic and heat transport through heat transfer by charge carriers. Direct electrical-thermal energy conversion for power generation, solid-state cooling [20, 21] and characterization of semiconductor materials [25] are the most common applications of thermoelectricity. Thermoelectricity can be observed as an open-circuit voltage across a temperature difference in a circuit of two different materials (Seebeck effect), heating or cooling at a current-passing junction between two different materials (Peltier effect) and heating or cooling along a current carrying homogeneous material under a temperature gradient (Thomson effect). The Seebeck voltage polarity and heating versus cooling for Peltier and Thomson effects depend on temperature-dependent thermoelectric properties of the material and directions of temperature gradient and electric current. The three thermoelectric effects are characterized by the Seebeck (S), Peltier (3 DQG7KRPVRQȕ FRHIILFLHQWVZKLFKDUHLQWHUUHODWHGE\WKHIXQGDPHQWDO.HOYLQUelationships [21]: 3

ST

E

T

, dS dT

(1) (2)

Thomson effect results in skewing of temperature profiles and is typically very small in macroscopic structures; however, it is significant in self-heated small-scale structures such as micro-lamps [22] and micro-heaters [23, 24] as mentioned above, as well as phase-change memory (PCM) elements [26], due to large current densities and temperature gradients. In all of these cases of self-heating at high temperatures, the hottest spot along the structures appears closer to the lower potential end (V-) for n-type structures and closer to the higher potential end (V+) for p-type structures, in agreement with expected hightemperature positive Thomson coefficient for n-type ȕ! and negative Thomson coefficient for p-type ȕ materials. DiCastro et al. [26] have calculated a Thomson coefficient of -1ȝ9.for SbTe above room temperature using an analytical solution for the hottest spot location and indicated that a 5% reduction in RESET current was obtained in

12 asymmetric PCM structures due to Thomson effect. However, changes in the material during the heating process can contribute to the asymmetry in the temperature profile and hence the observed asymmetries may be larger than what is due to the pure contribution of thermoelectric effects. In our experiments, we have recorded videos of light emission from self-heated nc-Si microwires using a high magnification optical setup and a commercial high-definition (full HD) camcorder at 30 frames per second. The wires self-heated to sufficiently high temperatures (T > 800 C [23]) emit light in the visible range. The speed of the measurement is limited by the sensitivity and the frame rate of the camera. Hence, the light emission from the wires was observed for low frequency AC signals at ~ 1 Hz. The light intensity profiles along the microwires and shift in the brightest (hottest) spot are extracted from the videos using MATLAB. Fig. 2a-b show glowing of a 2.5 ȝm long, suspended, n-type microwire during positive and negative cycles of an AC signal generated by the parameter analyzer. The hottest spot on the microwire alternates position as the current direction changes, confirming that the shift of the hottest spot is not caused by any asymmetric geometrical or thermal boundaries, but is due to thermoelectric effects. Fig. 2c shows current through the microwire and the shift in the hottest spot location as a function of time. The shift in the hottest spot for either cycle of the AC signal is approximately 250 nm (10% of the length).The shift in the hottest spot for the negative cycle gradually increases over time, showing a memory effect. Similar behavior is observed on other wires when they are biased with opposite polarity of the previous bias.

I (mA), 'x (Pm)

(a)

1.0

IWire : 0.95 mA

IWire : 0.93 mA

(b)

,

0.5

'x

0.0 -0.5

x

-1.0

(c)

20

21

22 time (s)

23

24

Fig. 2 A 2.5 ȝP long, suspended, n-type microwire during the (a) positive and (b) negative cycle of an applied square wave with ~ 0.95 mA (~3 MA/cm2) amplitude. Current levels and directions are as indicated. Wire center is located at x= 0. (c) Current (I) through the microwire and shift (ǻx) in the hottest spot location as a function of time [19]

Numerical modeling The experimental results are complemented by finite element analysis of a 2.5 ȝP long, suspended, n-type microwire using COMSOL Multiphysics software [27] including the thermoelectric effects, using the parameters available in the literature. The thermoelectric effects are included in both current continuity and heat transfer equations [28]: ’ .J

d Si C P

’ .(

dT dt

’V  S’T

U

 ’ .( k ’ T )

)

0

,

U J . J  TJ .’ S ,

(3) (4)

where dSi is the density, CP is the specific heat, k is the thermal conductivity, ȡ is the electrical resistivity and S is the Seebeck coefficient. The thermoelectric term (-TJ‫ ׏‬S) in Eq. 4 reduces to the Thomson heat for homogeneous structures (-dS/dTJ‫ ׏‬T). The resistivity of the microwire is modeled as an exponentially decaying function from its room temperature value of 23 PȍFPWRWKHPHOWLQJWHPSHUDWXUHYDOXHRIPȍFP [17], following the trend of the measured resistivity in the 300 - 650 K range (ȡ +195.5e-T/142 PȍFP). Temperature dependent thermal conductivity and Seebeck coefficient are not yet characterized for the heavily doped nc-Si used for the fabrication of the wires, nor are there any thermal conductivity or Seebeck coefficient data available in the literature on nc-Si, to the best of our knowledge. Hence, an inverse polynomial extrapolation function given in Ref. [29], fitting the experimental thermal conductivity of heavily-doped poly-Si in the 300 K to 800 K range, is used. Similarly, Seebeck coefficient of heavily doped poly-Si ([P] ~ 1020 cm-3) is used at low temperature

13 range (150 K ± 450 K) [30] and Seebeck coefficient of poly-Si with [P] = 6x 1017 cm-3 is used at high temperature range (700 K ± 1350 K) for modeling [31]. The Seebeck coefficient in the 450 K ± 700 K range is extrapolated linearly from these two poly-Si data sets which intersect at ~ 800 K, and it is also linearly extrapolated in the range between 1350 K ± 1690 K using the high temperature data. Density and specific heat of c-Si are close to those of poly-Si and a-Si [32] and change only slightly with temperature, therefore constant (room temperature) c-Si values [27] are used. The room temperature values of the modeling parameters of nc-Si, SiO2 and c-Si layers are shown in Table 1. Fig. 3a shows the 3D structure used for the modeling of the microwire and the electrical and thermal boundaries. A 5.8 V, 1 ȝs voltage pulse or square wave (AC) with increasing amplitude is applied across the wire. The current continuity and heat transfer equations including thermoelectric effects are solved self-consistently (Eq. 3 and 4). The modeling of pulsed wires is also performed without thermoelectric effects for comparison. Table 1 Room temperature values of the physical parameters used for the modeling

nc-Si SiO2 Si

ȡȍFP 23x10-3 d 1016 d 10-1

k (W/m.K) c 54 d 1.38 d 163

a,b

a

d (kg/m3) d 2330 d 2203 d 2330

CP (J/kg.K) d 703 d 703 d 703

S ȝ9/K) e,f -105 -

This work, bRef.[17], c Ref.[29], d Ref. [27],e Ref. [30], f Ref. [31]

Simulation results for the pulsed wire are seen in Fig. 3. The peak temperature on the wire reaches melting temperature of VLOLFRQ. LQȝVIRU91 ȝVYROWDJHSXOVHFig. 3b). The voltage pulse amplitude is chosen to keep the peak temperature on the wire below the melting temperature, since the phase change is not included in the modeling. The time to reach the melting temperature scales down as the voltage pulse amplitude is increased (Fig. 3c). The simulations suggest that the peak temperature on the wire can reach the melting temperature in less than 10 ns for voltage pulse amplitudes larger than 30 V. The cooling time of the wire is less than 250 ns for the given geometry. The simulated temperature profile along the wire just before melting is significantly skewed compared to the profile simulated without thermoelectric effects (Fig. 3d). The peak temperature is closer to lower potential end of the wire, which is in agreement with previous reports and our optical observations. Fig. 3d suggests that the melting of the wire starts on one end and continues until the whole wire melts. 1800

SiO2 (500 nm)

c-Si (5 ȝm)

(a)

0V 300 K

6 TMelt

1500

5 4

1200

3

900

2

600

1

300 (b) 0.0

0

1000

1800

0.5 1.0 1.5 Time (Ps)

VPulse (V)

Peak Temperature (K)

nc-Si (80 nm)

2.0

I 1200

T (K)

tmelt (ns)

1500

100

10

900 600

1

(c)

0

10

20 30 VP amplitude (V)

40

300

with TE effects

(d) -1.0

w/o TE effects -0.5

0.0 0.5 x (Pm)

1.0

Fig. 3 (a) 3D structure used for numerical modeling. A voltage pulse or a AC signal with increasing amplitude is applied to the square section of the left pad, while the square section on the right pad and the bottom surface of the substrate are set to 0 V. The temperature at these electrical boundaries is kept at 300 K. (b) Simulated peak temperature on the wire during the voltage pulse. (c) Simulated time required to reach the melting temperature of silicon (1690 K) on the wire as a function of voltage pulse amplitude. (d) Simulated temperature along the wire just before reaching melting temperature with and without thermoelectric effects. The arrow indicates the current direction (I: 0.74 mA) [19]

14 The light emission from the self-heated microwires is expected to be due to black-body radiation [22]. The light emission intensity profiles corresponding to the simulated temperature profiles are calculated using Eq. 5 [22] in the visible range to compare the simulated and experimental light intensity results. E (T )

³ H ( O , T ) E ( O , T )d O

,

(5)

O

where İȜ7 LVWKHHPLVVLYLW\ of the microwires which is assumed to be constant since it changes only very slightly throughout the visible range for silicon [33]. (Ȝ7 is the black-body radiation from the microwire as a function of radiation wavelength and temperature. The calculated light emission is convoluted using a point source approach to emulate the diffraction limited experimental light intensity profiles [34]. Each 1 nm segment of the microwire is assumed to be a point light source with a Gaussian intensity profile as given in Eq 6. I Gaussian ( x )

I ( x center ) 2 SV

2



( x  x center )

e

2V

2

2

,

(6)

where xcenter is the point where the Gaussian profile is evaluated, I(xcenter) is the black-body radiation from WKDWSRLQWDQGıLV the width for the profile. 7KHRSWLFDOUHVROXWLRQRIRXUV\VWHPFDOFXODWHGDVȜ ZKHUHȜLVthe wavelength of the emitted light [34]ZDVXVHGIRUı7KHintensity profiles from each point source are added together and scaled to have the same peak intensity as the experimental profile. Fig. 4c shows the experimental (I = 0.95 mA, J~3 MA/cm2) and simulated light intensity profiles (I = 0.96 mA) showing 250 nm and 154 nm of shift in the hottest spot (Fig. 4a-b), respectively. The simulated light intensity profiles are in good agreement with the experiments, showing the correct direction of the asymmetry and a comparable magnitude for the shift of the hottest spot location. The difference is expected to be due to a mismatch between the actual physical nc-Si parameters (electrical and thermal conductivities and Seebeck coefficient) and those used for the simulation from the literature for similar materials.

1200

(a)

100

IWire: 0.96 mA

1000

I

x (b)

600

Light Intensity (a.u.)

50

800

400 K

(c)

Experiment

0 100

Modeling

(d) I

50

IWire: 0.96 mA 0

-1.0

-0.5

0.0

0.5

1.0

x (Pm)

Fig. 4 (a, b) Simulated temperature profiles of the suspended, n-type microwire for indicated current level and direction. Experimental and simulated light intensity for (c) positive and (d) negative voltage cycles. Current direction for each cycle is as indicated. The simulated light intensity profiles are calculated as black-body radiation from the microwires in the visible range, at a current level (0.96 mA) that matches the experimental value [19]

Summary Nanocrystalline silicon microwires are self-heated, melted and crystallized by microsecond voltage pulses. The crystallized microwires are under tensile stress and typically acquire a cylindrical shape with smooth surfaces. Significant reduction in resistivity of pulsed, suspended microwires indicates crystallization of the microwires upon resolidification, with growth of large single crystal domains.

15 The extremely high current densities (1-100 MA/cm2) and temperature gradients (~ 1 K/nm) reached along the microwires result in strong thermoelectric effects as observed through asymmetric heating of the microwires. These thermoelectric effects are analyzed through capture of asymmetric light emission from both n- and p-type microwires during low-frequency AC signals. The hottest spot is always closer to the lower potential end for n-type microwires and closer to the higher potential end for p-type microwires. AC voltage applied to the microwires results in alternating location of the hottest spot, confirming the thermoelectric nature of the observed asymmetric self-heating, rather than being due to any asymmetric geometrical or thermal boundary condition. Numerical modeling of the thermoelectric transport in an n-type microwire during an AC signal, including temperature dependent physical parameters shows good agreement with the experiments. Simulation results for a microsecond voltage pulsed microwire show significantly skewed temperature profiles for temperatures close to melting temperature of Si, suggesting this model can be used to predict the heating and cooling of microwires during the rapid self-heating and crystallization process. The findings of this work are relevant for studies on crystallization techniques and thermoelectric effects under high current densities and thermal gradients. Higher performance may be achieved for small-scale electronic devices, such as phasechange memories, by accounting for thermoelectric effects in device design.

Acknowledgements The devices were fabricated at the Cornell NanoScale Science & Technology Facility. SEM imaging was partially performed at the Harvard Center for NanoScale Systems. We thank Nathan Henry, Mustafa Akbulut and Cicek Boztug for their help with design and fabrication of the microwires. We also thank the CNF staff for their support for the fabrication of the structures. This work was supported by the National Science Foundation (ECCS 0702307, 0824171 and 0925973), the Department of Energy (DE-SC0005038) and the University of Connecticut Research Foundation.

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Evaluation of Resistance Measurement Techniques in Carbon Black and Carbon Nano-tubes Reinforced Epoxy Venkat K. Vadlamani1, Vijaya B. Chalivendra1*, Arun Shukla2, Sze Yang2 1 University of Massachusetts, North Dartmouth, MA 02747, USA 2 University of Rhode Island, Kingston, RI, 02881, USA * Corresponding author, [email protected], 508-910-6572

ABSTRACT Two different resistance measurement techniques are used in an epoxy material reinforced separately with carbon black (CB) micro-particles and carbon nano-tubes (CNTs) to evaluate the effectiveness of both the techniques and type of reinforcement on damage detection under uni-axial tensile loading. Two techniques, namely traditional four-point probe (FPP) and fourcircumferential ring probe (FCRP) are employed and a constant current is applied through outer probes. The resulting voltage drop between inner probes is measured using a commercial high resolution electrometer based system. Since current density distribution in both techniques is different, the measured change in resistance (both qualitatively and quantitatively) is also different. In addition to change in current density due to different techniques, the size of conductive reinforcement also has significant impact on both current distribution and further change in resistance. CB reinforced epoxy showed very high percentage change in resistance against CNTs reinforced epoxy for both techniques. It was identified that CNTs reinforced epoxy showed no significant difference for both FPP and FCRP methods. However, for CB reinforced epoxy, significant difference in percentage change in resistance was observed for both resistance measurement methods.

1.

Introduction

Due to their high electrical conductivity, carbon black and carbon nanotubes were used as a sensory network in detecting damage initiation and growth in concrete [1-3] and in polymer composites [4-6] when they were subjected to mechanical loads. The damage initiation and growth was detected by measuring the change in resistivity of the above materials using traditional four point probe (FPP) measurement methodology [1-5]. In this methodology either constant current or voltage is supplied between two outer probes and respective change in voltage or current was measured through inner probes to record the change in material resistivity associated with the damage. To discuss few studies in this paper, Thostenson and Chou [4] recorded maximum percentage change in resistance of 300% due to damage at a peak load in glass fiber–epoxy composites. Nofar et al., [5] indentified a maximum percentage resistance change of about 40% due to damage in CNT reinforced laminated Bidirectional woven glass fibers epoxy composites during tensile and fatigue loading. However, traditional FPP methodology allows the current to flow though small depth below the surface and the damage detection zone is limited. However, to detect significantly large amount of damage inside the materials due to mechanical loads, we expected that a four circumferential ring probe (FCRP) methodology is a better choice. Although there are no many studies reported using FCRP approach, Park et al., [7] employed FCRP approach in determining change in resistivity due to damage during carbon fiber pull-out test of carbon nanotube reinforced epoxy composites. In this study, we conducted a comprehensive experimental investigation of both FPP and FCRP techniques in an epoxy material reinforced separately with carbon black (CB) micro-particles and carbon nano-tubes (CNTs) under uni-axial tensile loading. A constant current is applied through outer probes of above techniques and the resulting voltage drop between inner probes is measured using a commercial high resolution electrometer based system. Due to change in current density of above two techniques and also due to the size of conductive reinforcement, we expected to see significant change in resistance measurements (both qualitatively and quantitatively).

2. Experimental Procedures 2.1 Material Fabrication Given the simplicity of casting and low curing temperature, the matrix used in this study is an epoxy polymer based on bisphenol-A resin (Buehler Epothin (20-8140-128)) and an epoxy hardener (Buehler Epothin 20-8142-064). The mixing T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_3, © The Society for Experimental Mechanics, Inc. 2011

17

18 ratio of Part-A to Part-B was 50g to 18 g. The multi-wall carbon nanotubes (purity > 95%) used were supplied by NanoLab. The nanotubes had outside diameters of 30 ± 15 nm, lengths of 5 to 20 microns and a specific surface area of 200-400 m2/g. Two different weight fractions of CNTs 0.3 and 0.5% wt were tested to understand percolation threshold. Carbon black (CB) has irregular particle shape and has average size of 1-5µm and they have mass density of 1.8-2.0 gm/cm3. In this study a weight fraction of 10% was used in making composites. Due to high surface energy, carbon nanotubes tend to agglomerate into bunches. These agglomerations can act as defects rather than enhancements which directly affects the transport properties of the material [8]. To effectively disperse CNTs and enhance electrical response of the material under study, the present work implemented high-intensity ultrasonication and high-speed shear mixing.

Fig. 1. Schematic of nanocomposite fabrication procedure A schematic of the general procedure for material preparation is shown in Fig 1. Pre-measured amounts of Epothin Part-A Resin and carbon nanotubes were combined in a copper beaker. The mixture was mechanically stirred for 5 minutes. The mixture was then placed into a shear mixer (Ika Werke RW 16 Basic) outfitted with a 3-blade propeller stirrer (R1381 Propeller stirrer) operating at a speed of 450 RPM for 30 minutes. Following shear mixing, the mixture was then immediately irradiated. The ultrasonication process was applied for one hour on pulse mode, 4.5 sec on 9 sec off (Sonics & Materials Inc. VCX750). During the sonication process, the copper beaker containing the mixture was submerged into a cooling bath in order to maintain a mixture temperature of 18°C - 30°C. It is essential to control the temperature of the mixture during the entire process in order to prevent any avoidable damage that would occur to the nanotubes during the sonication process [9]. Any damage of the nanotubes would diminish the electrical properties of the final composite. Cooling bath was designed to control the temperature of the mixture by adjusting the flow rate of liquid nitrogen through a series of copper coils submerged in an anti-freeze solution. The weight fraction of CNTs in the solution may determine a required cooling rate for the temperature control. After the sonication process, the mixture was moved into a vacuum chamber to remove trapped air bubbles generated during the mechanical mixing process [10]. Once all air was removed from the mixture, it was combined with and mechanically stirred for 2 minutes. The mixture was once again placed back into the vacuum chamber for 5 minutes. Finally, the CNT-epoxy solution was slowly poured into pre-manufactured molds. The samples were allowed to cure for 24 hrs. In the case of carbon black, Epothin Part-A (Resin) and carbon black were combined in a copper beaker. The mixture was mechanically stirred for 5 minutes. The mixture was then placed into a shear mixer (operating at a speed of 450 RPM for 45 minutes). Then the mixture was placed in vacuum chamber until complete degassing was performed. Later the mixture was mixed with Part-B and shear mixed for 2 minutes. The final mixture was again placed in vacuum chamber for 5 min and after that the solution is poured in molds.

2.2 Electrical Characterization In the present study, dog bone specimen configuration was used for uni-axial testing. Two novel approaches four-point probe method and four-circumferential ring method were implemented to capture the electrical resistance change during mechanical loading. As seen in fig (4a), silver epoxy (MG Chemicals 8331-14G) was used for point method and as shown in fig (4b) silver paint (SPI-Paint 05001-AB) was used for circumferential ring method. A constant current was passed through the outer probes; voltage drop across two inner probes was measured to determine the electrical resistance of the middle section. Since

19 the current flow, i, was constant and the voltage change, V, between the two inner probes was measured, the instantaneous resistance between the two inner probes, R′, was calculated. Percent change in resistance was taken as,

R '− R 0 × 100 R0

(1)

where R0 is the initial resistance between the two inner probes. Due to the complexity and variability of the networks present within each specimen, the initial R value was served as a baseline resistance for each experiment. Suitable current must be chosen for the experiment. Various amount of current ranging from 100µA – 2nA passed and initial resistance is calculated for all currents. Within a range of currents the initial resistance will kept constant as seen in Table 1. A current should be selected from that range for experiment to avoid fluctuations in resistance measurements while applying mechanical loads. The experimental setup used in quasi-static tests is shown in Fig 2. A constant current source (Keithley Instruments Model 6220) was used to generate a constant current flow through outer probes. Two electrometers (Keithley Instruments Model 6514) measured the voltage reading at each of the two individual inner probe rings. The difference between the two voltage readings, which corresponds to the voltage drop across the two inner probes, measured by the electrometers would then be shown on a digital multimeter (Keithley Instruments Model 2000 DMM) and recorded using a LabView system.

Table 1. Selection of suitable current Current(amps)

Resistance(Ω)

100e-6

3.64e+5

75e-6

3.84e+5

50e-6

4.16e+5

25e-6

4.82e+5

200e-9

1.21e+6

175e-9

1.21e+6

150e-9

1.21e+6

125e-9

1.18e+6

100e-9

1.22e+6

75e-9

1.19e+6

50e-9

1.32e+6

25e-9

1.13e+6

2e-9

1.9e+6

Constant Current Source

Multimeter

Electrometer

Electrometer

Constant Current Source

(a)

Multimeter

Electrometer

Electrometer

(b)

Fig. 2. Experimental set-ups for measuring resistance change under quasi-static conditions (a) Four-Point, (b) Four circumferential ring

20

2.3 Quasi-Static Loading The quasi-static loading was implemented by a servo-hydraulic system (Instron 5582), as shown in fig (5). Specimens were loaded at a constant rate of 1 mm/min. The displacement of the loading head corrected by the machine compliance was utilized to calculate the strain of the specimen under quasi-static loading.

3. Results and Discussion 3.1 Percolation Behavior Study

Resistance(KΩ)

Prior to experimentally studying the electrical 3000 response of CNT- epoxy nanocomposites under loading, a detailed investigation was conducted to 2500 determine the percolation threshold of the fabricated composites under no loading conditions. This study 2000 was essential in order to determine the optimum duration of sonication as well as the concentration of 1500 CNTs for the manufacturing of the test specimens to ensure a proper network being formed within the 1000 material. Although the results are discussed here in this paper, we identified that 0.5% weight fraction 500 generates optimum percolation threshold. Previous 0 studies have shown similar electrical percolation 0 1 2 3 4 5 6 behavior in nanotube-epoxy composites [11]. Hours of sonication Beyond 0.5 wt% the percolation threshold, there is no further significant improvement in electrical Fig. 3. Experimental results of static resistance conductivity. Therefore, the concentration of CNTs measurements as a function of sonication duration was set to 0.5 wt. % in the present study. Using this 0.5% weight fraction, the effect of the duration of the sonication process on the base resistance of the material was determined. The resulting change in resistance with sonication time is shown in shown in Fig 3. 60 50

Stress (MPa)

While the base resistance show apprarent change immediately after one hour of sonication, it begins to drastically increase as sonication duration is further extended. This may be attributed to the nanotubes being damaged due to an excessive sonication. The high local temperatures and pressures during the sonication process may have damaged and weakened the nanotubes, thus creating a less efficient percolation network. From this observation, sonication was set to 1 hour during the specimen fabrication process in present study.

40 30 20

Epoxy Epoxy with CNT Epoxy with Carbon Black

10

3.2

Electro-mechanical response: 0

For statistical significance and consistency of the experimental data, minimum six experiments were conducted for specific case of material & technique. Having high confidence on our experimental data, we only present in this section, a representative data for each situation.

0

2

4

6 Strain (%)

8

10

Fig. 4. Engineering stress vs strain diagrams of pure epoxy, epoxy reinforced with CNT and carbon black

12

Before the electromechanical response of both CNT and carbon black reinforced epoxy is discussed in this section, typical engineering stress vs. strain diagrams of pure epoxy, epoxy reinforced with CNTs and carbon black is shown in Fig. 4. With the reinforcement of CNTs, the composite’s percentage elongation at break decreases to around 7.75% and the same for carbon black reinforced epoxy is at around 4.5%. There is no considerable change in tensile strength of all three materials. These stressstrain diagrams would be useful in explaining the nature of percentage changes in resistance of CNT & carbon black reinforced epoxy composites later in this section.

60

Stress (MPa)

4

200 30 150 20

100

10

50

0 1

2

3

4

5

6

8

Strain (%)

0 0

4

6

Strain (%)

Fig. 7. Typical stress-strain and electrical repsonse of CB reinforced epoxy using FPP methodology

Fig. 5. Typical stress-strain and electrical repsonse of CNT reinforced epoxy using FPP methodology

4.5 4

Stress (MPa)

50

3.5

40

3 2.5

30

2

20

1.5 1

10

0.5

0

0 0

2

4

6

8

Strain (%) Fig. 6. Typical stress-strain and electrical repsonse of CNT reinforced epoxy using FCRP methodology

50

200

40

160

30

120

20

80

10

40

0

0 0

1

2

3

4

5

Strain (%)

Fig. 8. Typical stress-strain and electrical repsonse of CB reinforced epoxy using FCRP methodology

Change in Resistance (%)

60

Change in resistance (%)

250

40

0 2

Stress (MPa)

300

2 20

0

Change in Resistance (%)

Stress (MPa)

50

3

0

Fig. 6 provides the variation of both applied stress and percentage change of electrical resistance against axial strain of CNT reinforced epoxy using FCRP methodology. A similar trend to that of FPP technique shown in Fig. 5 can be seen for FCRP case. All three stages as discussed for Fig. 5 can be noticed in Fig. 6 too. 350

40

1

Fig. 5 provides the variation of both applied stress and percentage change of electrical resistance against axial strain of CNT reinforced epoxy using FPP methodology. In the first stage (until 3% strain), as the applied strain increases, the resistance increases monotonically at rapid rate. In the second stage (beyond 3% strain until it reaches maximum stress value), the resistance of the specimen increases at a decreasing rate compared to stage-1. As soon as the maximum stress is reached, the resistance decreases (instead of further increase) due to relaxation of the material between maximum stress and breaking stress. As soon as the specimen breaks, the specimen realizes high resistance. The maximum percentage change in resistance recorded for CNT reinforced epoxy with FPP technique was about 4%.

60

5

Change in resistance (%)

21

22 The maximum percentage recorded for this technique is as well about 4%. Hence we conclude from Fig. 5 and 6 that both FPP and FCRP techniques resulted same stages and maximum value of change in resistance for CNT reinforced epoxy composites. Figs. 7 and 8 provide the variation of both applied stress and percentage change of electrical resistance against axial strain of CB reinforced epoxy using FPP and FCRP methodologies respectively. The first major difference between CB reinforcement against CNT reinforcement is that the maximum change in resistance in former case is 40 to 80 times higher than that of later case. The major reason for such a big change is severe voids formation that occurs around the CB particles and the resulting growth of damage. As it can be see from Fig. 4 that percentage elongation at break of CB reinforced epoxy is almost half that of pure epoxy and which is due to severe void formation around the CB particles. This phenomenon is significant in CNT reinforced epoxy. In can be noticed for both techniques for CB reinforcement, there exists again three stages of change of electrical resistance. Unlike in Figs. 5 and 6, in these both cases, the rate of change of resistance are less in the beginning until about 1% strain. In the second stage, after about 1%, the there is significant increase in the rate of change of resistance in both methods as shown in Figs.7 and 8. In the third stage, the maximum value of change in resistance happens before the mechanical axial load reaches maximum value. This is not the case for CNT reinforced epoxy as shown in Figs. 5 and 6. After reaching maximum value, the resistance varies about the maximum and tries to stay there again decrease that is seen in Figs. 7 and 8. The major significant difference that can be noticed in Figs 7 and 8, the FPP method notices higher change of resistance (about 315%) against maximum value (about 170%) in FCRP method for carbon black reinforced epoxy material under uni-axial tensile loading. We are not quite sure about the reasons for this difference and we would be able to explore them and present them in the conference.

4. Conclusions A comprehensive experimental study has been conducted to fabricate CNT and CB reinforced epoxy to verify the effectiveness of either four point probe or four circumferential probe measurement systems to capture electrical response during uni-axial tensile loading. Even though CB reinforcement generated very high percentage change in electrical resistance, CB reinforcement is recommended because the damage the reinforcement induces will corrupt the detection of actual damage of caused by the epoxy. Although CNT reinforcement induced reduction of percentage elongation to break by 30%, the resistance change can be directly attributed to damage of the epoxy matrix and may not be primarily due to CNT reinforcement itself. Moreover, both FPP and FCRP methods yielded similar qualitative and quantitative resistance changes, hence we recommend to use four-point probe methodology using CNT reinforcement as sensory network for detecting damage in polymer systems in future studies.

Acknowledgements This work was supported by the National Science Foundation (NSF) under grant number CMMI-0856463

References [1] H. Li, H-Q. Xiao, J-P. Qu, “Effect of compressive strain on electrical-resistivity of carbon black-filled cement based composites,” Cement and Concrete Composites, vol 28, pp. 824-828, 2006. [2] H. Li, J. Qu, “Smart concrete, sensors and self-sensing concrete structures,” Key Engineering Materials, vol 400-402, pp. 69-80, 2009. [3] L. Rejon, A. Rosas-Zavala, J. Porcoyo-Calderon, V.M. Castano, “Percolation phenomena in carbon black-filled polymeric concrete,” Polymer Engineering and Science, vol 40(9), pp. 2101-2104, 2000. [4] E.T. Thostenson, T-W. Chou, “Carbon Nanotube Networks: Sensing of Distributed Strain and Damage for Life Prediction and Self Healing,” Advanced Materials, vol 18, pp. 2837-2841, 2006. [5] M. Nofar, S.V. Hoa, M.D. Pugh, “Failure detection and monitoring in polymer matrix composites subjected to static and dynamic loads using carbon nanotube networks,” Composites Science and Technology, vol 69, pp.1599-1606, 2009. [6] M.A. Bily, Y.W. Kwon, R.D. Pollak, “Study of composite interface fracture and crack growth monitoring using carbon nanotubes,”Applied Composite Materials, vol 17(4), pp. 347-362, 2010. [7] J-M. Park, D-S. Kim, S-J. Kim, P-G. Kim, D-J. Yoon, K.L. DeVries, “Inherent sensing and interfacial evaluation of carbon nanofiber and nanotube/epoxy composites using electrical resistance measurement and micromechanical technique,” Composites: Part-B, vol 38, pp. 847–861, 2007.

23 [8] M.E. Kabir, M.C. Saha, S. Jeelani, “Effect of ultrasound sonication in carbon nanofibers/polyurethane foam composite,” Materials Science and Engineering A, vol. 459, iss. 1-2, pp. 111-116, 2007. [9] P. Ma, N.A. Siddiqui, G. Marom, J. Kim, “Dispersion and functionalization of carbon nanotubes for polymer-based nanocomposites: A review,” Composites Part A: Applied Science and Manufacturing, vol 41, iss. 10, pp. 1345-1367, 2010. [10] V.M.F. Evora VMF, A. Shukla, “Fabrication, characterization, and dynamic behavior of Polyester/TiO2 nanocomposites,” Materials Science and Engineering A, vol. 361, iss. 1-2, pp. 358-366, 2003. [11] W. Bauhofer, J.Z. Kovacs, “A review and analysis of electrical percolation in carbon nanotube polymer composites,” Composites Science and Technology, vol. 69, iss. 10, pp. 1486-1498, 2009.

A nano-tensile tester for creep studies

L.I.J.C.Bergers1,3,4 J.P.M. Hoefnagels1, E.C.A.Dekkers2, M.G.D. Geers1 1

Eindhoven Univ. of Technology, Dept. of Mech. Eng., P.O.Box 513, 5600 MB, Eindhoven, NL, 2 Eindhoven Univ. of Technology, GTD., P.O.Box 513, 5600 MB, Eindhoven, NL, 3 Foundation for Fundamental Research on Matter, P.O.Box 3021, 3502 GA Utrecht, NL, 4 Materials innovation institute, P.O.Box 5008, 2600 GA Delft, NL. E-mail: [email protected]

Abstract Free-standing metallic thin films are increasingly used as structural components in MEMS. In commercial devices, long-term reliability is essential, which requires determining time-dependent mechanical properties of these films. The uniaxial tensile test is a preferred method due to uncomplicated determination of the stress and strain state. However, at the MEMS-scale this method is not straightforward: specimen handling and loading, force and deformation measurement need careful consideration. Here we discuss the challenges of the application and measurement of nano-Newton forces, nanometer deformations and micro-radians rotation alignment ensuring negligible bending in on-chip tensile test structures during long periods. We then present a novel tensile-testing instrument with in-situ capabilities in SEM and Optical Profilometry. The design solutions to measure these small forces and deformations whilst ensuring a uniaxial stress state will be presented. Introduction Mechanical testing for material behavior characterization has brought much understanding into the mechanics of materials at the macro scale. Nowadays, however, miniature devices with dimensions at the sub-micrometer scale, such as MEMS, are processed routinely, which has revealed unexpectedly new mechanical micro-mechanisms. This has spurred research into new mechanical characterization techniques to understand the physical fundamentals at the (sub)-micron scale, e.g. nanoindentation [1], FIB-enabled in-situ micro-tensile testing [2], fully integrated and dedicated tensile test MEMS [3]. One important outcome of this research is that testing at the nano-scale is far from trivial [4;5]! To address this issue, a novel nano-tensile methodology is presented here for which all fundamental aspect of tensile testing have been reconsidered in its design. A suitable testing methodology faces a number of challenges. First of all, such a methodology needs to be sensitive enough to measure the nano-Newton forces and nanometer deformations involved at this scale. Well-defined loading conditions are preferred to facilitate interpretation of the deformation state, thus favoring the uniaxial tensile test. Boundary conditions should also be carefully controlled to minimize undesired influences, such as surface roughness or friction effects, while challenges of specimen handling, loading and alignment need to be addressed as well. Furthermore, easy specimen variation is required to enable systematic studies of the influences of, e.g., mechanical size-effects. Finally, in-situ SEM testing capability is necessary to unravel the physical origin underlying (the often complex) microscopic deformation mechanics [6]. Design of methodology The design of the methodology has the uniaxial tensile specimen at its heart. The specimen fabrication and variation determine the requirements for the loading method, force and deformation measurement. After establishing these requirements, suitable solutions to obtain them are discussed followed by their respective implementations in the design of the uniaxial tensile tester.

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_4, © The Society for Experimental Mechanics, Inc. 2011

25

26 Specimen fabrication A common method [7-9] to create tensile specimens is the micro-fabrication of dog bone shaped specimens on a substrate, with one end and the gauge section free-standing e.g., by under etching. Considering specimen handling and fabrication, it is highly preferred to test on-chip structures instead of separate μm-sized structures. Moreover, applying the same microfabrication procedure as done for the actual device guarantees the relevance of obtained results. Therefore, dog bone shaped tensile specimens are designed and fabricated on silicon chips, see Figure 1. The cross section dimensions of the gauge section are varied to probe size-effects from sub-micron into the micro range, because MEMS devices are designed this range. The specimen length is made as long as possible to facilitate the elongation measurement. Based on these dimensions and the desire to perform creep measurements at tensile stresses of 1-100 MPa, the force range is determined. Finally, a chip of 10x10 mm2 is filled with ~60 specimens. In short, this approach takes advantage of the precision and ease of reproduction of microfabrication, and the ease of geometrical variation within a chip design.

Figure 1 Chip layout and tensile specimen design Load application The loading of the specimens has to deal with applying desired forces to the specimen and ensuring a homogeneous uniaxial tensile stress is attained. The application of the forces is simplified to mounting a chip and gripping the free end of the tensile specimen. Several approaches to gripping have been reported: electro-static clamping, application of adhesives and mechanically locking. These methods have their pros and cons, but a choice is only possible after considering the effect of incorrect gripping, because this can lead to misalignment resulting in undesired bending stresses in the specimen. Some forms of misalignment can occur (see Figure 2): i) force and specimen's longitudinal axis are parallel, but not co-linear, ii) force and longitudinal axis are at an angle. Based on a straight forward analysis of statics and elastic beam theory, the initial ratio of maximum bending stress to desired tensile stress can be estimated. The bending stress from non-co-linearity can be assumed negligible, if the point of force application is in-line with the specimen's longitudinal axis. Furthermore, actuation of translations should be feasible at this scale with 5-10 nm precision, which is less than 1% of the specimen width and thickness. The bending stresses resulting from rotational misalignment can be minimized by reducing the ration l/t or by minimizing the misalignment angles. As it is desirable to increase l (for the elongation measurement), the angles need to be minimized. Allowing for σbend/σtensile < 5%, then already θ<10-4 rad for l/t=500 μm /0.5 μm! Therefore a precise mechanism is required to rotate the specimen and/or the gripper. To minimize the unwanted bending stresses, gripping is done mechanically by creating a hole in the pad at the free end of the specimen and a pin at the end of a stiff beam, the so-called gripper, see Figure 2. By using bulk silicon micro-machining of an SOI-wafer (200 μm handling layer, 50 μm device layer), the gripper can effectively be fabricated with sub-micron precision from the μm-scale at the specimen end to the mm-scale to facilitate instrument integration. The bending is minimized in two ways. First, the hole in the pad has a sharp feature that aligns the contact point of gripper and pad to the specimen's axis.

27 Second, the longitudinal axes of specimen and gripper can be translated in three directions and rotated about two axes with respect to each other with high precision to further minimize misalignment. Coarse translations (mm-range, μm resolution) are applied through manual thumbscrews, whilst fine translations are applied through a commercial 3-axis piezo stage (MadCityLabs, Nano-T225M: xy-parallel kinematics, z-axis separate), having in-plane and out-of-plane resolution of <1 over a range of respectively 200 μm x 200 μm and 50 μm and pitch, yaw, roll of ~10-6 rad. The rotations are carefully set through precision mechanisms based on elastic hinges with angular resolution of <10-4 rad.

Figure 2 Schematic illustration of (a) ideal uniaxial tensile test for the tensile specimen fixed at one end, (b) unwanted bending moment due to non-co-linearity of specimen's axis and force and (c) due to angular misalignment between specimen's axis and force The manipulation of the rotations needs to be measured to ascertain the bending stress contribution. Whilst in-plane rotations can be measured straightforwardly by top view imaging of the specimen with an (electron-) optical microscope and simple image processing, the out-of-plane rotation is not as straightforward. As an optical profilometer will only allow for measuring the misalignment to <10-3 rad, an electrical mechanism is included. Two electrical contact pads are placed on the substrate adjacent and parallel to the specimen's axis, spaced at a distance S=1 mm. Then a second pin is placed on the gripper at distance S from the loading pin. By grounding the pins and measuring the electrical currents through each contact pad, contact between the gripper and substrate can be monitored when the gripper approaches the substrate. In the case of no misalignment both contacts will be made simultaneously. If there is misalignment, this can be detected with δz,piezo / S < 5·10-5 rad. With this method of gripping and aligning of load to the specimen, it is estimated the bending stress contribution will be <10% of the desired tensile stress.

Figure 3 Load transfer using a ‘gripper’: pin-in-hole contact and alignment of axes minimizes moments and bending stresses

28 Load measurement The previous solutions yield a method of precisely loading the specimen. As indicated in Figure 1, the range of loads spans 5 decades, whilst 2 decades are additionally desired for nN-precision! Nano-indenters are currently the only instruments with such capabilities. Practically speaking it is not necessary to have nN-resolution for mN forces. Therefore, it is chosen to create three exchangeable load cells, each spanning part of the range. The load cells are simple parallel leaf spring mechanisms that are fabricated from a Ti-Al-V alloy through electric-discharge machining. The gripper is mounted at the end of the parallel leaf spring. The stiffness of these springs combined with the deflection measurement determines the measurable force range and resolution (see Table 1). By using a highly precise capacitive sensor (Lion Precision C5-D probe + CPL190 Driver), the leaf spring deflection u is measured. Calibration of the load cell is then achieved by tilting the load cell with a known angle and measuring the deflection caused by a component of the gravitational force exerted on the gripper of known mass. Finally, using accurate electronic readout ensures the long term stability of the load measurement. Table 1 Desired load cell characteristics Range Capacitive displacement sensor Force range 1: Force range 2: Force range 3:

250 μm

Resolution 5 nm @100 Hz

0.01 μN…10 μN 1 μN…1 mN 100 μN…100 mN

<0.01 μN <0.1 μN <10 μN

Precision <0.05 μN 0.5 μN 50 μN

Linearity 0.1% of full range

k [N/m] 0.08 8.0 800.0

Deformation measurement The measurement of deformation is feasible with microscopical tools like SEM or even optical microscopy, if dimensions across which deformations are to be measured are large enough. The foremost component of deformation measurement is the uniaxial strain. By placing markers along the length of the gauge, small enough to have negligible influence on the stress state, and on the substrate, the displacement of these markers can be measured yielding the uniaxial strain. With digital image correlation (DIC) this can be resolved to ~0.1 pixel for SEM images and ~0.01 pixel for light microscopy images [10] which yields strain resolutions of ~10-4 respectively ~10-5 for an image of 1000 pixel length. Furthermore, by employing SEM to obtain hi-resolution images at the micro-scale, not only in-situ qualitative observations of the deformation mechanisms are obtained, but also quantitative 2D deformation fields in combination with DIC. Positioning and actuation The last aspects of the design of the methodology are the chip mount, positioning and load actuation. The chip is mounted on a small platform through mechanically clamping. The platform is also equipped with a resistive heater and thermometer to heat the chip up to 150 °C. The design of the nano-tensile stage then integrates the chip platform, the load cell with gripper, and positioning and alignment mechanisms, see Figure 4. Positioning of the gripper and load cell is achieved by a coarse manual xyz-stage, and a fine electronic xyz-piezo stage. The x-actuator of the piezo stage also serves as the load actuator (200 μm stroke, <10 nm resolution). Alignment to minimize bending stresses as previously specified is done for 4 rotations: 1) θy and 2) θz of the specimen, 3) θz between x-piezo actuator and load cell's direction of deflection and 4) θy of the load cell and xyz-stage to set the load cell horizontal with respect to gravity. Based on these considerations, the alignment and test procedure is as follows: 1. Under an optical profilometer the load cell is leveled so it is in the center of its range. 2. Then the gripper is translated to the specimen with the manual manipulators followed by in-plane alignment by optically measuring the angle between the long side of the gripper and the beam and applying simple image processing. 3. The out-of-plane alignment can then be done by first using optical profiling to achieve alignment within 10-3 rad and then the electrical contacting mechanism to align within 10-4 rad. 4. After translating the gripper away from the specimen only using the piezo stage, the setup can be transferred to the SEM, where if necessary the load cell leveling is done again (required if SEM and profilometer are not exactly parallel). 5. Then in the SEM, the misalignment is checked before the gripper is hooked into the specimen with the piezo stage. 6. Finally the creep test can be performed by loading with the piezo stage, measuring the force with the load cell and recording the deformation through SEM imaging. This design succeeds in creating a compact setup that fits in a scanning electron microscope. By translating the gripper for specimen loading, the imaging of the specimen's deformation is greatly facilitated. Finally, the use of accurate electronics and a feedback loop to conduct force controlled creep experiments combined with the mechanical precision design will enable performing stable and precise long term in-situ measurements.

29

Figure 4 Schematic overview of the realized tensile tester, indicating the various actuated degrees of freedom, mounting of load cell and placement of chip with tensile specimens Conclusion In the authors' opinion, the here-presented nano-tensile methodology is the first technique that meets all of the requirements simultaneously: force resolution of 10 nN, strain resolution of 10-5, minimization of bending stresses to 10% of the desired uniaxial stress, easy specimen variation and handling and a compact and stable setup capable of in-situ SEM creep measurements. The strength of the methodology will be demonstrated through highly precise measurements of uniaxial stress-strain curves of on-chip μm-sized free-standing Al-(1wt%)Cu beams (used in RF-MEMS applications). References 1. Nix, W. D., "Mechanical properties of thin films," Metall.Trans.A., 20, 11, pp. 2217-2245, 1989. 2. Kiener, D. et al., "A further step towards an understanding of size-dependent crystal plasticity: In situ tension experiments of miniaturized single-crystal copper samples," Acta Mater., 56, 3, pp. 580-592, 2008. 3. Haque, M. A. and Saif, M. T. A., "In-situ tensile testing of nano-scale specimens in SEM and TEM," Exp. Mech., 42, 1, pp. 123-128, 2002. 4. Hemker, K. J. and Sharpe Jr, W. N., "Microscale characterization of mechanical properties," Ann. Rev. Mater. Res., 37, pp. 92-126, 2007. 5. Kang, W. and Saif, M. T. A., "A novel method for in situ uniaxial tests at the micro/nano scale part I: Theory," J. Microelectromech. Syst., 19, 6, pp. 1309-1321, 2010. 6. Legros, M. et al., "Quantitative In Situ Mechanical Testing in Electron Microscopes," MRS Bull, 35, 5, pp. 354-360, 2010. 7. Chasiotis, I. and Knauss, W. G., "A new microtensile tester for the study of MEMS materials with the aid of atomic force microscopy," Exp. Mech., 42, 1, pp. 51-57, 2002. 8. Tsuchiya, T. et. al., "Tensile testing system for sub-micrometer thick films," Sens. Actuators A Phys., 97-98, pp. 492496, 2002. 9. Sharpe Jr, W. N., "Murray lecture tensile testing at the micrometer scale: Opportunities in experimental mechanics," Exp. Mech., 43, 3, pp. 228-237, 2003. 10. Sutton, M. A. et al., Image Correlation for Shape, Motion and Deformation Measurements, 1st ed. New York City, NY: Springer Science+Business Media, LLC, 2009.

The Measurement of Cyclic Creep Behavior in Copper Thin Film Using Microtensile Testing K.-S. Hsu, *M.-T. Lin, C.-J. Tong

Graduate Institute of Precision Engineering, National Chung Hsing University, Taichung 402, Taiwan, R.O.C. *E-mail: [email protected]

ABSTRACT A micro-tensile testing for studying the cyclic fatigue mechanical properties of freestanding copper thin film with thickness of sub-micrometer application for MEMS was performed to observe its mechanical response under tension-tension fatigue experiments with a variety of mean stress conditions at cyclic loading frequencies up to 20 Hz. Tensile sample loading was applied using a piezoelectric actuator. Loads were measured using a capacitance gap sensor with a mechanical coupling to the sample. The experiments were carried out with feedback to give load control on sputter deposited 300, 500 and 900 nm copper thin films. Loading cycles to failure reached over 10^6 at low mean load with a trend of decreasing cycles to failure with increasing mean load as anticipated. The cyclic fatigue results provided clear evidence for a cyclic creep rate dependent and change in failure mechanism from crack formation to extended plasticity as the mean load is decreased. I.

INTRODUCTION

With the fast development of the microelectronics technology, the system and device design required further developing the complexity and packing density of micro-nano scale devices into the future allowing ever smaller in the range of nanometer scale and more densely packed structures to be fabricated. Continued growth of microsystem technology requires still further miniaturization, with a corresponding need to understand how length scales affect mechanical behavior. As a result, the mechanical properties of sub micron and nano scale thin films have become one of the most important issues. Moreover, MEMS (MicroElectroMechanical Systems) has become an important technology. The goal of MEMS is to integrate many types of miniature devices on a single chip and has been used in a variety of applications. To date, fabrication of MEMS devices has generally been performed using conventional integrated circuit fabrication techniques. Thus, materials properties play a role of importance in MEMS as it has performed in the integrated circuit applications. In recent study of MEMS fabrication, design, and testing confirms that devices whose fabrication, design, and operational attributes including environment have been optimized rarely exhibit bulk mechanical failure by fatigue or fracture [1]. Instead, MEMS failure mechanisms may associate degradation of reflecting MEMS thin films including surfaces, grain growth, deformation and time dependent deformation due to creep or fatigue. Among various materials application for microelectronics and MEMS, copper thin film is one of the most common used thin films materials since its electrical conductivity. In particular, cyclic behavior of copper thin films, could ultimately limit product lifetime in its applications. Example such as micro-machined copper thin film resonators requires a vacuum package to obtain the highly selective frequency response. However, the resonant frequency is strongly dependent upon the device dimensions and characteristics of deposited structural thin films. Thus, a reliable design parameter, such as mechanical properties of copper films is needed in order to overcome the process variation, inherent mechanical stresses as well as cycle fatigues. Here, the experimental testing technique whose characteristics represent nominal operating conditions is demonstrated. It is designed to use a specimen with electroplated frames, pins align holes, misalignment compensates springs and a load sensor beam connected to a freestanding microbeam. The specimen is then fitted into the microtensile apparatus to carry out a series of micromechanical uniaxial tensile and displacement controlled tension-tension fatigue experiments tests.

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_5, © The Society for Experimental Mechanics, Inc. 2011

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2. EXPERIMENTAL PROCEDURES The experimental setup consists of a tensile test chip, a piezoelectric actuator and a load sensing capacitor. The original design were reported previously [3,5 ], a number of changes were made both in the system and sample design and fabrication to make it more robust in terms of consistencies of process yields, tests reliability and operation efficiency. 2.1. Overview of the sample design and fabrication The sample design consists of a freestanding beam and a supporting frame connected to the piezoelectric actuator. Figure 1 shows the schematic of the test chip, the details specimen geometry and the dimension. The central part of the testing chip is the sputtered freestanding copper thin film (with a gage section measuring 600 μm in length and 100 μm in width, and preferred thickness of 0.3, 0.5, 0.9 μm) to be tested for its mechanical properties, held at one end by the displacement sensor beam to mount a Polytech PI high resolution capacitor sensor, which allows the measurement of in-plane deflections. Same thing as other small scale tension tests, the gripping of the specimen is due to the adhesion between the frame substrate and the specimen materials. This eliminates the necessity of an extra gripping mechanism for the specimen. The sample was placed flat, with copper thin film up (frame down), on horizontal mounting blocks, or mounts. Grips rise vertically out of the top faces of the mounts, fitting through the sample that extends through the frame at either end of the tensile sample. The mounts are held in position relative to one another and the two mounts could move independently of one another. The other end of the specimen is held by a set of grip which have the ability to reduce the misalign errors.

Fig. 1- The schematic of the test chip The details on fabrication of the sample, the loading fixture, as well as an analysis on the issue of alignment were provided in [2~5]. Figure 2 is a modified version of the fabrication sequence and is more robust in terms of process yields. The processing substrates are using 4” (100) silicon wafers. A silicon nitride layer in 1μm thick served as a sacrifice layer coated on top of it. Copper films with thickness of hundreds of nanometer thick were then being sputtered. The copper films were then being patterned in microlithography lift-off process. Total of 32 test samples can be obtained from each wafer. The thickness of each tested thin film is measured by a profilometer after sample fabrication.

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Fig. 2 -The sample fabrication sequence 2.2. Overview of the system The stage apparatus is custom design equipped with environmental cells and controlled by PC through National Instrument LabVIEW program. This assembly consists of a micromechanical testing system with height-adjustable grips, built-in piezoactuator with position sensor, load cell and temperature sensor. The control electronics include a closed-loop piezoelectric controller, amplifier and waveform generator. Monitored signals are conditioned and then fed into an A/D board which is located in a PC. Data acquisition is performed with LabVIEW software. The system is covered in a well insulated, temperature controlled box and is supported on a vibration isolation table. It consists of two aluminum blocks rigidly bolted to the vibration isolation table. The left block mounts a displacement controlled piezoelectric actuator. The right aluminum block mounts with height adjustable pin via an x–y–z stage to assure well alignment of the sample and also supports the capacitor load cell. The control electronics include a closed-loop piezoelectric controller with 0.1 um resolution and a waveform generator. The maximum displacement provided by the piezoelectric actuator has travel range over 50 um. Loading was applied through the retraction of piezoelectric actuator to pull the test chip through the pinhole. Loads were measured by a capacitor load cell with a resolution of less than 0.1 mN. The displacement is transmitted to the displacement sensor beam and the strain can be calculated from the difference of displacement in load sensor readout. Tensile force is applied on the specimen by adding a displacement on one end of the chip while the other end is held fixed. The displacement is transmitted to the displacement sensor beam by the specimen and causes a deflection on the displacement sensor beam. The force F on the film specimen is defined as F = kd, where k is the spring constant of the combination of force sensor beam and linked capacitor senor, and d is the beam deflection, it can also be measured from the capacitive displacement senor. Figure 3 shows the calibration figures of displacement versus voltage measurement of capacitive senor and thus the spring constant of the load versus senor measurement can be calibrated. For the stress and strain calculations of the freestanding thin film, the dimension of each test sample is individually measured. The thickness of each tested thin film is also measured by a profilometer. Strain is determined from that measure the distance between the left marker A and the right marker B with a resolution of ±10.0 nm.

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Fig. 3- the calibration figures of displacement versus voltage measurement of capacitive senor Simultaneously, external microscope with CCD camera is equipped to acquire in situ image for study during testing. Tension-tension type fatigue tests were utilized in this study due to the inability of thin film tensile structures to support compressive loads. Initial experimental parameters were determined based on results from monotonic tensile testing. Two parameters, displacement amplitude (A) and mean displacement (d) were varied in a systematic manner. Figure 4 and 5 schematically shows how the triangular waveform sent to the piezoelectric actuator was varied in the experiments. Figure 4 and Figure 5 show experiments where constant displacement amplitude, Ao was maintained while the mean displacement was varied from do to d1. One experimental constraint to note is that in order to maintain either tension-tension or tension-zero experiments, the displacement amplitude may not be more than two times the mean displacement.

Fig. 4

schematic of fatigue experiments I

Fig 5 schematic of fatigue experiments II

3. RESULTS 3.1 Tension-tension fatigue testing results The prior studies for fine grain size metal film fatigue [10] suggested that a free-standing tensile-type test, among other benefits, offers results which may be directly interpreted and affords ease of fatigue analysis. However, both qualities are important at a size scale where neither material properties nor testing methods are well established. Tension-tension type cyclic tests were utilized in this study due to the inability of thin film tensile structures to support compressive loads. It is clear that fatigue lifetime is dependent on both fluctuated load amplitude and overall mean stress. A detail study on mean stress versus loading cycles, fatigue cycles versus sample elongation of 500 nm and 900 nm thick copper thin film were

35

perform to investigate their tensile fatigue behavior. Initial experimental parameters were determined based on results from monotonic tensile testing to determine the fraction of its maximum stress. The mean stress (D) was varied with constant load amplitude (A) in a systematic test. In each tests, total of 15 cyclic tests set were performed from the mean stress of 20 percent maximum stress to 100 percent maximum stress with every 30 MPa extensions. Samples were run at a mean displacement corresponding to each load, including displacement amplitude corresponding to  20 MPa experiment, the maximum amplitude for this particular mean displacement (A/2≦d). A summary of the results on a loading cycles vs stress ratio curve of 500 nm and 900 nm copper films can be seen in Figure 6, 7.

Fig. 6 - loading cycles vs stress ratio curve of 500 nm copper films

Fig. 7 - loading cycles vs stress ratio curve of 900 nm copper films

36

In bulk copper materials, under constant stress amplitude, 1x102 ~103 cycles without failure is often defined as a fatigue limit. In this study, the fatigue tests on copper thin films with thickness of 500 nm and 900 nm, neither of the samples failed within 1x103 cycles. Although testing conditions are different, we consider both of our tested 500 nm and 900 nm samples to be past the fatigue limit. In particular, when the experimental mean stress was increased to 80 percent of maximum yielding stress, the fatigue life time can still reach over 1x104 cycles as shown in Figure 6, 7. This is contrary to the behavior of bulk copper materials where the low fatigue cycle leads to sample failure in such loading condition. Moreover, it was observed that the fatigue to failure cycles can exceed 1x105 cycles without fracture in the 20 percent maximum stress amplitude on both thickness of the tests samples. The results indicate a trend of increasing cycles to failure with decreasing thickness of copper down to submicrometer scale. However, the trend on fatigue cycles to failure between 500 nm and 900 nm was not clearly reflecting to the reduction of its thickness since the grain sizes were similar in both films. 3.2 Cyclic creep testing results Figure 8, Figure 9 summarized the sample elongation rate versus fatigue life for fixed stress amplitudes of 20MPa and at various mean load (stress) tests as indicated of 500nm and 900 nm copper films respectively. These sample elongation values were obtained from the value of DC offset of piezo feedback as described. In Figure 8, for the mean load value of 26.75 mN (estimated to be 535 MPa), the cyclic elongation of sample reaches 7.8um. In the contrast, for the mean load value of 35 mN (estimated to be 700 MPa), the cyclic elongation of sample is less than half micron. As well as Figure 9, for the mean load value of 12.6 mN (estimated to be 140 MPa), the cyclic elongation of sample reaches 6.8um. In the contrast, for the mean load value of 53.55 mN (estimated to be 595 MPa), the cyclic elongation of sample is less than half micron. For the data shown in Figures 8 and 9, cyclic plastic flow decreases with mean stress increases, indicating the sensitivity of cyclic creep to imposed mean stress and a trend in decreasing plasticity with increasing mean load is well described.

Fig. 8 - the sample elongation rate versus fatigue life for fixed stress amplitudes at various mean load (stress) tests of 500nm copper films

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Fig. 9 - the sample elongation rate versus fatigue life for fixed stress amplitudes at various mean load (stress) tests of 900nm copper films

4. CONCLUSIONS A novel experimental sample design and apparatus for uniaxially tensile testing microtensile of thin films under monotonic loading/unloading and tension-tension fatigue conditions has been designed and fabricated. Furthermore, it is capable of testing over a large range of displacement rates up to 20 m/s as well as a range of frequencies up to 25 Hz. The experiments are carried out with feedback to give load control on sputter deposited 500 and 900 nm Cu thin films. Loading cycles to failure reached as high as 10^5 at low mean load with a trend of decreasing cycles to failure with increasing mean load as anticipated. The cyclic creep results provided clear evidence for a creep rate dependent and change in failure mechanism from crack formation to extended plasticity as the mean load is decreased. REFERENCES 1. Miller, S.L., M.S. Rodgers, G. LaVigne, J.J.Sniegowski, P. Clews, D.M. Tanner, and K.A. Peterson, in Proc. 36th IEEE Int. Reliability Physics Symp. (NJ, 1998) 2. Haque, M.A. and Saif, M.T.A., “In Situ Tensile Testing of nano-scale Specimens in SEM and TEM,” EXPERIMENTAL MECHANICS, 42(1), 123-128 (2001) 3. Ming-Tzer Lin, Chi-Jia Tong & Chung-Hsun Chiang “Design and Development of Sub-micron scale Specimens with Electroplated Structures for the Microtensile Testing of Thin Films” MICROSYSTEM TECHNOLOGIES (Accept JAN 2007) 4. Haque, M.A. and Saif, M.T.A., “Application of MEMS force sensors for in situ mechanical characterization of nano-scale thin films in SEM and TEM”, Sensors and Actuators A 97-98, 239-245(2002). 5. Ming-Tzer Lin et al. (2006) Design an electroplated framefreestanding specimen for microtensile testing of submicron thin TaN and Cu Film, in materials, technology and reliability of low-k dielectrics and copper interconnects. Mater Res Soc Symp Proc 914, Warrendale 6. D.T. Read “Tension-tension fatigue of copper thin films”. Int. J. Fatigue Vol. 20, No. 3, pp. 203-209. (1998) 7. Nicholas Barbosa III, Paul El-Deiry, Richard P. Vinci “Monotonic Testing and Tension-Tension Fatigue Testing of Free-standing Al Microtensile Beams” Mat. Res. Soc. Symp. Proc. Vol. 795 © (2004) 8. Haque, M.A. and Saif, M.T.A., Sensors and Actuators A 97-98, (2002) pp.239-245. 9. Ming-Tzer Lin, Chi-Jia Tong & Kai-Shiang Shiu, Microsystems technologies, DOI 10.1007/s00542-007-0463-5 10. D.T. Read. Int. J. Fatigue Vol. 20, No. 3,(1998) pp. 203-209 11. O. Kraft, R. Schwaiger, P. Wellner, Materials Science and Engineering A319-321 (2001) 919-923.

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12. G. P. Zhang, Sun, K.H.; Zhang, B.; Gong, J.; Sun, C.; Wang, Z.G., Materials Science and Engineering A483-484 (2008)387-390. 13. R. D. Emery, G. L. Povirk, Acta Materialia 51 (2003) 2067-2078. 14. R. D. Emery, G. L. Povirk, Acta Materialia 51 (2003) 2079-2087. 15. Spolenak, R, Brown, W.L., Tamura, N.; MacDowell, A.A.; Celestre, R.S.; Padmore, H.A.; Valek, B.; Bravman, J.C.; Marieb, T.; Fujimoto, H.; Batterman, B.W.; Patel, J.R. Physical Review Letters, v 90, n 9, Mar 7, 2003,. 16. M. T. Lin, Paul El-Deiry, Richard R. Chromik, Nicholas Barbosa, Walter L. Brown Terry J. Delph, Richard P. Vinci, Microsyst Technol (2006) 12: 1045–1051. 17. E. Arzt, Acta Mater. 46, 5611 (1998). 18. S. P. Baker, Mater. Sci. Eng. A 319-321, 16 (2001). 19. J. R. Weertman, in Nanostructured Materials: Processing, Properties, and Applications, C. C. Koch, Ed. (William Andrews, Norwich, NY, 2002). 20. M. A. Haque, M. T. A. Saif, Sens. Actuators A 97-98, 239 (2002).

New Insight into Pile-up in Thin Film Indentation B.C. Prorok, B. Frye, B. Zhou and K. Schwieker Auburn University, Department of Mechanical Engineering 275 Wilmore Engineering Labs, Auburn, AL 36849, Email: [email protected] ABSTRACT A new method of accurately and reliably extract the actual Young’s modulus of a thin film on a substrate has been developed. The method is referred to as the discontinuous elastic interface transfer model. The method has been shown to work exceptionally well with films and substrates encompassing a wide range of elastic moduli and Poisson ratios. The advantage of the method is that it does not require a continuous stiffness method and can use the standard Oliver and Pharr analysis and the use of a predictive formula for determining the modulus of the film as long as the film thickness, substrate modulus and bulk Poisson ratio of the film are known. However, when there is much pile-up during the indentation process in a softer film, the experimental data does not follow the predictive formula but instead follows a similar model with a single Poisson ratio between the film and the substrate. INTRODCUTION In the scientific and engineering communities, there has been much effort to accurately determine the properties of thin film coatings by means of discretely intrusive indents using nanoindentation techniques. However, the task in determining the properties is not trivial a trivial one. The problem with the measurement methods stems from deformation fields originating from the indent propagating in both the film and the substrate; therefore any properties measured in the experiment are that of a composite value. It has been challenging for scientists and engineers to obtain a theoretical method of investigating a complete description of the discontinuous properties of thin film coatings. Recently, a new model has been proposed for a new model referred to as the elastic interface transfer model. The new Figure 1 (a) Schematic illustrating the concept of continuous model accounts for a discontinuity in elastic strain transfer transfer of strain between the film and substrate, (b) numerical between the film and the substrate. A schematic of the simulation indicating that strain is likely discontinuously theory underlying the elastic interface transfer model is transferred between the film and substrate, and (c) schematic shown in figure 1. The figure shows, based upon the theory, showing how the film and substrate components are decoupled that between the boundaries of the film and substrate, there in the discontinuous elastic interface transfer model is not a continuous transfer of strain. Figure 1: (a) is representative of what Doerner and Nix [2] and Gao [3] have presented in their works as a spherically symmetric strain field emanating from the indent across the film/substrate interface. According to Doerner and Nix, the values of strain on either side of the film/substrate interface are equal to one another, suggesting that there is a continuous transfer of strain. However, numerical simulations have found that there should be a discontinuous transfer of the elastic strain field at the film/substrate boundary, Fig 1(b) and (c). Figure 1:(c) indicates that there is actually a film component as well as a substrate component describing the discontinuous strain field. In the previous models, a single weight factor was used to describe the strain transfer, having the following form:

1 1 1 1  = ' +  ' − ' ΦD−N , E' E f  E s E f 

(1)

Here, E’ is the composite modulus, Ef’ is the film modulus = Ef /(1-υf2), Es’ is the substrate modulus = Es /(1-υs2), and ΦD-N is a weighting factor which accounts for the continuously changing contribution of the film and substrate made by the indenter, which is given as,

€

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_6, © The Society for Experimental Mechanics, Inc. 2011

39

40

Φ D−N = e

−α (t / h eff )

,

(2)

where, t is the film thickness, h is the indent depth and α is an empirically defined constant, usually around 0.25 according to Doerner and Nix. Different weighting factors have been applied to the previous model in order to describe the discontinuity in the elastic strain field in the following form:

€ ,

(3)

where,

Φf = e

−α f (t / h )

and

Φs = e−α s (t / h )

(4)

Here, Φf and Φs are the weighting factors to account for the effects of the film on the substrate and substrate on the film respectively and αf and αs are the constants. In previous works, the discontinuous elastic transfer model has been compared to experimental data from various combinations of thin film materials on different substrates and was found to match experimental curves accurately. Through investigation of the theoretical curves, it was found that the constants, αf and αs, in each weighting factor were essentially equivalent to the bulk scale Poisson’s ratios for the film and substrate respectively.

€

€

EXPERIMENTAL PROCEDURE In this work was AlOx deposited on five different substrates with a variable range of elastic moduli and Poisson ratios to investigate the discontinuous elastic interface transfer model. The substrates included <0001> sapphire (Al2O3), <100> magnesium oxide (MgO), <100> N-type undoped germanium (Ge), amorphous silicon (aSi) and silicon dioxide (SiO2). All substrates were previously polished to ensure a uniform contact at the film/substrate interface. Gold films were deposited onto the substrates using a Denton sputtering system with RF and DC power and the parameters used during the process were determined by previous experiments. The substrate platform was rotated at 50 RPM to ensure uniform deposition during the sputtering process. Secondly, gold (Au) was sputtered on Quartz using the same procedure previously stated. An adhesion layer of titanium (Ti) was sputtered first on the substrate before sputtering the Au thin film. The final thickness of the Au film on the substrate was approximately 480 nm. Material properties of each material are shown in table 1. For Au, the elastic modulus is 72 GPa and the Poisson ratio value for the bulk scale is 0.44. Table 1 Material properties for the substrates used

Substrate

Modulus (GPa)

Poisson’s Ratio [ref]

SiO2

70 ± 4

0.17 (quartz)

[39]

Ge

144 ± 7

0.27

[40]

Si

173 ± 9

0.28

[41]

MgO

249 ± 17

0.23

[42]

Al2O3

460 ± 28

0.21~0.27

[43]

Indentation tests on each sample were performed using an MTS Nanoindenter XP with a Berkovich diamond tip. Young’s modulus vs. displacement of the indenter into the sample was obtained using a continuous stiffness method (CSM) with a minimum thermal drift rate of 0.05 nm/s and a harmonic displacement target set to 2 nm. The depths of the indents were set to 500 nm. The Poisson’s ratio used in the CSM tests was that of the bulk value for gold. For each indentation test, 25 indents were made, each having the same parameters and indent depths, and averaged together for the final Young’s modulus vs. displacement data.

RESULTS AND DISCUSSIONS In the work, raw indentation data of aluminum oxide (AlOx) on 5 different substrates were calibrated and compared to the discontinuous elastic interface transfer model. Figure 2 illustrates the measured Young’s modulus vs. displacement into the surface on each of the five substrates. The data was shown to fit the curves accurately in all substrates. The quality of the fit for all five substrates is shown in Figure 3, which exhibits a flat region that can be

41 considered to represent the Young’s modulus of the film. The change in the value of Eflat for AlOx suggests that it is strongly dependent on the substrate modulus, increasing as the substrate’s modulus increases.

Figure 2 Plot comparing the measured Young’s modulus as Figure 3 Plot illustrating the quality fit of the discontinuous a function of displacement for the AlOx films on different elastic interface transfer model for the AlOx films and estimation of elastic homogeneity of the film/substrate substrates composite (dashed line) However, when choosing a film substrate combination with elastic moduli values close to each other, the experimental data did not match the theoretical data of the discontinuous elastic interface transfer model as well. The experimental data of Au on Quartz is shown in figure 4. According to the model, the experimental data should have rapidly increased as the indenter penetrated the film and slowly decreased upon further depth. The trend predicted by the model is a result of the difference in Poisson ratio’s between the film and the substrate. However, the experimental data followed the Doerner and Nix model, in which there is but one weighting factor. Because Au is a softer film, perhaps the behavior shown is due to pile-up of the film during the indentation process. Figures 5 and 6 show SEM micrographs of a single indent in the Au film on a quartz substrate. In the image, it is clear that there is significant pile-up of gold around the perimeter of the indent. Figure 4 Plot comparing the measured Young’s modulus of In other words, the effect of the differences in the Poisson Au on a quartz substrate to the discontinuous elastic ratio’s of the Au film and Quartz substrate did not make a interface transfer model as well as the Doerner and Nix difference in the experimental data as predicted by the model. model

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Fig 5 SEM micrograph of indent on Au film at 18,000X

Fig 6 SEM micrograph of same indention at 30,000X

CONCLUSIONS Indentation tests were conducted on various film and substrate combinations. It was found that the difference in material properties between the film and substrates had a large effect on the mechanical behavior of the film, as shown in the experimental data. The experimental data for AlOx films fit the discontinuous elastic interface transfer model accurately. However, when performing an indent on a soft film such as gold on a soft substrate such as quartz, the experimental data did not match the theoretical model but instead followed the model presented by Doerner and Nix. Because the data followed the D-N model, there is a single weight factor in effect which is related a single Poisson ratio. There was an indication of pile-up in the film around the indent of the Au film suggesting that the load of the indenter is directly transferred into the substrate as the depth of the indent increases. REFERENCES: 1. J.B. Pethica, R. Hutchings and W.C. Oliver: Hardness measurement at penetration depths as small as 20 nm. Philos Mag A 48 593 (1983). 2. M.F. Doerner and W.D. Nix: A method for interpreting data from depth-sensing indentation instruments. J. Mater. Res. 1 601 (1986). 3. H. Gao, C.-H. Chiu and J. Lee: Elastic Contact versus Indentation Modelling of Multi-Layered Materials. Int. J. Solids Structures 29 2471 (1992). 4. G.M. Pharr, D.L. Callahan, S.D. McAdams, T.Y. Tsui, S. Anders, A. Anders, J.W. Ager Iii, I.G. Brown, C.S. Bhatia and S.R.P. Silva: Hardness, elastic modulus, and structure of very hard carbon films produced by cathodic-arc deposition with substrate pulse biasing. Appl. Phys. Lett. 68 779 (1996). 5. X. Chen and J.J. Vlassak: Numerical study on the measurement of thin film mechanical properties by means of nanoindentation. J. Mater. Res. 16 2974 (2001). 6. R.B. King: Elastic Analysis of Some Punch Problems for a Layered Medium. Int. J. Solids Struct. 23 1657 (1987). 7. W.D. Nix: Mechanical properties of thin films. Met. Trans. A 20 2217 (1989). 8. J.A. Knapp, D.M. Follstaedt, S.M. Myers, J.C. Barbour and T.A. Friedmann: Finite-element modeling of nanoindentation. J. Appl. Phys. 85 1460 (1999). 9. H. Buckle, The Science of Hardness Testing and its Research Applications. (ASM, 1973) Pages. 10. J. Hay: Measuring substrate-independent modulus of dielectric films by instrumented indentation. J. Mater. Res. 24 667 (2009). 11. J. Menčík, D. Munz, E. Quandt, E.R. Weppelmann and M.V. Swain: Determination of elastic modulus of thin layers using nanoindentation. J. Mater. Res. 12 2475 (1997). 12. H. Xu and G.M. Pharr: An improved relation for the effective elastic compliance of a film/substrate system during indentation by a flat cylindrical punch. Scr. Mater. 55 315 (2006).

43 13. H. Li and J.J. Vlassak: Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation. J. Mater. Res. 24 1114 (2009). 14. S. Roche, S. Bec and J.L. Loubet: Analysis of the elastic modulus of a thin polymer film. Mater. Res. Soc. Symp. Proc. 778 117 (2003). 15. R. Saha and W.D. Nix: Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Mater. 50 23 (2002). 16. H.Y. Yu, S.C. Sanday and B.B. Rath: The effect of substrate on the elastic properties of films determined by the indentation test—Axisymmetrical Boussinesq problem. J. Mech. Phys. Solids 38 745 (1990). 17. S.M. Han, R. Saha and W.D. Nix: Determining hardness of thin films in elastically mismatched film-on-substrate systems using nanoindentation. Acta Mater. 54 1571 (2006). 18. S. Bec, A. Tonck, J.M. Georges, E. Georges and J.L. Loubet: Improvements in the indentation method with a surface force apparatus. Philos. Mag. A 74 1061 (1996). 19. T. Chudoba, M. Griepentrog, A. Duck, D. Schneider and F. Richter: Young’s modulus measurements on ultra-thin coatings. J. Mater. Res. 19 301 (2004). 20. N. Schwarzer, F. Richter and G. Hecht: The elastic field in a coated half-space under Hertzian pressure distribution. Surf. Coat. Technol. 114 292 (1999). 21. B. Zhou and B.C. Prorok: A Discontinuous Elastic Interface Transfer Model of Thin Film Nanoindentation. in press Exp. Mech.(2010). 22. G.M. Pharr, J.H. Strader and W.C. Oliver: Critical issues in making small-depth mechanical property measurements by nanoindentation with continuous stiffness measurement. J. Mater. Res 24 653 (2009). 23. Z. Wei, G. Zhang, H. Chen, J. Luo, R. Liu and S. Guo: A simple method for evaluating elastic modulus of thin films by nanoindentation. J. Mater. Res. 24 (2009). 24. B.C. Prorok and H.D. Espinosa: Effects of nanometer-thick passivation layers on the mechanical response of thin gold films. J. Nanosci. Nanotech. 2 427 (2002). 25. H.D. Espinosa, B.C. Prorok and M. Fischer: A methodology for determining mechanical properties of freestanding thin films and MEMS materials. J. Mech. Phys. Solids 51 47 (2003). 26. H.D. Espinosa, B.C. Prorok and B. Peng: Plasticity size effects in free-standing submicron polycrystalline FCC films subjected to pure tension. J. Mech. Phys. Solids 52 667 (2004). 27. H.D. Espinosa and B.C. Prorok: Size effects on the mechanical behavior of gold thin films. J. Mater. Sci. 38 4125 (2003). 28. L. Wang and B.C. Prorok: Characterization of the strain rate dependent behavior of nanocrystalline gold films. J. Mater. Res. 23 55 (2008). 29. L. Wang and B.C. Prorok: Investigation of the Influence of grain size, texture and orientation on the mechanical behavior of freestanding polycrystalline gold films. Mater. Res. Soc. Symp. Proc. 924E Z03 (2006). 30. H.D. Espinosa, B.C. Prorok, B. Peng, K.H. Kim, N. Moldovan, O. Auciello, J.A. Carlisle, J.A. Gruen and D.C. Mancini: Mechanical properties of ultrananocrystalline diamond thin films relevant to MEMS/NEMS devices. Exp. Mech. 43 256 (2003).

Measuring Substrate-Independent Young’s Modulus of Thin Films Jennifer Hay Factory Applications Engineer Agilent Technologies, Inc., Nano-Measurements Operation 105 Meco Ln., Suite 200 Oak Ridge, TN 37830

ABSTRACT Substrate influence is a common problem when using instrumented indentation (also known as nano-indentation) to evaluate the elastic modulus of thin films. Many have proposed models in order to be able to extract the film modulus (Ef ) from the measured substrate-affected modulus, assuming that the film thickness (t) and substrate modulus (Es) are known. Existing analytic models work well if the film is more compliant than the substrate. However, no analytic model accurately predicts response when the modulus of the film is more than double the modulus of the substrate. In this work, a new analytic model is reviewed. Using finite-element analysis, this new model is shown to be able to accurately determine film modulus (Ef) over the domain 0.1 < Ef/Es < 10. Finally, the new model is employed to determine the Young’s modulus of low-k and silicon carbide films on silicon.

Introduction The problem of determining intrinsic film properties from indentation data that are influenced by both film and substrate is an old one. If the film is thick enough to be treated as a bulk material, then the analysis of Oliver and Pharr (1992) is typically used [3]. When the film is so thin that indentation results at all practical depths are substantially affected by the substrate, the influence of the substrate must be accurately modeled in order to extract the properties of the film alone. Since 1986, many such models have been proposed [2, 4-13]. In 1992, Gao, Chiu, and Lee proposed a simple approximate model for substrate influence. They derived two functions, I0 and I1, to govern the transition in elastic properties from film to substrate[2]. Beginning in 1999, Song and his colleagues took an alternate solution path which was originally suggested by Gao et al. but not followed [8-10]. This alternate path yielded a simpler model which is called the “Song-Pharr model” in the literature. The Song-Pharr model predicts substrate effect reasonably well when the film is more compliant than the substrate. In 2011, Hay and Crawford developed a modified version of the Song-Pharr model which better handles the case of stiff films on compliant substrates[1]. In this article, the Hay-Crawford model will be explained and applied to material systems of broad interest: low-κ and silicon-carbide films on silicon. The Hay-Crawford model is a development of the Song-Pharr model, which in turn, draws from the Gao model. The HayCrawford model requires these inputs: • µa, the apparent (or substrate-affected) shear modulus of the film, • νf, the Poisson’s ratio of the film, • t, the film thickness, • µs, the shear modulus of the substrate, and • νs, the Poisson’s ratio of the substrate.

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_7, © The Society for Experimental Mechanics, Inc. 2011

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46 The output of the model is µs, which is the substrate-independent shear modulus of the film. (Throughout this work, the subscript “f” means “of the film,” the subscript “a” means “apparent,” and the subscript “s” means “substrate”.) All of the inputs to the Hay-Crawford model are readily available from a regular indentation test. The apparent shear modulus, µa, is simply that which is calculated by the Oliver-Pharr method [3, 14, 15]. It should be noted that most commercial indentation systems output Young’s modulus, E. To convert between Young’s modulus, E, and shear modulus, µ, one must assume and employ the general relation: µ = E/[2(1+ν)] (1) Although the model requires Poisson’s ratio for both film and substrate, the results are actually very insensitive to these parameters, so educated guesses are fine if definitive measurements are unavailable. (For glasses and ceramics, use ν = 0.2; for metals, use ν = 0.3; for polymers, use ν = 0.4.)

Theory The Hay-Crawford model is based on the supposition that, subject to an indentation force, the film has the potential to act both in series and in parallel with the substrate as illustrated schematically in Figure 1. It is rather intuitive that the film may act in series with the substrate. However, as the film becomes more and more stiff relative to the substrate, it begins to act more and more like a spring in parallel with the substrate. There are several ways to consider the sense of this configuration. First, as the film becomes stiff, it dominates the response, and this is what happens with parallel springs—the stiffer spring dominates. Second, as the film becomes thin and stiff, the deformation in the top layer of the substrate approaches that of the film. If two springs of different stiffness experience the same deformation subject to the same force, then they should be modeled as parallel. Finally, if the film provides significant lateral support, then it effectively acts on the indenter like the leaf springs which support the indenter column, and these leaf springs are well modeled by a parallel spring.

Fig. 1 Schematic of the proposed model allowing the film to act in series and in parallel with the substrate; the constant D = 4a/(1-νa) relates bulk modulus to stiffness; it cancels out of the expression derived from this model (Eq. 2)[1].

Springs in parallel are treated together by adding their stiffnesses. Thus, the Hay-Crawford model relates the apparent shear modulus to that of the film and the substrate through:

1

1 1 (2) = (1 − I ) +I 0 0 µa µ s + FI µ f µf 0 Eq. 2 contains two factors for moderating the film influence: an empirical constant F and a weighting function I0. A constant value of F = 0.0626 has been determined by finite-element analysis [1]. This single value for F holds for any film-substrate system. The weighting function, I0, is that of Gao et al [2]. The function I0 is plotted in Figure 2 and given by I0 =

2  t  1 + (t / a )  t/a  1 t arctan  + − (1 − 2ν a ) ln . 2  π a  (t / a )  1 + (t / a)2   a  2π (1 − ν a ) 

2

(3)

47 Eq. 2 gives us the right behavior in the limits of I0 → 1, I0 → 0, µf << µs, and µf >> µs. When I0 is close to 1, as it is at shallow penetration depths, the apparent modulus approaches that of the film. As I0 approaches 0, as it does at large depths, the apparent modulus depends on both the film and the substrate through the first term on the right-hand side of Eq. 2. In the case of a compliant film on a rigid substrate (µf << µs), Eq. 2 reduces to a model for two springs in parallel, which in fact, is the Song-Pharr model [8-10]. Finally, when the film modulus is very large, the apparent compliance goes to zero for all values of I0, as it should.

Fig. 2 Gao’s weighting functions I0 and I1 which govern the film-to-substrate transition for shear modulus and Poisson’s ratio, respectively [1, 2]

The shear modulus of the film is calculated from the apparent value by solving Eq. 2 for µf :

− B + B 2 − 4 AC , where 2A A = FI0 B = µs – (FI02 – I0 + 1)µa C = - I0 µaµs. Finally, the Young’s modulus of the film is calculated from the shear modulus and Poisson’s ratio as Ef = 2µf (1+νf).

µf =

(4)

(5)

Calculation of µa from standard indentation results for use in Eq. 2 requires a value for Poisson’s ratio. The weighting function I0 also utilizes Poisson’s ratio. But what value should be used—that of the film or that of the substrate? To be sure, this problem is of second order, but Gao et al. also provided a weighting function, I1, for handling the transition in Poisson’s ratio. Gao’s function I1 is also plotted in Figure 2 and given by [2]

I1 =

2  t  t / a  1 + (t / a )  arctan  + ln . 2  π a π  (t / a ) 

2

(6)

Using Gao’s weight function, the apparent Poisson’s ratio, νa, is calculated as [8-10]

(1−ν s )(1−ν f )  . 1 − (1 − I 1)ν f − I 1ν s  

ν a =1− 

(7)

Eq. 7 provides the value for Poisson’s ratio used in the calculation of µa and I0. It should be noted that if film and substrate have the same Poisson’s ratio (that is, if νs = νf =ν ), then Eq. 7 reduces to νa = ν.

Finite-element analysis Finite-element analysis (FEA) is essential to the development and verification of analytic contact models, because FEA idealizes experiment. In a finite-element model, the film thickness, film properties, and substrate properties are all well known, because they are required inputs. Also, there is little ambiguity about the true contact area under load, because it is determined from the last node(s) in contact. So before turning to experimentation, the worth of an analytic model is first assessed by means of FEA. For example, an elastic finite-element model may be constructed with a film of thickness t on a

48 substrate, with the input properties being the Young’s modulus and Poisson’s ratio of the film (Ef , νf ), and the Young’s modulus and Poisson’s ratio of the substrate (Es, νs). Then, indentation into the material is simulated, and the simulated force-displacement data are analyzed in order to achieve a value for the Young’s modulus of the film, i.e. Ef-out. What is the difference between this output value and the value that was used as an input to the finite-element model? FEA allows this question to be answered systematically over the domain of situations that might be encountered experimentally: thick films, thin films, stiff films on compliant substrates, compliant films on stiff substrates, etc. If an analytic model applied to simulated data fails to return the input properties with sufficient accuracy, it should not be expected to work well when applied to experimental data. Some simulation inputs were fixed, and some were systematically varied in order to investigate the domain of interest. Table 1 summarizes the 30 finite-element simulations performed in this work. The film thickness was set to 500nm for all simulations; indentation depth was varied in order to investigate the domain of 4% < h/t < 40%. All indented materials, both film and substrate, were assigned a Poisson’s ratio (ν) of 0.25 and a linear-elastic stress-strain curve. (Thus, neither the effect of plasticity nor of transition in Poisson’s ratio was investigated by FEA.) The Young’s modulus of the film was fixed at 10GPa. To achieve the desired variation in Ef/Es, the substrate modulus was varied between 100GPa (Ef/Es = 0.1) and 1GPa (Ef/Es = 10). The modulus ratios are the same whether expressed in terms of Young’s modulus or shear modulus, i.e. µf/µs = Ef/Es. For all simulations, the indenter was a cone having an included angle of 140.6o and an apical radius of 50nm. This shape is the two-dimensional analogue of the common Berkovich indenter. The indenter was defined to be a linear-elastic material having the properties of diamond: E = 1140GPa and νi = 0.07. Table 1 Summary of finite-element simulations, showing values for inputs that were varied. For all simulations, the indenter was a 2-dimensional version of a Berkovich diamond. For the sample, t = 500nm, Ef = 10GPa, and νf = νs = 0.25 [1].

Simulation

Es, GPa

1-10 11-20 21-30

100 10 1

Maximum indenter displacement (h), nm 20 20 20

40 40 40

60 60 60

80 80 80

100 100 100

120 120 120

140 140 140

160 160 160

166 180 180

174 200 200

The purpose of simulations 11-20 was to verify the finite-element model. For these ten simulations, the finite-element model had the mesh of a film-substrate system, but with film and substrate having the same modulus (i.e. Ef = Es =10 GPa), and so behaving as a bulk sample. Application of standard analysis to the simulated data from runs 11-20 (for which Ef/Es = 1) yielded an output modulus that differed from the input value by no more than 1%. Figure 3 shows the finite-element results for simulations 1-10 and 21-30 in terms of apparent compliance (1/µa) versus normalized contact radius (a/t). Indeed, the finite-element results for apparent compliance are well modeled by the Hay-Crawford model (Eq. 2). In this plot, the

Fig. 3 Comparison between Hay-Crawford model and finite-element results for the film/substrate systems having the most severe modulus mismatch

49 dashed centerline marks the true modulus for the film—the value that was used as an input to the finite-element simulations. FEA results are shown as discrete data points; each data point represents a single simulation of pressing the indenter into the film to a prescribe depth and withdrawing it, then analyzing the simulated force-displacement data by the Oliver-Pharr [3] method to achieve apparent compliance. FEA results for stiff films on compliant substrates (Ef/Es = 10) fall above true film compliance. For these simulations, the apparent compliance increases with increasing penetration depth due to the increasing influence of the compliant substrate. The FEA results for compliant films on stiff substrates (Ef/Es = 0.1) fall below the true film compliance. For these simulations, the apparent compliance decreases with increasing penetration depth due to the increasing influence of the stiff substrate. The solid curves in this plot show the apparent compliance as predicted by the Hay-Crawford model (Eq. 2) under the same circumstances. The excellent agreement between Eq. 2 and FEA justifies using Eq. 2 to interpret experimental results.

Experimental Procedure Samples Four samples were tested: • C1: 249nm low-κ on Si • C2: 488nm low- κ on Si • S1: 150nm silicon-carbide (SiC) on Si • S2: 300nm silicon-carbide (SiC) on Si. Film materials were typical for their respective applications, but these samples were chosen to illustrate the utility of the HayCrawford model. For the “C” samples, the film was expected to be substantially more compliant than the substrate; for the “S” samples, the film was expected to be stiffer than the substrate. Samples within a pair were comprised of the same film material, with the only difference being thickness. For all samples, the elastic properties of the silicon substrate were assumed to be Es=170GPa and νs = 0.2GPa. Equipment and Procedure All samples were tested with an Agilent G200 NanoIndenter (Chandler, AZ), utilizing continuous stiffness measurement (CSM) and a DCM II head fitted with a Berkovich indenter. Results were achieved using the NanoSuite test method “GSeries DCM CSM for Thin Films,” which includes an implementation of the Hay-Crawford model. At least 8 tests were performed on each sample. Loading was controlled such that the loading rate divided by the load (P’/P) remained constant at 0.05/sec. The excitation frequency was 75Hz, and the excitation amplitude was controlled such that the displacement amplitude remained constant at 1nm. Results and Discussion Figure 4 shows Young’s moduli for the two low-κ samples as a function of normalized indenter penetration. Each trace represents the average of all tests done on that sample. The gray symbols are the measurements obtained by applying the Oliver-Pharr analysis to continuous-stiffness data [3, 15]. As a function of normalized penetration, the apparent moduli (gray symbols) first decrease, then increase due to the increasing influence of the silicon substrate. It is difficult to know whether the initial decrease is the manifestation of a real variation in properties (stiffer surface layer) or an experimental artifact (high strain rate at contact). Either way, properties measured in this regime are not representative of the bulk of the film. The open

Fig. 4 Apparent modulus and film modulus as a function of normalized indenter penetration for low-κ samples

50 symbols in Figure 4 have the same underlying physical measurements as the gray symbols, but the open symbols show the results of applying Eqs. 2-7 to obtain the substrate-independent moduli of the films. When the indenter penetration exceeds 20% of the film thickness, the open traces also begin to rise. This is “substrate effect” only in an indirect sense: the hard substrate is causing the film material to “pile-up” around the face of the indenter. The analysis for determining contact area does not account for such deformation, and so calculated contact areas are too small, thus making calculated moduli too large. (This effect is also present in the gray traces, but it is overwhelmed by true substrate effect.) Figure 5 shows Young’s moduli for the two SiC samples as a function of normalized indenter penetration. Again, each trace represents the average of all tests done on that sample. The gray symbols show the results of applying the OliverPharr analysis to continuous stiffness data; the open symbols show the results of additionally using Eqs. 2-7 to calculation the substrate-independent moduli of the films. As a function of penetration depth, the apparent moduli first increase, then decrease due to the increasing influence of the silicon substrate. Again, it is difficult to know whether the observed change in the first few nanometers of contact is due to a real change in properties or experimental Fig. 5 Apparent modulus and film modulus as a function of normalized artifact. Experimental issues which could cause this indenter penetration for SiC samples gradual increase include surface roughness and errant area function. (The “area function” is a polynomial which relates distance from the apex of the diamond to cross-sectional area; it is used to calculate contact areas.) After the initial increase, however, the film moduli (open trace) remain constant with increasing penetration depth. Although this doesn’t absolutely prove the validity of the Hay-Crawford model, it is certainly reassuring. For these samples, the degree of modulus mismatch is not as extreme (as compared to the “C” samples). Thus, we choose to report report properties at 20% of film thickness, rather than at 10%. Young’s moduli for all four films are summarized in Table 2. Use of the Hay-Crawford model substantially changed the reported moduli for the films. For the low-k samples, the film modulus was about 17% lower than the apparent modulus at the same normalized displacement; for the Si-C samples, the film modulus was about 25% higher than the apparent modulus. Table 2 Summary of experimental results [1]

Sample ID

Description

t nm

Ef GPa

(Ef - Ea)/ Ea %

Ef/Es

C1 C2 S1 S2

low-κ on Si low-κ on Si SiC on Si SiC on Si

249 488 150 300

4.69±0.146 4.77±0.074 284±9.50 284±15.4

-18.4 -16.5 26.0 23.5

0.028 0.028 1.67 1.67

Conclusions The Hay-Crawford thin-film model (Eq. 2) has been shown to accurately relate the apparent modulus obtained from an instrumented indentation experiment to the moduli of film and substrate, thus allowing the extraction of film modulus if substrate modulus and film thickness are known. The model works well for both compliant films on stiff substrates and vice versa. Application of this model to low-κ and SiC films revealed substantial differences between apparent and film moduli.

51 Acknowledgements The author gratefully acknowledges the following contributors: Drs. Jeremy Thurn and Michael Kautzky at Seagate Technology for supplying the SiC-on-Si samples, Mr. Bryan Crawford for testing the SiC-on-Si samples, and SEMATECH for providing the low- κ samples.

References 1.

Hay, J.L. and Crawford, B., "Measuring Substrate-Independent Modulus of Thin Films," Journal of Materials Research, Accepted for publication in 2011.

2.

Gao, H.J., Chiu, C.H., and Lee, J., "Elastic Contact Versus Indentation Modeling of Multilayered Materials," International Journal of Solids and Structures 29(20), 2471-2492, 1992.

3.

Oliver, W.C. and Pharr, G.M., "An Improved Technique for Determining Hardness and Elastic-Modulus Using Load and Displacement Sensing Indentation Experiments," Journal of Materials Research 7(6), 1564-1583, 1992.

4.

Doerner, M.F. and Nix, W.D., "A Method for Interpreting the Data from Depth-Sensing Indentation Instruments," Journal of Materials Research 1(4), 601-609, 1986.

5.

King, R.B., "Elastic Analysis of Some Punch Problems for a Layered Medium," International Journal of Solids and Structures 23, 1657–1664, 1987.

6.

Shield, T.W. and Bogy, D.B., "Some Axisymmetric Problems for Layered Elastic Media: Part I, Multiple Region Contact Solutions for Simply Connected Indenters," Journal of Applied Mechanics 56(4), 798-806, 1989.

7.

Mencik, J., et al., "Determination of Elastic Modulus of Thin Layers Using Nanoindentation," Journal of Materials Research 12(9), 2475-2484, 1997.

8.

Song, H., Selected Mechanical Problems in Load- and Depth-Sensing Indentation Testing, 1999, Rice University: Houston.

9.

Rar, A., Song, H., and Pharr, G.M., "Assessment of New Relation for the Elastic Compliance of a Film-Substrate System," Materials Research Society Symposium Proceedings, 695, 431-436, 2002.

10.

Xu, H. and Pharr, G., "An Improved Relation for the Effective Elastic Compliance of a Film/Substrate System during Indentation by a Flat Cylindrical Punch," Scripta Materialia 55(4), 315-318, 2006.

11.

Bec, S., et al., "Improvements in the Indentation Method with a Surface Force Apparatus," Philosophical Magazine A-Physics of Condensed Matter Structure Defects and Mechanical Properties 74(5), 1061-1072, 1996.

12.

Roche, S., Bec, S., and Loubet, J.L., "Analysis of the Elastic Modulus of a Thin Polymer Film," 778, 117-122,

13.

Hay, J.L., "Measuring Substrate-Independent Modulus of Dielectric Films by Instrumented Indentation," Journal of Materials Research 24(3), 667-677, 2009.

14.

Hay, J.L., "Introduction to Instrumented Indentation Testing," Experimental Techniques 33(6), 66-72, 2009.

15.

Hay, J.L., Agee, P., and Herbert, E.G., "Continuous Stiffness Measurement during Instrumented Indentation Testing," Experimental Techniques 34(3), 86-94, 2010.

Analysis of Spherical Indentation of an Elastic Bilayer Using a Modified Perturbation Approach Jae Hun Kim, Department of Materials Science and Engineering Stony Brook University, Stony Brook, NY Andrew Gouldstone, Department of Mechanical and Industrial Engineering Northeastern University, Boston, MA Chad S. Korach, Department of Mechanical Engineering Stony Brook University, Stony Brook, NY ABSTRACT Accurate mechanical property measurement of films on substrates by instrumented indentation requires a solution describing the effective modulus of the film/substrate system. Here, a first-order elastic perturbation solution for spherical indentation on a film/substrate is presented. Finite element method (FEM) simulations were conducted for comparison with the analytical solution. FEM results indicate that the new solution is valid for a practical range of modulus mismatch, especially for a stiff film on a compliant substrate. It also shows that effective modulus curves for the spherical punch deviates from those of the flat punch when the thickness is comparable to contact size. The work is applicable in tribological films and other engineering systems requiring hard, protective coatings. 1. Introduction Measurement of mechanical properties of films deposited on substrates has long been an issue in thin- and thick-film technology. Although indentation is extensively used due to its relative experimental simplicity, analysis is complicated by the inevitable substrate effect. Rules of practice exist that state film properties may be isolated if contact dimensions are small compared to film thickness, but such simplifications are not useful for layers including microstructural size effects (e.g., where contact dimensions are smaller than dislocation spacing, or splat size for thermal sprayed coatings), or ultra-thin films. Thus, analyses that consider the relation between film and substrate properties are necessary.

F r t

 f , f  s , s

2a

z

Figure 1. Schematic of spherical indentation on film/substrate system Consider the indentation of an ideally elastic film/substrate system that is mechanically bonded (Figure 1). A proper description of the effective modulus eff of the film/substrate system, in the context of film and substrate moduli (  f and  s ) is essential to the accurate extraction of the film properties. Since there is no exact solution yet for this problem, a number of approximate models have been proposed to be fitted with data from experiments, and FEM simulations, or analytic solutions for several tip geometries. Those models have shown good yet limited applicability. Most of these approaches were based on the following simple formula: (1) eff  s  ( f  s ) (a / t ,  f / s )

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_8, © The Society for Experimental Mechanics, Inc. 2011

53

54 where a is contact radius, t is the thickness of the film and  is a weight function of contact size, tip geometry and modulus mismatch;  approaches 1 when a / t  0 and 0 when a / t   . Numerous forms of Eq (1) have been proposed for sharp and flat-ended cylindrical geometry:      

Doerner and Nix[1] first introduced an empirical equation of an effective modulus expressed as an exponential form and fit it with experimental data obtained with a sharp tip. King[2] performed a numerical analysis of flat-ended tip indentation and introduced a similar equation to Doerner and Nix’s. Jung et al.[3] developed a power law function based on their experimental results from nanoindentation with ceramic films on silicon substrates. The above empirical equations have adjustable parameters which must be determined by experiment, or numerically. Gao, et al.[4] performed a first order perturbation analysis on the flat-ended cylindrical punch problem, and presented a formula for effective modulus eff . Mencik, et al.[5] compared this and several empirical equations with experimental data from nanoindentation, and found that Gao et al.’s equation gave the best fit to their experimental data. Xu and Pharr[6] later modified the perturbation solution and comparison with FEM results showed better accuracy for a wide range of modulus mismatch.

The perturbation solution is attractive because it is given as a closed form and doesn’t include adjustable parameters. But its assumption on flat-ended cylindrical geometry limits the applicability for sharp or spherical tip indentation, particularly when a and t are comparable. Different tip geometries have been considered in other investigations:   

Perriot and Barthel[7] used numerical integration to get effective modulus curves for sharp and spherical tips, and showed they overlap closely, but differ from those for a flat-ended cylindrical tip. Clifford and Seah[8] conducted FEM simulations with spherical tip geometry to get effective modulus curves for compliant polymer films on stiff substrates and proposed a curve-fit equation. Finally, Hsueh and Miranda[9] presented an approximate, analytically derived equation of effective modulus under spherical tip indentation, based on an extension of the Boussinesq Green’s function. Using FEM simulations, they showed that their results were valid for a certain range of modulus mismatch, but most accurate for the case of a compliant film on a stiff substrate.

There is an opportunity to revisit the problem of spherical indentation of a bilayer, with particular attention to the stiff film on compliant substrate. From the above investigations it appears that inaccuracies may arise when tip geometry is assumed inappropriately (e.g., flat punch assumption for spherical punch indentation experiment). To investigate this, here we use the first-order perturbation solution, and modify it for a spherical tip geometry. 2. Perturbation analysis The full description of the perturbation analysis can be found in [10], here the approach is briefly described. In perturbation analysis, the film/substrate system is treated as a homogeneous material with (initially) properties of the substrate that undergoes a phase transformation to assume film properties in the region 0  z  t . During the transformation, the load F is fixed and the displacement h is allowed to change to h  h . The force-displacement relation for spherical indentation of an elastic material, is described by Hertzian relation[11] as

F

8 Rh3 / 2  3(1  )

(2)

Eq. 2 contains a single value for shear modulus and Poisson’s ratio, but a composite value is used to represent the film/substrate system [8, 9, 12]. Upon the phase transformation, the extra work done by the force F due to the displacement change h is thus calculated as [13]

W   Fh  

W 

2 Fh 5

8 Rh 3 / 2  2 h  Fh , 3(1   ) 5 (3)

The additional work is equal to the strain energy change due to moduli variation in the body, and the energy conservation equation can be written as

55

2 1 Fh    cijkl uio, j u ko,l dV 5 2 Vf

(4)

where cijkl is the change of moduli from substrate material to film material and u io is the known displacement field for the homogeneous substrate material. The right term of Eq. 4 is the energy variation due to a moduli transformation, and can be rearranged (following Gao, et al.) as

2 1 1  f  s Fh   es   ojj  kko dV  V f 5 2 2 s



Af

 ijo nio u oj dA ,

(5)

where  s is the Lame constant of the substrate,

e

 f ( f   s ) ,   s  s (1  2 f )

(6)

and  o and  o are the known stress and strain field for the homogeneous substrate material[4]. The terms V f and A f in Eq. 5 indicate the domain volume and the surrounding surface domain of the film region, respectively. The surface domain consists of two planes: z  0 and z  t . The surface stress and displacement solutions for spherical indentation of an elastic homogeneous material are known[11], and substituting into Eq. 5 leads to the following expression for h / h

h h



5 es 4 Fh



Vf

 ojj  kko dV 

 f  s s

 5   o o  o o 1  2 Fh 0 ( zz u z   rz u r ) z t rdr 

(7)

The original displacement h is calculated from the Hertz relation[10] such as

3F (1  ) 8a Since the total displacement ht is given as h  h , h

ht (a / t )  where

(8)

 f  s  3F (1   s )   f   s I 1 (a / t )  I o (a / t ) 1  s 8a s  1  s 

(9)

5   o o ( zz u z   rzo u ro ) z t rdr , 2 Fh 0 5  s (1  2 f )(1   s ) e s  ojj  kko dV . I 1 (a / t )  4  f (1  2 s )( f   s ) Fh V f I o (a / t )  1 

(10) (11)

Eq. 9 is thus the perturbation equation for spherical indentation. The terms I o and I 1 are weighting functions representing modulus difference and Poisson’s ratio difference, respectively. Here, the elastic solutions for the spherical punch problem given by Hamilton [14, 15] are used to obtain new I o and I 1 for spherical indentation:

Io  1 

5 4a (1   ) 5

 a  3  t  z ( aM  2 S )  NS (1  2 )   aM ' t    (2a 2  r 2 )(1   )  4       N ' dz  rdr   0 S S '   0  2       aM ' t   a2   a    3  N ' ar 1  2  (2a 2  r 2 ) Sin 1   (1   )  a S '   r    r    

(12)

t  z ( aM  2 S )  NS (1  2 )    2  dz  rdr 0 S       N' r H ' rt    2t   2 (3 N ' t 2  3r 2 t )(1   )  ( N ' S ' a 3  2 A' N ' )(1  2 )  3aM ' t 2  0 G'  H '    S' 30 t  2 I1    N  z  rdrdz ,





0 0

 rdr 

 (13)

56 where A' , S ' , M ' , N ' , G ' , H ' are variables at z  t found in [14,15]. Equations (12) and (13) can be substituted into the following equation [6]:

1       1  s  ( s  f ) I1  eff 



 (1  I 

o

)



s

Io    f 

(14)

Giving the normalized displacement after rearrangement as:

 (1   )   ht / h f      f

 (1   )       eff

  

2/3

(15)

This term, denoted as ht / h f compares tip displacement under identical loading conditions, between a composite material and a homogeneous material having film properties. 3. Results and Discussion Figure 2 illustrates the normalized displacement (Eq. 15) curves comparing the current work with FEM results and Hsueh’s model[9]. Note that Hsueh’s model gives a very similar result to the current solution when the modulus mismatch is small for the case of stiff films, but when the mismatch increases, it shows larger deviation. For  f /  s  10 , both Hsueh’s and the current solution deviate from the FEM results when a / t   . Hsueh et. al attributed this discrepancy to flexural stresses in the film. The current solution underestimates the modulus in the case of compliant films. We find this acceptable, as Hsueh’s solution is sufficiently accurate in those cases. In the case of stiff films, the current solution appears most accurate when a and t are comparable. Recently, work by Zhou and Prorok[16] has demonstrated that taking into consideration the discontinuity in strain at the film-substrate interface provides a better match with experimental data over the Gao and Doerner and Nix models. 1.0

4

Current work, Eq. 28 FEM (spherical) Hsueh (spherical)

f/s=10

0.8

ht/hf

ht/hf

f/s=0.5 3

f/s=4

2

f/s=0.4 0.4

f/s=2

Current work, Eq. 28 FEM (spherical) Hsueh (spherical)

f/s=0.1

0.2

1 0.01

0.6

0.1

1

aa/t /t

Figure 2. Normalized displacement, (a)

10

100

0.01

0.1

1

10

100

aa/t /t

ht / h f curves for the current work with comparison to FEM results and Hsueh’s model:

 f /  s  2 ,4 and 10, and (b)  f /  s  0.1 , 0.4 and 0.5.

4. Conclusions In this paper, we presented a new analytic solution for spherical indentation of a linear elastic film/substrate bilayer based on the perturbation approach previously used by Gao et al[4]. The new weighting functions ( I o , I 1 ) have similar shapes to those for flat punch, but deviate over most of the contact dimension range. We used the equation suggested by Gao et al.[4] and the one modified by Xu and Pharr[6] to combine weighting functions and give effective modulus curves. The new perturbation solution gives good agreement with FEM results for stiff layers on substrates, relevant for a number of engineering systems. Acknowledgements JHK and AG gratefully acknowledge the NSF Faculty Early Career Award CMS 0449268 for supporting this work; and CSK would like to gratefully acknowledge the NSF Award CMMI 0626025 for support.

57 References 1. M. F. Doerner and W. D. Nix: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986). 2. R. B. King: Elastic Analysis of Some Punch Problems for a Layered Medium. Int. J. Solids. Struct. 23, 1657 (1987). 3. Y. G. Jung, B. R. Lawn, M. Martyniuk, H. Huang and X. Z. Hu: Evaluation of elastic modulus and hardness of thin films by nanoindentation. J. Mater. Res. 19, 3076 (2004). 4. H. J. Gao, C. H. Chiu and J. Lee: Elastic Contact Versus Indentation Modeling of Multilayered Materials. Int. J. Solids Struct. 29, 2471 (1992). 5. J. Mencik, D. Munz, E. Quandt, E. R. Weppelmann and M. V. Swain: Determination of elastic modulus of thin layers using nanoindentation. J. Mater. Res. 12, 2475 (1997). 6. H. T. Xu and G. M. Pharr: An improved relation for the effective elastic compliance of a film/substrate system during indentation by a flat cylindrical punch. Scripta Mater. 55, 315 (2006). 7. A. Perriot and E. Barthel: Elastic contact to a coated half-space: Effective elastic modulus and real penetration. J. Mater. Res. 19, 600 (2004). 8. C. A. Clifford and M. P. Seah: Modelling of nanomechanical nanoindentation measurements using an AFM or nanoindenter for compliant layers on stiffer substrates. Nanotechnology 17, 5283 (2006). 9. C. H. Hsueh and P. Miranda: Master curves for Hertzian indentation on coating/substrate systems. J. Mater Res. 19, 94 (2004). 10. J.H. Kim, C.S. Korach, A. Gouldstone: Spherical Indentation of an Elastic Bilayer – a Modification of the Perturbation Approach. J. of Matls. Res. 23(11), 2935 (2008). 11. K. Johnson: Contact Mechanics (Cambridge University Press, New York, 1985). 12. I. Pane and E. Blank: Response to loading and stiffness of coated substrates indented by spheres. Surf. Coat. Tech. 200, 1761 (2005). 13. D. Maugis: Contact, adhesion, and rupture of elastic solids (Springer, Berlin, 2000). 14. G. M. Hamilton: Explicit Equations for the Stresses beneath a Sliding Spherical Contact. Proc. Inst. Mech. Eng. Part C - J. Mech. Eng. Sci. 197, 53 (1983). 15. G. M. Hamilton and L. E. Goodman: Stress field created by a circular sliding contact. J. Appl. Mech. 33, 371 (1966). 16. B. Zhou and B.C. Prorok: A Discontinuous Elastic Interface Transfer Model of Thin Film Nanoindentation. Exp. Mech. 50(6), 793 (2010).

Nano-indentation Studies of Polyglactin 910 Monofilament Sutures Leming Sun1, Vijaya Chalivendra2* and Paul Calvert1 1 Materials & Textiles Department 2 Department of Mechanical Engineering University of Massachusetts Dartmouth, MA 02747 *Corresponding author, [email protected], 508-910-6572 ABSTRACT Nano-indentation studies using atomic force microscopy (AFM) were introduced to investigate the effects of hydrolysis degradation on mechanical properties of polyglactin 910 monofilament sutures. The polyglactin 910 sutures were immersed in phosphate buffered saline (PBS) solution of pH 5, 7.4, 10 without enzyme and pH 7.4 with esterase enzyme. After that, the samples were incubated at 37 oC under an oscillation of 80 rpm. Samples were removed for testing after 7, 14, 21 and 28 days. The effects of degradation on gradation of Young’s modulus values across fiber cross-section were studied by doing progressive nano-indentation from center to surface of cross section of the sutures. Results indicate that the pH 7.4 condition hydrolysis degradation did not have a significant impact on variation of Young’s modulus values of the polyglactin 910 sutures from the center to the surface after different degradation times. And the Young’s modulus from the original samples to sutures after 4 weeks degradation have a decreasing trend, but not including the first week. Then the SEM, FTIR and Tensile test were conducted to investigate the mechanical and chemical properties of polyglactin 910 monofilament sutures.

1. INTRODUCTION At present, polyglycolide, polylactide and their copolymers are widely used as the biodegradable polymeric biomaterials [1]. For absorbable suture material, the two important factors considered are keep maximum original tensile strength as long as it is needed for wound healing and disappearance as soon as possible when the sutures have lost their tensile strength. The polyglactin 910 monofilament suture meets all the desired properties for the absorbable sutures. It is less reactive than catgut and better in tensile strength [2]. Polyglactin 910 monofilament suture is made by the copolymerization of lactide acid and glycolide acid, and it is composed of 90% polyglycolide and 10% polylactide. This suture can be used in general soft tissue approximation or ligation, including use in ophthalmic procedures, but not for use in cardiovascular or neurological tissues. As the sutures degradation, all absorbable sutures have two steps of absorption. The first is the loss of the tensile strength, and the second is the progressive loss of the suture mass until the suture is completely absorbed. Many studies have been done on the multifilament PGLA sutures of their mechanism and macromechanical properties. But it is far away from the comprehensive understanding of the

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_9, © The Society for Experimental Mechanics, Inc. 2011

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60

mechanism for the in vitro degradation of PGLA sutures, especially the micro-mechanical properties.

2. Experimental 2.1 Materials Polyglactin 910 monofilament sutures were purchased from Ethicon Company (V960G), which is a 10-0 size violet monofilament suture. It is composed of 90% polyglycolide and 10% polylactide, which structure shown in Fig. 1. This suture can be used in general soft tissue approximation or ligation, including use in ophthalmic procedures, but not for use in cardiovascular or neurological tissues.

Fig. 1 Repeated units of (a) polylactide, (b) polyglycolide.

2.2 In vitro degradation Polyglactin 910 monofilament sutures were purchased from Ethicon Company (V960G), which is a 10-0 size violet monofilament suture. It is composed of 90% polyglycolide and 10% polylactide. The polyglactin 910 sutures were immersed in phosphate buffered saline (PBS) solution of pH 7.4, and then the samples were incubated at 37 oC under an oscillation of 80 rpm. After 7, 14, 21 and 28 days, the samples were removed from the PBS for the following test. 2.3 Atomic force microscope 2.3.1 Sample preparation Sutures were vertically embedded in the mode as Fig. 2 with curing and low heat generation epoxy at room temperature for 12 hours. After that, the samples were cut with a ultra-microtome to get a very smooth cross section.

Fig. 2 Fibers embedded in Epoxy Matrix.

Fig. 3 Nano-indentation across the suture cross section.

2.3.2 Nano-indentation

The indentation was performed on the cross section of the sutures as Fig. 3, from the center to the surface. The contact mode scan was made to get the geometry images for the nanoindentation.

61

2.3.3 Surface topography The surfaces of the samples were scanned using non-contact mode to obtain the surface topography images. Then we can get the 3D images of the previous. 2.4 Scanning electron microscope Sutures were sputtered with gold and examined using a JEOL JSM 5610 scanning electron microscope, with a observation condition voltage of 10 kV. 2.5 Macro-scale tensile testing According to ASTM G3822 standard, a constant rate of extension 2.54 mm/min was used for 16mmgage length sample. The limited maximum force of the load cell is 2.5 N. As Fig. 4 shows, the blue dots are the epoxy adhesive.

Fig. 4 Schematic of tensile testing sample

2.6 Fourier transform spectroscope The sutures were arranged at the gold plate and carried out in the reflectance mode with Fourier transform infrared spectroscopy (Varian FTIR Bench and Microscope, CA, USA).

3. Results and Discussion 3.1 Nano-indentation Nano-indentation were performed across the fiber radius from center to surface in Fig. 5, from

Fig. 5 Young’s modulus at different places and different degradation times

Fig. 6 Topography images of the sutures at different degradation times

62

which we can get the Young’s modulus at different places and different degradation times seems almost at a same level. 3.2 Surface topography Using the non-contact mode of AFM, we can get the topography images of the sutures at different degradation times in Fig. 6. It is obvious that there are changes of hydrolytic degradation at the surface. The amorphous areas are easier for degradation than crystalline areas. It is possible that the peaks of the surface are crystalline areas. 3.3 Scanning electron microscopy SEM images of surfaces of the monofilament polyglactin 910 sutures at different degradation times are shown in Fig. 7. These images show no significant differences at different degradation weeks. Fig. 8 shows the difference between bulk and surface degradation. From Fig. 7, we can get the diameter of the sutures at different degradation times, and all of the diameters are around 27 microns, with no significant differences. It proved that the main effects of the hydrolytic degradation for polyglactin 910 monofilament sutures are bulk degradation.

Fig. 7 SEM results of polyglactin 910 sutures at different degradation days

Fig. 8 Schematic of bulk and surface hydrolytic degradation [3]

3.4 Tensile testing 800 0 weeks

700

Stress(MPa)

Fig. 9 shows the correlation between stress and strain of the sutures. It is shown that the samples have a high tensile strength and elongation at break. Also from Fig. 10 and Fig. 11, we can see the changes of the tensile strength and elongation at break on different degradation weeks. After 4 weeks degradation in PBS solution, just about 24% of its original tensile strength and 8% of its original elongation at break is left. The results shown above might be

1 weeks

600

2 weeks

500

3 weeks

400

4 weeks

300 200 100 0 0

0.05

0.1

0.15

Strain

0.2

0.25

0.3

0.35

Fig. 9 Stress-strain diagram at different degradation weeks

63

Elongation at break(%)

Tensile Strength(MPa)

the reason that the main degradation of the PGLA monofilament sutures in PBS solution is bulk degradation. 800 700 600 500 400 300 200 100 0 0

1

2

3

4

Degradation time(weeks)

Fig. 10 Tensile strength at break at different degradation weeks

35 30 25 20 15 10 5 0 0

1

2 Degradation time(weeks)

3

Fig. 11 Elongation at break at different degradation weeks

3.5 Fourier transforms spectroscopy Fig. 12 displays the IR spectrum of Polyglactin 910 monofilament sutures, from which we can see the C-H bonds are around 2900 cm-1 and 1400 cm-1. The C=O bonds are around 1750cm-1, and the special O-H bonds are near the area of 3500cm-1. From original sutures to 4 weeks degradation sutures, the scope of the O-H bonds are becoming wider and wider. It is the reason that the hydrolysis degradation let the breakage of the ester bonds, after that there will produce a lot of O-H bonds.

Fig. 12 FTIR spectrum of the polyglactin 910 suture at different degradation weeks

4. Conclusions The Young’s modulus of the in vitro degradation polyglactin 910 monofilament sutures from the center to the surface and at different degradation times don’t have significant differences. Also the tensile strength has a big change. The samples have a high tensile strength and elongation at break. After 4 weeks degradation in PBS solution, just about 24% of its original tensile strength and 8% of its original elongation at break is left. The 3D topography images from AFM show that there is surface degradation at the in vitro degradation. The SEM images show the constant level diameters of the sutures at different degradation times at in vitro degradation.The study shows that this degradation consists of bulk degradation and surface degradation, and the bulk degradation takes a main position in the degradation process.

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ACKNOWLEDGEMENT The authors greatly appreciate the financial support from the National Science Foundation through Grant CMS0618119 for acquiring an atomic force microscope. Also we would like to acknowledge the financial support from the National Textile Center through project number M08-MD13.

REFRENCES 1. M. Deng, G. Chen, D. Burkley, J. Zhou, D. Jamiolkowski, Y. Xu, R. Vetrecin. Acta Biomaterialia. 2008, 4, 1382-1391. 2. Sherrell J. Aston, Thomas D. Rees. Aesthetic Plastic Surgery. 1977, 1, 289-293. 3. D. Hofmann, M. Entrialgo-Castano, K. Kratz, A. Lendlein. ADV. Mater. 2009, 21, 32373245.

Analytical approach for the determination of nanomechanical properties for metals Kaushal K Jhaa, Nakin Suksawangb*, Arvind Agarwalc PhD candidate, Department of Civil and Environmental Engineering b Assistant Professor, Department of Civil and Environmental Engineering c Associate Professor, Department of Mechanical and Materials Engineering Florida International University, Miami, FL, 33174 a

*

Corresponding Author: Tel: 305-348-0110, Fax: 305-348-2802, E-mail address: [email protected]

ABSTRACT A modified form of the two-slope method used for the determination of mechanical properties of a material is presented in this paper. Modified expressions for the determination of slopes of the loading and unloading curves make use of the energy based parameters which are independent of the indentation size. A correction factor is also introduced to account for the inward radial displacement of material’s surface points which has important implications on the accuracy of the mechanical properties. Mechanical properties obtained after these modifications compares well with the experimental results. The elastic modulus and hardness obtained by the proposed method precisely describe the elasto-plastic behavior of the metals considered in this study which further confirms the accuracy of the method described herein. The proposed method enhances our understanding of the behavior of a material at very small scale of length and may be extended to determine the mechanical properties of materials other than metals.

1.

Introduction

Several methods for the analysis of nanoindentation data to determine the mechanical properties of thin films and bulk materials exist in the literature. All these methods may be classified based on: (1) how load-displacement curves are utilized in the determination process; and (2) how the analysis is performed. Based on first criterion nanoindentation data analysis procedure may be divided into three groups: (i) The unloading curve method (Oliver and Pharr method) [1-3]; (ii) the loading curve method (Methods by Hainsworth et al. [4, 5] and Malzbender et al. [6]) and (iii) the hybrid method (Cheng and Cheng [7, 8]; two-slope method [9, 10]; and finite element method [2]). On the basis of second criterion, these methods are classified as tools for either reverse analysis or forward analysis [11]. In the reverse analysis, mechanical properties are extracted from the experimental load displacement curve. On the other hand, mechanical properties are used to model the experimental load-displacement curve in the forward analysis. Loading curve method and finite element method are usually used as forward analysis tools. In all of these methods, the most important thing is to understand the information contained in the load-displacement curves. But, both the presence of non-uniform stress and displacement fields in the vicinity of contact and complex deformation processes that take place during indentation preclude us in gaining such understanding [2]. Therefore, these methods are either incomplete or heavily depend on the empirical observations. Oliver and Pharr method, also referred to as an area function technique, is the most widely used method for the determination of mechanical properties of a material. Determination of the contact area is a prerequisite of this technique which is generally obtained with large errors when the data from inhomogeneous samples or from materials that show significant pile up in the perimeter of contact during indentation. Second limitation of this conventional technique is related to computational efforts which are extremely important when grid indentation technique [12] is required to be performed on inhomogeneous samples. Attaf [13] has shown that the computational efficiency of the area function technique can be significantly improved if correlations among nanomechanical quantities dictated by the unified correlations diagram [13] are considered. On the other hand, Oliver proposed two-slope method [9] that does not require determination of contact area at all to determine the mechanical properties. Surprisingly, these studies have not received much attention of material scientist and engineers even though their findings may prove to be instrumental in developing an attractive alternative method to the area function technique. In the two-slope method, stiffness of the load displacement curves are determined by differentiating the algebraic expressions used to fit the loading/unloading curves and then evaluating the differential at peak indentation load. It has been shown that unloading curve parameters are dependent on indentation size [15] and thus pose difficulty in characterizing a material based on these parameters. For some brittle material, it is possible that the power law may not be a good choice to describe the unloading curve [15]. On the other hand, equation used to represent the loading curve itself depends on the indentation size. For instance, a parabolic representation for loading curve is suitable at large peak indentation load for T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_10, © The Society for Experimental Mechanics, Inc. 2011

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66 conical or Berkovich indenter. But at small peak indentation load, a second degree polynomial is the appropriate choice as bluntness in the tip of the indenter is more pronounced at this level of load [4]. This anomaly in the representation of loading and unloading curves may be overcome if functional analysis based expressions [16] are used to represent them. A Berkovich indenter does not confirm to an axisymmetric condition. Thus, a correction factor is required in order to apply Sneddons’ solution to determine the mechanical properties from the data acquired using this indenter. King [17] suggested that a value of 1.034 may be used for this correction factor. Recent studies by Meza et al [18], however, have shown that this factor is dependent on the penetration depth. Method that is based on Sneddon’s solution ignores one more correction factor that take proper deflected shape of the material surface points during indentation as introduced by Hay et al. [19]. This correction factor has important implication on the accuracy of the computed mechanical properties. The very intent of this study is to ameliorate the existing two-slope method by giving due consideration on the proper representation of loading/unloading curves and on the implementation of the correction factors described above. 2.

Experimental data

For the purpose of verification, nanoindentation data pertaining to aluminum, copper and tungsten is used. These materials may be considered as elastic perfectly plastic material as the percentage elastic recovery of these materials is less than 10%. First set of data are digitized from the literature [1, 4]. These data were obtained using a Berkovich indenter with peak indentation load greater than 100 mN. Second set of data were acquired by carrying out nanoindentation test on commercially available oxygen free copper using same indenter with peak indentation load of 1.0, 1.5, 2.0 and 2.5 mN. 3.

Two-slope method: background

As the name suggests, two-slope method essentially makes use of the slopes of the loading and unloading curves evaluated at the point of maximum depth of penetration. Oliver [9] derived expressions for reduced elastic modulus ( Er ) , contact area

( Ac )

and hardness ( H ) of a material in the following forms:

Er =

1  Su2 Sl    C 2 Pmax β  2Su − ε Sl 

π

2  2 Su − ε Sl  Ac = CPmax    Su Sl 

1  2 Su − ε Sl  H=   CPmax  Su Sl 

(1)

2

(2)

−2

(3)

where C is constant that relates the contact area and contact depth by the relation Ac = Chc2 and ε denotes the geometric factor which are respectively equal to 24.56 and 0.75 for a Berkovich indenter. The factor β appearing in Eq. (1) accounts for the lack axial symmetry of a Berkovich indenter. Sl and Su respectively denote slopes of the loading and the unloading curves as shown in fig 1. These slopes are usually evaluated by analytically differentiating the algebraic expressions (obtained by curve fitting) used to represent them. Two well known equations are used to derive above expressions: (i) fundamental relation among Su , Er and Ac ; and (ii) equation of loading curve capable of describing the elasto-plastic deformation of a material. In mathematical form; these equations may be written as

Su = β  1 P= Er   C 

2

π

Er ε + H β

Er Ac

π H   4 Er 

(4) −2

(h + ξ )

2

(5)

where ξ is a parameter supposed to be an indicator of bluntness in the tip of the indenter. The advantage of this method is that it does not require the computation of area function, a key requirement in the conventional Oliver and Pharr method, for the determination of mechanical properties. The essence of this method is that Eq. (5) must precisely predict the experimental loading curve when the values of mechanical properties determined using Eq. (1) and (3) are substituted in it.

67 4.

Energy dissipation and nanomechanical quantities

Energy dissipated during indentation may be employed to represent the load-displacement curves which, in turn, may be used to evaluate the slopes of these curves. Starting with the basic definition of the energy based parameters; a procedure for the determination of the loading/unloading slopes is described in the following. 4.1 Energy constants Total, elastic and plastic energy dissipated during indentation are found to be proportional to the absolute energy of indentation [20]. Absolute energy (WS ) is considered as the maximum possible energy that can be dissipated during indentation of a material. Mathematically, it is given by the area of the triangle OAhmax in the loading displacement diagram as shown in fig 1. The ratio of absolute to total and elastic energy are constant for a given material may be expressed as: vT =

WS WT

(6)

vE =

WS WE

(7)

Where vT and vE respectively describe the total and elastic energy constants and are primarily related to the curvature of the loading unloading curves. Large values of these constants simply mean that the loading and unloading curves have more curvatures. The elastic energy constant may also be related to the percentage elastic recovery of a material. The material which recovers less upon withdrawal of load has higher value of this constant.

Fig 1 Typical nanoindentation load-displacement diagram with terminology

68 4.2 Slopes of loading/unloading curves Attaf [15], using functional analysis, found that the loading and unloading curves may be respectively represented by the following expressions:

 h  P = Pmax    hmax 

2 vT −1

 h  P = Pmax    hmax 

2 vE −1

(8)

(9)

Where Pmax and hmax are peak indentation load and maximum depth of penetration respectively. The approximating power of the above expressions is shown in fig 2a and 2b for aluminum and tungsten respectively. Excellent agreement between experimental and theoretical curves could be seen in the figures. Note that, for the materials which recover more upon withdrawal, such an excellent agreement is normally not obtained for unloading curves. Knowing the expressions for loading and unloading curves, their slopes may be evaluated by analytically differentiating the above expression and then evaluating the derivative at the point of maximum depth of penetration as

Pmax hmax P = Su ( 2vE − 1) max hmax = Sl

( 2v

T

− 1)

(10) (11)

While Eq. (10) gives reasonable estimate of loading slopes, unloading slopes are overestimated if Eq. (11) is used. However, Eq. (11) may be used to determine the contact depth between the indenter and material to be indented in terms of elastic energy constant and maximum depth of penetration. Slope of the unloading curve can then be determined from the known value of contact depth following the procedure used to determine the contact depth from the known value of initial unloading stiffness in the conventional Oliver and Pharr method.

Fig 2 Modeling nanoindentation load displacement curves using functional analysis based expressions: (a) Aluminum; (b) Tungsten

69 4.3 Contact depth and elastic energy constant As mentioned, the initial unloading stiffness or slope of the unloading curve may be determined from the known contact depth which may be expressed as a fraction of maximum depth of penetration as [13]:

hc =

2 ( vE − 1) h ( 2vE − 1) max

(12)

Equation (12) is found to be applicable even for heterogeneous material such as concrete. For copper, an error of less than 3% was obtained. Total depth of penetration may be additively decomposed into material surface deformation and the contact depth. During indentation, material surface deformation is found to be proportional to the ratio of peak indentation load and initial unloading stiffness. Using these conditions one can obtain a relation for slope of the unloading curve in terms of elastic energy constant as

= Su ε ( 2vE − 1)

Pmax hmax

(13)

where ε is known as geometric constant and is equal to 0.75 for a Berkovich indenter. Note that it is the geometric constant that makes the difference between Eq. (11) and Eq. (13). Equation (11) overestimates the slope of the unloading curve by 25% for a Berkovich indenter than that given by Eq. (13). In this way, the main ingredients of the two-slope method i.e. loading and unloading slopes may be determined without resorting to curve fitting method. 5.

Modified two-slope method

The issue related to the representation of loading/unloading curves is already discussed in the preceding sections and we concluded that it is advantageous to use energy based expressions to determine their slopes. The second issue is related to the use of correction factors in the Sneddon’s solution and loading curve equation respectively given by Eq. (4) and Eq. (5). Role of these two correction factors have been studied from different perspectives by many researchers. However, no definite conclusions regarding their determination and implementation are found to exist in the literature. It would be reasonable to assume that the correction factors due to lack of axial symmetry and inward radial displacement of materials’ surface points exits simultaneously and may be employed simply by multiplying these two factors if a Berkovich indenter is used to obtain the load displacement curve. This assumption regarding implementation of correction factors is also used by Meza et al. [18]. By substituting Eq. (10) and (13) in Eq. (1) - (3) and by replacing β with βγ , following expressions for elastic modulus, area of contact and hardness is obtained respectively.

Er =

ε Pmax ( 2vT − 1)( 2vE − 1) 2 C 2 βγ hmax ( 4vE − 2vT − 1) π

Ac = Ch

 ( 4vE − 2vT − 1)     ( 2vT − 1)( 2vE − 1) 

P H = max2 Chmax

 ( 4vE − 2vT − 1)     ( 2vT − 1)( 2vE − 1) 

2 max

2

(14)

2

(15)

−2

(16)

In above expressions, factor γ is calculated according to the formulae given in Hay et al [19] for a Berkovich indenter. A value of 1.034 for the factor is used to check the validity of the proposed expressions when the peak indentation load is in excess of 100 mN. Knowing all the parameters appearing in above equations, the mechanical properties for aluminum, copper and tungsten were determined. As shown in table 1, the elastic modulus of all these materials compare well with that obtained from the conventional Oliver and Pharr method. But Eq. (15) yields higher values of the contact area for all these material than the conventional method. It is due to the fact that the initial unloading stiffness given by Eq. (13) is still larger than that obtained by the differentiation of the power law used to represent the unloading curve. The contact area determined by the conventional method cannot be questioned as it gives accurate value of contact area at least for materials like aluminum, copper and tungsten [1]. As a result, an area correction factor is used to obtain the accurate value of the contact

70 area and hence the hardness. We assume that this correction factor is equal to (αβ ) . With this assumption the hardness value 2

for each material is calculated (as shown in table 1) which is in reasonable agreement with that obtained by both Oliver and conventional methods. Elastic modulus and hardness are substituted back in Eq. (5) for each material and corresponding loading curve is modeled. Excellent agreement between theoretical and experimental loading curve could be seen in fig 3 which further ensures the accuracy of the mechanical properties determined using this method and validates our assumption concerning area correction factor.

Fig 3 Modeling nanoindentation loading curves using Eq. (4) with values of Er and H determined in this study. Following the above procedure, elastic modulus and hardness value of copper subject to different peak indentation load are calculated. Here different values for β are assumed successively, but best results were obtained when a value of 1.126 is selected. This is in agreement with the findings of Meza et al. which states that β depend on the maximum depth of penetration: it attains higher values at lower depth and remains constant when the depth of penetration is large. The elastic modulus and hardness values obtained using modified method and Oliver method are compared with those obtained experimentally as shown respectively in fig 4 and fig 5. It can be seen that the values obtained by the proposed method is in reasonable agreement (< ±10%) with experimental values. On the other hand, Oliver method gives error in excess of 10% for both elastic modulus and hardness as shown respectively in fig 4a and fig 5a. From this observation, it may be concluded that the proposed method gives consistent results regardless of the indentation size. Oliver method is more prone to error when indentation size is small. This is very important in case of thin films and coatings where depth of penetration is very small.

71

Fig 4 Comparison of modulus (in GPa): (a) Oliver method; (b) This study vs. experimental data for copper at loads less than 3 mN

Fig 5 Comparison of hardness (in GPa): (a) Oliver method; (b) This study vs. experimental data for copper at loads less than 3 mN

72 6.

Conclusions

Energy based parameters/expressions are employed to ameliorate the two-slope method used for the determination of elastic modulus and hardness of a material. The proposed method is validated using the nanoindentation data on elastic perfectly plastic materials such as aluminum, copper and tungsten. Elastic modulus and hardness of these materials compare well with experimental results with a relatives error of less than 10%. Main conclusions of this study may be enumerated as follows: •

•

•

Functional analysis based expressions are very accurate as far as the representation of load-displacement curves is of concern for the material which recovers less upon withdrawal of load. Expression for unloading curve, however, overestimates the initial unloading stiffness. Alternatively, it may be calculated from the known value of contact depth expressed in terms of elastic energy constant and maximum depth of penetration. The slope of the loading curve at the peak indentation load may be obtained directly by analytically differentiating the energy based expression. Correction factors due to the lack of axial symmetry and inward radial displacement of the material surface points have important implications on the accuracy of the mechanical properties determined by this method. The magnitude of β depends on the indentation size and has higher value at lower depth of penetration. In this study, a constant value equal to 1.034 is used at large peak indentation load. At low load level, a value which gives the least error is selected using hit and trial method. γ may be determined using the expression given by Hay et al. The proposed expression for the determination of the contact area overestimates its value as compared to the conventional method. For the material considered in this study, a very accurate value of contact area is usually obtained using the conventional Oliver and Pharr method. To correct this, a factor has been introduced in the expression which is 2 found to be approximately equal to (αβ ) for all the materials considered in this study regardless of indentation size.

Table 1 Comparison of mechanical properties in GPa obtained from three different methods.

Material Aluminum Copper Tungsten

This Study Er 70.44 130.00 320.16

H 0.194 0.894 4.470

Oliver Method Er 69.55 122.74 344.87

H 0.197 0.804 4.32

Oliver and Pharr Method Er H 72.42 0.21 136.50 0.970 320.4 3.80

Ref. 1 4 1

Acknowledgement Authors are thankful to Debrupa Lahiri, PhD candidate in the Department of Mechanical and Material Engineering at Florida International University, for helping us in carrying out the nanoindentation experiment on copper. References 1. Oliver WC, Pharr GM, An Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, Journal of Material Research, 7(6), pp. 1564-1583, 1992. 2. Pharr GM, Bolshakov A, Understanding nanoindentation unloading curves, Journal of Material Research, 17(10), pp. 2660-2671, 2002. 3. Oliver WC, Pharr GM, Measurements of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology, Journal of Material Research, 19(1), pp. 3-20, 2004. 4. Hainsworth SV, Chandler HW, Page TF, Analysis of nanoindentation load-displacement loading curves, Journal of Material Research, 11(8), pp. 1987-1995, 1996. 5. Jha KK, Suksawang N, Agarwal A, Analytical method for the determination of indenter constants used in the analysis of nanoindentation loading curves, Scripta Materialia, 63, pp. 281-284, 2010. 6. Malzbender J, de With G, den Toonder J, The P-h2 relationship in indentation, Journal of Material Research, 15(5), pp. 1209-1212, 2000.

73 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Cheng YT, Cheng CM, Relationship between hardness, elastic modulus, and work of indentation, Applied Physics Letters, 73(5), pp. 614-616, 1998. Cheng YT, Cheng, CM, Scaling relationship in conical indentation of elastic perfectly plastic materials, International Journal of Solids and Structures, 36, pp. 1231-1243, 1999. Oliver WC, Alternative technique for analysis instrumented indentation data, Journal of Materials Research, 16(11), pp. 3202-3206, 2001. Troyon M, Huang L, Critical examination of the two-slope method in nanoindentation, Journal of Material Research, 20(8), pp. 2194-2198, 2005. Fischer-Cripps AC, Nanoindentation, Second edition, Springer, 2004. Constatinides G, Ravi Chandran KS, Ulm F-J, Van Vliet KJ, Grid indentation analysis of composite microstructure and mechanics: Principles and validation, Materials Science and Engineering A, 430, 189-202, 2006. Attaf MT, New formulation of the nanomechanical quantities using the β-material concept and the indentation function, Materials Letters, 58, pp. 889-894, 2004. Attaf MT, A unified aspect of power-law correlations for Berkovich hardness testing of ceramics, Materials Letters, 57, pp. 4627-4638, 2003. Gong J, Miao H, Peng Z, Analysis of the nanoindentation data measured with a Berkovich indenter for brittle materials: effect of the residual contact stress, Acta Materialia, 52, pp. 785-793, 2004. Attaf MT, Step by step building of a model for the Berkovich indentation cycle, Materials Letters, 58, pp. 507-512, 2004. King RB, Elastic analysis of some punch problems for a layered medium, International Journal of Solids and Structures, 23(12), pp. 1231-1243, 1999. Meza JM, Abbes F, Troyon M, Penetration depth and tip radius dependence on the correction factor in the nanoindentation experiments, Journal of Material Research, 23(3), pp. 725-731, 2008. Hay JC, Bolshakov A, Pharr GM, A critical examination of the fundamental relations used in the analysis of nanoindentation data, Journal of Material Research, 14(6), pp. 2296-2305, 1999. Attaf MT, New ceramics related investigation of the indentation energy concept, Materials Letters, 57, pp. 4684-4693, 2003.

Advances in Thin Film Indentation

B. Zhou, K. Schwieker, B. Frye, and B.C. Prorok Auburn University, Department of Mechanical Engineering 275 Wilmore Engineering Labs, Auburn, AL 36849, Email: [email protected] ABSTRACT: A new method to accurately and reliably extract the actual Young’s modulus of a thin film on a substrate by indentation was developed. The method involved modifying the discontinuous elastic interface transfer model to account for substrate effects that were found to influence behavior even a few nanometers into a film several hundred nanometers thick. The method was shown to work exceptionally well for all 25 different combinations of 5 films on 5 substrates that encompassed a wide range of compliant films on stiff substrates to stiff films on compliant substrates. A predictive formula was determined that enables film modulus to be calculated as long as one knows the film thickness, substrate modulus and bulk Poisson’s ratio of the film and substrate. The calculated values of film modulus were verified with prior results that employed the membrane deflection experiment and resonance-based methods. The greatest advantages of the method are that the standard Oliver and Pharr analysis can be used and that it does not require the continuous stiffness method, enabling any indenter to be employed. The film modulus then can be accurately determined by simply averaging a handful of indents on a film/substrate composite. INTRODCUTION: Accurately assessing the properties of thin film coatings with modestly intrusive indents continues to remain a strong desire of the scientific and engineering communities. These measurements can be problematic as the deformation field emanating from the indent usually propagates in both the film and the substrate, rendering any property interrogated as a composite value influenced by both. Various experimental and theoretical-based approaches have been applied to decoupling these effects [1-20], yet a complete and accurate picture has been challenging to obtain. Recently, the authors proposed a new model called the discontinuous elastic interface transfer model [21] that accounted for an apparent discontinuity in elastic Figure 1: (a) Schematic illustrating the concept of strain transfer at the film/substrate interface. The continuous transfer of strain between the film and physical basis of this model is best illustrated in Fig. substrate, (b) numerical simulation indicating that strain 1, which shows that values of strain are not is likely discontinuously transferred between the film numerically equivalent across the film substrate and substrate, and (c) schematic showing how the film interface. Part (a) is a schematic of the spherically and substrate components are decoupled in the symmetric strain field emanating from an indent in a discontinuous elastic interface transfer model. film/substrate composite that is representative of the interplay of stress and strain between the film and substrate in the leading models of Doerner and Nix [2] and Gao [3], see our prior work for a discussion on this point [21]. In this case there is a continuous transfer of strain from the film to the substrate, in other words, values of strain are numerically equivalent on both sides at the interface. However, our numerical simulations indicated that a discontinuity in elastic strain transfer should exist at the film/substrate interface, see Fig. 1(b) and (c). The new model was constructed based on this discontinuity by adapting the Doerner and Nix and Gao model forms; whereby, separate weighting factors were applied to account for the influence of the substrate in strain developed in the film and vice-versa, see Fig. 1(c). It has the following form,

.

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_11, © The Society for Experimental Mechanics, Inc. 2011

(1)

75

76 2

2

Here, E’ is the composite modulus, Ef’ is the film modulus = Ef /(1-υf ), Es’ is the substrate modulus = Es /(1-υs ), and Φf and Φs are the weighting factors to account for the effects of the film on the substrate and substrate on the film respectively and are given as, and

,

(2)

where, t is the film thickness, h is the indent depth and αf and αs are the constants for the film and substrate respectively. This form resembles that of Doerner and Nix [2] and Gao [3] with the exception that they both applied a single weighting factor (ΦD-N and ΦGao respectively) equally to each compliance component, see our prior work for a discussion on this point [21]. It should be noted that this form deals only with the film/substrate composite modulus (E’) and not the reduced modulus (Er) that is affected by the indenter properties (Ei’) as per (1/ Er) = (1/ E’) + (1/ Ei’). In most cases the indenter component is negligible and can be ignored because of the very low compliance of a diamond indenter. However, when the film/substrate compliance becomes comparable to diamond, the indenter component should be included. The discontinuous elastic interface transfer model was compared to experimental data from thirteen different amorphous thin film materials on a silicon substrate and was found to match the all experimental curves with high fidelity. Furthermore, our prior work discovered that the α constants in each weighting factor were found to have physical significance in being numerically equivalent to the bulk scale Poisson’s ratios of the film (αf) and substrate (αs). The model proved to be adept at revealing the interplay between the film and substrate during indentation. Given that the model was investigated with only one substrate there was some question as to whether the model is applicable to other film/substrate combinations. This point is investigated in the following work employing 5 films and 5 substrates for 25 different combinations that encompass a wide range of compliant films on stiff substrates and stiff films on compliant substrate cases. It will determine whether the original discontinuous elastic interface transfer model is applicable to most film/substrate combinations. EXPERIMENTAL PROCEDURE: In this work five different films and five different substrates were selected with a variable range of elastic moduli. The ability to deposit amorphous films was also a selection criterion so as to avoid microstructural effects and the films should not possess high modulus to hardness ratios to avoid loss of contact effects when employing the continuous stiffness method during indentation [22]. The films included chromium oxide (CrOx), amorphous silicon (a-Si), aluminum oxide (AlOx), aluminum nitride (AlN), and silicon carbide (SiC) and the substrates were amorphous silicon dioxide (SiO2), <100> germanium (Ge), <100> silicon (Si), <100> magnesium oxide (MgO), and <0001> sapphire (Al2O3), see Table 1 for material properties. The materials compose twenty five combinations of film/substrate modulus ratios. The substrates were all polished to a mirror surface to ensure uniform contact between the film and substrate. A Denton sputtering system was employed to deposit the films using DC or RF power. Here, optimum deposition parameters were determined from previous experiments [21] based upon those resulting in the “most” amorphous in structure. The substrate holder was rotated at a speed of 50 RPM to perform a uniform deposition. The achieved thickness of each film is listed in Table 1. Table 1: Material properties and their source for the substrates and films selected for the indentation experiments. Substrate

Modulus (GPa)

Poisson’s Ratio [ref]

SiO2

70 ± 4

0.17 (quartz)

Ge

144 ± 7

Si

Poisson’s Ratio [ref]

Thin Film

Thickness (nm)

[39]

SiC

460 ±13

0.3

[44]

0.27

[40]

AlN

1050 ± 27

0.26

[45]

173 ± 9

0.28

[41]

AlOx

260 ± 9

0.27

[43]

MgO

249 ± 17

0.23

[42]

a-Si

540 ± 6

0.25

[46]

Al2O3

460 ± 28

0.21~0.27

[43]

CrOx

135 ± 15

0.25

[47]

The indentation tests were performed with an MTS Nanoindenter XP system with a Berkovich type diamond tip. The continuous stiffness method (CSM) was employed to obtain Young’s modulus versus displacement with a harmonic displacement target set at 2 nm and a minimum thermal drift rate of 0.05 nm/s. The Poisson's ratios of

77 the films were assumed as the bulk values for all the amorphous thin films. For each film/substrate combination, 25 or more CSM tests were run with same final indent depth. Quasi-static simulation of nanoindentation was performed using ANSYS 11 with the tip movement controlled by displacement. The model was built-up using 2-D elements and assuming material properties and film thicknesses listed in Table 1. Detailed information can be found in our previous work [21]. To simplify the simulation the film roughness and residual stress were assumed to be negligible. RESULTS AND DISCUSSIONS: The raw indentation data for the 25 film/substrate combinations were calibrated and compared in groups of each film material. Fig. 2 shows the measured Young’s modulus-displacement curves of the AlOx films on the five substrates, encompassing a range of compliant-on-stiff to stiff-on-compliant film/substrate situations. Each curve exhibited a so-called “flat region,” that many in the thin film indentation community consider to represent the Young’s modulus of the film, before increasing gradually to the substrate modulus with displacement into the surface, or decreasing when the substrate was softer. However, in this case, the value of the modulus in the flat region, E’flat, for the AlOx film appears to strongly depend on the substrate

Figure 2: Plot comparing the measured Young’s modulus as a function of displacement for the AlOx films on different substrates.

Figure 3: Plot illustrating the quality fit of the discontinuous elastic interface transfer model for the AlOx films and estimation of elastic homogeneity of the film/substrate composite (dashed line).

modulus, increasing with increasing substrate modulus. The other 4 films exhibited the same trend. Wei and coworkers have reported similar behavior in Al and W films on different substrates [23]. It should also be noted that we examined the curves for signs of loss of contact at low penetration depths in accordance with effects recently identified by Pharr et al. [22] and did not find any significant evidence of this effect. In applying our previously developed discontinuous elastic interface model, Eq. (1), each of the AlOx curves can be matched rather well, see solid lines in Fig. 3. Here, using the substrate modulus and Poisson’s ratios in Table 1, each AlOx/substrate combination yielded a different value for the film modulus, Ef’, which increased with substrate modulus (108 GPa for SiO2, 123 GPa for Ge, 138 GPa for Si, 141 GPa for MgO, and 149 GPa for Al2O3), see Table 2. These values match well with the value of E’flat for each curve. The procedure was repeated for the remaining film/substrate combinations and the results are also listed in Table 2. It is clear from the data of all 5 films that the measured modulus in the flat region is not wholly determined by the film alone and that the substrate plays a significant role even very early in the indentation process. It is worth noting that while there were stiff-on-compliant and compliant on-stiff film/substrate combinations, the films and substrates used had Poisson’s ratios from 0.17 to 0.3, with none in the lower or higher range. To further investigate the above conclusion that the substrate plays a role very early in the indentation process, finite element simulations were performed on all five AlOx/substrate combinations, see Fig 4. The simulations employed the material properties listed in Table 1 and a film thickness of 260 nm. Each simulation showed the elastic strain intensity distribution from an indent only 5 nm into the film/substrate composite for AlOx

78 Table 2 List of E’flat values for each film/substrate specimen compared with the E’f values obtained from Fig. 4. Values of Ef’ and Eflat (GPa) for the Films Substrate

SiC

AlN

AlOx

a-Si

CrOx

SiO2

196 ± 17

136 ± 13

108 ± 6

83 ± 6

64 ± 5

Ge

222 ± 19

149 ± 11

123 ± 10

85 ± 7

80 ± 6

Si

230 ± 23

146 ± 9

138 ± 13

88 ± 5

73 ± 5

MgO

260 ± 16

153 ± 10

141 ± 20

87 ± 11

75 ± 14

Al2O3

281 ± 19

160 ± 14

149 ± 21

97 ± 7

72 ± 4

Estimated E’f from Fig. 4

259

144

121

82

64

E’f calculated From Eq. 3.

255 ± 19

140 ± 12

119 ± 9

84 ± 4

66 ± 4

Figure 4: Finite element analysis of the AlOx film/substrate composites showing the elastic strain distribution for an indent penetrating 5nm into each film; (a) SiO2, (b), Ge, (c) Si, (d) MgO, and (e) Sapphire. films on; (a) SiO2, (b), Ge, (c) Si, (d) MgO, and (e) Figure 5: Plot E’flat versus the substrate Young’s Sapphire, with (b) through (e) representing soft-on-hard modulus for all 5 films illustrating that for each film, a combinations. In all cases a discontinuous transfer of point of elastic homogeneity or the actual film elastic strain was observed at the interface consistent modulus can be suggested. with our model and previous work. It is clear that in all combinations a significant elastic strain field has developed in the substrate, even when the indenter has penetrated less than 2% of the film thickness. In case (a), the stiff-on-compliant combination, a significant amount of strain energy is absorbed by the more compliant substrate, resulting in the film appearing to possess less stiffness than it actually does. On the other hand, in the compliant-on-stiff cases, (b) through (e), the substrates absorb lesser and lesser amounts of strain energy as the substrate modulus increases. Here, the films appear stiffer than they actually are. This concept is consistent with the trend in AlOx E’flat values in Fig. 3 and in the data of the other films. The actual Young’s modulus of the AlOx film should lie between the E’flat of the SiO2 and Ge substrates. One may consider then the hypothetical case of elastic homogeneity existing between the AlO x film and substrate,

79 both possess the same Young’s modulus. Saha and Nix [15] illustrated this experimentally for tungsten films on sapphire substrates. The dashed line in Fig. 3 represents this case as a rough interpolation between the compliant-on-stiff to stiff-on-compliant curves. Unfortunately, this interpolation is not an exact practice and a more precise method is desired. Using the concept of elastic homogeneity, one can plot the values of E’flat for the films versus the substrate modulus to better estimate the film modulus, see Fig. 5. Here the dashed line represents elastic homogeneity between the film and substrate. The trend of each film indicates that an intersection with elastic homogeneity should exist that identifies the film modulus. Linear regression was employed to identify these intersections, which are listed in Table 2. However, given the variability of the data, it is not clear that this is the most appropriate method. Furthermore, it is desired to obtain the Young’s modulus of the film from a handful of indents on a single film/substrate composite rather than depositing and indenting the film on several substrates. Figure 6: Plot of ΔE’f versus the substrate modulus, With any elastically mismatched film/substrate both are normalized by E’f to directly compare each composite there will exist a difference between the film film. modulus and the measured modulus in the flat region, ∆Ef’, such that ∆Ef’ = E’flat -Ef’, that scales with the film/substrate mismatch. Values of ∆Ef’ were calculated using the film values estimated in Fig. 5 and the flat region values in Table 2. One can plot this difference versus the substrate modulus to assess whether the trend can be predicted and by normalizing both with the film modulus the different films can be compared, see Fig. 6. The data from all of the films appear to follow a uniform trend with the top half of the plot containing compliant-onstiff combinations and the bottom half stiff-on-compliant combinations. A power function can be used to describe this behavior, and in conjunction with Eq. 1 lead to,

(3) Here, the factor accounting for the early influence of the substrate is the ratio of the film to substrate modulus to the 0.1 power. It is unclear at this time as to the physical basis of the 0.1 power, but it matches the experimental data rather well for all 25 film/substrate combinations. This equation encompasses all aspects and enables the film Young’s modulus to be extracted from a single indent as long as one knows the film thickness, the substrate modulus, and the bulk Poisson’s ratios of the film and substrate. The Young’s modulus of all of the films studied can be determined from the experimental data for any Fig. 7 shows single film/substrate combination. application of it to the AlOx films for the Si (compliant-onstiff) and SiO2 (stiff-on-compliant) substrates. The solid line is the original equation, Eq. 1, for the discontinuous elastic interface transfer model and the open symbols are the calculated film modulus for each data point using the modified version, Eq. 3. The calculated values of the AlOx film are relatively uniform with displacement into the surface for both substrates. Both also agree fairly well with less than two percent difference between their average values for the two substrates. The average

Figure 7: Experimental curves for AlOx films on Si and SiO2 substrates showing the uniformity of film modulus calculated from each data point with Eq. 3.

80 values were calculated for all five films on all substrates and are listed in Table 2. The modulus from this method agrees well with that estimated from Fig. 5. This developed model appears adept at describing the complex interaction between the film and substrate during indentation. It was shown to work for amorphous and crystalline films with the wide range of film/substrate combinations investigated. Although most of the films investigated here where relatively hard in terms of plastic behavior, the results with gold and the soft alloys FeB and Metglas films in our prior work [21] indicate promising application to a variety of material classes. The method appears to provide a straightforward opportunity to accurately assess the Young’s modulus of a film or coating from mildly intrusive indents and employing the standard Oliver and Pharr method [38], while not requiring continuous stiffness measurements. The model though does not consider effects from residual stress or pile-up/sink-in. It may however, offer new opportunity to study these effects in more depth. CONCLUSIONS: Indentation tests were conducted on five films on five different substrates and revealed that the so-called “flat” region often seen in the Young’s modulus versus displacement signatures of many indented films was not entirely representative of the film response alone. By tracking the response of each film on the different substrates, the magnitude of this flat region was found to depend and scale with the substrate modulus. Furthermore, the data indicated that the substrate significantly influenced the mechanical behavior even at penetration depths less than 2 % of the film thickness. All 25 film/substrate combinations were found to follow a consistent trend and a power law description of behavior was determined. This formula was incorporated into the discontinuous elastic interface transfer model of thin film indentation and was shown to be adept at extracting the actual film modulus from the experimental data while employing the standard Oliver and Pharr analysis. It also does not require the continuous stiffness method, enabling virtually any existing indenter to employ it. The values matched rather well and confirm the validity of extracting Young’s modulus of indents in film/substrate composite with high fidelity. REFERENCES: 1. J.B. Pethica, R. Hutchings and W.C. Oliver: Hardness measurement at penetration depths as small as 20 nm. Philos Mag A 48 593 (1983). 2. M.F. Doerner and W.D. Nix: A method for interpreting data from depth-sensing indentation instruments. J. Mater. Res. 1 601 (1986). 3. H. Gao, C.-H. Chiu and J. Lee: Elastic Contact versus Indentation Modelling of Multi-Layered Materials. Int. J. Solids Structures 29 2471 (1992). 4. G.M. Pharr, D.L. Callahan, S.D. McAdams, T.Y. Tsui, S. Anders, A. Anders, J.W. Ager Iii, I.G. Brown, C.S. Bhatia and S.R.P. Silva: Hardness, elastic modulus, and structure of very hard carbon films produced by cathodic-arc deposition with substrate pulse biasing. Appl. Phys. Lett. 68 779 (1996). 5. X. Chen and J.J. Vlassak: Numerical study on the measurement of thin film mechanical properties by means of nanoindentation. J. Mater. Res. 16 2974 (2001). 6. R.B. King: Elastic Analysis of Some Punch Problems for a Layered Medium. Int. J. Solids Struct. 23 1657 (1987). 7. W.D. Nix: Mechanical properties of thin films. Met. Trans. A 20 2217 (1989). 8. J.A. Knapp, D.M. Follstaedt, S.M. Myers, J.C. Barbour and T.A. Friedmann: Finite-element modeling of nanoindentation. J. Appl. Phys. 85 1460 (1999). 9. H. Buckle, The Science of Hardness Testing and its Research Applications. (ASM, 1973) Pages. 10. J. Hay: Measuring substrate-independent modulus of dielectric films by instrumented indentation. J. Mater. Res. 24 667 (2009). 11. J. Menčík, D. Munz, E. Quandt, E.R. Weppelmann and M.V. Swain: Determination of elastic modulus of thin layers using nanoindentation. J. Mater. Res. 12 2475 (1997). 12. H. Xu and G.M. Pharr: An improved relation for the effective elastic compliance of a film/substrate system during indentation by a flat cylindrical punch. Scr. Mater. 55 315 (2006). 13. H. Li and J.J. Vlassak: Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation. J. Mater. Res. 24 1114 (2009). 14. S. Roche, S. Bec and J.L. Loubet: Analysis of the elastic modulus of a thin polymer film. Mater. Res. Soc. Symp. Proc. 778 117 (2003). 15. R. Saha and W.D. Nix: Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Mater. 50 23 (2002).

81 16. H.Y. Yu, S.C. Sanday and B.B. Rath: The effect of substrate on the elastic properties of films determined by the indentation test—Axisymmetrical Boussinesq problem. J. Mech. Phys. Solids 38 745 (1990). 17. S.M. Han, R. Saha and W.D. Nix: Determining hardness of thin films in elastically mismatched film-onsubstrate systems using nanoindentation. Acta Mater. 54 1571 (2006). 18. S. Bec, A. Tonck, J.M. Georges, E. Georges and J.L. Loubet: Improvements in the indentation method with a surface force apparatus. Philos. Mag. A 74 1061 (1996). 19. T. Chudoba, M. Griepentrog, A. Duck, D. Schneider and F. Richter: Young’s modulus measurements on ultrathin coatings. J. Mater. Res. 19 301 (2004). 20. N. Schwarzer, F. Richter and G. Hecht: The elastic field in a coated half-space under Hertzian pressure distribution. Surf. Coat. Technol. 114 292 (1999). 21. B. Zhou and B.C. Prorok: A Discontinuous Elastic Interface Transfer Model of Thin Film Nanoindentation. in press Exp. Mech.(2010). 22. G.M. Pharr, J.H. Strader and W.C. Oliver: Critical issues in making small-depth mechanical property measurements by nanoindentation with continuous stiffness measurement. J. Mater. Res 24 653 (2009). 23. Z. Wei, G. Zhang, H. Chen, J. Luo, R. Liu and S. Guo: A simple method for evaluating elastic modulus of thin films by nanoindentation. J. Mater. Res. 24 (2009). 24. B.C. Prorok and H.D. Espinosa: Effects of nanometer-thick passivation layers on the mechanical response of thin gold films. J. Nanosci. Nanotech. 2 427 (2002). 25. H.D. Espinosa, B.C. Prorok and M. Fischer: A methodology for determining mechanical properties of freestanding thin films and MEMS materials. J. Mech. Phys. Solids 51 47 (2003). 26. H.D. Espinosa, B.C. Prorok and B. Peng: Plasticity size effects in free-standing submicron polycrystalline FCC films subjected to pure tension. J. Mech. Phys. Solids 52 667 (2004). 27. H.D. Espinosa and B.C. Prorok: Size effects on the mechanical behavior of gold thin films. J. Mater. Sci. 38 4125 (2003). 28. L. Wang and B.C. Prorok: Characterization of the strain rate dependent behavior of nanocrystalline gold films. J. Mater. Res. 23 55 (2008). 29. L. Wang and B.C. Prorok: Investigation of the Influence of grain size, texture and orientation on the mechanical behavior of freestanding polycrystalline gold films. Mater. Res. Soc. Symp. Proc. 924E Z03 (2006). 30. H.D. Espinosa, B.C. Prorok, B. Peng, K.H. Kim, N. Moldovan, O. Auciello, J.A. Carlisle, J.A. Gruen and D.C. Mancini: Mechanical properties of ultrananocrystalline diamond thin films relevant to MEMS/NEMS devices. Exp. Mech. 43 256 (2003).

Cyclic Nanoindentation Shakedown of Muscovite and Its Elastic Modulus Measurement

Hang Yin1 and Guoping Zhang1 1

Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803

ABSTRACT A series of cyclic loading nanoindentation experiments with varied maximum loads (Fmax) of 0.05 to 2.0 mN were performed on a nanostructured, layered muscovite with loading direction normal to its basal plane. A critical load (e.g., 0.5 mN) exists that leads to distinct load-displacement curves: when Fmax is greater than this load, the loading/unloading curves, after a few initial cycles, become characteristic closed hysteresis loops, suggesting that shakedown process occur quickly; otherwise, only nonlinear elastic, completely overlapped hysteresis loops were observed. These phenomena result in two representative elastic moduli that depend on indentation depth. For Fmax (e.g., 0.05 and 0.1 mN) smaller than the critical load, the obtained elastic modulus at the nonlinear elastic state is nearly 88 GPa, which agrees with the reported Young’s modulus of the material; However, when Fmax exceeds the critical value, the measured modulus decreased to a lower constant value around 55 GPa, close to the bulk modulus of muscovite. The transition from a higher, true Young’s modulus to a lower bulk modulus can be attributed to the three dimensional confinement around the indenter tip after plastic shakedown at relatively larger depth, where significant alteration to the originally layered structure of muscovite has taken place.

INTRODUCTION Phyllosilicate minerals, major constituents of soils and rocks, are ubiquitous in the Earth’s crust. They consist of either discrete or mixed-layered sequences of fundamental, continuous 1:1 or 2:1 layers of 0.7 or 1.0 nm in thickness, respectively, with distinct sub-nanometer thick interlayers, thus phyllosilicates can be treated as naturally occurring nanostructured layered materials. These materials are usually platy in shape with high aspect ratios (e.g., diameter to thickness ratio ranges from 10:1 to 100:1). Their platy morphology and complex layered structure render them significant anisotropic properties and make it difficult to measure the elastic and plastic properties. For instance, the Young’s moduli at different directions (e.g., directions perpendicular to (001) or (010) plane) are expected to vary significantly. In nature, some of these materials (e.g., mica) occur as macrocrystals, thus rendering them a suitable analog material for the study of nanomechanics of synthesized or manufactured nanostructured multilayers [1-5]; while others may exist as micro to nano crystallites, and the measurement of their bulk

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_12, © The Society for Experimental Mechanics, Inc. 2011

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modulus is a difficult, challenging task. Further, accurate determination and better understanding of their mechanical properties are of essential relevance to geomechanics, geophysics, and other disciplines related to subsurface explorations and the design and construction of foundations to civil infrastructure. Muscovite is a non-expandable dioctahedral 2:1 phyllosilicate mineral with an ideal crystal formula K(Si3Al)Al2O10(OH)2 [6]. Its 2:1 layers typically possess a negative layer charge of ~1.0 per O10(OH)2 unit, which are balanced by non-hydrated or unsolvated interlayer K+ cations that tightly hold adjacent layers together. Figure 1 shows a schematic illustration of the crystal structure of muscovite. The interlayer bond can affect the material’s compressibility significantly, as further elaborated below. ~0.7 nm ~1.0 nm

~0.3 nm

Fig. 1 Schematic illustration of the ideal crystal structure of muscovite

The isothermal bulk modulus of muscovite was experimentally examined by isotropic compression testing. Comodi and Zanazzi [7] studied the high-pressure structural variations and compressibility of both K-muscovite and Na-muscovite and observed that the bulk moduli of these two muscovites are 49 and 54 GPa (±3 GPa), respectively. They further pointed out that the smaller bulk modulus of Kmuscovite when compared with Na-muscovite is due to the higher compressibility along the [001] direction and higher compressibility of the K-O bonds in the interlayer region. These results also agree with the compressibility data (i.e., 56 GPa) of Catti et al. [8] obtained on 2M1 K-muscovite sample using powder neutron diffraction at room temperature. Other Brillouin scattering measurements, which can examine the 13 independent elastic moduli of monoclinic crystals, have also shown that the elastic modulus of muscovite along the c-axis is about 58.6 [9] or 61 GPa [10]. Sekine et al. [11] used a shockwave equation of state to estimate the bulk modulus of natural muscovite sample, which is 52 GPa. All these modulus values are statistically identical, given that the examined samples may vary in chemical composition and crystal structure. Prior research has also found that muscovite exhibits interesting and distinct mechanical behavior under nanoindentation. For example, Barsoum et al. [12] observed the occurrence of fully reversible, superimposed stress-strain hysteresis loops when a muscovite single crystal was subjected to indentation repeated loading under a spherical indenter, and attributed the nonlinear elastic hysteresis loop to the formation and annihilation of incipient kink bands (IKBs). They further pointed out that muscovite and other layered minerals and materials (e.g., graphite, layered ceramics) belong to a group of kinking nonlinear elastic solids. Zhang et al. [13,14] observed that the elastic modulus of muscovite exhibits an apparent indentation size effect (ISE) based on a series of nanoindentation experiments conducted with a sharp Berkovich indenter. Furthermore, this kind of ISE, or in other words, the decrease in the measured elastic modulus with increasing indentation depth, is not typically observed for metals or other stereotypical crystalline materials. Yin and Zhang [15] examined the nanoindentation behavior of muscovite subjected to repeated loading. They found that a critical maximum load exists, which marks

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the material’s completely different responses to repeated loading, resulting in different values of elastic modulus. This paper aims to investigate the influence of cyclic nanoindentation shakedown observed on muscovite under repeated loading on the estimation of its elastic moduli, including both Young’s modulus and bulk modulus. Following the conclusions in Yin and Zhang [15], this paper further extends the experimental observations and discusses the transition of the measured Young’s modulus along the [001]* direction to the bulk modulus. If cyclic nanoindentation shakedown occurs, a smaller stiffness along the [001]* direction results from a large number of loading/unloading cycles. A particular focus is on the influence of load level on the nanoscale deformation of this mineral under cyclic nanoindentation loading and the resulting change in elastic modulus. It is hoped that the experimentally derived phenomenological behavior can help future analytical work to establish a more theoretical understanding of the aforementioned transition of the elastic modulus.

SAMPLE PREPARATION The muscovite sample chosen for this study was collected from Panasqueira, Portugal. Its chemical composition and crystal structure were well analyzed previously [16]. It is a 2M1 mica polytype and has a layer charge of -1.05 with a chemical formula 2+ (K1.00Na0.03Ca0.01)(Al1.93Fe 0.01Mg0.01Mn0.01)(Si3.09Al0.91)O10(OH)1.88F0.12. A carefully selected small fragment with an in-plane dimension of > 2 mm and a thickness of > 0.1 mm was gently cleaved off the muscovite rock chip and then used for subsequent sample mounting. A piece of single-crystal silicon wafer (100) (MTI Corporation, Richmond, CA) with a dimension of 10 × 10 × 0.6 mm (length × width × thickness) was used as substrate that provides atomically flat surface for sample mounting. A regular aluminum puck was first heated to 130 oC on a hot plate and then a thin layer of Crystalbond 509 amber resin (Aremco Products, Inc., New York), which melts at a temperature of 130 oC or higher, was applied to the puck surface. This was followed by carefully placing the silicon wafer substrate onto the puck surface where the resin was applied. To avoid trapping air between the resin and wafer interface, the wafer was gently pressed into the melted resin with a continuous rotation along one straight edge. Sufficient time was allowed for the wafer to be heated to 130 oC. Then another thin layer of amber resin was applied onto the silicon wafer surface, followed by carefully placing the muscovite sample onto the silicon wafer in a similar manor. Moreover, to prevent overheating the muscovite sample, immediately after the sample placement, the entire sample set (i.e., including alumina puck, silicon wafer, and muscovite) was removed off the hotplate to a leveling table for cooling. Finally, a very thin layer was cleaved off top of the muscovite sample with a razor blade so that a fresh and intact surface was exposed for nanoindentation loading. Before indentation testing, the sample was first examined under an optical microscope to check the sample dimension and quality of sample mounting. No cracks are observed within the sample, indicating that this fragment is most likely a single crystal. The surface topography of the sample was further characterized using an Agilent 5500 atomic force microscope (AFM) (Agilent Technologies, Inc., Chandler, AZ). Figure 2 shows a typical AFM micrograph for an area of 100 × 100 m on the muscovite surface. It is normal that an air-cleaved mica may not yield atomically flat surface due to surface contamination by the atmosphere and the reaction of interlayer K+ with atmospheric water and CO2 [17]. The blurred lines, divided into several parallel sets, are either very tiny scratches caused by a cotton swap during sample surface cleaning or the edge and screw dislocations that are previously

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present in the crystal or newly introduced by cleaving [18-20]. Again, no cracks are observed in the scanned area.

Fig. 2 The surface topography of the tested muscovite fragment (AFM image)

NANOINDENTATION TESTING An MTS Nano XP indenter (MTS Nano Instruments, Inc., Oak Ridge, TN) was employed for all nanoindentation experiments. Totally six tests, which used two different loading methods including the MTS standard method, and the cyclic loading method modified from the MTS standard method, were performed with a dynamic contact module (DCM) head equipped with a diamond Berkovich tip of < 20 nm in tip radius. The DCM head has a load resolution of 1.0 nN and displacement resolution of < 0.01 nm. For each test, typically 2-9 duplicate indents at a spacing of 100 µm were performed to ensure measurement repeatability. All tests were run with an allowed thermal drift rate of < 0.05 nm/s. th = 10 s

FP,5 = Fmax

th

Unloading at a constant rate F&5

Load, F

Loading at a constant rate F&5

Load, F

Unloading at a constant rate

Loading at a constant rate

FP,4 100 s

FP,3

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Time, t

(a) (b) Fig. 3 The loading profile for (a) the MTS standard method and (b) cyclic loading method modified form the MTS standard method

The MTS standard method applies indentation load at a constant loading rate under load control mode. Figure 3a depicts the loading sequences for this method. The maximum load (Fmax) and loading time (tL)

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were preset to 2.0 mN and 30 s, respectively. It takes 5 cycles of loading and unloading (L/U) to reach the Fmax. For the i-th cycle (where i = 1, 2, …, 5), the peak load FP,i and loading rate to peak load F&i are given by FP ,i = Fmax

2i 2N

(1)

F F 2i F&i = P,i = max N tL tL 2

(2)

where N is the total number of L/U cycles or 5 for this test. For the unloading section of each cycle, the unloading rate was kept the same as that of loading section of that same cycle, and the load was reduced to the 90% of the peak load of that cycle. Also, at the peak load, a holding time (th) of 10 s was allowed in all L/U cycles. At the end of the 5th cycle unloading, a holding time of 100 s was allowed for thermal drift correction. The MTS standard method was modified to perform cyclic loading tests (Figure 3b). Three modifications were made, including keeping the peak load of each cycle the same as the Fmax, reducing the holding time to zero at all peak loads, and changing the percentage of unloading from 90% in the MTS standard method to 100% in the repeated loading method. All other parameters remained the same. Totally 5 tests with different Fmax and loading time tL were performed. ANALYSES OF RESULTS 2.0

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Fig. 4 The relationship between maximum load and maximum displacement for all cyclic loading tests

Figure 4 collectively summarizes the relationship between the Fmax and maximum indentation depth hmax for all tests performed under cyclic loading, including the one by the MTS standard method (see inset).

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It is clearly shown that the data points can be categorized into two groups according to the Fmax: (1) When Fmax ≤ 0.25 mN, superimposed points are observed, indicating that the hmax remains the same in spite of multiple L/U cycles; (2) When Fmax ≥ 0.5 mN, the data points at a given Fmax are scattered over a wide band whose width increases with the Fmax. The observed data scattering is attributed to the popins whose accumulative extension usually increases with Fmax [15]. Figure 5 illustrates how pop-ins affect the indentation depth with two representative tests at Fmax = 1.0 and 0.1 mN. Pop-ins of varying extensions occur randomly in the first few loading sections of the L/U cycles when the Fmax exceeds the critical value (Figure 5a). With these pop-ins, the L/U hysteresis loops start to disperse and move toward the right side. After a few cycles, the L/U loops tend to converge to a stabilized one, and this phenomenon is named “shakedown” [21-23]. It refers to the process, under repeated loading, whereby the plastic deformation caused by initial L/U cycles introduces a system of residual protective stresses which make the steady cyclic state purely elastic [22] or cyclically plastic [23], leading to elastic shakedown or plastic shakedown, respectively [23]. During the process of shakedown, the occurring frequency and extension of the pop-ins also tend to decrease and even disappear with the number of L/U cycles increasing. This also suggests that pop-ins be the major cause of non-recoverable or permanent deformation during nanoindentation loading for the tested mineral. This phenomenon is in accordance with the observed increase of the L/U loop width and of the pop-ins number or occurring frequency. 1.0

0.12

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(a) (b) Fig. 5 The load-displacement curves of Tests performed under cyclic loading: (a) Fmax = 1.0 mN, (b) Fmax = 0.1 mN

The occurrence of random pop-ins and accordingly shakedown behavior of the tested muscovite can lead to significant variation in elastic modulus E, if the accumulative hmax is used to estimate the projected contact area and contact stiffness by following the Oliver and Pharr [24,25] method. Further details can be found in Yin and Zhang [15]. Because the loading direction is normal to the basal plane of the phyllosilicate mineral, the derived elastic modulus is referred to the [001]* direction. Figure 6 summarizes the elastic modulus obtained from all tests. As a reference, the continuous E-h curve obtained by the continuous stiffness measurement (CSM) method [15] is also shown here. For smaller Fmax (i.e., ≤ 0.25 mN), the E values obtained by the repeated loading method lie above the continuous E-h curve by the CSM method. For higher Fmax (i.e., > 0.5 mN), the majority of the E values lie below the continuous curve. Moreover, for a given large Fmax (> 0.5 mN), the E values fall inside a scattered band and decreased significantly with indentation depth. Overall, the derived elastic modulus

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values range widely from 55 to 115 GPa, indicating that the apparent indentation size effect exists for this mineral’s Young’s modulus. Furthermore, the E values decrease significantly during the first few L/U cycles and quickly stabilize to a single value, which agrees with the observed overlapped L/U loops very well. Another important feature is that at the same Fmax for cyclic loading, the E values also decrease with the number of L/U cycles, leading to two different characteristic points: •

When Fmax > 0.5 mN, the measured elastic modulus at the final shakedowned cycles is around 55 GPa, and this value agrees very well with the reported bulk modulus of muscovite, which ranges from 49 to 62 GPa. It should be noted that, although the derived elastic moduli at the final shakedowned cycles are around 55 GPa, some variations exist for this value, e.g., 70 GPa for Indent 2 and 65 GPa for Indent 3 at Fmax = 1.0 mN. According to the general relationship between an isotropic material’s Young’s modulus (E) and bulk modulus (K): E = 3K(1-2ν)), if the Poison’s ratio (ν) of the muscovite is 0.25 [26] and the above bulk modulus of 55 GPa is used, then the E value is 83 GPa,

•

When Fmax ≤ 0.25 mN, the derived elastic modulus after 20 L/U cycles is around 88 GPa, which is close to the E value (83 GPa) estimated based on the bulk modulus. 120

0.05 mN CSM Cyclic Indent 1 Cyclic indent 2 Cyclic Indent 3 Cyclic Indent 4 MTS Standard

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110

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100 90

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80

2.0 mN 0.25 mN

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150

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Fig. 6 The elastic modulus of the muscovite derived from all tests

DISCUSSION The nanostructured layered muscovite exhibits, when subjected to cyclic nanoindentation loading, multiple modes of complex nanoscale deformation in response to different levels of load. A critical load exists that leads to distinctly different load-displacement curves: when Fmax is greater than this load, the observed curves exhibit characteristic closed hysteresis loops, after a few initial loading/unloading cycles, suggesting that shakedown process occur quickly in muscovite; otherwise, only nonlinear elastic, completely overlapped hysteresis loops were observed. These phenomena lead to two representative elastic moduli that depend on indentation load or depth. At smaller Fmax (e.g., 0.05 and 0.1 mN), the obtained elastic modulus at the nonlinear elastic cyclic loops was nearly 88 GPa, which agrees with the reported Young’s modulus, ranging from 79-84 GPa [13,27]; However, when the Fmax exceeds the

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critical value (e.g., >0.5 mN), the measured elastic modulus decreased to a lower value around 55 GPa, close to the bulk modulus of muscovite. This transition from a higher Young’s modulus obtained from smaller indentation load to a lower bulk modulus obtained from larger indentation load can be attributed to the three dimensional confinement around the indenter tip at a relatively larger depth, where significant alteration to the original layered structure of muscovite has taken place. The alteration to the layered structure, as reflected by the cyclic plastic shakedown, leads to changes in the elastic behavior of the material in the region affected by the cyclic indentation loading. In general, three mechanisms contribute to this phenomenon: the protective residual stress induced by plastic deformation of prior L/U cycles; the increased contact area along with accumulated plastic deformation, leading to reduced contact stress (even though the indentation load remains the same); and the strain-hardening of the material. For the tested muscovite, the former two mechanisms may be dominant. During the process of shakedown, the occurring frequency and extension of the pop-ins tend to decrease and even disappear, resulting in non-recoverable or permanent deformation for the tested layered material. Similar phenomena have also been reported on mica and other layered materials (e.g., Ti3SiC2)[12,28]. Basal plane reorientation

Incipient Kink Band (a)

Layer delamination

Basal plane rupture (b)

Fig. 7 Schematic of the nanoscale modes of deformation at (a) small maximum load where only IKBs but no plastic deformation occurs; and (b) large maximum load where layer delamination and basal plane rupture take place

As pointed out by Comodi and Zanazzi [7], the compressibility of anisotropic K-muscovite is highly dependent upon the compressibility of dioctahedral layer and the strength of interlayer K-O bond. The layer structure also results in the nonlinear kinking elastic deformation, resulting from the incipient kink bands (IKBs), when the indentation load is relatively small (Figure 7a). Therefore, the Young’s modulus of the [001]* direction, as obtained from the cyclic loading indentation under smaller Fmax, is affected by the kinking elastic deformation. Whether this modulus reflects the true Young’s modulus or the definition of the traditional Young’s modulus should include nonlinear kinking elasticity needs further investigation. When the Fmax is greater than the critical load, after certain cycles of loading/unloading, the initially generated IKBs are forced to separate from each other and move away from the indenter tip, resulting in the formation of kink bands. The movement of kink boundaries can further result in the delamination and even rupture of basal planes [29]. Once the layer delamination occurs, significant alteration to the original layered structure of muscovite has taken place, leading to the rearrangement of the muscovite layers around the indenter tip, just like a 3-D confinement of the tip at a greater depth (Figure 7b). Therefore, the elastic indentation unloading is very similar to the 3-D unloading, and the derived Young’s modulus based on the indentation unloading approximates the bulk modulus.

91

CONCLUSIONS This study has examined the elastic moduli of muscovite derived from cyclic nanoindentation loading at [001]* direction. The maximum indentation load affects the mineral’s response to cyclic loading, resulting in two different elastic moduli that correspond to the nonlinear kinking elasticity and the cyclic plastic shakedown. These nanoscale modes of deformation are closely related by the intrinsic layered structure of muscovite. In particular, the following conclusions can be drawn: (1) The elastic modulus, 88 GPa, obtained from the nonlinear kinking elastic hysteresis loops is close to the Young’s modulus. However, whether this value is the true Young’s modulus needs further research; (2) The elastic modulus, 55 GPa, obtained at the cyclic plastic shakedown stage approaches the bulk modulus. This is caused by the layer delamination and basal plane rupture, accompanied by the 3-D confinement of the indenter tip at a larger depth (under a larger load). (3) The reported experimental observation may lead to the development of a cyclic nanoindentation technique for determining the bulk modulus of certain materials with layered structure that are prone to plastic shakedown when subjected to cyclic loading.

REFERENCES [1] Chen H., Zhang G., Wei Z., Kevin C. M., and Luo J., 2010, “Layer-by-layer assembly of sol-gel oxide "glued" montmorillonite-zirconia multilayers,” J. Mater. Chem., 20(23), pp. 4925-4936. [2] Li X., Chang W., Chao Y. J., Wang R., and Chang M., 2004, “Nanoscale structural and mechanical characterization of a natural nanocomposite material: The shell of red abalone,” Nano Lett., 4(4), pp. 613-617. [3] Podsiadlo P., Kaushik A. K., Arruda E. M., Waas A. M., Shim B. S., Xu J., Nandivada H., Pumplin B. G., Lahann J., Ramamoorthy A., and Kotov N. A., 2007, “Ultrastrong and stiff layered polymer nanocomposites,” Science, 318(5847), pp. 80-83. [4] Rubner M., 2003, “Materials science: Synthetic sea shell,” Nature, 423(6943), pp. 925-926. [5] Tang Z., Kotov N. A., Magonov S., and Ozturk B., 2003, “Nanostructured artificial nacre,” Nat. Mater., 2(6), pp. 413-418. [6] Fanning D., Keramidas V., and El-Desoky M., 1989, “Micas,” Minerals in Soil Environments, J. Dixon, and S. Weed, eds., Soil Science Society of America, Wisconsin, pp. 551-633. [7] Comodi P., and Zanazzi F. P., 1995, “High-pressure structural study of muscovite,” Phys. Chem. Miner., 22(3). [8] Catti M., Ferraris G., Hull S., and Pavese A., 1994, “Powder neutron diffraction study of 2M 1 muscovite at room pressure and at 2 GPa,” Eur. J. Mineral., 6(2), pp. 171-178. [9] Vaughan M. T., and Guggenheim S., 1986, “Elasticity of muscovite and its relationship to crystal structure,” J. Geophys. Res., 91(B5), pp. 4657-4664. [10] McNeil L. E., and Grimsditch M., 1993, “Elastic moduli of muscovite mica,” Journal of Physics Condensed Matter, 5, pp. 1681-1690. [11] Sekine T., Rubin A. M., and Ahrens T. J., 1991, “Shock wave equation of state of muscovite,” J. Geophys. Res., 96(B12), pp. 19675-19680. [12] Barsoum M., Murugaiah A., Kalidindi S., and Zhen T., 2004, “Kinking nonlinear elastic solids, nanoindentations, and geology,” Phys. Rev. Lett., 92(25). [13] Zhang G., Wei Z., and Ferrell R., 2009, “Elastic modulus and hardness of muscovite and rectorite

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determined by nanoindentation,” Appl. Clay Sci., 43(2), pp. 271-281. [14] Zhang G., Wei Z., Ferrell R. E., Guggenheim S., Cygan R. T., and Luo J., 2010, “Evaluation of the elasticity normal to the basal plane of non-expandable 2:1 phyllosilicate minerals by nanoindentation,” American Mineralogist, 95(5-6), pp. 863-869. [15] Yin H., and Zhang G., “Nanoindentation Behavior of Muscovite Subjected to Repeated Loading,” Journal of Nanomechanics and Micromechanics, In press. [16] Guggenheim S., Chang Y., and Koster van Groos A. F., 1987, “Muscovite dehydroxylation; hightemperature studies,” Am. Mineral., 72(5-6), pp. 537-550. [17] Ostendorf F., Schmitz C., Hirth S., Kühnle A., Kolodziej J. J., and Reichling M., 2008, “How flat is an air-cleaved mica surface?,” Nanotechnol., 19(30), p. 305705. [18] Amelinckx S., 1952, “Screw dislocations in mica,” Nature, 169(4301), pp. 580-580. [19] Amelinckx S., and Delavignette P., 1960, “Observation of dislocations in non-metallic layer structures,” Nature, 185(4713), pp. 603-604. [20] Hull D., and Bacon D., 2001, Introduction to dislocations, Butterworth-Heinemann, Ltd., Oxford, Boston. [21] Cross G. L. W., Schirmeisen A., Grütter P., and Dürig U. T., 2006, “Plasticity, healing and shakedown in sharp-asperity nanoindentation,” Nat. Mater., 5(5), pp. 370-376. [22] Johnson K., 1987, Contact mechanics, Cambridge University Press, Cambridge, New York. [23] Williams J., Dyson I., and Kapoor A., 1999, “Repeated loading, residual stresses, shakedown, and tribology,” J. Mater. Res., 14(4), pp. 1548-1559. [24] Oliver W., and Pharr G., 1992, “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments,” J. Mater. Res., 7(6), pp. 1564-1583. [25] Oliver W., and Pharr G., 2004, “Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology,” J. Mater. Res., 19(1), pp. 3-20. [26] Mavko G., Mukerji T., and Dvorkin J., 2009, The Rock Physics Handbook, Cambridge University Press, Cambridge. [27] Zhang G., Wei Z., Ferrell R. E., Guggenheim S., Cygan R. T., and Luo J., 2010, “Evaluation of the elasticity normal to the basal plane of non-expandable 2:1 phyllosilicate minerals by nanoindentation,” Am. Mineral., 95(5-6), pp. 863-869. [28] Murugaiah A., Barsoum M., Kalidindi S., and Zhen T., 2004, “Spherical nanoindentations and kink bands in Ti3SiC2,” J. Mater. Res., 19(4), pp. 1139-1148. [29] Barsoum M., Murugaiah A., Kalidindi S., Zhen T., and Gogotsi Y., 2004, “Kink bands, nonlinear elasticity and nanoindentations in graphite,” Carbon, 42(8-9), pp. 1435-1445.

Assessment of Digital Holography for 3D-Shape Measurement of Micro Deep Drawing Parts in comparison to Confocal Microscopy Nan Wang, Dr. Claas Falldorf, Dr. Christoph von Kopylow and Prof. Ralf B. Bergmann Dept. of Optical Metrology, BIAS GmbH, Klagenfurterstr. 2, 28359 Bremen, Germany

Abstract Fast and accurate measurement of the 3D-shape of mass fabricated parts is increasingly important for a cost effective production process. For quality control of mm or sub-mm sized parts tactile measurement is unsuitable and optical methods have to be employed. This is especially the case for small parts which are manufactured in a micro deep drawing process. From a number of measurement techniques capable to measure 3D-shapes, we choose Digital Holography and confocal microscopy for further evaluation. Although the latter technique is well established for measuring of micro parts, its application in a production line suffers from insufficient measurement speed due to the necessity to scan through a large number of measurement planes. Digital Holography on the other hand allows for a large depth of focus because one hologram enables the reconstruction of the wave field in different depths. Hence, it is a fast technique and appears superior to standard microscopical methods in terms of application in a production line. In this paper we present results of shape recording of micro parts using Digital Holography and compare them to measurements performed by confocal microscopy. The results prove the suitability of Digital Holography as an inline quality control instrument. 1 Introduction Modern mass production processes have to be cost-effective regarding the percentage of error-free manufactured parts. Therefore an adequate quality control by means of a fast and accurate measuring technique has to be established. Respecting the object under investigation in this paper, we will focus on a mm or sub-mm sized micro deep drawing part, which is produced and investigated in the Collaborative Research Centre “Micro Cold Forming” [1] at the University of Bremen, Germany. In Fig. 1 two examples of this bowl-like part are presented, which have dimensions of about 0.5 mm height and 1 mm width. Especially fast production process of this micro part must be inspected continuously because an unperceived failure in the forming process leads to a high number of defect parts.

© BIAS GmbH

200 μm

Fig. 1 Two micro deep drawing parts, scanning electron microscope (SEM) image [1] In order to control the quality of this part, tactile measurement is unsuitable and rapid non-destructive optical methods should be considered [2]-[8]. For example, confocal microscopy can provide precise inspection of micro objects. But concerning the necessity to scan through a large number of measurement planes, its integration in a production line does not appear practicable due to insufficient measurement speed. Currently there are no commercially available solutions, which at the same time provide a rapid and non-invasive investigation of microscopic objects. One of the major problems is the limited depth of focus, which is a common characteristic for any microscopic imaging technique. Here, Digital Holography is chosen due to the reasons below: a.

It is able to enhance the depth of focus considerably by means of combining several reconstructed wave fields associated with different observation planes from a single measurement [6];

b.

It needs only one or two recordings of the holograms to recover the object wave field [7], [8].

In this paper we present a 3D-shape measurement of micro deep drawing parts by means of Digital Holography and compare them to results obtained by confocal microscopy. The results show that Digital Holography can be employed as an inline quality control instrument. 2 Principles In this section the basic principles used for the digital-holographic measurement of the micro deep drawing part will be described. Firstly Digital Holography, including recording and reconstruction, will be introduced. Then we will present how to extract the 3D-shape from the holographically reconstructed phase information in the object domain. The micro parts investigated in this paper are mm or sub-mm sized and thus extremely large compared to the wavelength range of a normal laser, so that an ambiguity of the object shape derived from the reconstructed phase information arises. In order to solve this problem, we will finally discuss a method by means of contouring with two illumination directions.

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_13, © The Society for Experimental Mechanics, Inc. 2011

93

94 2.1 Digital Holography: Recording In terms of scalar diffraction theory, an optical wave field can be described by a real amplitude as well as a phase distribution. The light wave at a point r in space can be generally described as E(r)=A(r)exp[iij(r)] with A(r) being its real amplitude distribution and ij(r) its phase distribution [7], [8]. In practice all sensors can only capture light intensity, defined by I(r)=|E(r)|2=E(r)E*(r)=A2(r). Please note that in this process its phase ij(r) is lost. In this section we will present how Digital Holography records the phase information into the intensity and in the next section how it numerically reconstructs the object wave field, which holds both the amplitude and the phase distribution. A basic holographic setup shown in Fig. 2(a) is used to record the wave field reflected from an object, which is called the object wave. It is superposed by a second wave field, the reference wave. In order to be coherent both have to originate from the same source of a laser. The resulting interference pattern, the hologram, is electronically captured by a CCD-camera and stored in a computer. In the following the holographic process will be mathematically described using the coordinate system shown in Fig. 2(b). As an example in the object volume an arbitrary object plane {x,y} is denoted by the area Ȉ. The complex amplitude of the object wave can be described by EO(r)=AO(r)exp[iijO(r)] and the one of the reference wave by ER(r)=AR(r)exp[iijR(r)]. Both waves interfere in the hologram plane {ȟ,Ș} with z=0 at the surface of the CCD. The corresponding intensity, i.e. the hologram, is calculated by [6], [8]: H ([ ,K )

E R ([ ,K )  EO ([ ,K )

2



(1)

I R  I O  EO E R  E R EO ,

where IR and IO denote the individual intensities and * means the complex conjugate. The hologram H(ȟ,Ș) is recorded by the CCD, digitized into a N×M pixel array and digitally stored in the computer. In the next section, we will see how to numerically reconstruct the object wave field from H(ȟ,Ș). (a) Laser

(b)

y

Ș Ȉ

x

ȟ z

zj

0

ȡ

Object Object Wave Reference Wave

Reconstruction Plane

CCD

Hologram Plane

Fig. 2 Digital Holography: (a) basic holographic setup [7] and (b) the coordinate system [8] 2.2 Digital Holography: Reconstruction Throughout the past decades a number of ways to digitally reconstruct the hologram have been developed [8]. The reconstruction method applied in this paper will be presented in this section. Based on the Rayleigh-Sommerfeld formulation of diffraction the wave field u(ȟ,Ș) in the hologram plane z=0 propagated from the wave field u(x,y) in the object plane z can be described by [9], u ([ ,K )

z iO

³³

6

u ( x, y )

exp( ikU )

U2

(2)

dx dy.

Here, ȡ is the distance between a point in the object volume and a point on the hologram plane {ȟ,Ș} given by ȡ=[(x-ȟ)2+(y-Ș)2+z2] ½. When the aperture in the hologram plane {ȟ,Ș} is small compared to the distance z, the Fresnel approximation can be applied, which means ȡ§z+(x-ȟ)2/2z+(y-Ș)2/2z inside the exponential function as well as ȡ§z outside of it can be considered. By means of this approximation and Eq. 2 we will define the propagation operator P [9]: u ([ ,K )

Pzo0 {u ( x, y )} Q1, z Q2 , z ([ ,K ) ˜ F{u ( x, y ) ˜ Q2 , z ( x, y )}(

[ K , ), O z Oz

(3)

which includes a single Fourier transform denoted by F. The terms Q1 as well as Q2 are spatially varying phase factors, defined by: Q1, z

1 exp( ikz ), Q2 , z ([ ,K ) iO z

ª ik º exp « ([ 2  K 2 ) » and Q2 , z ( x, y ) ¬2z ¼

ª ik º exp « ( x 2  y 2 ) ». ¬ 2z ¼

(4)

Here, Q2 is a quadratic-phase exponential function, which is known as the chirp function. Positive z corresponds to propagation into the direction of the hologram plane, while using the inverse Fourier transform and conjugating the terms Q1 as well as Q2 results in back propagation P-1 into the direction of the reconstruction plane [9]. Since the phase information is encoded inside the two multiplicative terms EOER* and EREO* of the hologram H(ȟ,Ș) given in Eq. 1, we will look at these terms in more detail. Using the propagation operator P, we can describe the wave field EO and ER in the hologram plane {ȟ,Ș} by [8] EO ([ ,K ) E R ([ ,K )

Pz o0 {EO ( x, y )} Q1, z Q2 , z ([ ,K ) ˜ F{EO ( x, y ) ˜ Q2 , z ( x, y )}( PzR o0 {E R ( x, y )}

[ K , ), Oz Oz

Q1, zR Q2 , zR ([ , K ) ˜ F{G ( x  x R , y  y R ) ˜ Q2 , z R 2

[ K ( x, y )}( , ) Oz R Oz R

ª ik º Q1, zR Q2 , zR ([ ,K ) exp « ( x R[  y RK ) » , ¬ zR ¼

(5)

95 where the coordinates (xR,yR,zR) denote the source point of the spherical reference wave. When the reference wave is located close to the object with z=zR, the interesting term EOER* in Eq. 1 can be described by: EO ([ ,K ) E R ([ ,K ) *

exp[ 

ik ( x R[  y RK )] [ K z F{EO ( x, y ) ˜ Q2 , z ( x, y )}( , ), O2 z 2 Oz Oz

(6)

while EREO* in Eq. 1 can be described simply by conjugating Eq. 6. In order to obtain one of these two terms from the hologram, we can further filter the hologram simply by inverse Fourier transform [8] F 1{H ([ , K )}

*

*

F 1{I R  I O}  F 1{E O E R }  F 1{E R E O } F 1{I R  I O}  F 1{I R  I O} 

1

O2 z 2 1

O2 z 2

G 2 (u  x R , v  y R ) … ( EO Q2, z )  1

EO Q2, z (u  x R , v  y R ) 

O2 z 2

1

O2 z 2 *

(7)

G 2 (u  x R , v  y R ) … ( E O * Q 2 , z * ) *

EO Q2 , z (u  x R , v  y R ),

where … denotes the convolution. Here, IR is assumed to be constant and IO is a speckle field of the object wave. Their inverse Fourier transform in regard to the first term is located in the center. The second term contains EOQ2,z, which is shifted by (-xR,-yR); While the third term contains the conjugate of the EOQ2,z, which is oppositely shifted by (xR,yR). Hence, they are center-symmetrically located and can be spatially separated by selecting the coordinates of the reference wave (xR,yR) appropriately. According to it, we can take one of these two symmetric terms simply by means of eliminating the other two terms and then back filter the remaining result by means of Fourier transform to get EOER* or EREO* in the hologram plane {ȟ,Ș}. Based on it and the back propagation, we can reconstruct the object wave field in any reconstruction plane z=zj by using for example [8], P0o1 z j {EO ([ ,K ) E R ([ ,K ) ˜ E R ([ ,K )}

I R P0o1 z j {EO ([ ,K )}.

*

EO( j ) ( x, y )

(8)

2.3 Relation between the reconstructed Phase and the 3D Shape We want to extract the 3D shape of the object under measurement from the reconstructed object wave field EO(j)(x,y) in the j-th reconstruction plane z=zj with its complex amplitude EO(j)(x,y)=AO(j)(x,y)exp[iijO(j)(x,y)]. The scheme we used for this process is briefly presented in Fig. 3, where P is an arbitrary point on the surface of the object with the position rP=(x,y,z) and S is a point source with the position rS. Let us assume that any point P on the surface can be associated to a specific point B in the corresponding j-th reconstruction plane z=zj. This is especially true for those parts of the image, when the object appears to be in focus [4]: U3

M O ( j ) ( x, y ) M ( ) 

2S

( z j  z) .

O

(9)

The distance between the object and the source point is further assumed to be large compared to the dimensions of the object. In this case the light incident on any arbitrary point on the surface of the object can be described as a plane wave. Its phase ij(rP) is given by ij(rP)=k(rP-rS)= krP+c0. Here, the product between the position of the light source rS and the wave vector k is written by a constant c0, because the shape information of the object does not depend on it. When the components of the wave vector k=(kx,ky,kz) are introduced, the phase ij(rP) can be rewritten by ij(rP)=kxx+kyy+kzz+c0, where the first two terms can be ignored, because the shape of the object is only related to the coordinate z. The coordinate x and y constitute a phase ramp, which can either be determined by the geometrical parameters of the setup or by a calibration process using a flat surface. According to this and Eq. 9, if the angle of the illumination direction ș is known and c0 is set to be c0=0 we obtain [4]:

M O ( j ) ( x, y )

kz z 

2S

O

( z j  z)

2S

O

[ z j  (1  cos T ) z ].

(10)

From this equation we see, that the height information of the object in z direction is related to the reconstructed phase. Reconstruction Plane

y

P

B

x rP

zj rS

k

z

S

Fig. 3 Schematic describing the relation between the reconstructed phase ijO(j)(x,y) and the 3D shape of the object: P is a point on the surface of the object, which is associated to a point B on the reconstruction plane. The distance between the object and the light source should be large in comparison to the dimension of the object, so that the light incident on the point P can be regarded as a plane wave [4]

96 2.4 Contouring with two Illumination Directions The contour of the object is encoded in the phase ijO(j)(x,y) as seen from Eq. 10. If the contour exceeds the range of the wavelength, the phase value becomes ambiguous in terms of fringes. In our case, the surface roughness of the object already exceeds that range, so that the phase value appears noisy and the geometry of the object can not be resolved. In order to solve this problem we use the contouring method by means of two illumination directions in this paper, which is a well established method to measure the shape of a diffusely reflecting object [8]. Generally this technique is based on two sequentially reconstructed phase distributions of the object wave ijO,1(j)(x,y) and ijO,2(j)(x,y), associated with shifting of a point source from position S1 to S2. According to Eq. 10, the shape information of the object can be calculated from the phase difference of these phase distributions ijO,1(j)(x,y) and ijO,2(j)(x,y) [4]: 'M O ( x , y ) ( j)

2S

O

cos T1  cos T 2 z

2S z. /

(11)

Here, ȁ denotes the synthetic wavelength, which is strongly larger than the wavelength Ȝ and can be adjusted by selecting the angles of these two illumination directions ș1 and ș2 accordingly. It has to be noted, that this phase difference is independent from the distance of the reconstruction plane zj. That means the phase difference can be digitally reconstructed in any arbitrary reconstruction plane zj to obtain the fringes, which are associated to the height z according to Eq. 11. From the phase difference, the desired 3D shape information of the object can be directly extracted. 3 System Setup A schematic setup for digital holographic contouring by means of two illumination directions [6] is presented in Fig. 4. A micro deep drawing part, which has the same dimensions as the parts shown in Fig. 1, is our object under measurement. It is illuminated by a plane wave, provided by an optical fiber in the front focal plane of a collimating lens. The angle of the plane wave can be changed by either shifting the source point or the lens. A second fiber is located close to the object and provides a spherical reference wave. In order to capture the hologram arising from the superposition of the reference wave and the light scattered from the object, an analyzer (polarization filter) is located in front of the camera which equalizes the polarization states of the interfering wave fields. For our investigations we used a dye-laser with a wavelength of Ȝ=582 nm and the sensor of the camera has 2208 × 2208 pixels with a size of 3.5×3.5 μm2. The distance between the object and the camera is set to be about 3 cm, in order to obtain a suitable speckle size compared to the pixel size of the camera. Considering the maximum frame rate of 9 Hz of this camera at its full resolution, recording the holograms with two different illumination directions takes less than 0.3 seconds. Reference Wave

Object Object Wave

CCD Laser

Fig. 4 Sketch of the setup for digital holographic contouring by means of two illumination directions [6] 4 Experimental Results In order to show the capability for fast 3D-shape measurement by means of Digital Holography we have numerically reconstructed the complex amplitude EO(j)(x,y) of the object wave field. From the corresponding reconstructions in one plane we can calculate the phase differences ǻijO(j)(x,y) of the corresponding phase distributions associated with the two illumination directions. Unfortunately these data contain noise due to the limited depth of focus across a single reconstruction plane (see Eq. 11) in the out-of-focus areas. But all necessary information is stored in one set of two measurements and can be reconstructed numerically, which is the significant advantage of Digital Holography. The reconstruction of the phase differences in two different planes is shown in Fig. 5(a) and Fig. 5(b). Here, these noisy areas are marked by the white boxes. In order to recover an uncorrupted phase difference for the whole micro deep drawing part, we reconstructed the phase differences in four different reconstruction planes (j = 1, …, 4) and calculated a combined phase difference with all regions in focus, which is presented in Fig. 5(c). This procedure can be implemented in any reconstruction plane because of the independence of the phase difference ǻijO(j)(x,y) from the distance of the reconstruction plane zj.

97

(a)

(b)

ʌ

(c)

-ʌ (1)

(4)

Fig. 5 The phase differences of two phase distributions exemplarily (a) ǻijO (x,y) in the lower, (b) ǻijO (x,y) in the top observation plane and (c) an all-in-focus combined phase difference, obtained in only one set of two holographic measurements with regard to two illumination directions. All distributions are sampled by 690 × 540 pixels To retrieve the 3D-shape from the combined phase difference, it has to be low-pass filtered [7] and then unwrapped, e.g. the discontinuous 2ʌ-jumps arising from the sinusoidal nature of the phase have to be eliminated by adding multiples of 2ʌ [10]. After subtracting the known phase ramp as mentioned in Section 2.3 and then cutting the noisy data in the surrounding areas off by means of a mask, the unwrapped phase values are inserted into Eq. 11. The real amplitude of the filtered hologram F-1{H(ȟ,Ș)} is shown in Fig. 6(a), which has a center-symmetric distribution mentioned in Section 2.2. Cutting the area marked by the yellow box in Fig. 6(a), the final 3D-shape map with respect to the height z is shown in Fig. 6(b), which is sampled by 500 × 390 pixels and has a lateral resolution of about 2 μm2. For comparison a measurement of the same region of this micro part is performed by confocal microscopy. In Fig. 6(c) the microscopic image is shown. Its shape map presented by Fig. 6(d) is masked with the same mask, which is sampled by 1500 × 1170 pixels and has a lateral resolution of about 0.7 μm2. Although this microscopic measurement has a better resolution compared to the holographic one, it takes a considerable long time of about 6 minutes in this case to scan through the whole object. Please note, since the image of this micro part in Fig. 6(a) takes only half of the full quarter space, the resolution of this digital-holographic measurement can be further increased up to 1 μm2, either by decreasing the distance between the object and the camera, or by applying an objective between the object and the camera in our setup [8]. (a)

(b)

600 μm

0 100 μm

(c)

(d)

600 μm

0 100 μm

Fig. 6 The top row shows the digital-holographic measurement of the micro deep drawing part: (a) the real amplitude of the filtered hologram F-1{H(ȟ,Ș)} and (b) the 3D-shape map from the created phase difference after subtracting the phase ramp, which is sampled by 500 × 390 pixels. In the bottom row is the confocal-microscopic measurement of the same region of this micro part for comparison: (c) the microscopic image and (d) its 3D-shape map, which is sampled by 1500 × 1170 pixels. Both of them have the same mask and a similar measuring direction. The yellow boxes in (a) and (c) mark the corresponding cutting areas in (b) and (d).

98 In order to compare these two shape maps in more detail, they have to be aligned iteratively by calculating the average error, while the microscopic measurement is fixed as reference and the holographic one is shifted as test step by step. In the case of holding the minimal average error with ca. ±13 μm, we will assume that the two maps are in a best fit alignment. Based on it, a complete 3D shape comparison is presented in Fig. 7. The deviation of the holographic measurement compared to the microscopic reference is displayed in a colored map. Here the maximal error is between ca. ±50 μm and appears mostly in the boundary areas due to the speckle noise. z

y

+ 50 μm

x

0

- 50 μm 100 μm

Fig. 7 The 3D comparison between the digital-holographic and the confocal-microscopic shape map displayed in a false color representation. The maximal error is between ca. ±50 μm, while the average error is between ca. ±13 μm 5 Conclusion In this paper we investigated Digital Holography as a tool for inline quality control in a fast manufacturing process like micro deep drawing. As an example the 3D-shape of a micro bowl with a diameter of 1 mm has been measured, which principally requires only a set of two recorded holograms. The evaluation of the data shows the strength of Digital Holography: In contrast to other techniques especially in microscopic applications, the focused area of the measurement can be arbitrarily changed during the data evaluation numerically by selecting the corresponding reconstruction plane of the measured wave field. The measurement has been compared to a measurement using confocal microscopy which is a well established standard method for measuring the shape of micro parts. The deviation between the two methods was less then ±50μm, though the resolution of the Digital Holography setup was not exactly adapted to the size of the object. Hence Digital Holography is well suited for the inline quality control of the micro parts. In the future the measurement velocity can even be increased by using a spatial light modulator for shifting the illumination direction automatically. 6 Acknowledgement The authors gratefully acknowledge the financial support by the DFG (German Research Foundation) within the frame of subproject B5 Sichere Prozesse of the SFB 747 (Collaborative Research Center) "Mikrokaltumformen - Prozesse, Charakterisierung, Optimierung" [1]. 7 References Collaborative Research Center 747 Micro Cold Forming - Processes, Characterization, Optimization. URL: http://www.sfb747.unibremen.de, release date Sep. 01, 2008 [2] Pawley JB, (2006) Handbook of Biological Confocal Microscopy (3rd ed.). Berlin: Springer [3] Su X, Zhang Q, (2010) Dynamic 3-D shape measurement method: A review. Optics and Lasers in Engineering, Volume 48, Issue 2, Fringe Projection Techniques, February, 191-204 [4] Agour M, Huke P, Kopylow Cv, Falldorf C, (2009) Shape measurement by means of phase retrieval using a spatial light modulator. In Proc. On Advanced Phase Measurement Methods in Optics and Imaging, Locarno, Switzerland [5] Falldorf C, Kopylow Cv, Agour M, Bergmann RB, (2010) Measurement of Thermally induced Deformations by means of Phase Retrieval. In Proc. Internati. Sympo. on Optomechatronic Technologies (ISOT), 1-5 [6] Wang N, Kopylow Cv, Falldorf C, (2010) Rapid optical inspection of micro deep drawing parts by means of digital holography. In Proc. 36th Internati. Matador Conf., 45-48 [7] Kreis T, (2005) Handbook of Holographic Interferometry: Optical and Digital Methods. Weinheim, Wiley-VCH [8] Schnars U, Jueptner W, (2005) Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques. New York, Springer [9] Goodman JW, (2005) Introduction to Fourier Optics. McGraw-Hill [10] Robinson DW, (1993) Phase unwrapping method. In Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, 194299 [1]

Full-Field Bulge Testing Using Global Digital Image Correlation Paper number 206

Jan Neggers1 ([email protected]), Johan Hoefnagels1, François Hild2, Stéphane Roux2 and Marc Geers1 1)

Eindhoven University of Technology, Department of Mechanical Engineering, Den Dolech 2, 5612 AZ Eindhoven, Netherlands 2) LMT Cachan, avenue du Président Wilson 61, 94235 Cachan Cedex, France

ABSTRACT The miniature bulge test is an acknowledged method for characterizing freestanding thin films. Nevertheless, some discrepancies in the quantitative results from such tests can be found in literature, explained in part by erroneous assumptions in the analytical description used to compute the global stress and strain from the membrane pressure and deflection. In this research, a new method is presented which renders the analytical description obsolete. A specialized Global Digital Image Correlation technique on high resolution, confocal microscopy, surface height maps of bulged membranes, has been developed. This method is able to capture full-field continuous deformation maps, from which local strain maps are computed. Additionally, local stress maps are derived from full-field curvature maps and the applied pressure. The local stress-strain maps allow the method to be used on inhomogeneous, anisotropic membranes as well as on exotic membrane shapes. INTRODUCTION Current micro-electronic devices or integrated systems often consist of an abundance of different thin films, typically selected on their electronic properties [1-3]. However, due to the inherent large range of thermal expansion coefficients in these materials, large stresses occur during processing or in the lifetime of the product. To improve the reliability of these products the mechanical properties of the individual thin films are required. Since these thin films often have one dimension smaller than the intrinsic micro-structural length scale of the material, they exhibit a so-called size effect which means that the thin film material response is different than their bulk counterparts [4-6]. Therefore, experimental methods that can characterize these thin films in the same form as they are produced and used are invaluable. An important experiment in this class is the bulge test experiment. In a bulge test experiment a thin film or membrane is deflected using a pressure medium. From the pressure and deflection at the apex of the bulge, the stress-strain response is calculated by means of an analytical descriptions of the membrane deformation, called the bulge-equations [7-8]. These bulge equations are very sensitive to the membrane geometry which has been a large source of inaccuracy in the past. Nonetheless, with the currently available (lithographic) Si micro-machining techniques the bulge membranes can be produced with such accuracy that this is no longer a problem. These micro-machining techniques are the same techniques as used to create the micro-electronics, as a result, allowing for the creation of bulge test samples which had a very similar processing history as the real products. The bulge test experiment is recognized as a powerful method to characterize thin-films mechanically, allowing for the measurement of full (isothermal) stress-strain curves, including the plastic regime, of freestanding thin films [9]. Nevertheless, some discrepancies occur in literature when comparing the results quantitatively. The reasons for these discrepancies are most likely due to the fact that the membrane deformation is actually more complex, including (i) localized deformation, mainly close to the membrane boundaries, (ii) inhomogeneous membrane deformation, typically the deformation state ranges from plane strain to plane stress, varying over the membrane, and (iii) anisotropic material behavior. None, of the before are taken into account in the bulge-equations, and are always assumed to be negligible. The membrane deflection is often measured with a single spot, laser interferometric, measurement. In contrast, also full-field surface profilometric measurement techniques are becoming ever more available, e.g. atomic force microscopy or confocal

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100 optical microscopy. Using such a technique to measure the membrane deflection profile allows for the application of Digital Image Correlation (DIC) to obtain the full-field strain, i.e. the strain at every spot on the membrane. Additionally, the applied pressure, underneath the membrane, is constant over the entire membrane, and the membrane is in static equilibrium. This means that from the applied pressure and the measured curvature field the stress-field can be obtained if the membrane thickness is known and the local bending stresses are small. It should be noted that this reasoning did not include any assumptions on the membrane shape, i.e. this method is applicable to any shape bulge membrane without making any assumptions on boundary conditions etc. As a result, a custom bulge test setup has been build that fits underneath the optical confocal microscope (figure 1).

Fig 1 Experimental setup: a miniature plane strain bulge test setup, placed under a confocal optical profilometer.

GLOBAL DIC To obtain the curvature-field typically the position field, i.e. surface map, has to be differentiated twice, which is rather noise sensitive and in-accurate, especially when the curvatures are small, which is the case for strains relevant for typical microelectronic materials. To solve this, a highly specialized DIC method is developed based on the currently quickly developing Global DIC method [10-11]. With this method an infinitely differentiable deformation field is obtained which is extremely insensitive to micro-fluctuations from which high accuracy curvature fields can be computed. In DIC, the goal is typically to find the displacement field u (x) , described by the degrees of freedom u , between two im ages, the references image f (x) and the deformed image g (x) . The main characteristic of global DIC or GDIC is that u is  being solved for globally, as opposed to locally. In this way GDIC typically enforces a continuity of u (x) . The degrees of freedom can be similar to the nodal degrees of freedom in a Finite Element Method (FEM) model, and if Quadrilateral Four node (linear) elements are used in GDIC, the method is typically named FEM-DIC or Q4-DIC [11]. However, in GDIC it is not necessary to use a FEM basis. To capture an infinitely differentiable deformation field, the deformation field is discretized using a set of polynomial functions

= ϕ n x a y b , a , b = [0, 1, 2, … ] A GDIC approach consists of the minimization of the mean squared difference

(0.1)

101

∫ ( f (x) − g {x + u (x )}) dx 2

η2 =

ROI

(0.2)

where the displacement field is expressed in a chosen basis

u ( x) = ∑ un φ n ( x)

(0.3)

n

where φn are chosen vector functions, and un are associated degrees of freedom, which if combined in a column are denoted as φ and u respectively. The minimization of η 2 with respect to the unknowns u is solved iteratively using an ex   plicit procedure, assuming u i += u i + d u i . Linearizing this system of equations allows the minimization to be rewritten as 1 a matrix-vector product as ∂η 2 = M i du − b= 0 i ∂ui   

(0.4)

where M can be considered as a mass matrix with vector components M= i

∫

ROI

φ·∇f (x)·∇f (x)·φ t  d x    

(0.5)

and b as a column with vector components  = bi 

∫

ROI

( f (x) − g {x + ui (x)})·∇f (x)· φ d x  

(0.6)

Solving this system iteratively until convergence results in the discretized deformation field from which the strain field and curvature fields can easily be determined. The development of the method is still in progress, nevertheless, there are no foreseen reasons why it would not be possible to capture the full-field local stress and strain maps. RESULTS As an early result the method was applied to 100 nm thick SiN free standing bulge membranes which are created by back a (1 × 6 mm) rectangular opening in the Si below the SiN layer. On top of this membrane a pattern is applied using etching spherical Ag particles with a distributed size between 80-500 nm. The membrane is then stretched to 5% and 10% strain yielding to correlation images f and g respectively (Figure 2). The method was able to directly correlate between the two strain steps without using intermittent steps. The resulting displacement fields in the x, y, and z directions are shown in figure 3.

102

Fig. 2 Two measured bulge test profiles f and g at 5% and 10% strain respectively. A pattern is applied on the surface using 80-500 nm Ag particles. In global DIC, the image g is mapped onto f by fitting its deformation u (x).

Fig. 3 The displacement fields in x, y and z directions (subfigures a, b, c) obtained from the global DIC method, using basis functions of the type ϕn = x a y b , where a = [0,1, 2,3, 4] and b = [0,1] .

CONCLUSIONS A specialized global DIC method is developed which can cope with the semi-3D data obtained from surface profilometry measurement techniques. The method has proven very robust and able to correlate directly between large strain steps, yielding continuous full-field displacement fields with sub-pixel displacement resolution. The displacement fields are insensitive to micro-fluctuations, e.g. measurement noise, and are therefore especially capable in capturing small curvature variations. From the full-field curvature fields and the applied bulge test pressure the local full-field stress can be determined. The proposed method allows the capturing of full-field stress-strain information of the entire bulge membrane. More importantly it allows for measuring only a part of the membrane, i.e. away from the boundary. As a result the measurement can be performed in a region where the deformation state is well understood allowing for easier extraction of important constitutive material parameters. An elaborate description of the method including proof of principle experiment is currently under development and will be published within respectable time.

103 REFERENCES [1] W.D. Nix, Mechanical properties of thin films, Metallurgical transactions A, vol 20A, 2217-2245 (1989) [2] A.J. Kalkman, A.H. Verbruggen G.C.A.M. Janssen and S. Radelaar, Transient creep in free-standing thin polycrystalline aluminum films, Journal of Applied Physics, Vol. 92-9, 4985-4957 (2002) [3] C.V. Thompson, The yield stress of polycrystalline thin films, Journal of Materials Research, Vol. 8-2,237-238 (1993) [4] P.A. Gruber, J. Böhm, F. Onuseit, A. Wanner, R. Spolenak, E. Arzt, Size effects on yield strength and strain hardening for ultra-thin Cu films with and without passivation: A study by synchrotron and bulge test techniques, Acta Materialia, Vol. 56, 2318-2335 (2008) [5] E. Arzt, Size effects in materials due to microstructural and dimensional constraints: a comparative review, Acta Materialia, Vol. 46-16, 5611-5626 (1998) [6] L.B. Freund and S. Suresh, Thin film materials: stress, defect formation, and surface evolution, Cambridge University Press, New York, (2003) [7] R.P. Vinci and J.J. Vlassak, Mechanical behavior of thin films, Annual Review of Materials Science, Vol. 26, 432-462 (1996) [8] J.J. Vlassak and W.D. Nix, A new bulge test technique for the determination of Young's modulus and Poisson's ratio of thin films, Journal of Materials Research, Vol. 7-12, 3242-3249 (1992) [9] Y. Xiang, X. Chen, J.J. Vlassak, Plane-strain bulge test for thin films, Journal of Materials Research, Vol. 20-9, 23602370 (2005) [10] F. Hild and S. Roux, Digital Image Correlation: from Displacement Measurement to Identification of Elastic Properties a Review, Strain, 42, 69–80 (2006) [11] G. Besnard, F. Hild and S. Roux, “Finite-Element” Displacement Fields Analysis from Digital Images: Application to Portevin-Le Châtelier Bands, Experimental Mechanics, 46: 789-803 (2006)

Experimental Investigation of Deformation Mechanisms Present in UltrafineGrained Metals

Adam Kammers, Samantha Daly The University of Michigan, Department of Mechanical Engineering 2350 Hayward, Ann Arbor, MI 48109 ABSTRACT Ultrafine-grained (UFG) metals possess grain sizes on the order of hundreds of nanometers and display a remarkable capacity for high strength, high ductility, and enhanced superplasticity. This paper presents the preparatory steps necessary for a highresolution experimental investigation into the deformation mechanisms active in UFG metals. A new experimental methodology is used, in which an optical metrology known as Digital Image Correlation (DIC) is combined with scanning electron microscopy to track the quantitative development of full-field strains on the length scale of the microstructure. The micro-scale field of view and use of a SEM for image capture require the development of novel specimen patterning methods and of image distortion corrections prior to experimentation. The results obtained through the combined SEM and DIC approach, and corresponding pre- and post-mortem electron backscatter diffraction (EBSD) analysis, enable the analysis of the real-time, micro-scale evolution of Lagrangian strains at an unprecedented spatial resolution, and the quantification of the surface deformations inside grains and across grain boundaries as the material is subjected to thermo-mechanical loading. TECHNICAL APPROACH To track the in-situ development of strain, the optical method Digital Image Correlation (DIC) is used to measure displacements on the surface of the test sample from which Lagrangian strains can be calculated. DIC requires the sample surface to have isotropic, high contrast random variations in surface features, taken generally as brightness or roughness. The surface is broken up into subsets, and the displacements and thus Lagrangian strains are then calculated by tracking the change in surface features at each subset as the sample is deformed, as shown in figure 1. For macroscopic testing, patterning is most commonly achieved by applying a random speckle pattern with an airbrush. This work will utilize a SEM for smallscale imaging of the tensile sample as it is heated and strained in a tensile/compression stage. As a result of the small size scale investigated in this work, it was necessary to develop new patterning techniques, which are detailed in the sample preparation section of this paper. Tensile samples fabricated by wire ElectroDischarge Machining (EDM) from extruded superpurity (99.99%) aluminum and 6061-T6 aluminum sheets were used for development of the techniques necessary for this combined SEM-DIC investigation. The 99.99% Al and 6061-T6 Al tensile samples have 2.5 x 4 mm and 1 x 4 mm gage cross sections respectively, and 6 mm gage Fig. 1 Illustration of a DIC subset tracking surface brightness as a test lengths. sample is deformed SAMPLE PREPARATION The first step following fabrication of the tensile samples is preparing the surface for microstructural analysis through Electron Backscatter Diffraction (EBSD). This is achieved by polishing with 400, 600, and 800 grit SiC papers with water. Buehler MetaDi Supreme polycrystalline 9, 3 and 1 µm diamond suspensions are then used followed by Buehler MasterMet colloidal silica suspension. After polishing, the test Field of View (FOV) is marked with a FEI Quanta 200 3D SEM equipped with a Focused Ion Beam (FIB) and Gas Injection System (GIS). Through the use of the GIS, platinum markers are deposited on the surface of the test sample at the corners of the desired FOV as shown in figure 2. One additional marker is placed outside of the field of view to assist in the determination of the test sample orientation.

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106 The dark rings surrounding the markers in figure 2 are a result of the ion beam current being set too high and can be removed by reducing the current accordingly. The platinum markers adhere very well to the surface of aluminum test samples and are capable of withstanding light polishing with colloidal silica as well as ultrasonic cleaning. Following the application of the platinum markers to the test sample, a pretest EBSD map of the sample surface is collected. The markers assist in aligning both the pre- and post-test EBSD area with the test image FOV. There have been a limited number of papers on the application of a small-scale pattern suitable for DIC in a SEM [1-3]. Therefore a full survey of patterning methods has been performed to determine the most suitable methodology. The first method investigated was a chemical vapor thin film rearrangement method [1]. After multiple attempts and variations in film thickness, vapor temperature, and sample surface roughness, repeatable results could not be achieved by the investigators. Small areas of the film appeared to break up as desired, but the islands were dispersed and the majority of the film remained intact. Previous work by Sabaté et al. [4] used a FIB to mill a Fig. 2 Platinum markers applied to the surface of a 6061-T6 random pattern into the surface of a test sample. The aluminum test sample to mark the area of interest method described is semi-destructive and cannot be used in   in areas. However, through the use of a GIS equipped FIB, current tests as the surface of the sample is actually milled away platinum markers were instead deposited onto the surface of the test sample in order to create a random tracking pattern. The   pattern shown in figure 3 was created by drawing a random block pattern in the FIB user interface and depositing it in patches that were translated and rotated to cover the surface. Due to the damage that results from the ion beam, the limitation on the minimum speckle size, and time demand required by this method, it is no longer being used. Evaporating metal through TEM grids has been successfully used by Biery et al. [5] in the past to apply a regular grid to the surface of a test sample. In an attempt to generate a random pattern using a similar method, alumina and polycarbonate filter membranes acted as templates for the evaporation of gold onto test sample surfaces. While this method was successfully applied to TEM grids consisting of 7.5 x 7.5 µm holes, the aspect ratio (Thickness:Pore Diameter, alumina: 325:1, polycarbonate: 25:1) of the pores in the alumina and polycarbonate membranes proved too large and this technique did not yield a suitable pattern. Patterning is currently being performed successfully with gold nanoparticles (NPs). Gold NPs can be purchased in sizes ranging from 2-200 nm and have high contrast when imaged with a SEM, making them good candidates for patterning for DIC-SEM experimentation. In the current work, concentrated solutions of gold NPs supplied by Ted Pella are used to create DIC tracking patterns. Numerous methods have been investigated to determine the effect of drying temperature, angle, airflow, and atmospheric pressure on the NP distribution. Additionally, layering methods have been investigated, such as applying a second NP layer to a previously dried layer, and alternating NP layers with sputtered carbon layers. NP patterning has been successful in providing a suitable tracking pattern for DIC-SEM and is a quick process, requiring only the time for the solution to dry, results in a broad distribution of speckle sizes, and provides a high contrast pattern when imaged with the secondary or backscatter electron detector as shown in figure 4.

Fig. 3 FIB pattern created by translation and rotation of a small user generated pattern. The white spots are platinum and the substrate is pure aluminum    

To pattern with NPs, droplets of the NP solution are applied with a micro-pipette or plastic dropper. Prior to application, the NP solution is held in an ultrasonic cleaner for 15 minutes to break up aggregates and distribute the NPs throughout the solution. It has been determined that drying time is a critical parameter in the quality of the speckle pattern generated by NPs. A long drying time encourages the NPs to clump and results in an inhomogeneous dispersion with the majority of the

107 NPs formed as large aggregates at the outer edge. Additionally, the drying behavior of the NP solution varies greatly depending on the surface energy of the substrate to which it is applied. For example, the droplet has a very small contact angle with freshly polished pure aluminum. However, over time the oxide layer adsorbs polar water molecules from the atmosphere, which results in a decreased surface energy [6,7]. As a result, the contact angle between the aluminum substrate and the NP droplet increases. This large contact angle increases the drying time and results in more aggregates. Different drying methods have seen more success on copper and ceramics, therefore it is difficult to predict the drying behavior on different substrates. To accurately calculate surface displacements, the NPs must remain securely attached as the sample is strained. It has been determined that the NPs strongly adhere to the surface of Al test samples, ensuring fidelity of the deformation tracking. Tests were performed in which the FIB was used to mill markers on the surface of 99.99% Al and 6061-T6 Al Fig. 4 DIC appropriate 100 µm field of view SEM image of a test samples. NPs were deposited in the marked area and 100 nm diameter gold nanoparticle pattern on a polished the sample was strained in a tensile stage inside the SEM Aluminum sample chamber. Average strain values calculated from the NPs by the DIC program matched the values calculated from measuring the motion of the FIB milled markers used as an “extensometer”. Additionally, in later tests, there was no noticeable change in NP density after rinsing the sample surface with a strong jet of water from a squirt bottle. NPs were also not observed outside of the original droplet area, further verifying that the rinse did not remove particles from the surface. To remove the NPs from the surface for post-test EBSD, the sample is held in de-ionized water in an ultrasonic cleaner for ten minutes. Even after this cleaning, NPs still remain on the surface but their distribution is so diffuse that they interfere only minimally with the EBSD mapping. Shortcomings of NP patterning include difficulty in preventing aggregates and the difficulty in achieving consistent results on different substrates. However once the drying behavior on the desired substrate is determined, it is a fast and cost effective patterning method. Electron beam lithography is currently being investigated as a patterning methodology for comparison with NP patterning. SEM DISTORTION CORRECTION Two forms of distortion exist in images captured by a SEM; drift or temporal distortion and spatial distortion. If not corrected, these distortions will unacceptably affect displacement and strain calculations. Drift distortion arises from errors in the positioning of the electron beam as it raster scans across the field of view. It varies with time and appears as displacements between pixels that vary throughout the image scan. Spatial distortion results from the complex focusing mechanism used in the SEM and appears as curvature of the displacement field that is nearly constant throughout all images. In this work, it was observed that changes in chamber pressure and scan speed as well as sample charging all have a significant effect on drift distortion. Low chamber pressure at the beginning of the imaging process for a 100 µm Horizontal Field Width (HFW) led to apparent displacements of 4 pixels in a single image. In images of non-conducting alumina filters that had been sputter coated with gold, apparent displacements of up to 25 pixels in a single image were observed. For a 100 µm HFW, 25 pixels corresponds to over 2 µm of drift. Charging artifacts were not seen in the images, but are most likely responsible for the large apparent drifts. Drift distortion accumulates over the period of the test leading to inaccurate results. To correct for distortion, the procedure as outlined in references [8,9] was followed

Fig. 5 Drift velocity at one pixel location over the calibration phase and the best-fit quadratic curve

108 and subsequently built upon. In summary, 20-30 images of a speckle patterned surface are captured using a FEI Quanta 3D 200 SEM with the time as well as the pressure at which each image is captured being recorded. The images are captured in pairs where the specimen remains stationary in the pair. Between image pairs, the specimen is translated a known distance in the horizontal and vertical directions. Translations are performed manually with the stage control knobs since translations by inputting the desired value in the SEM user interface prove too aggressive and result in additional unknown displacements being incorporated in the images. DIC is performed on each image pair through the use of VIC2D software developed by Correlated Solutions Inc. The raw displacement data exported by VIC2D is then imported into a custom Matlab code created by the investigators for distortion correction. The Matlab code first determines the time that passed between each DIC data point being scanned in the first and second image of every image pair. The u and v drift velocity at the midtime of each stationary image pair at every data point is calculated and plotted against time allowing for visualization of the change in drift velocity over the time of the calibration phase. A Fig. 6 Spatial distortion fields for a 300 µm horizontal field width quadratic function is then fit to the velocity data for each data point and integrated over time so that the drift distortion can be determined over any time frame. Using each data point’s unique drift function, all of the calibration image data is corrected for drift distortion before being used for spatial distortion correction. A plot of the u drift velocity at one data point and the quadratic best-fit curve is shown in figure 5. By capturing calibration image pairs throughout the test phase, the drift distortion function for each pixel can be modified as needed to account for any changes in drift. The relationship between the chamber pressure and drift is currently being investigated as a means to better characterize the evolution of drift. Spatial distortion does not vary between test images, but it can change between tests due to the replacement of the SEM filament or aperture alignment. It is corrected by correlating the images captured before and after each translation. Since the sample has only experienced rigid body motion, the displacement fields should be flat and any deviation from the correct, flat displacement field is determined at each data point and subtracted from the displacement data in all calibration and test images. A typical u and v spatial distortion field for a 300 µm HFW is shown in figure 6. Pixel displacement values for a stationary image pair before and after distortion correction can be seen in figure 7. Note that the displacement average is shifted to zero and the magnitude of the variation in displacement is reduced by an order of magnitude. After correcting all of the VIC2D displacement data for distortion the Matlab code calculates the Lagrangian strain Fig. 7 Raw horizontal (u) displacement and distortion corrected u displacement for a stationary image pair. The distortion correction code shifts the displacement average at each data point. closer to zero and reduces the magnitude of the variation in displacement by an order of magnitude

109 TEST ON COARSE-GRAINED 6061-T6 ALUMINUM In order to validate the developed procedures, tests have been performed on coarse-grained 6061-T6 Al. A tensile samples with a gage cross section of 0.6 x 4 mm and gage length of 6 mm was polished as outlined in the sample preparation section. Immediately after polishing, platinum parkers were applied with a FIB and a pre-test EBSD map of the surface as shown in figure 8a was collected using a step size of 2 µm. After EBSD, 200 nm diameter gold NPs were deposited on the sample with a micropipette. Following drying of the NP solution, the sample was loaded into a Kammrath & Weiss tensile/compression stage in the FEI Quanta 200 3D SEM. Calibration images were captured, and the sample was strained to an elongation of 13.75%, resulting in visible deformation in the area of interest. The sample was strained in steps of on average 20 µm or 6.7% of the HFW, which allowed for good correlation in VIC2D. After each step, the sample was held for approximately 30 seconds to allow the load to stabilize. Every 5 to 10 images, image pairs were captured to compare to the drift distortion quadratic fit. Upon reaching the maximum elongation, the load was removed and a final image was captured of the unloaded sample. Following the tensile test, the NPs were removed and a post-test EBSD map was collected as shown in figure 8b.

a

b

c

Fig. 8 a) Pre-test EBSD map of 6061-T6 Al sample. b) Post-test EBSD map corresponding to the unloaded sample FOV that was captured in the final test image. c) εxx overlaid EBSD map showing areas of high strain primarily at grain boundaries. The black rectangles are covering up the locations of the platinum markers.

Figure 8c shows the post-test EBSD map overlaid with the distortion-corrected strain (εxx) along the loading axis (x), showing the highest strains occurring primarily at the grain boundaries. Through the use of DIC, the evolution of strain can be observed throughout the test. This allows the investigators to pinpoint location of strain concentrations as they develop and observe the strain evolve throughout the loading. Work is currently underway to develop a method to determine the relative displacements at areas of high strain. This will allow the determination of active deformation mechanisms, and the characterization of the development and interaction of these mechanisms as the sample is thermomechanically loaded.

110 CONCLUSIONS Significant work has been performed to develop the novel experimental methodologies required for successful DIC-SEM analysis of deformations on the scale of the microstructure. From work performed thus far, the following conclusions have been made: 1. 2.

3.

Gold nanoparticles can effectively be used to create a DIC pattern for SEM imaging. Patterning methods for deformation tracking will continue to be investigated, including improvements on nanoparticle patterning and the use of electron beam lithography as a secondary patterning methodology. The developed distortion correction codes successfully remove both drift and spatial distortions from SEM micrographs. The fit equations generated during calibration correctly predict the distortion throughout the test period. The code also accurately calculates the Lagrangian surface strains from these distortion corrected displacements. Through the use of platinum markers to mark the area of interest, OIM maps of the sample surface can be accurately matched up with test images and the DIC calculated strain field. This methodology will enable the quantification of deformation mechanisms active in UFG metals.

It has also been displayed that distortion correction is critical to obtain accurate results from DIC experiments performed in an SEM. Future experiments will be performed on UFG 99.99% pure aluminum through the use of the outlined methodologies. ACKNOWLEDGEMENTS The authors gratefully acknowledge the funding provided by the NSF CMMI grant number 0927530 and the University of Michigan’s Rackham Non-Traditional Student Fellowship. The authors would also like to acknowledge the financial support of the DOE, Office of Basic Energy Sciences (Contract No. DE-SC000396) who funded a portion of the coding work. This work was performed in part at the Lurie Nanofabrication Facility, a member of the National Nanotechnology Infrastructure Network, which is supported in part by NSF. This work was also performed in part in the University of Michigan’s Electron Microbeam Analysis Laboratory. REFERENCES [1] W.A. Scrivens, Y. Luo, M.A. Sutton, S.A. Collete, M.L. Myrick, P. Miney, P.E. Colavira, A.P. Reynolds, X. Li, “Development of patterns for digital image correlation measurements at reduced length scales,” Exp. Mech., vol. 47, pp. 63-77, 2007. [2] T.A. Berfield, J.K. Patel, R.G. Shimmin, P.V. Braun, J. Lambros, N.R. Sottos, “Micro- and nanoscale deformation measurement of surface and internal planes via digital image correlation.” Exp. Mech., vol. 47, pp. 51-62, 2007. [3] S.A. Collette, M.A. Sutton, P. Miney, A.P. Reynolds, X. Li, P.E. Colavita, W.A. Scrivens, Y. Luo, T. Sudarshan, P. Muzykov, M.L. Myrick, “Development of patterns for nanoscale strain measurements: I. Fabrication of imprinted Au webs for polymeric materials.” Nanotechnology, vol. 15, pp. 1812-1817, 2004. [4] N. Sabaté, D. Vogel, J. Keller, A. Gollhardt, J. Marcos, I. Gràcia, C. Cané, B. Michel, “FIB-based technique for stress characterization on thin films for reliability purposes.” Microelectronic Eng., vol. 84, pp. 1783-1787, 2007. [5] N. Biery, M. DeGraef, T.M. Pollock, “A Method for Measuring Microstructural-Scale Strains Using a Scanning Electron Microscope: Applications to γ-Titanium Aluminides.” Metall. & Mat. Trans. A, vol. 34A, pp. 2301-2313, 2003. [6] B.D. Yan, S.L. Meilink, G.W. Warren, P. Wynblatt, “Water Adsorption and Surface Conductivity Measurements on a-Alumina Substrates.” IEEE Trans. on Comps. Hybrids & Manuf. Tech., vol. CHMT-10, pp. 247-251, 1987. [7] S. Sasaki, J.B. Pethic, “Effects of surrounding atmosphere on micro-hardness and tribological properties of sintered alumina.” Wear, vol. 241, pp. 204-208, 2000. [8] M.A. Sutton, N. Li, D. Garcia, N. Cornille, J.J. Orteu, S.R. McNeill, H.W. Schreier, X. Li, A.P. Reynolds, “Scanning Electron Microscopy for Quantitative Small and Large Deformation Measurements Part II: Experimental Validation for Magnifications from 200 to 10,000,” Exper. Mech., vol. 47, pp. 789-804, 2007. [9] M.A. Sutton, N. Li, D. Garcia, N. Cornille, J.J. Orteu, S.R. McNeill, H.W. Schreier, X.D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation.” Meas. Sci. Technol., vol. 17, pp. 2613-2622, 2006.

Characterization of a Variation on AFIT’s Tunable MEMS Cantilever Array Metamaterial

Matthew E. Jussaume, Peter J. Collins, Ronald A. Coutu, Jr. Air Force Institute of Technology 2950 Hobson Way Wright-Patterson AFB, OH 45433 [email protected] Abstract Metamaterials are devices with embedded structures that provide the device with unique properties. Several applications for metamaterials have been proposed including electromagnetic cloaks, lenses with improved resolution over traditional lenses, and improved antennas. This research addresses an obstacle to practical metamaterial development, namely the small bandwidth of current metamaterial devices. This research characterizes the effectiveness of several metamaterial designs. The basic design incorporates a microelectromechanical systems (MEMS) variable capacitor into a double negative (DNG) metamaterial structure. One set of devices is fabricated with the MEMS capacitor in the gap of the split ring resonator (SRR) of the DNG metamaterial. Applying voltage to the MEMS device changes the effective capacitance, thereby adjusting the resonant frequency of the device. Additionally, similar devices with three possible capacitor layouts are examined with stripline measurements and computer models. Recommendations for design improvements are provided. The initial capacitor layout with MEMS capacitors in the split ring gaps is recommended for future design iterations with adjusted gap capacitance values. Introduction Metamaterial devices have received much attention over the past two decades. There are many definitions for metamaterials. For this research effort, a metamaterial is defined as an “arrangement of artificial structural elements designed to achieve advantageous and unusual properties" [1]. In spite of the attention garnered by metamaterials, the science behind their apparent unusual properties is not settled. According to some researchers, metamaterials can be viewed to have a set of macro effective parameters for the medium, much as a molecular lattice interacts with incident electromagnetic fields. These effective constituent parameters produce quantities such as the effective index of refraction and effective impedance. These quantities dictate the behavior of the electromagnetic fields inside a metamaterial and are what gives a metamaterial its unusual properties. The effective permittivity and permeability are controlled by the geometry of the structural building blocks, the unit cells. When both the permittivity and permeability are negative, the material is referred to as a double negative (DNG) material and takes on a negative index of refraction [7]. Commonly, DNG materials are constructed with wire lattices and a pair of split ring resonator (SRR) particles. The unique properties associated with DNG materials are limited to the resonance regions of the metamaterial devices. Previous research has shown a myriad of ways to adjust the dispersive resonance region of metamaterial devices. The metamaterial designs in [3] and [4] depend on the inclusion of tunable magnetic and dielectric material respectively to adjust the resonant frequency. In [5], the authors propose a design that employs a varactor diode to adjust the resonant frequency; however the varactor is large, leading to a perturbation of the pure SRR and complicating structure scalability for manufacturing. The authors in [6] and [7] present a similar design with alternate placements of the varactor. This diode is controlled by the incident electric field, automatically adjusting based on the incident power. Similar to the design examined in this paper, the structures in [8] use a MEMS device to control the resonance of an SRR particle, but their MEMS device is a switch, not a variable capacitor. The authors of [9] present an alternate structure with series capacitors that are controlled with T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_16, © The Society for Experimental Mechanics, Inc. 2011

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112 a static electric field, which is similar to the method used to control the capacitance of the metamaterial presented in this paper, however, their capacitance changes are based on changes to the permittivity of the dielectric present. The metamaterial design analyzed in this paper uses a microelectromechanical systems (MEMS) variable capacitor that has six distinct states. It has a small footprint that is fabricated as part of the SRR element and is independent of the incident electromagnetic field. Based on the work of Lundell in [10], the intra-ring capacitance is expected to have a greater impact than the gap capacitance with the larger structures. Variants of the proposed structure with different MEMS capacitor layouts are examined using computational and measurement techniques. Theory The devices analyzed in this paper attempt to adjust the resonant frequency of the metamaterial device by including an additional circuit element in the equivalent circuit model of the structure. Using the equivalent circuit model, the particle’s resonant angular frequency is given in the microwave frequency regime by [8]

1

ω0 =

Leq C eq

.

(1)

The capacitance (Ceq) and inductance (Leq) of an SRR is dependent on the material it is made of as well as its dimension and shape. A novel metamaterial structure that achieves frequency adaptability was proposed in a previous research effort [11]. The structure is based on a basic DNG unit cell. The proposed structure also incorporates a MEMS variable capacitor across the gaps of the SRR particles. Fig. 1 shows the proposed initial design layout. The presence of the cantilever beams on the SRR creates a new source of capacitance which modifies the resonance of the structure. The cantilever beams are pulled down by applying voltage to the cantilever control lines. With no voltage applied, all of the cantilever beams are in the up state. With all the beams raised, the cantilevers can be modeled as two capacitors in series, one with an air gap (C1) and the other with a dielectric gap (C2). The first capacitor has a separation distance (d1) equal to 2 µm, the ideal raised height of the cantilever beams. The second capacitor has a separation distance (d2) equal to the thickness of the dielectric layer, ideally 0.3 µm. The capacitance of the un-actuated beams is calculated by [12]

Ctotal =

1

1 1 + C1 C2

=

ε oε r A

ε r d1 + d 2

where ε r is the permittivity of the dielectric, silicon nitride, and A is the area of the capacitor. As the beams pull down, they no longer behave as two capacitors in series but rather one capacitor with a separation equal to the thickness of the dielectric. The additional capacitances provided by the six different beam configurations are summarized in Table 1. For this paper, high frequency capacitance measurements of the cantilever structures were unable to be completed, making the calculated capacitance values the best initial estimate for the additional gap capacitance. For this research, models are examined with cantilever structures positioned in various locations around the general SRR cell. Computational models are presented in this paper to characterize and evaluate the frequency adaptability of the various capacitor layouts of the basic structure. The basic structure without the cantilever structures is designed to resonate around 3 GHz. The models are simulated using CST Microwave Studio® (MWS®), a commercial full wave electromagnetics solver employing the finite integration technique. The basic unit cell model is refined to model the physical devices as measured in a laboratory environment. For the different layouts, only the simulation results that take the measurement setup into account are presented in this paper. The simulations provide results for comparison to measurements without modeling the physical dimensions of the sets of cantilevers thereby balancing the need for simulations that accurately model the physics of the samples with the requirement for timely simulation data.

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Fig. 1: An adaptive DNG metamaterial design that uses cantilever beam variable capacitor [10]. Table 1: Calculated additional capacitance values for MEMS cantilevers. State Activated Beams Capacitance (pF) C0 None 0.195456 C1 300 μm 2.2282 C2 300 and 325 μm 4.26095 C3 300, 325, and 350 μm 6.29369 C4 300, 325, 350, and 375 μm 8.32644 C5 300, 325, 350, 375, and 400 μm 10.3592 Computational Models and Measurement Results There are four different capacitor layouts examined for the SRR samples, shown in Fig. 2. The first layout (layout A) has the cantilevers with one cantilever set in each of the split ring gaps. Based on the work of Lundell in [12], the intra-ring capacitance is expected to have a greater impact than the gap capacitance with the larger structures. Layout B is created to examine this conclusion, having two sets of intra-ring cantilevers on each side of the cell for this layout. Layout C is a combination between layouts A and B, with sets of cantilevers in each of the split ring gaps as well as two sets of intra-ring cantilevers per side of the unit cell, six sets of cantilevers in total. Layout D is similar to layout B, having three sets of intra-ring cantilevers on each side of the cell. The variable capacitors are modeled as lumped element capacitors, depicted as the blue objects in Fig. 2. The AFIT adaptive metamaterial structures are designed to be tested using a stripline waveguide designed for operation up to 4 GHz. To match experimental conditions, the devices are modeled in the simulated waveguide structure. The simulated cross sectional dimensions of the waveguide model match the physical dimensions of the waveguide. All metal pieces are modeled as perfect electrical conductor (PEC), and all boundaries are set to open. The length of the stripline is greater than three times the length of the longest sample to be measured in the physical stripline. The number of port modes simulated is set to four for all simulations of the AFIT adaptive metamaterial structures in the simulated waveguide. It is assumed that the physics of the structures is captured within these four modes and that higher order modes will have decayed before reaching the waveguide ports. The simulated device with capacitor Layout A is shown in Fig. 3.

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Fig. 2: AFIT metamaterial unit cell variants. (a) Layout A with cantilevers in the gaps of the split rings. (b) Layout B with two set of cantilevers between the inner and outer split ring per side of the cell. (c) Layout C with sets of cantilevers in the split ring gaps and two sets per side of the cell. (d) Layout D with three sets of intra-ring cantilevers per side of the cell.

Fig. 3: Model of the AFIT adaptive metamaterial structure with capacitor layout A in the model of the physical stripline.

115 The simulation and measurement of the structure with capacitor layout A are shown in Fig. 4(a) and Fig. 4(b) respectively. The simulation results show an area of resonance above 2 GHz for C0, which shifts to below 0.5 GHz by C3. The stripline measurements were taken at 0 volts applied and then at every volt from 5 to 21 volts. The measured transmission data from the 3 GHz sample with capacitor layout A is shown in Fig. 4(b). A region of shifting resonance is seen around 2 GHz. The resonance is seen to shift from 1.98 GHz at 0 volts applied to 1.89 GHz at 21 volts applied, a difference of only 0.11 GHz or 5.5% of the original resonance frequency. The small shift is due to the small range of voltages applied. In the interest of sample preservation, the range of applied voltages was limited to fewer than 22 volts, as previous samples with capacitor layout A shorted at 25 volts.

Fig 4: (a) Simulation and (b) measurement results from AFIT metamaterial device with layout A. Simulated and measured transmission results for the AFIT metamaterial structure with cantilever layout B are depicted in Fig. 5. The transmission data is clouded by multiple resonance areas. There appears to be a shifting resonance area at 2.25 GHz that shifts downward with increasing capacitance. At C0, the single region is seen around 2.25 GHz. For C1 and C2, two shifting regions are seen. For C3 through C5, the resonance appears to have shifted below 0.5 GHz. The stripline measurements were taken at 0 volts, 5 volts, and every two volts from 10 volts to 30 volts. The measured transmission data is shown in Fig. 5(b). With increased voltage, the transmission nulls are seen to shift slightly, only 0.052 GHz and 0.050 GHz for the 2 and 3 GHz resonance regions respectively. Simulated and measured transmission results for the AFIT metamaterial structure with cantilever layout C are shown in Fig. 6. From the simulation data, the C0 results show two resonance regions at 1.75 GHz and 3.5 GHz which shift to 0.75 GHz and 2.25 GHz for C1, respectively. There is also a third resonance region for C1 at 2.75 GHz. The resonance regions shift out of the frequency range as the capacitance values increase. The increased number of capacitors adds to the complexity of the transmission data. The stripline measurements were taken at 0 volts applied then at every 5 volts from 10 to 40 volts, where the sample shorted out. The measured transmission data from the 3 GHz sample with capacitor layout C is shown in Fig. 6(b). A large oscillation is present in the transmission data above 2 GHz; therefore data above 2 GHz should be disregarded. Transmission nulls are seen around 0.5 GHz and just below 2 GHz. The transmission data does not change with applied voltage at the 0.5 GHz transmission null; however there are changes at the 2 GHz transmission data. Even with the changes at the 2 GHz transmission data, no appreciable null shift is seen, only a slight decrease in the transmission amplitude is observed. In this region, the calibration appears poor, with transmission measurements above unity, a non-physical result. It should be noted that this set of measurement data was obtained without applying time domain gating to the measured data. Simulated and measured transmission results for the AFIT metamaterial structure with capacitor layout D are shown in Fig. 7. Similar to capacitor layout C, multiple resonance areas are seen in the simulation results. There is an area of resonance at 2 GHz for C0 that appears to shift below the frequency range for greater capacitance values. There is also a resonance region around 2.75 GHz for C1 that shifts to around 1.25 GHz for C5. The stripline measurements were taken at 0 volts and at every volt from 5 to 15 volts. The measured transmission

116 data from the 3 GHz sample with capacitor layout D is shown in Fig. 7(b). Transmission nulls are seen around 1 and 2 GHz; however here is no shifting seen as the voltage is increased.

Fig 5: (a) Simulation and (b) measurement results from AFIT metamaterial device with layout B.

Fig 6: (a) Simulation and (b) measurement results from AFIT metamaterial device with layout C.

Fig 7: (a) Simulation and (b) measurement results from AFIT metamaterial device with layout D. Having reviewed simulated results from all four variants of the larger AFIT metamaterial structure, recommendations can be made for design improvements. While there are clear resonance shifts observed for the structures simulated with additional intra-ring capacitance, the multiple resonance areas complicate analysis.

117 Also, cell to cell variance of additional capacitance in the physical devices can limit the strength of the resonances. The single resonance frequency provided by layout A provides transmission results that are easily evaluated for resonance frequency shifts. The effective capacitance change required to achieve a shift within the frequency range of the stripline is examined. Various capacitance values are simulated and the resonance frequencies are calculated. Based on the simulated resonance frequencies for layout A, a non-linear increase in effective capacitance values is recommended. To achieve a shift from 2.3 GHz to 1.0 GHz, a change of capacitance from 0.1 pF to 1.5 pF needs to occur. The other layouts are not recommended for further design improvements. As the number of capacitors is increased, the strength of resonant mode coupling is decreased because of the variance in actual effective additional gap capacitance provided by the physical cantilever structures, leading to little shift of the resonance frequency observed in the measured results. Conclusions Full wave electromagnetic simulations and measurements of larger scale AFIT metamaterials are combined in this research to determine the most promising structure for changing the resonance frequency. For the four capacitor layout variants created, a single cell model is refined to represent the structures as measured, 4-cell long columns in a stripline. The single resonance frequency provided by capacitor layout A provides transmission results that are most easily evaluated for resonance frequency shifts. To achieve a resonance frequency shift from 2.3 GHz to 1.0 GHz, a change of effective additional gap capacitance of 0.1 pF to 1.5 pF needs to occur. To achieve a linear step decrease in the resonance frequency, thicker cantilever beams with geometries that will provide the additional capacitance are recommended. The thicker beams would provide a more discrete change in additional capacitance and therefore a more discrete change in resonance frequency. The remaining layouts are not recommended for further design improvements. As the number non-uniformly actuating capacitors is increased, the strength of resonant mode coupling as decreased, as seen in measurements of the samples. Stronger resonance regions would be achieved if the MEMS structures actuated uniformly across the cells. References [1] Lapine, M. and S. Tretyakov. “Contemporary notes on metamaterials". IET Microwaves Antennas Propag., 1(1):3{11, Feb. 2007. [2] Engheta, N. and Richard W. Ziolkowski. Metamaterials: Physics and Engineering Explorations. Wiley, Hoboken, N.J., 2006. [3] J. N. Gollub, D. R. Smith, and J. D. Baena, “Hybrid resonant phenomenon in a metamaterial structure with integrated resonant magnetic material,” Opt.Express, vol. 17, no. 4, pp. 2122–2131, 2008. [4] G. Lunet, V. Vigneras, H. Kassem, and L. Oyhenart, “Meta-material with tunable thin film material for the conception of active radome,” in Microwave Conference, 2009. EuMC 2009. European, 2009, pp. 602–605, iD: 1. [5] I. Gil, J. Garc´ıa-Garc´ıa, J. Bonache, F. Mart´ın, M. Sorolla, and R. Marqu´es, “Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies,” Electron.Lett., vol. 40, no. 21, pp. 1–2, Oct. 2004. [6] I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, “Tunable split-ring resonators for nonlinear negative-index metamaterials,” Opt.Express, vol. 14, p. 9344, 2006. [7] D. Huang, E. Poutrina, and D. R. Smith, “Analysis of the power dependent tuning of a varactor-loaded metamaterial at microwave frequencies,” Applied Physics Letters, vol. 96, no. 10, pp. 104 104–104 104–3, 2010, iD: 1. [8] T. Hand and S. Cummer, “Characterization of tunable metamaterial elements using MEMS switches,” IEEE Antennas Wireless Propag.Lett., vol. 6, pp. 401–404, Jan. 2007.

118 [9] K. J. Nicholson and K. Ghorbani, “Design, manufacture and measurement of a metamaterial with tunable negative-refractive index region,” in Microwave Conference, 2009. APMC 2009. Asia Pacific, 2009, pp. 1231 1233, iD: 1. [10] Lundell, C. A, Collins, P. J, Starman, L. A., Coutu, R. A. “MEMS integrated metamaterial structure capable of variable resonance for RF applications.” Proceedings of the SEM Annual Conference. 2010. [11] L. Rederus, “A MEMS multi-cantilever variable capacitor on metamaterial,” Master's thesis, Air Force Institute of Technology, Air University, Wright Patterson AFB OH, 2009. (ADA497157). [12] C. Lui, Foundation of MEMS. Upper Saddle River, New Jersey: Pearson Prentice Hall: Pearson Prentice Hall, 2006.

MEMS for real-time infrared imaging

I. Dobrev, Marc Balboa, Ryan Fossett, C. Furlong, and E. J. Harrington Center for Holographic Studies and Laser micro-mechaTronics  CHSLT NanoEngineering, Science, and Technology  NEST Mechanical Engineering Department Worcester Polytechnic Institute 100 Institute Road, Worcester MA, 01609, USA ABSTRACT This project investigates an innovative approach to imaging with Micro Electro-Mechanical Systems (MEMS) based devices. By using a Linnik interferometer and advanced phase unwrapping algorithms for processing data, the feasibility of generating high-resolution grayscale images in real-time was proven with an array of individually addressable MEMS micro-mirrors. Further investigations on a thermal imaging detector consisting of an array of pixels defined by surface micromachined bimaterial beam structures were carried out. A thermal loading fixture was manufactured and incorporated into the interferometer setup, which was also optimized to provide high measuring resolution. Interferometric images were collected at several temperatures in order to determine the beams’ response as a function of temperature, which successfully demonstrated the suitability of the detector to imaging with high-sensitivity and with a linear response. Experimental results were used with analytical and computational models to further predict the thermo-mechanical characteristics of the beams and to perform parametric investigations and optimization of their design. Further developments will consist of integrating the detector into a highly advanced, completely mechanical, imaging device having mK thermal resolution. The availability of such device will greatly improve current thermal imaging technology. Keywords: interferometry, infrared imaging, MEMS, metrology, thermoelasticity, micromachining

1. Introduction This project investigates an innovative approach to thermal imaging using MEMS devices with laser interferometry, a technique that allows for the generation of continuous grayscale variations that are proportional to temperature differences. The current state of the art thermal imaging devices use CMOS and CCD sensors - digital devices which are only able to identify quantized levels of infrared radiation. Since this radiation is emitted from any warm body, these devices are subject to high levels of noise; even from the devices themselves. As a result the device requires expensive cooling systems in order to maintain high thermal resolutions, thus limiting them to stationary use. These cameras have digital resolution on the order of 25-30mK, which is insufficient for some of today’s thermal imaging applications such as development of advanced circuitry and long range infrared detection devices for homeland security. Higher resolutions can be obtained using MEMS devices that react to infrared radiation. These devices use micro scale, bimaterial cantilever beams, which react to changes in temperature by deflecting out of plane. Naturally, the scale of these variations is on the order of nanometers, so highly sensitive measurement techniques with high resolution must be utilized.

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_17, © The Society for Experimental Mechanics, Inc. 2011

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120 We have developed a Linnik interferometer for measuring changes in position with sub-nanometer resolution. Changes in optical path-length of the object beam shown in Fig. 1, create constructive and destructive proportional to the position of a sample. The principal of operation of the setup is that thermally induced deflections of microcomponents can be quantified interferometrically as grayscale patterns that encode temperature information.

Fig. 1. Linnik interferometer configuration used in our developments [1].

2. Interferometric measurements 2.1. Principle of operation A four phase stepped algorithm with a quarter wavelength step is used to extract optical phase information corresponding to the shape of the micro-components of interest. Therefore, the phase distribution across an object is determined with,

 I ( x, y ) 4  I ( x , y ) 2  ( x, y )  tan 1  ,  I ( x, y )1  I ( x, y )3 

(1)

with to corresponding to images from 0 to step positions of the phase shifter and λ is the wavelength of the laser diode used for illumination. By using Eq. 1, it is possible to determine deformations, Lz, with L z ( x, y) 

  ( x, y) . 4

(2)

While this algorithm is useful for absolute measurements of shape and deflection of the surface of an object, the algorithm can be used in double-exposure mode to measure changes in displacement rather than absolute positions [1]. This allows for measurements of very small displacements relative to the initial shape of the surface of an object. 2.2. Calibration and accuracy of the system A crucial part on the quality of the measurements is the positioning accuracy of the phase shifting reference mirror, which is driven by a piezo-based nanopositioner. Calibration of the nanopositioner is achieved by implementing a high-resolution Hariharan algorithm [2] that leads to positioning resolutions on the order of . After calibration, the interferometric system was tested for accuracy and resolution with a standard calibration flat plate having a flatness in the Å range. The demonstrated measured resolution achieved is on the order of 0.25nm. The setup was also tested for accuracy and mechanical stability and they were found suitable for our measurements.

121 2.3. Proof of concept system for real-time interferometric imaging Initial experimentation consisted of a proof of concept to determine the feasibility of using an interferometer for real time grayscale pattern generation. To test this, a sample array of pixels was required that could predictably be moved in and out of plane. A commercially available micro-mirror array manufactured by Boston Micromachines Corporation [3] was acquired for testing. The chip consists of an array of 18×18 individually addressed 600×600μm2 micro mirrors; each having a maximum out-of-plane displacement of approximately 400nm. The actuation of the mirrors is completely analog and can therefore be used to demonstrate the interferometer’s ability to measure continuous displacements. Figure 2 shows an example of a pattern generated with our interferometer measuring unwrapped optical phase in double-exposure mode while 6 micro-mirrors are operated independently

(b) (a) Fig. 2. (a) MEMS generation of the letter "J", viewed using interferometry; Top view (b) of the micro-mirror array.

3. Realization of thermally induced pattern generation using MEMS bi-material beam arrays 3.1. Analytical and FEM characterization of a bi-material beam Full characterization of the beams requires a combined analytical computational and experimental approach. However due to the complex shape of the bi-material beams used in the MEMS device [4, 5] no closed form analytical solution is available. To overcome that an indirect method was implemented by initially calibrating a FEM model of a simply supported bimaterial beam against an analytical model [6, 7]. The computational model of the simple cantilever beam yielded a sensitivity of 24.1 nm/K while the analytical model predicts a sensitivity of 23.8 nm/K – less than one percent error between the solutions for 64µm long beam. Both models predict completely linear thermal sensitivity. The FEM model was then further modified to match the true geometry of the bi-material pixels in the MEMS array [8]. 3.2. FEM model characterization of MEMS bi-material beam Our computational model of a simple cantilever beam validated that the FEM model could be reliably expanded to predict the behavior of beams with more complex shapes, such as the ones in the MEMS bi-material beam array that was implemented in our system [9, 10, 11]. Shown in Fig. 3, note the presence of release holes, a trademark of the surface micromachining process. Figure 3b shows the release holes (and corner fillets) modeled, although the FEM model does not take these into consideration. These features affected the computation by only 1-3 pico-meters, thus these features were deemed negligible.

122

(b) (a) Fig. 3. 50x magnified images: (a) of a section of bi-material cantilever pixel array; Graphic representation (b) of bi-material cantilever pixel from FEM model. 4. Experimental characterization of MEMS bi-material beams array Experimental data was collected using the Linnik interferometer; the data were processed and analyzed using a collection of softwares for data capturing [12] and phase unwrapping [13]. Raw data was first masked using a MATLAB program to avoid errors when using the unwrapping software. The raw masked data was then phase-unwrapped using a fluid unwrapping algorithm. Finally, unwrapped data was exported to MATLAB for analysis; with this data, both absolute and relative position could be determined. By relating these displacements to the temperature of the beams at the time of the experiment and taking several readings at different temperatures, the sensitivity of the beams was calculated. Then, by combining the thermal sensitivity of the array with the resolution of the interferometer, the thermal resolution of the system was determined. In order to conduct an experiment with such a thermally sensitive MEMS device a special thermal loading station was designed and built [14] to accurately determine the temperature of the experimental array of beams. Figure 4 shows a CAD model of this setup while of Fig. 5 shows its realization and use. Two thermoelectric cooling devices (TECs) were used to generate a temperature difference between the base plate and a heat sink fastened below it. There were two major considerations in the design of this setup: first, that the experimental array is to be kept stationary during the heating and cooling process, and second, that the two thermal bodies – the MEMS array and the support plate, be thermally isolated to ensure thermal stability.

Fig. 4. CAD model of thermal loading station

Fig. 5. Design realization of thermal loading station

Data sets were collected by first capturing a reference image at an initial temperature and then taking ten images at even intervals as the array was either heated or cooled. Data sets were taken at a variety of starting temperatures, both heating and cooling, and with the ten images captured in temperature ranges from 1°C to 5°C. Two high sensitivity thermistors inserted in the support plate were used to provide feedback for temperature of the beams.

123 After obtaining the raw experimental data it was noticed that directly applying unwrapping algorithm to it resulted in errors mainly because of data noise at the edges of the beams. The noise was due to irregular illumination of the edge areas of the beams which caused errors in readings of the surface at these points. This was accounted for by creating a MATLAB program than automatically masks the raw data so that only the surface of the beams is visible along with some of the surface of the substrate. The substrate areas were used as a reference for the unwrapping process so that the true deflection of the beams can be calculated. The mask greatly reduced the noise in the data and thus allowing for the unwrapping algorithm to produce much smoother surface representing the surface of the beam. Figure 6 shows the final result of the unwrapping algorithm of two pixels, while Fig. 7 shows the 3D representation of that data of one pixel.

Fig. 6. Masked unwrapped phase data of two beams, which correspond to two pixels of the array tested

Fig. 7. 3D representation of the shape of a beam at a detected temperature of 17.49oC

The unwrapping algorithm produces a continuous grayscale image so that the grayscale intensity of each pixel corresponds directly to the displacement of the beam at that point. This allows for full-field of view measurements of the thermally induced displacement of the bi-material pixels as well as their shape. Based on this information, the curvature of the beam was extracted by tracing a line on the 3D surface of the beams. This technique was applied for the extraction of the curvature of the beam at several temperatures. By reading the position of the surface near the tip of the beam, a data for the thermal sensitivity of the beams can be extracted. While beams are 136.5μm long, information at 122 μm from the base of the beams was sampled to minimize noise associated with inaccuracies of the readings at the tip of the beam. A graph of the experimentally measured beams’ displacement with respect to temperature along with FEM predictions are shown in Fig. 8.

Fig. 8. Beam sensitivity comparison for FEM and experimental results According to Fig. 8 it can be clearly observed that computationally predicted thermal response of the beams is within the error margin of the experimentally predicted response. The FEM model yields a sensitivity of 87.4nm/K and the experimental characterization shows a sensitivity of 85.5nm/K – a difference of only 2.2%.

124 This gives confidence that the experimental procedures were done with high degree of accuracy. Having the sensitivity of the MEMS bi-material beams array and the sensitivity of the interferometric measurement system, the resulting overall thermal resolution of the system is determined to be 3mK. By comparing this value to the resolution of existing high-end infrared imaging systems – 25mK [15], the proposed system offers more than 8 times increase in thermal resolution. 5. Conclusions and future work In our project we successfully demonstrated that interferometry can be used for real time gray-scale imaging proportional to temperature. We also managed to characterize MEMS thermally actuated bi-material beam array. With our analytical and FEM model of the thermal sensor we allow for future design optimization of the beams array for specific applications. Overall, our system demonstrated a thermal resolution not achievable by any currently available conventional commercial technologies. Future work should be focused on miniaturization and full system integration of the system. Further investigations on achieving full system mobility should be conducted. 6. Acknowledgements The authors gratefully acknowledge the support provided by Boston Micromachines Corporation as well as the support of the NanoEngineering, Science, and Technology (NEST) program at the Worcester Polytechnic Institute, Mechanical Engineering Department. We would also like to acknowledge our colleagues at the CHSLT labs. REFERENCES [1] Furlong, C. and Pryputniewicz, R. J., “Optoelectronic characterization of shape and deformation of MEMS accelerometers used in transportation applications,” Opt. Eng., 42 (5):1223-1231, 2003. [2] Hariharan, P., Oreb, B. F., and Eiju, T., "Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm," Appl. Opt. 26: 2504-2506, 1987. [3] Boston Micromachines Corp., [4] Pal, S. Kemiao, J., Xie, H., “An Electrothermal Micromirror with High Linear Scanning Efficiency”,Proc. IEEE, 9858694, pp. 914-915, 10.1109/LEOS.2007.4382707, 2007. [5] Hsu, T-R, MEMS & Microsystems: design and manufacture, McGraw-Hill, NY, 2002. [6] Hibler, R. C., Mechanics of Materials, 6th ed. Pearson, Upper Saddle River, NJ, 2005. [7] Timoshenko, S., “Analysis of bi-metal thermostats,” J. Opt. Soc. Am., 11:233-255, 1925. [8] Balboa, M., Dobrev, I., Fosset, R., MEMS for Real Time Imaging Applications, Major Qualifying Project, Mechanical Engineering Department, 2009 [9] ANSYS Inc., Ansys User’s guide v 9.0, Canonsburg, PA, 2007. [10] Moaveni, S., Finite Element Analysis: Theory and Application with ANSYS, Pearson, Upper Saddle River, NJ, 2003. [11] Pelesko, J. A., and Bernstein, D. A., Modeling MEMS and NEMS, CRC Press, Boca Raton, FL, 2003. [12] Harrington, E., Dobrev, I., Bapat, N., Mauricio Flores, J. M., Furlong, C., Rosowski, J. J., Cheng, J. T., Scarpino, C., Ravicz, M., "Development of an optoelectronic holographic platform for otolaryngology applications", Proc. SPIE, 7791, 77910J; doi:10.1117/12.862130, 2010 [13] Kolenovic, E., Furlong, C., Jüptner, W., “Inspection of micro-optical components by novel digital holographic techniques,” Proc. SEM: pp. 470–475, 2004. [14] Norton, R. L., Machine Design: An Integrated Approach, Pearson, Upper Saddle River, NJ. , 2006. [15] Flir Thermal Imaging, Inc.,<www.flir.com> 

New Insights into Enhancing Microcantilever MEMS Sensors

S. Morshed and B.C. Prorok Auburn University, Department of Mechanical Engineering 275 Wilmore Engineering Labs, Auburn, AL 36849, Email: [email protected] ABSTRACT: Damping effects on different geometries were investigated by testing them in air at different 5 -2 pressure levels, ranging from the atmospheric pressure of 10 Pa to 10 Pa. The resulting responses of these geometries followed the same trend as the analytical plot for the rectangular shape structure. As the relative resonant frequency of the structure is proportional to the intrinsic resonant frequency, measured at the lowest pressure levels achieved by the AFM system, different shapes showed different amount of responses as a function of pressure. As the intrinsic resonant frequency of the triangular shape was the highest, its relative resonant frequency was the highest; the modified geometry showed intermediate responses among the three geometries. INTRODUCTION: In recent years, Microcantilever based sensors have been applied to detect different physical quantities, such as acceleration of automobiles to deploy airbags, and different chemical [1-8] and biological species [8-17] present in different environments. Sensors consist of two elements: sensing and transduction elements. The sensing element measures the measurand, which can be a physical quantity, property or a certain condition, from the input signal that can be magnetic, chemical, electromagnetic, mechanical, thermal etc. Microcantilever based sensors use two types of detection schemes, one of them involves deflection of the cantilever beam structure due to the mass loading on the beam in static condition, while the other one involves the change in the resonant frequency of the cantilever beam structure due to the mass loading on the beam under dynamic conditions. Biosensors usually use acoustic wave based sensing devices for detection. They use elastic waves at frequencies well above the human audible range propagating through the sensing structures. Microcantilever based sensor devices fall into this category. Datskos et al. [18], Oden [19] and Stern et al. [20] have compiled and compared performances of acoustic wave based sensors based upon mass sensitivity, which can be expressed by the equation 1,

Sm =

1 Δf f Δm smin

,

(1) min

where, f is the resonant frequency, Δf the resonant frequency shift and Δms the minimum detectable surface mass density. In prior work [21], we reported on a simplistic approach for significantly enhancing the mass sensitivity of microcantilever acoustic sensors by modifying the cantilever geometry. The approach involved € modifying the geometry to minimize the effective mass at the free end of the microcantilever. Polystyrene beads were attached at specific locations and the resonant behavior and mass sensitivity was compared between geometries. Resonance behavior was assessed via the laser reflection method. Mass sensitivity was found to increase by nearly an order of magnitude for the new geometrical shapes over the rectangular geometry, which is the standard shape for microcantilever acoustic sensors. Triangular geometries yielded the best performance increase over the standard rectangular geometry; however a compromise was made to ensure there was sufficient area at the microcantilever free end to capture target species in frequency shift by mass addition applications, see Table 1. Resonant frequency shifts that result from the attachment of a single bioparticle are shown in Figure 1. Our results indicated that modifying the geometry of a microcantilever to reduce the amount of effective mass at the end of the microcantilever was successful in significantly enhancing its performance. Mass sensitivity was increased by 8.77 times that of a standard rectangular microcantilever when in a triangular shape of the same length and geometry and 4.55 times for the adapted geometry. Another aspect to consider is how damping influences these geometries, as these types of sensors for biological agents are almost exclusively operated in liquid environments. An initial thought experiment would seems to conclude the modified geometries would be less influenced by damping as their cross-sectional interface with the surrounding medium is less than the standard rectangular cantilever. One can then

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_18, © The Society for Experimental Mechanics, Inc. 2011

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126 conceptually generate a schematic of how the relative resonant frequency shift would behave with viscosity of the medium, see Figure 2.

Figure 1: Frequency spectrum for the different shapes indicating the resonant frequency both with and without the attached polystyrene bead.

Figure 2: Schematic figure showing expected viscosity dependence on different geometrical shapes.

127 This range of viscosity can be divided into three separate regions [22-27]. At low pressure levels the vibrating cantilever beam structure loses energy due to internal damping, known as the intrinsic regime. At this pressure level air molecules can be considered non-interacting with the vibrating structure. Thus, the damping effect due to the medium can be neglected. At higher pressure levels, near the atmospheric pressure, the damping effect is dominated by the external effect imposed by the molecules present in the medium. This region of external damping is referred to as the viscous regime. In between these two regimes, there is a transition regime where both the internal and the external damping effects play roles. This work is aimed at experimentally determining how damping influences the mass sensitivity of the different geometrical shapes. EXPERIMENTAL PROCEDURE: The devices fabrication was identical to that described in out prior work [21]. The microcantilevers were fabricated using standard surface and bulk micromachining techniques. Silicon-oninsulator (SOI) wafers were used that possessed a 1 µm SiO2 layer 4.3 µm below the wafer surface. The process is summarized in 5 steps, see Fig. 2: (1) Spin coat photoresist on the top side, pattern and develop; (2) deep reactive ion etching (DRIE) of the exposed silicon on the top-side; (3) spincoat photoresist on the top and bottom side and pattern and develop the bottom side; (4) DRIE etching of silicon from the bottom side using the ‘Bosch’ process27-29 until the silicon oxide layer is met; and (5) etching of the SiO2 layer with an H2O:HF solution (10:1) to release freestanding microcantilever structures. Complete fabrication procedures are described elsewhere. [21] The resonance behavior of the microcantilevers was measured at ambient air pressure via the laser reflection method. A JEOL 5200 Scanning Probe Microscope operating in non-contact AC mode was employed to excite the microcantilevers and measure their resonant properties. Temperature was maintained at a 24.7°C to ensure that it did not influence the measurement and the microcantilevers were placed in the test rig 1 hour before testing to allow them to equilibrate. Microcantilevers were initially characterized to determine their resonance frequency and then remeasured after application of the polystyrene beads. Polystyrene beads 10 µm in diameter, obtained from Polysciences Inc., were attached on the free end of the microcantilever beam where it is most sensitive to mass attachments [21]. The beads were manipulated with a probe station tip to a location on the central axis of the microcantilever approximately 20 µm from its free end. In order to rigidly affix the beads to the microcantilevers, they were annealed above the bead’s glass transition temperature, 95°C, at a temperature of 120°C for a period of 15 minutes. The result was bead attachment suitable for the resonance measurements. The nominal diameter of each bead was 9.8 ± 0.2 µm with a mass of 513.5 ± 0.2 pg. To investigate the damping effect on these geometries and their performances the A, F and I shaped cantilevers were tested and compared. The resonant frequency of these geometries was measured in air at 5 different pressure levels, starting from atmospheric pressure to the lowest vacuum pressure attainable (of 10 to -2 10 Pa) by a JEOL SPM 5200 Scanning Probe Microscope system. The laser diode and photodetector of the system were employed to measure resonance frequency. RESULTS AND DISCUSSIONS: The relative resonant frequencies were calculated from the experimental data for each of the samples of all three geometries and plotted in Figures 3. To make a comparison, an analytical model for a rectangular cantilever was attached to each of the plots for different shapes (solid line). Sandberg et al. [38] had developed this analytical expression for pressure dependence of the resonant frequency of a regular rectangular shaped cantilever beam structure: −1/ 2 ⎛ πMwp ⎞ f = f 0 ⎜1 + , ⎟ 4 RTρh ⎠ ⎝

(2)

Here, f0 = intrinsic resonant frequency, M = molar mass of the medium (in this case 28.97 gm/mol for air), p: = pressure, R = gas constant (8.314 J/mol.K), T = temperature (room temperature, approximated as 300 K), ρ = 3 density of the beam material (for Si it is 2.329 gm/cm ), and h = bean thickness. From equation (2), the relative € resonant frequency can be calculated using the following expression: −1/ 2 ⎡⎛ ⎤ πMwp ⎞ Δf = f 0 ⎢⎜1 + −1⎥ , ⎟ 4RTρh ⎠ ⎢⎣⎝ ⎥⎦

(3)

where, the intrinsic resonant frequency was assumed to be the same as the maximum resonant frequency that was measured at the lowest pressure attained by the system during testing for each samples. To calculate the

€

128 analytical results for a rectangular shape cantilever, the average value of the thickness of the samples and the average value of the intrinsic resonant frequencies of the samples were used. The separate plots in Figure 3 were combined into a single figure to better enable comparison, see Figure 4. From these plots it can be seen that there are no significant differences among the three geometries, in terms of relative resonant frequencies. Proving the expectation to be wrong which was summarized in the schematic plots attached in Figure 2. This may be due to the fact that the relative resonant frequency is highly dependent on the intrinsic resonant frequency, as can be seen from the Equation (3). Although the damping effects on the triangular shape might be the smallest, its intrinsic resonant frequency was the highest. Thus, the change in the resonant frequency became comparable to that of the other shapes. On the other hand, the rectangular shape had the largest surface area for damping effect to take place, while it had the lowest intrinsic resonant frequency. Thus, the change in the resonant frequency due to damping became comparable to the other shapes.

Figure 3: Relative resonant frequency as the function of pressure for the 3 shapes. It is interesting to note that the triangular shape was significantly more influenced by damping than the standard rectangular shape. Our initial assumption was that its reduced cross-sectional interface with the medium would reduce damping effects. However, it appears to be the opposite effect. The reason involved their significantly different resonant frequencies, 194 KHz for the rectangular and 390 KHz for the triangular. The triangular has twice the vibration rate as the rectangular shape, meaning it possesses twice as much contact time with the medium. Even though the triangular shape possesses less cross-sectional contact, its higher resonant frequency producs more contact with the medium and is there for damped to a larger degree. Unfortunately this erodes, in part, the benefits gained in mass sensitivity by changing the geometry.

129

Figure 4: Relative resonant frequency as the function of pressure comparing all three shapes. CONCLUSIONS: Our prior work revealed that changing the standard rectangular shape of microcantilever sensors to more triangular-like shapes can significantly improve the mass sensitivity, by nearly an order of magnitude. However, this work revealed that this change can significantly increase damping effects that erode some of the performance enhancement that triangular-based geometries offer. REFERENCES: 1. Alvarez, M, Calle, A., Tamayo, J., Lechuga, L.M., Abad, A., Montoya, A.; Development of nanomechanical biosensors for detection of the pesticide DDT; Biosensors & Bioelectronics, Vol. 18, 2003. 2. Baselt, D.R., Fruhberger, B., Klaassen, E., Cemalovic, S., Britton, C.L., Jr., Patel, S.V., Mlsna, T.E., McCorkle, D, Warmack, B.; Design and performance of a microcantilever-based hydrogen sensor; Sensors & Actuators B, Vol. 88, 2003. 3. Gunter, R.L., Delinger, W.D., Porter, T.L., Stewart, R., Reed, J.; Hydration level monitoring using embedded piezoresistive microcantilever sensors; Medical Engineering & Physics, Vol. 27, 2005. 4. Ji, H.-F.,Thundat, T; In-situ detection detection of calcium ions with chemically modified microcantilevers; Biosensors & Bioelectronics, Vol. 17, 2002. 5. Pinnaduwage, L.A., Thundat, T., Hawk, J.E., Hedden, D.L., Britt, P.F., Houser, E.J., Stepnowski, S., McGill, R.A., Bubb, D.; Detection of 2,4-dinitrotoluene using microcantilever sensors; Sensors & Actuators B, Vol. 99, 2004. 6. Porter, T.L., Eastman, M.P., Macomber, C., Delinger, W.G., Zhine, R.; An embedded polymer piezoresistive microcantilever sensor; Ultramicroscopy, Vol. 97, 2003. 7. Zhou, J., Li, P., Zhang, S., Huang, Y., Yang, P., Bao, M., Ruan, G.; Self-excited piezoelectric microcantilever for gas detection; Microelectronics Engineering, Vol. 69, 2003. 8. Tamayo, J., Humphris, A.D.L., Malloy, A.M., Miles, M.J.; Chemical sensors and biosensors in liquid environment based on microcantilevers with amplified quality factor; Ultramicroscopy, Vol. 86, 2001. 9. Rodolphe, M., Jensenius, H., Thaysen, J., Christensen, C.B., Boisen, A.; Adsorption kinetics and mechanical properties of thiol-modified DNA-oligos on gold investigated by microcantilever sensors; Ultramicroscopy, Vol. 91, 2002. 10. Baselt, D.R., Lee, G.U., Colton, R.J.; Biosensor based on force microscope technology; Journal of Vacuum Science & Technology B, Vol. 14, 1996. 11. Raiteri, R., Grattarola, M., Butt, H.-J., Skaladal, P.; Micromechanical cantilever-based biosensors; Sensors & Actuators B, Vol. 79, 2001. 12. Ilic, B. Czaplewski, D., Zalalutdinov, M., Craighead, H.G., Neuzil, P., Campagnolo, C., Batt, C.; Single cell detection with micromechanical oscillators; Journal of Vacuum Science & Technology B, Vol. 19, 2001. 13. Gunter, R.L., Delinger, W.G., Manygoats, K., Kooser, A., Porter, T.L.; Viral detection using an embedded piezoresistive microcantilever sensor; Sensors & Actuators A, Vol. 107, 2003. 14. Kooser, A., Manygoats, K.,Eastman, M.P., Porter, T.L; Investigation of the antigen antibody reaction between anti-bovine serum albumin (a-BSA) and bovine serum albumin (BSA) using piezoresistive microcantilever based sensors; Biosensors & Bioelectronics, Vol. 19, 2003.

130 15. Yan, X., Ji, H.-F., Lvoy, Y.; Modification of microcantilevers using layer –by-layer nanoassembly film for glucose measurement; Chemical Physics Letters, Vol. 396, 2004. 16. Ilic, B., Yang, Y., Craighead, H.G.; Virus detection using nanoelectromechanical devices; Applied Physics Letter, Vol. 85, 20004. 17. Alvarez, M., Tamayo, J.; Optical sequential readout of microcantilever arrays for biological detection; Sensors & Actuators B, Vol. 106, 2005. 18. Datskos, P.G., Sauers, I., Detection of 2-mercaptoethanol using gold-coated micromachined cantilevers, Sensors and Actuators B, Vol. 61, 1999. 19. Oden, P.I., Gravimetric sensing of metallic deposits using an end-loaded microfabricated beam structure, Sensors and Actuators B, vol. 53, 1998. 20. Stern, R., Levy, M., Acoustic wave sensors, Academic Press, 1997. 21. Morshed, S., Baldwin, K.E., Zhou, B., Prorok, B.C., Modifying Geometry to Enhance the Performance of Microcantilever-Based Acoustic Sensors, Sensor Letters, vol. 7, (2009). 22. Sader, J.E.; Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope; Journal of Applied Physics, Vol. 84, 1998. 23. Sandberg, R., Molhave, K., Boisen, A., Svendsen, W.; Effect of gold coating on the Q-factor of a resonant cantilever; Journal of Micromechanics & Microengineering, Vol. 15, 2005. 24. Southworth, D.R., Craighead, H.G., Parpia, J.M.; Pressure dependent resonant frequency of micromechanical drumhead resonators; Applied Physics Letters, Vol. 94, 2009. 25. Ikehara, T., Lu, J., Konno, M., Maeda, R., Mihara, T.; A high quality-factor silicon cantilever for a low detection-limit resonant mass sensor operated in air; Journal of Micromechanics & Microengineering, Vol. 17, 2007. 27. Bianco, S., Cocuzza, M., Ferrero, S., Giuri, E., Piacenza, G., Pirri, C.F., Bich, D., Merialdo, A., Schina, P., Correale, R.; Silicon resonant microcantilevers for absolute pressure measurement; Journal of Vacuum Science & Technology B, Vol. 24, No. 4, 2006. 27. Sandberg, R., Svendsen, W., Molhave, K., Boisen, A.; Temperature and pressure dependence of resonant in multi-layer microcantilevers; Journal of Micromechanics & Microengineering, Vol. 15, 2005

A Miniature MRI-Compatible Fiber-optic Force Sensor Utilizing Fabry-Perot Interferometer Hao Su*§1, Michael Zervas§2, Cosme Furlong2 and Gregory S. Fischer1 1

Automation and Interventional Medicine (AIM) Robotics Laboratory

Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA, USA 2

Center for Holographic Studies and Laser micro-mechaTronics

Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA, USA *Corresponding author: [email protected], (508)-831-5191. §Shared first authorship. ABSTRACT Magnetic resonance imaging provides superior imaging capability because of unmatched soft tissue contrast and inherent three-dimensional visualization. Force sensing in robot-assisted systems is crucial for providing tactile feedback and measuring tissue interaction forces in needle-based percutaneous procedures in MRI. To address the issues imposed by electromagnetic compatibility in the high-field MRI and mechanical constraints due to the confined close-bore space, this paper proposes a miniaturized fiber optic force sensor utilizing Fabry-Perot interferometry. An opto-electromechanical system is designed to experimentally validate the optical model of the sensor and evaluate its sensing capability. Calibration was performed under static and dynamics loading conditions. The experimental results indicate a gage sensitivity on the order of 40 (mV/με) of the sensor and a sensing range of 10 Newton. This sensor achieves high-resolution needle insertion force sensing in a robust and compact configuration in MRI environment.

Keywords: Optical Force Sensor, Fabry-Perot Interferometer, MRI Compatibility, Needle Insertion I.

INTRODUCTION

Magnetic resonance imaging (MRI) is a multi functional imaging modality with unmatched soft tissue contrast that allows for accurate delineation of the pathologic and surrounding normal structures and inherent three-dimensional visualization that permits dynamic imaging plane control and surgical tool tracking. Comparing with ultrasound and computerized tomography, it has an unparalleled potential for guiding, monitoring and controlling therapy in real-time. D'Amico et. al [1] reports that the positive predictive value of transrectal ultrasound-guided needle biopsy is only 18% to diagnose prostate cancer, while MRI-guided prostate brachytherapy and biopsy procedure achieved 100% dose coverage within the prostate without exceeding the maximal allowable doses using a 0.5T open-MRI scanner. In general, MRI allows for interventional surgery in an efficient and high-accuracy manner. Due to intrinsic MRI compatibility, there are significant research efforts on optical force sensing recently. It is immune to electromagnetic signal and resistant to harsh environment. The intensity modulated optical sensor, based on optical micrometry or reflected mirror [2-3], is convenient to design and manufacture. However, it is sensitive to environment change and usually bulky thus impractical for a large range of force sensing to be integrated with surgical tools (e.g. needles, electrodes and catheters). Fiber Bragg Grating (FBG) sensor [4], a wavelength modulated approach, provides an amiable solution with high sensing senility and miniaturization. FBG directly correlate the wavelength of light and the change in the desired strain. If the fiber is strained from applied loads then these gratings will change accordingly and allow a different wavelength to be reflected back from the fiber. Nevertheless, the costly optical source and spectral analysis equipment (usually more than $20K) present formidable application for medical instrumentation. Based on our previous efforts on MRIcompatible piezoelectric actuation and robot design [5-10], the aim of this paper is to design a miniaturized fiber optic force sensor that can be integrated with the robotic systems. This paper investigates Fabry-Perot interference (FPI) fiber optic sensor for several advantages over other fiber optic sensors [11]. First, in contract to intensity modulated techniques, FPI is phase modulated and provides absolute force measurement, independent of light source power variations. Second, because it takes advantage of multimode fiber and minimizes adverse

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effect of thermal and chemical changes. Besides, it can be miniaturized in meso-scale and integrated to surgical tools. In addition to biocompatibility, it is sterilization tolerant with ethylene oxide and autoclave. The operating temperature is −40oC to 250oC. The sensing strain ranges from ±1000 με to ±5000με with resolution1 0.01% of full scale. To our knowledge, the work in this paper is the first investigation of FPI sensors in needle insertion force measurement with a focused application in MRI-guided prostate interventions. This paper is organized as follows: Section II describes the FPI sensing principle of Fabry-Perot interference sensor. Section III presents the design and mechanical modeling of FPI sensor. Opto-mechanical design to implement FPI is presented in Section IV. Sensor calibration and experimental validation is presented in Section V. In Section VI, we conclude with a discussion of FPI sensor and future work.

II.

SENSING PRINCIPLE OF FABRY-PEROT INTERFEROMETER

In a Fabry-Perot strain sensor, light propagates through a cavity containing semi-reflective mirrors. Some light is transmitted and some is reflected. As shown in Fig. 1, the distance between the two fiber tips is generally on the order of nanometers and depends on the gauge length (the active sensing region, defined as the distance between fusion welds). Lcavity is the original cavity length. d is the change in the cavity length from a given load. The returning light interferes resulting in black and white bands known as fringes caused by destructive and constructive interference. The intensity of these fringes varies due to a change in the optical path length related to a change in cavity length when uni-axial force is applied.

   Fig. 1: Light Propagation through FPI Cavity

This phenomenon can be quantified through the summation of two waves [12]. By multiplying the complex conjugate and applying Euler’s identity, we obtain the following equation of reflected intensity at a given power for planar wave fronts: I = A12 + A22 + 2A12A22 cos(f1 - f2 )

[1]

with A1 and A2 representing the amplitude coefficients of the reflected signals. The above equation can be changed to represent only intensities by substituting Ai2 = I i (i = 1,2) and f1 - f2 = Df as I = I 1 + I 2 + 2 I 1I 2 cos(Df)

III.

[2]

MECHANICAL MODELING OF FABRY-PEROT INTERFEROMETER SENSOR

An FPI fiber optic strain sensor (FISO Technologies, Canada) [13] was used to evaluate the systems resolution and potential integration into the robot. As shown in Fig. 2, the main component of the FPI is the sensing cavity, measuring 15.8 mm wide. A glass capillary covering the sensing region is fusion welded to the fiber in two locations and encapsulates the sensor. There is an air gap of approximately 100.5 mm wide. The total length of the FPI sensor, including the glass capillary, and bare fiber is approximately 20mm. Besides immune to electromagnetic and RF signal and substantially cheaper than FBG, the advantages of this sensor includes: 1) static/dynamic response capability, 2) high sensitivity and resolution, 3) no interference due to cable bending and 4) robust to a large range of temperature variation (-40º-250º) due to air gap insulation to the sensing region.

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  Fig. 2: Miniaturized Fabry-Perot Interferometer Strain Sensor (a) Commercially Available FISO Technologies FPI strain sensor (b) Fiber tip under microscope (c) Size perspective of sensor (d) Expanded view of components of FPI strain sensor

Finite element analysis software, ANSYS Workbench [14], was utilized to develop a three-dimensional model of FPI sensor. A CAD model was imported into ANSYS Workbench with the correct constraints, applied force, and material properties just as in the analytical model as seen in Fig. 3 (left). The ANSYS contained a great deal more elements and nodes than the analytical model with 8076 elements and 22,183 nodes. After the complex model was tested and the results were analyzed, comparisons between the analytical and computational calculations were made.

  Fig. 3: (left) ANSYS Computational Model of FPI, and (right) Analytical and Computational Agreement of Linearity of FPI Sensor

As Fig.3 (right) depicts, there is a nearly perfect agreement between the analytical and computational calculations with less than 1% error between them. Since the FPI sensor’s linearity was verified using two different finite element methods, we now had to set out on designing an opto-mechanical setup for use of our FPI sensor.

IV.

OPTO-MECHANICAL DESIGN

The opto-mechanical setup begins with a pigtailed laser diode (PLD) which emits light in the 830nm band of the infrared line with a power of 1mW. This diode is controlled by a laser diode controller (LDC) which has a PID built in which helps stabilize the temperature and current of the diode when attached to laser cooler. The output of the pigtailed laser that exits the FC connector (FC) at the end of the sensor’s fiber is connected to a Z-axis translator (ZT). This Z-axis translator helps focus the divergent light onto a 20× objective lens mounted to an X- Y-axis translator (20XYT). This collimated light is sent into a 50:50 beam splitter cube (BS) where fifty percent of the light is split towards the FPI and the other fifty percent is not used. The light that is sent to the sensor is focused onto the 50μm core of the sensor’s multimode fiber. This focusing is accomplished with the help of another 20× objective lens mounted to an X-Y-axis translator which focuses the light onto the fiber core which is able to adjust via a Z-axis translator which has the FPI fiber’s ST connector (ST) attached to it. The light travels through the fiber and into the sensing cavity and then back reflects out the same optical axis it came in. This back reflected light passes through the 20X objective lens and is collimated into the beam splitter and once through the beam splitter the light is sent into the photodetector (PD). The photodetector’s output is digitized by a 16-bit data acquisition system (DAQ) and a processing computer (PC) is used to calculate the strain values.

134

 

 

Fig. 4: (left) Schematic diagram of the opto-mechanical design to implement FPI sensor and (right) the bench top evaluation system of opto-mechanical design to implement FPI sensor.

V.

FIBER OPTIC FORCE SENSOR CALIBRATION

Calibration was performed by attaching the FPI to a manufactured cantilever beam made of aluminum 6063-T5. Strain on the beam was calculated in terms of the applied force F: exx =

12FLc

[3] bt 3E where L is the length of the beam, c is the distance from the center of the beam along the y-direction, b is the width of the base, t is the thickness, and E is Young’s modulus. In order to calibrate the FPI, the relationship between the intensity of light at the output and the strain was derived. A hanger system was employed at the end of the cantilever beam to statically apply the load in increments of the 5 grams. Each of the weights used were weighted on a calibrated scale. The opto-mechanical setup was used to measure the output light intensity from the FPI and was recorded using the LabView program [15]. Recall in equation 2, the change in phase Df of the intensity equation is equal to the wave number

2p , multiplied by the l

length of the sensing cavity region and the strain in the x -direction:

Df =

2p(exx Lcavity )

[4] l This value for the change in phase was substituted into intensity equation and it is now possible to predict the output intensity of light as a function of the induced strain: 2p(exx Lcavity ) [5] )] l The calibrated system can be seen in the voltage-strain graph shown in Fig. 5. The theoretically predicted relationship is superimposed in the figure. The output voltage follows a sinusoidal pattern that repeats over an increasing applied force. A LabView program is built to count cycles as the interference pattern repeats between a maximum and minimum voltage range, which allows users to accurately determine the applied force. The discrepancy between the measurement and theoretical model is due to the ambient light disturbance to the opto-mechanical prototype which is not shielded during experiment. An optical packaging system with compact structure and light shielding is under development. Depending on the p required resolution, the FPI sensor can be calibrated to remain within a cycle for a maximum applied force of 10 Newton 4 that directly correlates voltage to force and avoids counting cycle. A gage factor of 40mV/με was calculated and when using a 16 bit data acquisition system, the FPI sensor is able to measure a minimum strain value of approximately 6.4 nano strains. I = 2I 0 [1 + cos(

135

Fig. 5: Calibration results showing voltage versus strain of the FPI sensor overlaid with the theoretical model.

VI.

CONCLUSION AND DISCUSSION

A fiber optic force sensor based on Fabry-Perot interferometry is modeled and calibrated. Comparisons between the fiber optic sensor and a typical foil strain gauge proved the FPI was superior in aspects including immunity to electromagnetic waves and resolution. Future testing should be done on this sensor to evaluate its performance and durability in MRI scanner room. The next step of this work will focus on packaging the opto-mechanical system and attain robust and portable interface with the robot controller. The measured needle insertion force can be used to inferred tissue stiffness properties and increase the cancer detection rates.

VII.

REFERENCES:

[1] D’Amico A. V., Cormack R. A. and Tempany C. M., “MRI-guided diagnosis and treatment of prostate cancer”. New England Journal of Medicine, volume 344(10), pp. 776-7, 2001. [2] Polygerinos P., Puangmali P., Schaeffter T., Razavi R., Seneviratne L., and Althoefer K., “Novel miniature MRIcompatible fiber-optic force sensor for cardiac catheterization procedures,” in Robotics and Automation (ICRA), 2010 IEEE International Conference on, pp. 2598–2603, May 2010. [3] Su H. and G. Fischer, “A 3-axis optical force/torque sensor for prostate needle placement in magnetic resonance imaging environments,” 2nd Annual IEEE International Conference on Technologies for Practical Robot Applications, (Boston, MA, USA), pp. 5–9, IEEE, 2009. [4] Park Y.-L., Elayaperumal S., Ryu S., Daniel B., Black R. J., Moslehi B., and Cutkosky M., “MRI-compatible Haptics: Strain sensing for real-time estimation of three dimensional needle deflection in MRI environments,” in International Society for Magnetic Resonance in Medicine (ISMRM), 17th Scientific Meeting and Exhibition, (Honolulu, Hawaii), 2009. [5] Su H. and Fischer G. S., “High-field MRI-Compatible needle placement robots for prostate interventions: pneumatic and piezoelectric approaches,” in Advances in Robotics and Virtual Reality (T. Gulrez and A. Hassanien, eds.), SpringerVerlag, 2011. [6] Huang H., Su H. and, Mills J., “Force Sensing and Control of Robot-Assisted Cell Injection”, eds. T. Gulrez and A. Hassanien, Advances in Robotics and Virtual Reality, Springer-Verlag, 2011 [7] Wang Y., Cole G., Su H., Pilitsis J., and Fischer G., “MRI compatibility evaluation of a piezoelectric actuator system for a neural interventional robot,” in Annual Conference of IEEE Engineering in Medicine and Biology Society, (Minneapolis, MN), pp. 6072–6075, 2009. [8] Cole G., Harrington K., Su H., Camilo A., Pilitsis J., and Fischer G.S., “Closed-Loop Actuated Surgical System Utilizing Real-Time In-Situ MRI Guidance,” in 12th International Symposium on Experimental Robotics - ISER 2010, (New Delhi and Agra, India), Dec 2010. [9] Wang Y., Su H., Harrington K., and Fischer G. S., “Sliding mode Control of piezoelectric valve regulated pneumatic actuator for MRI-compatible robotic intervention,” in ASME Dynamic Systems and Control Conference - DSCC 2010, (Cambridge, MA, USA), 2010. [10] Su H., Camilo A., Cole G., Tempany C.M., Hata N. and Fischer G. S., “ High-Field MRI Compatible Steerable Needle Driver Robot for Percutaneous Prostate Intervention”, Proceedings of MMVR18 (Medicine Meets Virtual Reality), Newport Beach, California, USA, February, 2011

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[11] Lemay J., White F., Zervas M., “Evaluation and Application of a High Resolution Fiber-Optic Strain Sensor”, Major Qualifying Project, Dept. of Mechanical Engineering, Worcester Polytechnic Institute, April. 2010. [12] Gangopadhyay T. K., “Prospects for fiber Bragg gratings and Fabry-Perot interferometers in fiber-optic vibration sensing,” Sensors and Actuators A: Physical, vol. 113, no. 1, pp. 20 – 38, 2004. [13] RocTest Limited, FISO Technologies, Inc., Sensoptic Fiber-Optic Strain Sensors - Fabry-Perot Strain Gage – FOS Series. Quebec, Canada: RocTest, 2000 [14] ANSYS, “ANSYS Academic Teaching Mechanical,” Accessed 15 February 2010 [15] National Instruments. Retrieved April 12, 2010, from www.ni.com

Micromechanical Structure With Stable Linear Positive And Negative Stiffness

Jeffrey P. Baugher1 and Ronald A. Coutu, Jr.2 1

Wright State University, 311 Russ Engineering, 3640 Colonel Glenn Highway, Dayton, OH 45435 2 Air Force Institute of Technology, 2950 Hobson Way, WPAFB, OH 45433

Abstract We introduce a novel micromechanical structure that exhibits two regions of stable linear positive and negative stiffness. Springs, cantilevers, beams and any other geometry that display an increasing return force that is proportional to the displacement can be considered to have a “Hookean” positive spring constant, or stiffness. Less well known is the opposite characteristic of a reducing return force for a given deflection, or negative stiffness. Unfortunately many simple negative stiffness structures demonstrate either unstable buckling which can require extraneous moving constraints during deflection, so as not to deform out of useful shape, or are highly nonlinear such as the disk cone spring. In MEMS, buckling caused by stress at the interface of silicon and thermally grown SiO2 causes tensile and compressive forces that will warp structures if the silicon layer is thin enough. The structure presented here utilizes this effect but overcomes its limitations and empirically demonstrates linearity in both regions. The structure is manufactured using only common micromachining techniques and can be made in situ with other devices. Introduction The correct electrical operation of many MEMS devices can depend on spatial changes between surfaces or even bending of materials which change electrical properties. Small changes in distances can easily be detected through capacitive sensing circuits and flexing of piezoresistive materials can be measured through changes in electrical potential. MEMS inertial sensors are normally blocks of material suspended by tethers from surrounding bulk material [1]. The tether’s thickness, length, shape and material are determined by the desired stiffness for a needed displacement sensitivity (formula 1) and resonant frequency (formula 2).

sd =

f res =

ma k

π 2

(1)

k m

(2)

where a is the acceleration, m is mass and k is stiffness. Since a change in mass has opposite effects on sensitivity and resonance, it will be considered as a constant. As a simple example, the displacement (y) formula for a single fixed end cantilever beam, where the force is applied to the free end, is

Disclaimer: The views expressed in this paper 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.

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_20, © The Society for Experimental Mechanics, Inc. 2011

137

138

y=

FL3 3EI

(3)

F is the applied force, L is the length of the beam, E is the Young’s Modulus of the beam material and I is the moment of inertia. Considering only rectangular structures,

I=

BH 3 12

(4)

B is the width of the cantilever and H is the thickness that is in the axis of the bending moment. Solving for the stiffness k, we arrive at

k=

EBH 3 . 4 L3

(5)

Negative Stiffness Looking through the parameters, it is apparent that for a given material (fixed Young’s Modulus), the standard way to mechanically modify the stiffness is by changing the geometry of the cantilever. This modification could be impractical due to size constraints or have undesirable effects on off axis mechanics and the displacement sensitivity. Another method to decrease the overall effective stiffness is by offsetting it with negative stiffness. Negative structural stiffness is fundamentally a reduction in return force for a given displacement. The mechanical realization of this concept has been used and studied for over 80 years [2]. Many objects which demonstrate this are prestrained, in a post-buckled state, require potential energy through pre-loading [4] and can only produce it non-linearly. Dynamic modeling of these devices are generally constrained to small relative displacements so that linearization can be assumed allowing for easier design. Figure 1 is a simple spring system which demonstrates a typical theoretical load deflection plot (Figure 2) of a negative stiffness system.

Fig. 1 Simple spring system that demonstrates negative stiffness [4]

139

Fig. 2 Typical load deflection plot of negative stiffness system [4] Stiffness, also known as a spring constant, is the slope at any point in the plot. Initially all springs are in a non-loaded state with the upper and lower ends attached to fixed pivots. The center portion is only free to move horizontally. As point a, in Figure 1, is deflected to the left, the springs are compressed, potential energy is added to the system and force increases to the right. This is demonstrated as the linear positive stiffness of k3=10 shown in Figure 2. When the spring forces are in equilibrium around the midpoint, no force is produced right or left, and the system is at the unstable zero point. Any deflection past this point will result in the springs developing force to the right and popping through. The negative stiffness is demonstrated after the inflection point up to the zero point. Other research has concentrated on using active systems to produce a negative stiffness, such as with electrostatic forces. These systems of course require external power, and development of effective controls systems is ongoing [5]. This paper presents some the preliminary results from the modification of a passive system, the buckled oxide membrane. Results A buckled oxide membrane is an axially symmetric dome that resembles the geometry of Figure 1 if rotated around the k2 spring. A Silicon-On-Insulator (SOI) wafer from Ultrasil Corporation was masked with oxide and bulk micromachined through 1mm x 1mm windows into the substrate (handle) using the DRIE process. The wafer device and handle layers were n type <100> monocrystalline silicon of 5 and 400um thicknesses respectively. The 2um buried oxide layer was used as the stop etch for the DRIE process. The oxide had been thermally grown on the device layer before chemical mechanical polishing and bound to the handle layer per Ultrasil. The oxide layer, due to a different coefficient of expansion than the silicon, is under compressive stress and causes a buckled membrane dome of it and the device layer once released from the handle layer via the DRIE process. The produced membrane is on average 15um higher or lower than the surrounding device layer. The membrane is bistable in that it could either be pushed into or out of the substrate and retain its position (Figure 3). A calibrated capacitive force sensor with .4uN resolution was mounted to a piezo-electric actuator with a 20um range (Figure 4). The force sensor was displaced 200nm at 500ms intervals through the substrate into and away from the crown of a pushed in membrane. The load deflection curve shape was typical of other structures with similar geometry (Figure 5), except for the extended zero stiffness region around the inflection point. The plot gives a general idea of the largest returnable deflection that was achievable without pop through.

140

Fig. 3 Image of buckled oxide membrane using Zygo White Light Interferometer

Fig. 4 Calibrated capacitive force sensor mounted to piezo electric actuator

141

Fig. 5 Load deflection plot of pushed in buckled oxide membrane A second set of membranes were manufactured but with thin film metallic layers. Prior to DRIE, a 300Å titanium adhesion layer and 3000Å gold layer were evaporated onto the device layer. This step reduced the height of the domes to approximately 11um but retained bistability. The deflection test was repeated again, with the results shown in Figure 6.

Fig. 6 Load deflection plot of Au-Ti buckled oxide membrane The inflection point is now sharper and the negative stiffness portion has been highly linearized. Curve fitting produces a stiffness of -.39un/nm (-390N/m) over a 4um deflection range in the negative portion (Figure 7).

142

Fig. 7 Linear curve fit of negative stiffness portion Au-Ti buckled oxide membrane

A literature search has turned up one MEMS structure that exhibits similar load deflection characteristics. A centrally clamped bistable silicon mechanism (Figure 8) produced the plot in Figure 9 [6]. Although the structures have many differences, similarities in their operation may provide insights into operation of the membrane.

Fig. 8 The centrally-clamped parallel-beam bistable mechanism, and its deflection and snap through behavior [6]

143

Fig. 9 Load deflection plot of the centrally clamped bistable MEMS mechanism [6] Conclusions Negative stiffness is potentially useful for selectively tuning the spring constant of micro-mechanical beams found in MEMS sensors and actuators. This paper analyzed buckled oxide membranes, fabricated from SOI wafers, as a test structure for realizing stable negative stiffness. Future work will include investigating other MEMS test structures for optimized negative spring constant tuning. Acknowledgements Thanks to Paul Cassity, Rich Johnston, and Rick Patton of the Air Force Institute of Technology for cleanroom support during device fabrication. 1. Maenaka, K. , "MEMS inertial sensors and their applications". INSS 2008, 5th International Conference on Networked Sensing Systems, 2008, pp.71-73, 2008 2. Almen, J.O. and Laszlo, A., "The uniform-section disc spring". Trans ASME , pp. 305–314, 1936 3. Lakes, R.S., T. Lee, A. Bersie, and Y.C. Wang, "Extreme Damping in Composite Materials with Negative-Stiffness Inclusions". Nature, pp. 565-567, 2001 4. Wang, Y. C., Lakes, R. S., "Extreme stiffness systems due to negative stiffness elements ". American Journal of Physics, Volume 72, Issue 1, pp. 40-50, 2004 5. Handtmann, M., Aigner, R., Meckes, A., Wachutka, G. K. M., "Sensitivity enhancement of MEMS inertial sensors using negative springs and active control ". Sensors and Actuators , Vol. 97-98, pp. 153-160, 2002 6. Qiu, J., Lang, J.H., Slocum, A.H.; , "A centrally-clamped parallel-beam bistable MEMS mechanism," The 14th IEEE International Conference on Micro Electro Mechanical Systems, 2001. MEMS 2001., pp.353-356, 2001

Terahertz Metamaterial Structures Fabricated by PolyMUMPs

Elizabeth A. Moore, Derrick Langley and Ronald A. Coutu, Jr. 1

Air Force Institute of Technology, 2950 Hobson Way, Wright Patterson Air Force Base, Ohio 45433

ABSTRACT We present a novel approach for the fabrication of terahertz (THz) metamaterial structures utilizing PolyMUMPs, a foundry process commonly used in the fabrication of microelectricalmechanical systems (MEMS) devices. The structure has an alternating composition consisting of three polysilicon layers and two silicon dioxide layers each with a unique thickness. A split ring resonator (SRR) structure was fabricated with dimensions to support resonance around 5 THz. The structures were arrayed to cover a 1 cm2 area. The backside of the samples was polished to improve the transmission characteristics of the material during Fourier transform spectroscopy measurements. The data indicates a transmission null around 3.7 THz due to the periodic arrangement of the SRR structures. These results are encouraging for future use of PolyMUMPs in terahertz metamaterial designs which is ideal for the repeatability the manufacturing process lends to the design.

Keywords: metamaterial, negative refractive index, fabrication, terahertz

INTRODUCTION Metamaterials are engineered materials designed to exhibit electromagnetic responses that do not occur naturally. A metamaterial is created by patterning materials, typically dielectrics, metals, or semiconductor substrates, in a periodic array of resonators of a particular size depending on the wavelength of the incident radiation. The structured materials are considered an effective medium and are therefore governed by Maxwell’s macroscopic equations and described by their effective electric permittivity and effective magnetic permeability. Tailoring structures to take advantage of the electromagnetic properties of materials enables the possibility of fabricating negative refractive index materials [1-2], the perfect lens [3], and cloaking materials [4].

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.

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_21, © The Society for Experimental Mechanics, Inc. 2011

145

146 Metamaterials are a composite material of a metallic structure (of specific shape and size) immersed on a host medium, usually a dielectric or semiconductor. Metamaterials, operating from radio to terahertz (RF to THz), are generally designed with sub-wavelength resonators, such as split ring resonators (SRRs). Pendry was the first to propose the use of the SRR as a means of creating a negative magnetic permeability [5]. The resonators collectively respond to the incident electromagnetic field altering the behavior of the radiation. The SRR has a fixed narrow resonant frequency based on the dimensions of the SRR capacitive gap and the self-inductance from the metal trace. The material will only exhibit a negative permeability just above resonance [6]. Through scaling of the resonators, metamaterials that function in the near visible and the radio frequency range of the electromagnetic spectrum have been demonstrated. Recently, strides have been made to develop metamaterials in the terahertz (THz) regime since most natural materials do not have a response to THz radiation. The lack of natural materials has created what is known as the THz gap. Metamaterials tailored towards THz frequencies provide a means for developing THz devices, such as filters, modulators, amplifiers, transistors, and resonators [7]. For THz generation, resonator structures need to be fabricated with dimensions on the order of 30 µm. The aforementioned THz gap covers from 100 GHz to 4 THz of the electromagnetic spectrum, which lies just above microwaves and below infrared waves. Developing THz technology has been on the forefront of research as scientist try to close this gap. Thus far, development of THz sources and detectors has resulted in THz imagers, semiconductor characterization, and new methods for chemical and biological sensing [8]. Many THz applications (communications, security, imaging, and chemical and biological sensing) have been identified and are currently being researched [9]. However, there is still a great deal of advancement required to fully exploit this region of the electromagnetic spectrum. These applications would undoubtedly benefit from materials that enhance our ability to manipulate, control, and detect THz radiation. Metamaterials have played an increasingly important role in the development of THz devices [10]. For instance, planar arrays fabricated on various semiconductor and insulator substrates have shown a response to THz radiation both electrically [8, 11] and magnetically [12-13]. Based on current research, metamaterials are ideal candidates for THz devices because they can be scaled and show a resonant frequency response that can be tunable by design. This work focuses on the modeling, design, and fabrication of SRRs fabricated from PolyMUMPs to operate around 5 THz. The PolyMUMPs process is a commonly used foundry process used to fabricate microelectronics [14]. Taking advantage of a foundry process allows for increased reliability and repeatability in the design of the THz structures.

MODEL, DESIGN, AND FABRICATION The design for the SRRs was initially laid out in L-Edit ©, a subset circuit layout editor program of the MEMS Pro software suite, the design is based on MatLab calculations to determine the resonant frequency considering the design parameters. Once the design was complete it was transferred to the PolyMUMPs foundry who then fabricated the devices given our design specifications. The MatLab code was written to aid in choosing the SRR dimensions. The dimensions of the SRR are determined by first deciding on a target resonant frequency. The main two contributing factors to the resonance are the structures inductance and capacitance, as shown in Equation 1

ω0 ≈

1 , LC

(1)

where L in the self inductance from the metal trace and C is the overall capacitance , however since the gap in the SRR is the dominating source of capacitance it is the only capacitance that is considered. The inductance of the trace and the gap capacitance are given by

L = µ0

l2 t

and

C = ε 0ε r

wt g

(2)

where µ0 is the vacuum permeability, l is the length of the side of the SRR, t is the thickness of the material, ε0 is the permittivity of free space, εr is relative permittivity, w is the width of the trace, and g is the gap separation. Note the resonant frequency is not a function of the sample thickness. The parameter having the most affect on the resonant frequency will be

147 the length of the SRR, which has a linear relationship with the resonant frequency. The resonance will be inversely proportional to the gap separation and proportional to the square root of the width of the trace and the relative dielectric constant. While these parameters will still affect the resonant frequency their contributions are minimal compared to altering the size of the SRR. Considerations must be made to ensure the design dimensions do not exceed the qualifications of the effective medium theory. Based on the polysilicon and silicon dioxide material, the dimensions of the single split ring resonators were chosen to support a resonate frequency of approximately 5 THz. A layout of the SRR structures and its dimensions are shown in Figure 1. The SRRs have a square shape with a height and length of 40 µm. The width of the trace is 10 µm on all sides. The capacitive gap opening is 17 µm, such that the length of the trace on either side of the gap is 11.5 µm.

Fig. 1 A schematic of a top down view of a single unit SRR with the dimensions indicated.

The SRR structures were arranged such that there were four to a unit cell as shown in Figure 2. The lattice period is 80 µm. The PolyMUMPs structures were arrayed to cover a 1 cm2 area to make the design large enough for characteization. The resonance frequency for the SRR shown in Figure 1 using the dielectric constant of silicon dioxide (3.9) was calculated to be 5 THz.

Fig. 2 3D diagram of a unit cell of the patterned metamaterial shows the 3 polysilicon and 2 silicon dioxide alternating layers grown on a silicon wafer with a thin silicon nitride buffer layer.

148 The SRRs for this study were fabricated with the PolyMUMPs process which uses polysilicon and silicon dioxide in alternating layers. The polysilicon layers act as a metallic structure and the silicon dioxide layers are used as a dielectric. These materials were chosen due to the high plasma frequency of the polysilicon and the dielectric constant of the silicon dioxide. The PolyMUMPs samples consist of alternating polysilicon and silicon dioxide layers grown on top of a single side polished crystalline silicon wafer with a small nitride buffer layer. At the foundry, the alternating layers are capped with a thin layer of chromium followed by a thin layer of gold. The layout of the material layers along with each layer thickness are shown in Figure 3. The gold and chromium layers were removed with a wet etch prior to the metamaterial testing. A detail review of the PolyMUMPs fabrication process can be found on their website [14].

Fig. 3 A schematic illustrating the layers and their corresponding dimensions used in the PolyMUMPs process.

RESULTS Fourier transform spectroscopy (FTS) was conducted on 3 metamaterial samples and 1 sample with no SRR structures. The transmission was captured by a Fourier transform spectrometer equipped with THz optics at a resolution of 4 cm-1. The measurements were performed in a vacuum at room temperature. The transmission was calculated from the ratio of the reference spectrum and the sample spectrum. Three samples were measured all with identical structures but with varying degrees of surface quality sample 1 having the worst quality while sample 3 has the best. The varying degree of surface quality is a result of the residual gold and chromium that remains on the surface following the wet etch removal. The FTS transmission spectrum for the sample without SRRs, shown in Figure 4, has 0% transmission in the frequency range investigated. This is expected considering silicon dioxide is not transparent in the far IR. The transmission spectra of all three structured samples shown in Figure 5, have an off resonance transmission of about 25 % which drops off at the resonant frequencies. The spectra for all three samples have a small resonance around 3.7 THz due to the LC response of the SRRs where the transmission drops to approximately 15%. Also present in all the spectra is a resonance at 18.4 THz where the transmission decreases to 5% or 10% depending on the sample surface quality. The resonance null deepens as the surface quality of the material improves. The MatLab calculations determined the resonant frequency would be around 5 GHz using a dielectric constant of 3.9 for silicon dioxide. The material stacks also contain a thin layer of silicon nitride which may affect the dielectric properties of the material. Calculating the resonance using a dielectric constant of 7.8 for silicon nitride yields a resonant frequency of 3.5 THz, which is much closer to that measured with FTS. The layered materials and different dielectric constants make it difficult to predict the resonant frequency of the samples. The overall low transmission amplitude is most likely a result of the layered material. Layered materials are known to cause a decrease in the transmission and to broaden the resonance however the resonant frequency remains constant [15]. The weak resonance could also be a result of the substrate used in the fabrication process. The samples are grown on single side polished crystalline silicon. The unpolished backside of the samples resulted in too much scatter for measurements to be obtained. The following transmission spectrum was only obtained after the backside of the samples was polished to a highly reflective surface.

149

40

Reference Sample: No SRRs

35

Transmission (%)

30 25 20 15 10 5 0 -5 -10

4

6

8

10

12

14

16

18

20

Frequency (THz)

Fig. 4 Transmission spectra of the PolyMUMPs material without the SRRs showing zero transmission across the measured frequency range. 40

Sample1 Sample2 Sample3

35

Transmission (%)

30 25 20 15 10 5 0

4

6

8

10

12

14

16

18

20

Frequency (THz)

Fig. 5 Transmission spectra of the PolyMUMPs samples fabricated with SRRs showing a transmission of about 25% and a resonance at 3.7 and 18.4 THz

150

CONCLUSION We demonstrated a quasi three dimensional metamaterial by fabricating SRRs from alternating layers of polysilicon and silicon dioxide. This is the first use of a foundry process, to our knowledge. All the fabricated PolyMUMPs samples show a resonant response around 3.7 THz and another resonance at 18.4 THz. These results show that a polyMUMPs fabrication approach can be used to produce 3D metamaterials with minimal alterations. However, further research needs to be conducted to determine the overall dielectric constant of the material stacks.

ACKNOWLEDGEMENTS The financial support and sponsorship of this project were provided by Drs. Katie Thorp and Augustine Urbas from the Air Force Research Laboratory (AFRL), Material and Manufacturing Directorate.

REFERENCES [1] Smith, D.R., Padilla, W.J., Veir, D.C., Nemet-Nasser S. C., and Schultz, S. “Composite medium with Simultaneous Negative Permeability and Permittivity,” Physics Review Letters 84:4184-41-87, 2000. [2] Shelby, R.A., Smith, D. R., and Shultz S. “Experimental Verification of a Negative Index of Refraction,” Science 292:77-79, 2001. [3] Pendry, J.B. “Negative Refraction Makes a Perfect Lens” Physics Review Letters 85:3966-3969, 2000 [4] Schurig, D., Mock J.J., Justice, B.J., Cummer, S.A., Pendry J.B., Starr A.F., and Smith D.R. “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314:977-980, 2006. [5] Pendry, J.B. “Negative Refraction Makes a Perfect Lens” Physics Review Letters 85:3966-3969, 2000 [6] D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, and S. Schiltz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Physics Review Letters 84 (18): 4184-4187 (2000). [7] Han, Jiaguang, Lakhtakia, Akhlesh, and Qui, Cheng-Wei. “Terahertz Metamaterials with Semiconductor Split-Ring Resonators for Magnetic Tunability,” Optical Society of America 2008. [8] Chen, Hou-Tong, O’Hara, John F., Taylor, Antoinette J., and Averitt, Richard D. “Complementary Planar Terahertz Metamaterials,” Optics Express 15(3), pp 1084-1095, 2007. [9] Peralta, Xomalin G., Smirnova, Evgenya I., Azad, Abil K., Chen, Hou-Tong, Taylor, Antoinette J., Brener, Igal, and O’Hara, John F. “Metamaterials for THz Polarimetric Devices,” Optical Society of America 17(2), pp 773-783, 2009. [10] Tao, Hu, Padilla, Willie J., Zhang, Xin, and Averitt, Richard D. “Recent Progress in Electromagnetic Metamaterial Devices for Terahertz Applications,” IEEE Journal of Selected Topics in Quantum Mechanics, 2010. [11] Azad, A.K., Dai J., and Zhang, W. “Transmission Properties of Terahertz Pulses Through Subwavlength Double Split Ring Resonators,” Optics Letters 31: 634-637, 2006. [12] Yen, T.J., Padilla, W.J., Fang N., Vier, D.C., Smith D.R., Pendry J.B., Basov D.N., and Zhnag X. “Terahertz Magnetic Response from Artificial Materials,” Science 303:1494-1496, 2004. [13] Driscoll, T., Andreev, G.O., Basov, D.N., Palit, S., Ren, T., Mock, J., Cho S.Y., Jockerst N.M., and Smith D.R. “Quantitative Investigation of a Terahertz Artificial Magnetic Resonance Using Oblique Angle Spectroscopy.” Applied Physics Letters 90:092508, 2007. [14] PolyMUMPs process, http://www.memscap.com/en_mumps.html [15] Azad, Abul K, Chen, H.T., Lu, X., Gu, J., Weisse-Bernstein, N.R., Akhodov, E., Taylor, A., Zhang, W., and O’Hara, J.F. “Flexible Quasi-Three-Dimensional Terahertz Electric Metamaterials,” Terahertz Science and Technology 2(1):15-22, 2009.

Investigations Into 1D and 2D Metamaterials at Infrared Wavelengths Jack P. Lombardi III and Ronald A. Coutu, Jr. Air Force Institute of Technology, 2950 Hobson Way WPAFB, OH 45433-7765

Abstract Investigations are made into the characterization of 1D metamaterials consisting of stacks of metal and dielectric. These stacks are modeled and designed to have a permittivity approaching zero. Simulation, fabrication and testing are conducted to verify the design of the layered material. These stacks are fabricated using magnetron sputtering and tested using Fourier Transform Infrared Spectroscopy (FTIR). Comparison between modeled and measured reflection and transmission are used to determine if the fabricated structure is behaving like a homogeneous material. Collected results indicate that a homogeneous structure was structures were formed, one with a possible low permittivity. Introduction Metamaterials are designed materials that can provide tailored material properties that are not found in nature. These materials hold promise for many different applications, from advanced imaging systems that can resolve beyond the diffraction limit to electromagnetic invisibility [3], [5], [12]. These unique properties are derived from the substances used and structure of the fabricated material. The dimensions of these structures are on the order of tens to hundreds of nanometers, so that they are orders of magnitude smaller than the micrometer-long infrared wavelengths they are interacting with, and the overall interaction of the material and the light can be seen as bulk properties, as if it were a homogeneous material [11]. This can be used to create an artificial permittivity, using a layered structure with metals, which can naturally have a negative permittivity when the wavelength of the incident light is shorter than the material’s plasma wavelength, and dielectrics, which have a positive permittivity [3],[4]. By combining these metals and dielectrics in a certain proportion, the positive and negative permittivity can effectively cancel each other out and result in an effective permittivity approaching zero [3]. This type of metamaterial is also commonly known as an epsilon near zero (ENZ) material. another type of metamaterial, a 2D “fishnet” metamaterials, which consist of periodic strips of metal and dielectric, can be used to create materials with a negative index of refraction. Unlike the ENZ materials which used thin layers of materials to create their material properties, these materials derive their properties from a negative permeability, created by resonant magnetic strips, and non-resonant electric strips, which have a negative permittivity from the metal uses in them [3],[1]. When these two pieces, negative permeability and permittivity are combined, a negative index is formed. 1D Metamaterial Design and Modeling For a metal dielectric stack to have a low permittivity, the amount of metal and dielectric for this to occur need to be determined. Since this structure can be thought of as periodic, this can be done by taking one period of the structure, with a thickness, d, and finding the filling fraction, f, fraction of the period thickness taken up by each material, such that f1 + f 2 = 1, (1) where f1 and f2 and are the filling fractions for the dielectric and metal. The thickness of each material layer is then the filling times the period thickness. An illustration of this can be seen in Fig. 1.

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.

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_22, © The Society for Experimental Mechanics, Inc. 2011

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Fig. 1 Example of a 1D metamaterial consisting of a metal dielectric stack d is the period of the material, and is made up of a layer of metal and a layer of dielectric The thickness of each layer is found from the filling fraction, f , multiplied by the period, d Using the filling fractions and the permittivity of the structure can be determined using the Maxwell-Garnett approximation for the effective permittivity[6]

ε eff ≈ f1ε '1 + f 2ε '2

(2)

where εeff is the effective permittivity of one period, with electric field of the incident light parallel to the layer and the light propagating into the structure, ε'1, ε'2 are the real part of the complex permittivity, ε'+iε'', of each layer, and f1, f2 are the filling fractions. If a low, approaching zero, effective permittivity is desired, Equation (2) can be rearranged to form f1ε '1 = − f 2ε '2 , (3) providing everything needed to determine the filling fractions and thickness of each metal or dielectric layer, given the period of the stack and the permittivity of each material [3], [6]. Once the effective permittivity and filling fractions are set, the structure can then be modeled. The approach taken was to model the fabricated structure in two different ways, as either a layered material or as a homogeneous material. Using these treatments, the reflection and transmission for each case would be calculated, and the calculated results compared to the measured reflection and transmission. Comparisons can then be made between the two models and the measured reflection and transmission, and a determination could be made on whether the structure is behaving as a homogeneous or layered material. These two different methods of modeling can be seen in Fig. 2.

Fig. 2 Comparison of structures analyzed as layers (a) and a homogeneous media (b) Note how both structures have the same overall thickness To calculate the reflection and transmission for these models, methods developed for layered media using the Fresnel equations, based on the methods described in [6], and [2]. This method takes into account non-normal incident angles and the TE and TM polarizations as well as the substrate. The model for a homogeneous material uses an effective index, derived from the complex effective permittivity, which is the similar to the effective permittivity described in Equation (2), but with the complex parts of the permittivity included.

neff=

ε eff complex=

f1 (ε1 '+ iε1 ") + f 2 (ε 2 '+ iε 2 ").

(4)

153 Results Structures were then fabricated using a Denton Discovery 18 magnetron sputtering system to deposit thin film of metal and dielectric to create the structures. The metals were deposited using a DC and RF bias for the metals and dielectrics, respectively, without substrate heat. Three unique combinations of materials were used, titanium (Ti)-alumina (Al2O3), titanium-magnesium fluoride (MgF2), and nickel (Ni)-amorphous/poly silicon(Si). These material combinations were chosen based on their index and permittivity of each material, which would allow layers of at least 10nm, and period thicknesses of no larger than 500nm to be used in producing a ENZ in the range of 2.5-8μm. To the best of the authors’ knowledge, ENZ materials have not been attempted with these material combinations. The period, filling fractions, layer thicknesses and deposition parameters can be seen in tables for each fabrication. After fabrication these structures were then tested using a Bomem 157S FTIR, with the reflection and transmission measurements being made at 61.3˚ and . 0˚ angle of incidence, respectively. These results are then plotted with the results from the layered and homogeneous model, where the models used literature values for the indices of the materials. Each combination will be described individually. Titanium-Alumina Table 1shows the settings used for the deposition of materials and filling fractions. A four layer, two period structure is fabricated. A scanning electron micrograph of a cleaved piece this structure can be seen in Fig. 3. Table 1 Sputtering setting and layer parameters for Ti- Al2O3 structure Period: Pre-sputter Deposition Voltage/Power 150nm Voltage/Power Ti 500V 315V Al2O3 200W 200W

Deposition Thickness

Filling Fraction

10nm 140nm

.067 .933

Fig. 3 Micrograph of fabricated Ti- Al2O3 structure This micrographs was taken of a cleaved piece, and shows a cross section of the structure, with two layers of Ti and Al2O3 visible on top of the silicon wafer used as substrate

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This structure as then modeled as a layered and homogeneous material, and the reflection and transmission calculated. For these calculations, published data on the index of refraction of these materials was used, with the numbers coming from Kirillova and Charikov found in [9] and in [10], for Ti and Al2O3, respectively. The index for the crystalline silicon substrate was found using a dispersion relation found in [8]. Additionally, a thin 2nm thick silicon dioxide layer was put into the model above the silicon substrate. This was added to include the thin oxide that forms on a wafer due to exposure to air. The index for this layer came from data published in [10]. Using these numbers, this structure was calculated to give a zero permittivity at 4.45μm. The modeled and measured results are plotted and can be seen in Fig. 4.

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Looking at the collected data, it is seen that the modeled and measured values in both reflection and transmission curves have a similar shape and values. It can also be noted that the models are give results that are close to each other, indicating that the size of the structure in relation to the wavelength is such that homogeneous model is accurate in describing the structure. Another point of interest is the peak that can be seen in the transmission near 3μm. This peak is due to the index of the structure changing and going to a value that is the square root of the substrate, allowing the structure to act as an antireflection coating. This is not directly indicative of an ENZ, however, it does suggest that the structure is behaving as a homogeneous layer, and has a changing index which could have a zero permittivity [6]. Though the modeled and measured results are similar, there still are differences, especially at the longer wavelengths. These differences in the model are the result of differences between the material parameters used in the modeling and the parameters of the deposited materials. These differences in material parameters are not unexpected, as the properties thin films often vary from literature values, and even among different facilities and deposition systems. Titanium-Magnesium Fluoride Table 2 shows the settings used for the deposition of materials and filling fractions. An eight layer, four period structure is fabricated. A scanning electron micrograph of a cleaved piece this structure can be seen in Fig. 5. Table 2 Sputtering setting and layer parameters for Ti-MgF2 structure Period: Pre-sputter Deposition Voltage/Power 167nm Voltage/Power Ti 400V 340V MgF2 200W 200W

Deposition Thickness

Filling Fraction

12nm 155nm

.072 .928

Fig. 5 Micrograph of fabricated Ti-MgF2 structure This micrographs was taken of a cleaved piece, and shows a cross section of the structure, with four layers of Ti and MgF2 visible on top of the silicon wafer used as substrate The modeled reflection and transmission of the structure as layered and homogeneous were then calculated. The values used for the Ti, SiO2 and Si substrate in the Ti- Al2O3 structure were also used here. A dispersion equation for MgF2 found in [8] was used, where an average of the indices for the ordinary and extraordinary axes is used. Using this data, this structure was calculated to give a zero permittivity at 3.66μm. The results from the modeling and measurements are then plotted, and can be seen in Fig. 4. 80

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155 Looking at the above plots, there are a couple things that noted. First, the two modeled results line up very well, with a difference of no more than about 5% between them, indicating that the idea of this material being homogeneous is valid. Comparing the modeled results to the measured data, however, does not show much agreement, as the reflection curves have the same general shape, but values that differ by as much as 40%, and the transmission curve not showing the peak present in the models at 3.75μm, the peak from the structure acting as an antireflection coating. The lack of a peak does not mean that the fabricated structure is not behaving as a homogeneous material, but it does mean that the models, and the materials parameters they are using, are not accurate to the deposited materials. Further work into determining the material properties of the materials would allow for a better modeling and the determination of what is happening in this structure. Nickel-Silicon Table 3 shows the settings used for the deposition of materials and filling fractions. An eight layer, four period structure is fabricated. A scanning electron micrograph of a cleaved piece this structure can be seen in Fig. 7. Table 3 Sputtering setting and layer parameters for Ni-Si structure Period: 100nm Pre-sputter Deposition Voltage/Power Voltage/Power Ni 400V 360V Si 200W 200W

Deposition Thickness

Filling Fraction

11nm 89nm

.11 .89

Fig. 7 Micrograph of Ni-Si structure This micrographs was taken of a cleaved piece, and shows a cross section of the structure, with four layers of Ni and Si visible on top of the silicon wafer used as substrate Note that a thin silicon dioxide layer on top of the wafer is visible in this micrograph The modeling used index data for Ni from Lynch et al and found in [9], while the properties for amorphous Si were found in [10]. The values used for SiO2 and Si substrate in the Ti-Al2O3 structure were also used here. Using these numbers, the structure was calculated to give a zero permittivity at 3.16μm. The results from the modeling and FTIR are plotted, and can be seen in Fig. 8. 7

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Fig. 8 Plots of the measured and modeled reflection and transmission from the Ni-Si structure Theses plots show a comparison between the modeled and measured data for both reflection and transmission The comparison between the two models, and the collected and modeled data for the reflection and transmission shows that the models are not agreeing. The values for the two models are not as close as they were in previous structures, indicating

156 that the structure may not have homogeneous behavior, while the lack of agreement between either model and the measured data is due to the differences between indices of the deposited materials and the literature values. Though there is little correlation between the models and data, an interesting feature can be seen near 5μm in the reflection, where the minimum value is reached. This dip may be caused by the fabricated structure acting homogeneous and becoming an antireflection coating, however, it cannot be determined if this is the case, as there was essentially no transmission through the stack to indicate if this was happening. This lack of transmission is likely due to losses in the materials. 2D Metamaterial Design In addition to investigating 1D metamaterials, patterned fishnet metamaterials capable of producing a negative index were also investigated. This procedure could be used to find the dimensions needed to create a negative index structure at infrared wavelengths. This structure was designed with the thought that it is able to be fabricated with standard photolithographic processes, using masks and techniques such as etch back of deposited layers. A diagram of this structure and, the dimensions needed, can be seen in Fig. 9.

Fig. 9 Illustration of the fishnet metamaterial (a) shows a top view and the electric and magnetic strips, along with the widths of each and the period of the structure, 2w (b) shows a side view with the layers of the structure and their thicknesses, t and d The first step in the design is to pick the materials to be used as the metal and dielectric. A metal that has a negative permittivity at the design wavelength is needed, and one with low losses is desired [3]. A dielectric with a high index and permittivity are desired, as this would helps to keep the electric field between the magnetic strips and helps them to resonate [3]. To meet these requirements, the materials of gold and hafnium oxide are proposed, since Au has a high conductivity, negative permittivity in the infrared, and can easily be etched, and HfO2 due to its high permittivity and index. After materials are the next step is the design of the negative permeability elements was done first, using a relation found in [3] describing the dimensions and material properties needed to have a magnetic resonance occur at a given wavelength. The equation, given below, is

n2   dκ   ε '(λm ) = 1 − d 1 + coth    tκ   2 

(5)

where λm, is the wavelength at which the strips are resonant, ε'(λm) is the real part of the metal permittivity at the resonant frequency, nd is the index of the dielectric spacer, d is the thickness of the dielectric spacer, t is the thickness of the metal, and κ is defined as

157 2

2

 π   2π nd   .   −  w   λm 

= κ

(6)

Using these equations a MATLAB script is written to help determine the width of the resonator. Since it is more difficult to solve the above equations exactly, and the range of values for the sizes and thicknesses are restricted to certain ranges and are not continuous, due to fabrication and mask making restrictions, the MATLAB code was written to compute values for the right hand side of Equation (5), with t, w, and d being incremented. The values for λm, nd, and ε'(λm) are all fixed, based on the wavelength the resonance is desired to occur at. The value of each combination is calculated following the right side of Equation (5), and then subtracted from the value of ε'(λm) and the difference stored. The script then selects and displays the combinations that have the smallest difference, which are the structures that most closely fit the model in Equation (5). If the proposed materials are run with this script, using the permittivity of Au found in [9] and index of HfO2 found in [7], a few different combinations of layer thickness and widths were found for a wavelength of 4.45μm, of which one of the best was w=1.12μm, t=78nm and d=93nm. The width of the electric strips is then chosen to be a width that will not resonate like the magnetic strips, and will not add a lot of loss, so a width thinner than that of the magnetic strips should then be chosen [3]. A width of 1μm is suggested, as this is the smallest dimension able to be produced at AFIT. The period of 2w=2.24μm is also suggested, for both x and y directions to keep the structure periodic. A finite difference, time domain (FDTD) simulation was then run using the Lumerical® FDTD software, using periodic boundary conditions in the x and y directions to simulate this structure as one in an array of many. Two simulations were done, one for each polarization of light with respect to the structure, and averaged to give the response to unpolarized light. A screen shot of the setup used in the simulation can be seen in Fig. 10. Planewave Source and polarization

Au-HfO2 Structure

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Fig. 10 Screen shots showing the layout of the Lumerical simulation, with (a) showing a top view of the structure, and (b) a side view The results of the simulation can be seen in Fig. 11. These results show a peak in adsorption at 3.25μm, which is indicative of a resonance occurring and a possible negative index occurring [3]. % Reflection, Transmission, Absorption

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158 Conclusions and Future Work Investigations into metamaterials at infrared wavelengths using novel material combinations have been made. 1D, ENZ metamaterials were fabricated and tested, with materials shown to exhibit homogeneous, and possibly ENZ behavior. The lack of fit between either the layered or homogeneous model and the collected data from the fabricated structures is due to differences between the optical properties of deposited materials and their descriptions found in literature. This difference is not surprising, as material values for thin films often have a wide variation and differ from lab to lab. A fishnet metamaterial is proposed, and a simulation of the structure, with literature values for the materials, indicates that a resonance in the structure is occurring, and a negative index may be formed at 3.25μm. A few areas exist for future work, one area of which is characterizing the thin films of materials deposited by sputtering, and providing indices of refraction that could be used to allow for more accurate modeling and design of ENZ and fishnet structures. These properties can be found through a few different means, though one of the easiest is through spectroscopic ellipsometry of a single layer of deposited material. Work could also be done in fabricating the proposed fishnet structure using standard lithography and etching holes in the deposited layers to form a fishnet structure that could be tested. Acknowledgements The research would not have been possible without the help of many people. Those included are Dr. Michael Marciniak, and Jason Vap for all their help in modeling and analysis. Thanks also go to Paul Cassity, Rich Johnston, and Rick Patton. 1. Boltasseva A, Shalaev VM (2008) Fabrication of optical negative-index metamaterials: Recent advances and outlook. Metamaterials. doi: DOI: 10.1016/j.metmat.2008.03.004. 2. Born M, Wolf E (2005) Principles of Optics. University Press, Cambridge. 3. Cai W, Shalaev VM (2010) Optical Metamaterials: Fundamentals and Applications. Springer Science+Business Media, LLC, New York. 4. Chettiar UK, Kildishev AV, Cai W, Yuan H, Drachev VP, Shalaev VM (2008) Optical Metamagnetism and Negative Index Metamaterials. 5. Chettiar UK, Kildishev AV, Yuan H, Cai W, Xiao S, Drachev VP, Shalaev VM (2007) Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm. Opt Lett. 6. Karri J, Mickelson AR (2009) Silver dielectric stack with near-zero epsilon at a visible wavelength. Nanotechnology Materials and Devices Conference, 2009 NMDC '09 IEEE. 7. Khoshman JM, Kordesch ME (2006) Optical properties of a-HfO2 thin films. Surface and Coatings Technology. doi: DOI: 10.1016/j.surfcoat.2006.08.074. 8. Klocek P (1991) Handbook of Infrared Optical Materials. Marcel Dekker, New York. 9. Ordal MA, Long LL, Bell RJ, Bell SE, Bell RR, Jr. RWA, Ward CA (1983) Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared. Appl Opt. doi: 10.1364/AO.22.001099. 10. Palik ED (1985) Handbook of Optical Constants of Solids 1, 2. 11. Ramakrishna SA, Grzegorczyk TM (2009) Physics and Applications of Negative Refractive Index Materials. Taylor & Francis Group, LLC, Boca Raton, FL. 12. Wood B (2009) Metamaterials and invisibility. Comptes Rendus Physique. doi: DOI: 10.1016/j.crhy.2009.01.002.

MEMS integrated metamaterials with variable resonance operating at RF frequencies

Derrick Langley, Elizabeth A. Moore, Ronald A. Coutu, Jr., Peter J. Collins Air Force Institute of Technology, 2950 Hobson Way, Bldg 641, Wright-Patterson AFB OH 45433

ABSTRACT Metamaterials are engineered materials with integrated structures designed to produce a resonant response at specific frequencies. The capacitive and inductive properties of metamaterials effect the overall refractive index of the media in which an RF signal propagates by generating a resonant frequency response. Incorporating microelectromechanical systems (MEMS) into the structure adds the ability to tune metamaterials and generate a variable resonance. In this investigation, a resonant response is achieved for the 1 – 4 GHz range with tuning. Employing processing techniques to create microelectronic devices, different metamaterial designs are fabricated on quartz substrates. Using these modifications, a design which provides the ideal shift in resonance is selected to incorporate into future RF systems. This paper reports on the modeling, design, fabrication and testing of various designs of metamaterials incorporated with MEMS. Keywords: Metamaterials, Split Ring Resonator, MEMS

INTRODUCTION Metamaterials ability to induce a negative refractive index at certain frequencies has gained attention within the last decade. The research covers areas of the electromagnetic spectrum from acoustic to optical frequencies. Metamaterial research began with Pendry’s postulation that the split ring resonator (SRR) could be used to create an effective negative permeability [1]. This concept was first verified by Smith et al.[2] and the SRR has since become a staple in metamaterial designs [3-9]. The resonant frequency of the SRR depends on the structure dimensions, material composition, and frequency of the incident radiation. The design of the SRR structure will determine the capacitance and inductance which define the resonant frequency [4]. The permittivity of the host material used to fabricate the SRR will also affect the resonance. However, the resonance and therefore the region in which the structure will exhibit a negative permeability, generally covers a narrow portion of the electromagnetic spectrum. Developing a method to tune the resonant frequency is desirable for extending the range of negative permeability. Through this research, variable resonance of split ring resonators is realized by incorporating microelectromechanical systems (MEMS) cantilever arrays into the SRR design to varying the overall capacitance and inturn adjusting the resonance frequency.

DESIGN Combining the MEMS cantilevers with the baseline SRR offers a unique way to create variable resonance from an otherwise static design. Incorporating MEMS into the SRR structure brings functional mechanical capabilities to the designs at the micro-level which is essential for varying capacitance of the small structures.

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.

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_23, © The Society for Experimental Mechanics, Inc. 2011

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160 A SRR without cantilevers was modeled, fabricated, and tested to verify the design process and use as a reference. The SRR design along with the voltage and ground traces is shown in Figure 1a. The unit cell includes the SRR along with the voltage and ground traces. The traces are also affected by the electromagnetic field which induces low frequency plasma on the traces. The baseline SRR was arranged in a 1 x 4 periodic array for RF testing to establish the base resonant frequency of the modified designs. The RF transmission spectrum is shown in Figure 1b. The spectrum shows a narrow resonance at 2.83 GHz and the transmission drops to zero. The off resonance transmission is 100%. The reference split ring resonator aids in determining the inductance and capacitance parameters inherent to the structural design and material composition that establish the resonant frequency.

Figure 1 (a) Diagram of the baseline SRR with additional traces, and(b) the RF transmission spectrum showing resonance at 2.83 GHz The model of the baseline SRR is used to determine the initial dimensions of the design to create a resonance at the desired frequency. From this design, the requirements necessary to change the capacitance of the structure to smoothly shift the resonant frequency are identified. The analytical model for the resonant frequency is given below,

1

, (1) ( LOuter + LInner ) 2π (COuter + CInner + CLeft _ Trace + CRight _ Trace ) 2 where LOuter is the inductance of the outer resonator ring, LInner is the inductance of the inner resonator ring, COuter is the capacitance for the outer resonator ring, CInner is capacitance of the inner resonator ring, CLeft_Trace is the capacitance for the left trace, CRight_Trace is the capacitance for the right trace. ωres =

Two design options were used to vary the capacitance of the SRRs. The first option incorporates cantilevers in the gap of the SRR that are actuated through electrostatic force and will increase the gap capacitance. The second option utilizes the cantilevers to increase the capacitance between the inner and outer ring by connecting them as the cantilevers are actuated. The first design, shown in Figure 2a, integrates cantilevers into the gaps of both the inner and outer resonator rings. The cantilever array consists of five cantilevers 300 μm wide that vary in length. The length of each cantilever varies by 50 μm to have beam lengths ranging from 300 to 500 μm. Each beam tip extends over the gap to opposite side of the SRR overlapping the SRR by 75 μm. The cantilever is isolated from the SRR by a 0.3 μm layer of silicon nitride. The cantilever has a gap height of 2.0 μm. The actuation pad under each cantilever is shifted to vary the pull-in voltages. The pull-in voltage is calculated with 2z km , (2) Vp = 0 3 1.5C0 where z0 is the initial gap height, km is the material spring constant, and C0 is the capacitance of the cantilever at the initial gap [10]. The dominating parameter for the pull-in voltage is the spring constant km defined as Ewt 3 , (3) km = 4l 3 where E is the Young’s Modulus, w is the cantilever width, t is cantilever thickness, and l is the cantilever length. From Equation (3), it can be seen that the cantilever thickness and length determine the pull-in voltage. The cantilever thickness

161 will be varied to determine the ideal thickness for minimizing the stress in the electroplated layer. The capacitance each cantilever contributes is based on the area that it comes into contact with the SRR. For these cantilevers, the area is 300 x 75 μm. As each beam pulls in, it contributes approximately 0.6 pF to the overall capacitance. The next design modification incorporates cantilevers between the inner and outer resonator rings, as shown in Figure 2b. Four cantilevers make up a set of variable capacitors for the design which is laid out around the resonator rings in four locations. There are two sets of cantilever arrays located on the adjacent sides of the SRR from the gap. For this design, the cantilever arrays consist of 4 beams each 300 μm wide, whose length varies from 350 to 500 μm in 50 μm steps. The beams extend from the inner SRR across the gap to the outer resonator ring, overlapping the outer SRR by 75 μm. The actuation pads are placed between the rings at locations to vary the pull-in voltage. The longest beams on all four arrays should pull-in at the same voltage, thus creating four shifts in the resonant frequency. The third design modification, shown in Figure 2c, places cantilevers in the SRR gaps as well as in between the resonator rings. The cantilever arrays in this design have the same dimensions as those of the first and second design. The overall intention of this design is to increase the range in which the resonance frequency shifts by incorporating more cantilevers for a larger increase in the capacitance. With all the cantilevers at the same length having the same pull-in voltage, the design has a larger shift in resonance per cantilever. Figure 2d is a diagram of the fourth design. In this design, three cantilever arrays consisting of four beams were placed in between the resonator rings. The widths of each cantilever array are varied to change the capacitance area of each array. One set of the cantilevers has a width of 300 μm while the other cantilevers sets are 400 and 500 μm wide. Increasing the area creates a broader change in capacitance than the other designs. Developing the modified structures from the baseline design presented some design challenges. For instance, the actuation pads and interconnects add unnecessary capacitance and inductance which shifts the resonant frequency. To alleviate this problem, the interconnects are scaled to smaller sizes to minimize the additional capacitance and/or mutual inductance. In the modified designs, the metal components are fabricated with gold to improve: conductivity, ease of micro fabrication, and prevent oxidation of the material. A quartz substrate was used as a base for the metal components to increase electrical isolation [10]. All four different designs were fabricated based on the two modification options in order to test the effect of integrating MEMS cantilevers into the SRR structure and determine the configuration that offered the widest tunable range.

Figure 2 Layouts of the four design variations integrated with (a) cantilevers in the gap, (b) cantilevers between rings, (c) cantilevers in the gap and connecting the rings, and (d) cantilevers with varying widths between the rings

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MODELING CoventorWare, a design and simulation suite for all phases of MEMS production, was used to simulate the designs created by Coventor Inc [11]. CoventorWare performs finite element modeling and boundary element modeling to simulate the functionality of the MEM cantilevers used for each SRR design. The CoventorWare Analyzer provides a method to simulate electrical and mechanical response of MEMS. The simulation tests for: capacitance, inductance, temperature, resistance, current density, pull-in voltage, and release voltage of the cantilevers. Using CoventorWare to optimize the design before fabrication saves time and material. All four designs were modeled with CoventorWare at 0 VDC to determine the initial capacitance and inductance of each design so that the starting resonance frequency could be calculated. Figure 3 is a CoventorWare diagram of Design 1 with insets showing the cantilevers up and again with an applied voltage to actuate the longest cantilever. The CoSolveEM Analyzer was used to simulate the capacitance for the design with all the beams in the initial state. The inner and outer ring capacitance is 0.668 and 1.301 pF, respectively. The left and right trace capacitance is 0.269 and 0.518 pF, respectively. The other designs were simulated with CoventorWare at 0VDC obtaining the values given in Table 1. The inductance for the designs is simulated using the MEMHenry Analyzer. Inductance values calculated for the inner and outer resonator ring for Design 1 are 9.295 and 18 nH, respectively. The capacitance and inductance values along with Equation (1) were used to calculate a resonant frequency of 2.06 GHz for Design 1. Table 1 lists the capacitance, inductance, and resonant frequency for all four design layouts.

Figure 3 CoventorWare diagram of Design 1, an SRR with cantilevers in the gap. The insets show the cantilevers in a) the initial state and b) a state with the longest beam pulled-in Table 1 Simulated capacitance and induction parameters of the different designs at 0 VDC; along with the calculated resonant frequency for each design Design 1 2 3 4

LOuter (nH) 18 18 18 18

LInner (nH) 9.295 9.295 9.295 9.295

COuter (pF) 1.301 1.478 1.877 2.53

CInner (pF) 0.668 1.136 1.338 1.947

CLeft_Rod (pF) 0.269 0.271 0.251 0.321

CRight_Rod (pF) 0.518 0.312 0.304 0.277

ωres (GHz) 2.06 1.91 1.76 1.53

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TESTING Device characterization is performed on the SRR array and test devices of cantilevers. Characterization is performed in two phases. Phase one characterization consists of testing the cantilevers for DC voltage response by applying voltage to the actuation pads. The DC testing is conducted with a DC power supply, multimeter, and a Zygo white light interferometer. The Zygo instrument helps to inspect the cantilevers while stepping up the DC voltage on the actuation pads. This method of testing helps determine the pull-in voltages of the design and provides a quick method to inspect the actuation of the cantilevers. By completing the DC testing, the test results can be compared to the simulation and see how well results obtained from the modeling analysis fit for the cantilevers. Figure 4 shows an image obtained with the Zygo instrument while applying 15 VDC to the actuation pads which caused the longest cantilever to pull-in.

Figure 4 Cantilevers from Design 1 with the 500 μm cantilever pulled-in. Image obtained with the Zygo while applying 15 VDC to actuation pads through the DC traces Phase two characterization consists of RF testing on the SRR arrays and test devices. The test devices were used to test how each cantilever set contributes to the change in capacitance. The test devices also serve in process development of the fabrication steps. The SRR arrays were tested using a 4 GHz strip-line and Agilent Programmable Network Analyzer (PNA). Figure 5 shows Design 1 inserted in the strip-line for testing. In order to test the samples, the PNA was calibrated with the 4 GHz strip-line and shorting straps. The calibration ensures the measured RF spectrum from 10 MHz to 4 GHz have low signal noise and reduces any attenuation. After completing the calibration, the samples are inserted in the strip-line and measured at 0 VDC up to the voltage necessary to pull-in all the cantilevers. The measurements are analyzed to determine which SRR design provided the greatest variation of the resonance response.

Figure 5 Experimental setup showing 4 unit cells of Design 1 in the strip-line with the DC wires bonded to the actuation pads. The array is suspended between the inner conductor and outer conductor by Styrofoam.

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RESULTS Each design was thoroughly tested to ensure the functionality of the cantilevers as well as to identify the initial resonant frequency and the shift in the resonance due to the cantilever actuation. The cantilevers on each layout performed in a uniform manner; they actuated one at a time, longest to shortest, and within the calculated range for the pull-in voltage. The RF measurements on the other hand produced varying results for each of the four layouts. The transmission results for Design 1 (cantilevers in the SRR gap region) with an applied voltage of zero to 20 Volts are shown in Figure 6. This layout has an initial resonance at 2.06 GHz, matching the resonance calculated using the capacitance and inductance from the CoventorWare simulations. Applying the DC actuation voltage caused the resonant frequency to shift to lower frequencies as expected. At the applied 20 VDC, the resonance frequency is 1.88 GHz, for an overall shift of 0.18 GHz. The CoventorWare simulations predicted an overall shift of 0.27 GHz for this design. This discrepancy could be due to the lack of uniformity in the cantilevers at pull-in which can cause the SRRs not to produce an identical capacitance.

21

Transmision (S ) - Magnitude

1

0.98

0.96

0.94

0.92 00V 05V 10V 15V 20V

0.9

0.88 1.5

1.6

1.7

1.8

1.9

2

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2.3

2.4

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Frequency (GHz) Figure 6 Transmission results of Design 1 obtained from strip-line measurements Design 2, the cantilevers connecting the inner and outer SRRs, has an initial resonance of 1.92 GHz. This resonance is in good agreement with that calculated with Equation1. Figure 7 shows the transmission spectrum design of Design 2 plotted as a function of the actuation voltage. The sample has a thicker electroplated gold layer which resulted in much higher pull-in voltages to actuate the beams. The applied DC actuation voltage only created a minor shift in the resonance. The simulation predicted a much larger tuning effect from this design. The differences between the measurements and the simulations could be a result of the gap spacing for the cantilevers not being uniform. This would affect the overlap area and gap spacing of the cantilevers and the SRR significantly reducing the added capacitance of each cantilever. The transmission spectra for the third and fourth designs did not have a resonant frequency. Design 3 (cantilevers in both the SRR gaps and inner ring spacing) had a predicted initial resonance of 1.76 GHz based on the simulation. Even though a resonance was not observed, a voltage was applied to actuate cantilevers to look for any type of signal disturbance. Similar to Design 3, the fourth design (cantilevers with varying widths connecting the SRR rings) also did not display an initial resonance at the calculated value of 1.5 GHz, or within the frequency range measured. The transmission was not disturbed nor could any resonance shift be observed as the applied voltage was increased.

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Figure 7 Transmission data measured for Design 2 showing resonance at 1.92 GHz but shifting only 0.04 GHz as the voltage is increased from 0 to 110 VDC. The cantilever thickness was increased to 5.0 μm which increases the pull-in voltage. CONCLUSION The SRR has a static resonant response based on the material composition, geometric layout, and type of propagating signal. Adapting the baseline SRR design with cantilevers provides a method to tune the resonant response by changing the capacitance associated with the SRR. Conducting research on the four designs provided valuable information about the design method, modeling, fabrication and testing of the modified SRRs. From these results, Design 1 is chosen for the fabrication of a bulk array to test the structure within a focused beam system and observe the two dimensional effects of a bulk SRR system integrated with cantilevers. FUTURE WORK Future projects will focus on deeper understanding of the theory used to create variable resonant structures. Modifying structures with materials having various dielectric properties will be a focus of future investigations. And the use of bulk structures to isolate or block structures from propagating RF signals will be a topic of future investigations. Acknowledgements: The financial support and sponsorship of this project were provided by Drs. Katie Thorp and Augustine Urbas from the Air Force Research Laboratory (AFRL), Materials and Manufacturing Directorate. The authors are also thankful to the AFRL, Sensors Directorate for assistance and advice during device fabrication. REFERENCES: [1] Pendry, J. B., Holden, A. J., Stewart, W. J., Youngs, I., “Extremely low frequency plasmons in metallic mesostructures,” Physical Review Letters, Vol. 76, No. 25, pp. 4773-4776, 1996. [2] Smith, D. R., Padilla, W. J., Vier, D. C., Nemat-Nasser, S. C., Schultz, S., “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Physical Review Letters, Vol. 84, No. 18, pp. 4184-4187, 2000. [3] Pendry, J. B., Holden, A. J., Robbins, D. J., and Stewart, W. J., “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Transactions on Microwave Theory and Techniques, Vol. 47, No. 11, pp. 2075-2084, 1999. [4] Ramakrishna, S. A., Grzegorczyk, T. M., Physics and Applications of Negative Refractive Index Materials. Washington: SPIE PRESS, 2009.

166 [5] Liu, R., Ji, C., Mock, J. J., Chin, J. Y., Cui, T. J., Smith, D. R., “Broadband Ground-Plane Cloak,” Science, Vol. 323, pp. 366-369, 2009. [6] Martel, J., Marqués, R., Falcone, F., Baena, J. D., Medina, F., Martín, F., Sorolla, M., “A new LC series element for compact bandpass filter design,” IEEE Microwave and Wireless Components Letters, Vol. 14, No. 5, pp. 210-212, 2004. [7] Hand, T. H., Cummer, S. A., “Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings,” Journal of Applied Physics, Vol. 103, No. 066105, pp. 066105-1 – 066105-3, 2008. [8] Luke, R. A., “A MEMS Multi-Cantilever Variable Capacitor On Metamaterial,” Master’s thesis, Air Force Institute of Technology, 2008. [9] Lundell, C. A., Collins, P. J., Starman, L. A., Coutu, Jr., R. A., “Characterization and testing of adaptive RF metamaterial structure using MEMS,” Proceedings of the 2010 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, paper 461, 2010. [10] Langley, D, Coutu, Jr., R. A., LaVern, S. A., Collins, P. J., “MEMS integrated metamaterial structure having variable resonance for RF applications,” Proceedings of the 2010 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, paper 313, 2010. [11] www.coventor.com/coventorware.html.

Creep measurements in free-standing thin metal film micro-cantilever bending

L.I.J.C.Bergers1,2,3 J.P.M. Hoefnagels1, M.G.D. Geers1 1

Eindhoven Univ. of Technology, Dept. of Mech. Eng., P.O.Box 513, 5600 MB, Eindhoven, NL, 2 Foundation for Fundamental Research on Matter, P.O.Box 3021, 3502 GA Utrecht, NL, 3 Materials innovation institute, P.O.Box 5008, 2600 GA Delft, NL. E-mail: [email protected]

Abstract Creep is a time-dependent deformation mechanism that affects the reliability of metallic MEMS. Examples of metallic MEMS are RF-MEMS capacitors/switches, found in wireless/RF applications. Proper modeling of this mechanism is yet to be achieved, because size-effects that play a role in MEMS are not well understood. To understand this better, a methodology is setup to study creep in Al-Cu alloy thin film micro-cantilevers micro-fabricated in the same MEMS fabrication process as actual RF-MEMS devices. The methodology entails the measurement of time-dependent deflection recovery after maintaining cantilevers at a constant deflection for a prolonged period. Confocal profilometry and a simple mechanical setup with minimal sample handling are applied to control and measure the deformation. Digital image correlation, leveling and kinematics-based averaging algorithms are applied to the measured surface profiles to correct for various errors and improve the precision to yield a precision <7% of the surface roughness. A set of measurements is presented in which alloy microstructure length scales at the micrometer-level are varied to probe the nature of this creep behavior. Introduction The difference between micro- and macro scale creep is generally attributed to the size-effect: the interaction between microstructural length scales and dimensional length scales [1;2]. The physical micro-mechanisms of creep are, however, not nearly understood, let alone implemented in models. In the literature some reports can be found discussing creep and relaxation effects in thin aluminum films [3-8]. However, specifically for free-standing thin films not much research has focused on determining size-effects in time-dependent material behavior [9]. Therefore, there is a clear need for detailed studies into the physical micro-mechanisms underlying the size-effects in creep in metallic MEMS. As a first step towards such studies, the goal of the current work is to apply an experimental mechanical methodology to quantify creep, of μm-sized free-standing cantilever beams for various alloy microstructures, see Figure 1.

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Figure 1: Scanning electron micrograph illustrating the type of cantilever specimens used in the microbeam deflection recovery experiments Methodology Mechanical characterization of this behavior at the micro-scale is not trivial. Recently we developed a suitable methodology [10,11] to measure time-dependent deflections of μm-sized cantilevers (tf= 4.8 μm, w=24 μm, l=115 μm). A fully mechanical deflection-controlling mechanism is designed, a so-called micro-clamp, see figure Figure 2 . Combined with in-situ confocal profilometry, cantilever deflection is precisely controlled and measured. Following a period of prolonged constant deflection, time-dependent deflection recovery is measured once deflected cantilevers are released, see Figure 3. Applying digital image correlation and kinematics-based averaging algorithms to the measured surface profiles corrects for various errors and yields a precision of < 7% of the surface roughness, i.e. precision <3 nm. Further details of the setup and methodology can be found in [10,11]. With this methodology a study is conducted into the effect of the alloy structure length scales on the deflection recovery behavior. Alloy structure variations are achieved by aging as received Al-(1wt%)Cu thin metal films (tf= 4.8 μm) at elevated temperatures, 400 °C, for durations of 2, 4, 6 and 8 hours. Subsequently the specimens are loaded at room temperature to various depths, which correspond to different levels of initial stress. The load is applied during 24 hours, followed by release and measurement of the deflection recovery behavior for another 12 hours, which is observed to be long enough to observe no more change in deflection recovery.

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Figure 2 Schematic of the micro-clamp. A chip with test cantilever structures is placed under the knife edge and positioned with adjustment screws. The micro-clamp is placed under a confocal optical profilometer, which captures the deformation as function of time. The height of the knife edge is controlled by the thumb screw attached to an elastic mechanism: a leaf spring attached to an elastic hinge. The fully mechanical design and appropriate thermal compensation features result in a highly stable setup insensitive to thermal fluctuations

Figure 3 Sequence of a micro-beam deflection recovery experiment. (A) The knife edge controlled by the mechanism approaches the beam. (B) The knife edge deflects the beam to a depth of δloading and holds it there for a certain period of time. (C) The edge is raised, releasing the beam, after which the deflection recovery is measured over time using an optical surface profilometer Results Observations of the tip deflection immediately after release, see Figure 4, and at 12 hours after release, when no change in deflection occurred anymore, see Figure 5, show a remarkable yet clear trend that micro-cantilevers of aged alloys show more permanent deflection than that of the un-aged original material. The amount of permanent deflection is also seen to depend on the aging duration. These observations seem to be in line with precipitation strengthening [8]. An interesting observation is the difference in deflection behavior for the 4 hour-aged specimens and the other aged specimens. The results suggest the applied load needs to surpass a certain level for significant additional deflection to occur: an ‘elastic limit’ might be thought around -1500 nm of applied load. Finally, when considering the difference between tip deflection just after release and after 12 hours, the amount of recovered deflection is larger for aged specimens than for the specimen in original state. However, a more detailed analysis is required to quantify this.

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Figure 4 Deflection of tip as captured directly after releasing the applied load for specimens having undergone various lengths of aging

Figure 5 Permanent deflection of tip as captured after 12 hours after releasing the applied load for specimens having undergone various lengths of aging Conclusion Through fully mechanical microbeam deflection experiments creep recovery measurement on Al(1wt%)Cu-alloy cantilevers were conducted, with variations of the alloy microstructure achieved through aging as received specimens at 400 °C for various durations. Observations of the tip deflection immediately after release and at 12 hours after release, when no change in deflection occurred anymore, leads to the conclusion that the aging affects the instantaneous plastic behavior: depending on the duration a stronger or softer response is observed. More data analysis and experiments are required to further quantify this effect and the effect on the creep recovery behavior. This will be the subject of future work. Acknowledgements This research was carried out under project number M62.2.08SDMP12 in the framework of the Industrial Partnership Program on Size Dependent Material Properties of the Materials innovation institute M2i (www.m2i.nl) and the Foundation of Fundamental Research on Matter (FOM), which is part of the Netherlands Organisation for Scientific Research (NWO). References 1. 2.

Dehm G., et al., "Mechanical size-effects in miniaturized and bulk materials," Adv. Eng. Mater., 8, 11, pp. 1033-1045, 2006. Arzt E., "Size effects in materials due to microstructural and dimensional constraints: A comparative review," Acta

171 Mater., 46, 16, pp. 5611-5626, 1998. Lee H. J., Zhang, P. and Bravman, J. C., "Stress relaxation in free-standing aluminum beams," Thin Solid Films, 476, 1, pp. 118-124, 2005. 4. Kalkman, A. J., Verbruggen, A. H. and Janssen, G. C. A. M., "Young's modulus measurements and grain boundary sliding in free-standing thin metal films," Appl. Phys. Lett., 78, 18, pp. 2673-2675, 2001. 5. Kalkman, A. J., et al., "Transient creep in free-standing thin polycrystalline aluminum films," J. Appl. Phys., 92, 9, pp. 4968-4975, 2002. 6. Hyun S., Brown, W. L. and Vinci, R. P., "Thickness and temperature dependence of stress relaxation in nanoscale aluminum films," Appl. Phys. Lett., 83, 21, pp. 4411-4413, 2003. 7. Modlinski R., et al., "Creep characterization of al alloy thin films for use in mems applications," Microelectron. Eng, 76, 1-4, pp. 272-278, 2004. 8. Modlinski R., et al., "Creep-resistant aluminum alloys for use in MEMS," J. Micromech. Microengineering, 15, 7, p. S165-S170, 2005. 9. Connolley T., McHugh P.E., and Bruzzi M., "A review of deformation and fatigue of metals at small size scales," Fatigue Fract. Eng Mater. Struct., 28, 12, pp. 1119-1152, 2005. 10. Bergers, L.I.J.C., et al., "Measuring time-dependent deformations in metallic MEMS" Microelectron.Reliab.,(submitted), 2011. 11. Bergers, L.I.J.C., et al., “Measuring time-dependent mechanics in metallic MEMS", Proceedings of EuroSimE2010; pp. 1-6, 2010. 3.

MEMS Reliability for Space Applications by Elimination of Potential Failure Modes through Analysis

Rohit Soni S.E.(Mechanical Engineering) Mechanical Engineering Department Nagesh Karajagi Orchid College of Engg & Tech.,Solapur Maharashtra, INDIA

ABSTRACT As the design of Micro-Electro-Mechanical System (MEMS) devices matures and their application extends to critical areas, the issues of reliability and long-term survivability become increasingly important. This paper reviews some general approaches to addressing the reliability and qualification of MEMS devices for space applications. The failure modes associated with different types of MEMS devices that are likely to occur, not only under normal terrestrial operations, but also those that are encountered in the harsh environments of space, will be identified. Keywords: MEMS devices, reliability, qualification, failure mode, analysis, space environments.

1. INTRODUCTION Micro-Electro-Mechanical System (MEMS) devices have successfully been used in terrestrial applications for many years. Light-weight, low-cost, functionally-focused MEMS sensors and actuators promise to revolutionize space exploration in the next millennium. While the potential applications of MEMS are vast, the utilization of MEMS technologies in space missions have been limited thus far due to concerns of reliability and qualification of MEMS devices. Long-term reliability and survivability of MEMS devices for space applications require effective ground demonstration of reliable and robust operation in the hostile environment of space since they cannot be brought back to Earth for service. The establishment of qualification requirements and guidelines has been made difficult in part due to many types of MEMS devices, with different sets of failure modes stemming from different fabrication and construction techniques. Most of the research on MEMS devices in the past couple of decades have focused on developing advanced fabrication techniques and improving their functional performance. It is only in the past few years when MEMS technologies and device performance have advanced sufficiently and the applications have become so critical that researchers have paid more attention to the issues of reliability and long-term survivability. This paper focuses on the identification of the failure modes that can potentially occur in MEMS devices.

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2. FAILURE MODES 2.1. Material Incompatibility: A number of materials are used for the construction of MEMS devices. Even before evaluation of the functional performance of a design, selection of the materials and their compatibility are the first considerations that determine the reliability of the device. MEMS devices often use silicon and other electronic materials as mechanical structures. In addition to single crystal silicon, polycrystalline silicon (polysilicon) of different impurity concentrations and grain structures is another common structural material used for MEMS fabrication. Silicon is a monocrystal, mechanically-strong material that does not show creep or exhaustion and is well-suited for MEMS elements requiring bending. Polysilicon is readily compatible with micromachining processes. Sputtered thin films and traces of various metals, such as aluminum, tungsten, platinum, and gold, are used as electrical conductors and wires. Both silicon dioxide and silicon nitride have traditionally been used for electrical and thermal isolation, masking, and encapsulation. Silica glass is also increasingly being used for this purpose. Other materials used primarily for electrical isolation are aluminum oxide and polyimide. In addition to these structural materials, there has been an increasing interest of the use of amorphous and diamond-like carbon films and diamond structures in MEMS devices. 2.2. Fracture and Fatigue: Fracture occurs when the load on a device is greater than the strength of the material. Fracture is a serious reliability concern, particularly for brittle materials, since it can immediately or would eventually lead to catastrophic failures. Additionally, debris can be formed from fracturing of microstructure, leading to other failure processes. For less brittle materials, repeated loading over a long period of time causes fatigue that would also lead to the breaking and fracturing of the device. In principle, this failure mode is relatively easy to observe and simple to predict. However, the fatigue properties of thin films is often not known, making fatigue predictions error prone. There are several ways to avoid fracture failure from occurring. One approach is to design the device with the maximum applied stress safely below the stress at which failure occurs or use a material that has a material strength far exceed the maximum stress expected. 2.3. Stiction:

Fig.01: Cantilever beams stuck at the free end

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One of the biggest problems in MEMS has been designing structures that can withstand surface interactions. This is due to the fact that, when two polished surfaces come into contact, they tend to adhere to one another.While this fact is often unimportant in macroscopic devices due to their rough surface features and the common use of lubricants.MEMS surfaces are smooth and lubricants create, rather than mitigate, friction. As a result, when two metallic surfaces come into contact, they form strong primary bonds, which joins the surfaces together. This is analogous to grain boundaries within polycrystalline materials, which have been found to be often stronger than the crystal material itself. However, adhesive boundaries are usually not as strong as grain boundaries, due to the fact that actual area of contact is limited by localized surface roughness and the presence of contaminants, such as gas molecules. Adhesion is caused by Van der Waals forces bonding two clean surfaces together. The Van der Waals force is a result of the interaction of instantaneous dipole moments of atoms. In most MEMS devices, surface contact causes failure. When MEMS surfaces come into contact, the Van der Walls force is strong enough to irrevocably bond the two surface. 2.4. Vibration:

Fig.02 (a, b): Cracks in single crystal silicon support beams caused by vibrations from a launch test Vibration is a large reliability concern in MEMS. Due to the sensitivity and fragile nature of many MEMS structures, external vibrations can have disastrous implications. Either through inducing surface adhesion or through fracturing the device support structures, external vibrations can cause catastrophic failure. Long-term vibration will also contribute to fatigue. For space applications, vibration considerations are important, as devices are subjected to large vibrations in the launch process. 2.5. Friction and Wear: Many MEMS devices involve surfaces contacting or rubbing against one and other, leading to friction and wear.The operation of micromachined devices that have contacting joints and bearings is significantly affected by friction and wear of the contact surfaces involved. Friction and wear properties of materials used in the fabrication of contact surfaces must be improved for the long-term reliability and high performance. Adhesive wear occurs when elements in a device rub together causing small pieces to rip off. These pieces attract and stick to each other, particularly in high-humidity environments, resulting in regions where micromachines get jammed up and fail. Adhesive wear was found to be a major contributor to MEMS failures. Abrasive wear is a cutting or material removal of the surface increasing its roughness. Silicon is a widely used material for MEMS fabrication. However, friction and wear properties of silicon may not be adequate for many sliding applications. The mechanical and tribological properties may have to be improved to meet the functional performance and reliability requirements. One method to improve mechanical properties and possibly tribological properties is by ion implantation.

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2.6. Thermal Effects: Temperature changes are a serious concern for MEMS. Internal stresses in devices are extremely temperature dependent. The temperature range in which a device will operate within acceptable parameters is determined by the coefficient of thermal expansion. In devices where the coefficients are poorly matched, there will be a low tolerance for thermal variations. Since future space missions anticipate temperatures in the range of –100 to 150°C, thermal changes are a growing concern in MEMS qualification efforts. Beyond these issues, there are other difficulties caused by temperature fluctuations. Thermal effects cause problems in metal packaging, as the thermal coefficient of expansion of metals can be greater than ten times that of silicon. For these packages, special isolation techniques have to be developed to prevent the package expansion from fracturing the substrate of the device. Another area that has yet to be fully examined is the effect of thermal changes upon the mechanical properties of semiconductors. It has long been known that Young’s modulus is a temperature-dependent value. While it is more or less locally constant for a terrestrial operating range, it may vary significantly for the temperature ranges seen in the aerospace environment. 3. CONCLUSION The acceptance of MEMS devices for space and critical applications depends largely on their reliability. In this paper, the predominant failure modes of MEMS devices operating in different environments have been identified. 4. REFERENCES [1] Kayali.S., Lawton.R. and Stark.B., “Mems Reliability Assurance Activities”, JPL Publication,1998. [2] Merlijn van Spengen.W., “MEMS reliability from a failure mechanisms perspective”, Microelectronics Reliability 43, Pg.1049–1060, 2003. [3] Stark.B.,“MEMS reliability assurance guidelines for space applications”, JPL Publication, Vol.99-1, pg.21-47, 1999. [4] Shea.H., “Reliability of MEMS for space applications”, Proc. of SPIE, Vol.6111 61110A, 2006. [5] Osiander.R. and Ann Garrison Darrin.M.,“Reliability Practices for Design and Application of Space-Based MEMS”, MEMS and Microstructures in Aerospace Applications, Taylor & Francis Group, LLC, pg.327-346, 2006.

Analysis and Evaluation Methods Associated with the Application of Compliant Thermal Interface Materials in Multi-chip Electronic Board Assemblies John Torok, Shawn Canfield, David Edwards and David Olson IBM Corporation 2455 South Road Poughkeepsie, NY 12601 Michael Gaynes and Timothy Chainer IBM T. J. Watson Research Center 1101 Kitchawan Road Yorktown Heights, NY 10598 Abstract: Increased demands on large scale server system packaging density have driven the need for new, more challenging electronic component cooling solutions. One such application required the development of a large form-factor printed circuit board assembly with multiple power transformer devices to be cooled via a common heat spreader. Thermally coupling the multiplicity of devices to the heat spreader was completed using a compliant thermal interface material. Given the mechanical tolerance range, the strain rate dependency of the interface material and the mechanical load limitations of the electronic devices, finite element analysis and empirical evaluation techniques were applied to ensure the anticipated interface gaps were established and that the initial and residual mechanical loading effects were understood. A characterization of the thermal interface material’s mechanical properties was completed for analysis input. Coupling this input with the geometric and stiffness properties of the assembly’s structural elements provided predictions of both the initial as well as the residual mechanical assembly loads. Once completed, experiments using pressure sensitive film and piezoresistive film load cells were completed to correlate with the acquired analytical predictions. Key Words: electronic assembly, thermal interface material, pressure sensitive film, piezo-resistive film Introduction & General Application Description: As high-end computer electrical designs have evolved, so must their cooling solutions. To address this, advanced techniques must be developed to analyze and verify the performance of these cooling solutions, early in the computer’s development. As an example, a new high-end server was recently developed utilizing a large array of voltage transformer modules (VTMs) mounted to a common printed circuit board (PCB). Traditionally, voltage transformation had been previously performed within the power supplies remote to the source of load, but in this case, is performed closer to semiconductor chips, to increase end-to-end power delivery efficiency by reducing the physical distance of the power distribution network (i.e., path lengths of high current flow). In the specific application, an array of 37 VTMs, each measuring approximately 22 mm x 33 mm in size was attached to a PCB that is approximately 380 mm x 760 mm in size. These VTMs dissipate power in use, and need to be sufficiently cooled to maintain proper functionality and reliability. The selected cooling solution employed a thin layer of thermal interface material (TIM) that individually thermally coupled the back of the VTMs to a common, global, heat spreader. The heat spreader was slightly larger than the PCB. The nominal TIM material design thickness was 1.5 mm, but because of assembly tolerances, can vary by approximately +/-0.5 mm. The TIM was carefully selected for its thermal and mechanical properties, which were required to be sufficiently stable to ensure cooling of the VTMs for the life of the product. By our definition, thermal reliability includes the material not breaking down, nor migrating out of the gap between the VTMs and the heat spreader during the life of the product. The compression and separation characteristics of the TIM were also carefully determined and used as the basis for the process placing the TIM between the VTMs and the heat spreader, and then compressing the TIM (in a controlled manner), until the heat spreader was assembled in its final position. In this manner, the TIM was compressed in a means that (1) assured proper VTM-TIM coverage and (2) prevented excessive (damaging) compressive loads imparted to the VTMs. Given the assembly’s complexity, it was anticipated that some assemblies would fail in-line manufacturing testing. In these cases, a cost effective rework solution was required. Once again, understanding the TIM characteristics was critical to ensure the selected TIM would support heat spreader removal without imparting high (damaging) tensile loads on the VTMs or the PCB.

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Early in the design process, finite element (FE) analysis was performed to confirm the viability of the mechanical aspects of the cooling solution. This analysis evaluated the stresses during initial assembly, during the life of the assembly and during rework operations. The primary advantage of this FE analysis was its ability to identify any design concerns prior to initial hardware build. This FE analysis (as well as the TIM selection) relied heavily on experimental mechanical characterization of the TIM. Special fixtures were used to carefully measure the TIM response to compression and separation. These measured characteristics were then used to develop the equations used as inputs to the FE analysis. and reworked, without damaging any of the components. Besides post test destructive analysis, two in situ measurement during the assembly process. Inherently, PSF had the advantage of being readily applied at each module location, but had the disadvantage that it only showed the maximum pressure during a process. In addition, it also did not show when (time at occurrence) that maximum pressure was or if the pressure decayed with time. As such, after learning which module locations load ramped up (during the assembly process), and later decayed. This technique provided an enhanced understanding of the had to rely on the FE analysis. Finite Element Model of the PCB Assembly:

mechanical loading effects were understood.

soldered J-lead connections with a linearized, material modulus. The finite element analysis was setup to proceed in four steps as follows: 1. The heat spreader was brought down to the PCB, compressing the TIM at a specified strain rate 2. The screws securing the heat spreader to the PCB were preloaded to their specified torque level 3. Initial VTM compression forces are recorded (VTM T0 compression loads) 4. TIM allowed to relax for 120 minutes, then compressive forces recorded (VTM residual loads)

(a)

(b)

Figure 1. (a) CAD Geometry of PCB Assembly (Heat Spreader not shown) (b) Assembly Finite Element Model

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TIM VTM Solder PCB

(a) (b) Figure 2. (a) Simplified TIM, VTM and PCB assembly (b) Detailed View of FEM components

Unit Area Thermal Resistance, [C mm2/W]

TIM Material - FEM Inputs: A thermally conductive, pre-cured, silicone gel was characterized and selected for use in this application. The thermal conductivity was measured to be 2.4 +/-0.1 W/mK (Figure 3), however, because of its high viscosity (> 40,000 Poise), wettability at interfaces was poor, adding approximately 300C-mm2/W to unit thermal resistance. For a nominal bond-line of 1.5 mm, this represented an approximate 5 percent increase in the interface’s resistance. Besides acceptable thermal performance, this material also required an inherently low compression mating force as well as administered low tensile separation strength. These were key requirements to protect the functional integrity of the VTMs during heat spreader mating and during rework (i.e., when it is necessary to remove the common heat spreader). TIM characterization was completed in two phases. The first phase focused on acquisition of time zero material properties and processing, while the second phase assessed the long term stability of the material after exposure to a variety environmental stress conditions.

Bond Line, [um] Figure 3. TIM Thermal Conductivity vs. Applied Bond-line Thickness Parallel plate rheometry was used to measure the storage modulus versus temperature. (Figure 4). The room temperature modulus of 70-80 Pa was used in finite element modeling to estimate stresses at critical locations. The storage modulus was also measured during a temperature ramp of 30C/min up to 1500C and it was

determined that there was no significant decrease in flow to warrant using heat during the attachment of the heat spreader.

Figure 4. TIM Storage Modulus vs. Temperature The mating force applied to the heat spreader was limited to 250 kg; determined by assuming a uniform loading of all 37 modules to 90% of the compressive limit. Figure 5 is a plot of the TIM bond line vs. time and mechanical loading. As shown, the ultimate bond lines were not achieved with 250 kg mating force and time alone, but only after engaging the screws and securing to the standoffs were stable bond lines achieved (i.e., 1.2 to 1.7 mm). Given the typical strain rate dependency of the TIM with respect to stiffness during compression, instantaneous loads can be very high when the screws were engaged. Therefore, in order to ensure that the individual compressive loads on individual VTMs remained within the force limits, in situ force measurements were made. This work defined the required screw fastening sequence and rate to keep the instantaneous loading on any single VTM within the safe region.

Figure 5. Bond Line Measurement During Assembly vs. Time

181 Next, tensile adhesion testing was conducted on bonded samples of single components and aluminum plates. The tensile stress to separate the aluminum plate was consistently less than 0.04 MPa, which is below the upper limit rating of 0.05 MPa for the component. In addition, two cells of adhesion samples were exposed to 1000 hours of 1250C and 675 hours of 500C/80% RH, respectively. Again, tensile stress to separate remained stable at less than 0.04 MPa, thus assuring that the heat spreader could be removed without damage to components even after long periods of time under operational conditions. Given the above TIM stiffness properties, a piece-wise, multi-linear material model was used to approximate the modulus of the TIM. Force versus deflection data, for a variety of strain rates, was obtained from INSTRON® material tests on a sample that was of similar dimension to the actual application. A different material model was used as input to the FEM for each actuation strain rate case. To model the TIM’s force decay rate, seen in the INSTRON® tests, a pseudo-thermal contraction was enforced. This was accomplished by creating an artificial coefficient-of-thermal expansion for the TIM, which when combined with a small decrease in temperature, enforced only on the TIM, matched the Force vs. Time INSTRON® data (Figure 6). Force (lb) 24

T636 Peak 23.3 lbs

22 20 18 16

T636 Peak 13.0 lbs

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ptl08 094653-1hold 1 ptl08 094653-2 hold 1 ptl08 094653-1hold 2

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-2

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Figure 6. Force Decay Rate of TIM vs. Time at Different Applied Rates of Strain

Finite Element Analysis Results: The finite element model was subjected to a three separate total assembly times: 5 sec., 30 sec. and 120 seconds. The VTM loads at each site were recorded at T0 and at 120 minutes after assembly, to examine the initial and residual compressive loads on the VTM’s. Figure 7 shows the VTM site numbering scheme. Figure 8 and Figure 9 show a comparison of the VTM loads per site for the T0 and 120 minute assembly times, respectively. The results in Figure 8 show that slower actuation time reduces peak compression loading. The final actuation time was selected to provide the necessary VTM mechanical loading safety margin, while optimizing manufacturing throughput. In addition, examining the residual VTM loads showed that none of the sites resulted in a tensile force on the TIM material (a key indicator for interface reliability).

Figure 7. VTM Site Numbering

Figure 8. Initial VTM Compressive Loads

Figure 9. Residual VTM Compressive Loads Empirical evaluation techniques: Experiments were performed on prototype hardware to characterize detailed part dimensions, assembly tolerances and assembly forces. With regards to part characterization, investigations included non-contact laser scanning measurements of part details and assemblies, part flatness measurements during

183 subassembly construction, TIM gap measurements, PCB board strain measured through assembly operations, each completed during global heat spreader attachment. In addition, during this assembly assessment the applied forces on VTMs were measured. The heat spreader characterization was completed using a laser based scanning system. Analysis software was used to compare laser scanning data to the 3D model. Figure 10 shows a sample measurement on an initial prototype heat spreader demonstrating about 1.9 mm flatness variance across the entire surface. In practice, this part will bend during assembly to conform to the PCB assembly (i.e., stiffener to board, with mounted VTM components).

Figure 10. Heat Spreader Flatness (sample) Implemented as a design feature, the heat spreader incorporated fixed stand-offs (i.e., limited travel screw attach points) to establish the required TIM gaps. The stand-off dimensional height tolerance to individual pockets where TIM is applied is closely held during final machining of the heat spreader. These stand-offs make contact to the PCB surface when assembled. The PCB is also attached to a larger stiffener. Flatness data and VTM component height date were collected on six PCB subassemblies with the VTM component height being demonstrated to be within established tolerance limits. Following the aforementioned characterization, an effort was completed to understand the gap variation, a parameter critical for control of heat transfer (thermal resistance), forces exerted on VTMs through TIM

184 during assembly and volume of TIM to dispense during manufacturing. Several methods were employed and compared to characterize the gap. One method used putty assembled into the gap which was subsequently measured upon disassembly by laser scanning. The method, shown in Figure 11, is a side view of planes formed by the component and putty surface. As shown in Figure 12, the data gathered for various VTM sites indicate gaps for this set of initial parts that were on the low end of designed tolerance allowance and therefore provided an ideal worst case test vehicle for measurement of forces during assembly. Note, a capacitive bond line testing technique was also employed to quantify these gaps thereby correlating the putty gap measurements [2].

Figure 11. Putty Gap Laser Scan (sample)

Heat Spreader to VTM gap Metron measurements using putty in gap 2.2

Gap (mm)

2

Gap Nominal Upper Tol Lower Tol Min Max

1.8 1.6 1.4 1.2 1

ge Av er a

VT M

0 VT 1 M 0 VT 3 M 0 VT 4 M 0 VT 5 M 0 VT 6 M 1 VT 3 M 2 VT 7 M 3 VT 4 M 3 VT 5 M 3 VT 6 M 37

0.8

VTM location

Figure 12. VTM TIM Gap Measurement vs. Design Specification With the gap understood, two techniques were used to quantify the mechanical loads imparted to the VTMs. The first technique employed a pressure sensitive film [3]. Given the range of expected loads, this work was completed using the Extreme Low film (7.2-28 psi usage range). As required, two sheets were cut to size and deployed at each VTM site and stand-off locations. The two-sheet type of pressure sensitive film is composed of two polyester bases, one being coated with a layer of micro-encapsulated color forming material and the other containing a layer of the color-developing material. Figure 13 shows sample results of the PSF study. The deeper coloration represents areas of higher pressure (therefore force) and the color variation from VTM site to VTM site represents the load variation across the assembly. These results were compared to a known load vs. coloration calibration study and yielded reasonable correlation to the predicted loads indicated in Figure 8.

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Figure 13. Pressure Sensitive Film Study (sample) In order to fully understand both the dynamic load magnitude and load distribution during assembly, a force sensor employing pressure sensitive ink was used [4]. The sensor in this case is created on two films with pressure sensitive ink artwork forming a matrix of sensor elements. Each element is sampled and recorded. Note, pressure sensitive ink sensors need to be carefully calibrated for use with selected substrates (i.e., using a material’s test load frame and small capacity load cell). Specific to this application, the sensors were calibrated using a discrete VTM and dispensed TIM under various compression rates (i.e., TIM strain rates). Once calibrated, theses sensors were mounted in-situ to monitor forces during heat spreader assembly. Note, care was taken to ensure sensors did not block free flow of TIM paste as this would result in high hydrostatic pressures where the paste is dammed. During loading, the sensor element sums the data acquired for a given area of interest and plotted in time (Figure 14). As shown, a peak force of about six (6) pounds was observed on the VTM, with this force quickly decaying to two (2) pounds in approximately two (2) minutes. Correspondingly, a colorized pressure contour map of individual sensor elements shows areas of higher pressure on the VTM at the time of peak loading. As shown in Figure 15, a band of highest pressure (14 psi) is represented by the deep orange color, a band of green represents a pressure of 7 psi while the average load is shown in the upper right corner (i.e., six lb).

Figure 14. Individual VTM Site; Applied Force vs. Time

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Figure 15. I-Scan® Colorized Pressure Map Expanding beyond the single site noted above, Figure 16 depicts an example of four individual VTM sites being simultaneously mapped. In each case, peak and residual loads are recorded. These, again, correlated well with the predicted results noted in Figure 8.

Figure 16. Multi-VTM Site; Applied Force vs. Time

187 Summary and Conclusions: A new cooling solution for a new high-end, energy-efficient server has been developed and verified. In early conceptual phases of the design, detailed material characterization of candidate TIMs was performed and response models developed. The material characteristics were a critical input to FEM analysis to verify the design point and to start to develop manufacturing tooling and assembly processes. Later in the development process, prototype hardware was used with PSF and pressure sensitive ink sensors to verify the design, the material response and the assembly process on form factor hardware. The combination of these early analysis techniques was the development of an aggressive cooling solution without delaying the product introduction. Acknowledgements: The authors would like to thank Edward Yarmchuk retired member of the IBM Research team for his support with the development and execution of the CBLT test methodology and Robert Walsh and Ronald Spolverino of the IBM System and Technology Group for their assistance in data acquisition and analysis of the TIM gap and VTM loading measurements. References: [1] ANSYS v12.1, ANSYS, Inc., Canonsburg, Pa [2] Using In Situ Capacitive Measurements to Monitor the Stability of Thermal Interface Materials in Complex PCB Assemblies, M. Gaynes et al, IMAPS Conference 2010, 43rd International Symposium on Microelectronics, pg 450-57. [3] Fujifilm Pressure Sensitive Film, Prescale Features; http://www.fujifilm.com/products/prescale/prescalefilm/features/ [4]Tekscan, Inc., I-Scan System®, http://www.tekscan.com/pressure-distribution-measurement-system

Hierarchical Reliability Model for Life Prediction of Actively Cooled LED-Based Luminaire Bong-Min Song†, Bongtae Han and Avram Bar-Cohen Mechanical Engineering Department, University of Maryland College Park, MD 20742 Rajdeep Sharma1 and Mehmet Arik2 1 Lifing Technologies Laboratory 2 Thermal Systems Laboratory GE Global Research Center Niskayuna, NY 12309 The interest in light-emitting diodes (LEDs) for illumination applications has been increasing continuously over the last decade due to two key attributes of long lifetime and low energy consumption compared to the conventional incandescent light and compact fluorescent light. Although LEDs are attractive for lighting applications due to the aforementioned advantages, unique technical challenges, such as the extreme sensitivity of luminous output and useful lifetime to LED junction temperature, need to be overcome for their large-scale commercialization. Among various types of lamps recess downlights are the most common luminaire type in new residential construction. Several LED-based luminaires incorporating more than a single LED chip have been developed to provide the required luminous flux of recess downlight while offering the advantage of higher luminaire efficacy (i.e., higher light output using the same power or lower power consumption for the same light output) over conventional luminaires [1]. Although increasing the number of LEDs in recess downlight results in higher luminous flux (higher total lumens), the overall cost of the final luminaire also increases because of the high cost of LEDs. More importantly the luminaire efficacy remains the same for the same level of drive current. In practice it will be most likely reduced due to the possibly higher junction temperature. There are two approaches for achieving higher luminous efficacy. An ideal and long-term solution is improvement of the internal and external quantum efficiency of LED chips. An alternative approach relies on lowering the LED junction temperature by utilizing advanced cooling techniques. Indeed, the latter approach has resulted in the development of several cooling solutions for LEDs to enhance the luminaire efficacy of LED-based recess downlights. Passive cooling solutions have been implemented for several LED-based recess downlights. Due to the limited cooling capacity offered by passive cooling, the maximum total lumen is limited to approximately 600 lumens with the highest luminaire efficacy of about 54 lm/W. In order to be accepted more widely for general illumination, the LED-based luminaires should reach face lumens of 1200-1500 lm with luminaire efficacy higher than 60 lm/W at acceptable cost while maintaining reliability [2]. These requirements necessitate development of active cooling solutions. The basic requirements of active cooling solutions for the recess downlight are cost and reliability. The cooling solutions have to be innovative to satisfy the specific requirements, including (1) low power consumption (the power

†

Participant in the University of Maryland/Pusan National University Joint Doctoral Program

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consumed by cooling solutions reduces the luminaire efficacy); (2) low cost (LED chips are expensive and any substantial extra cost is not desired), (3) compact size (the recess downlight has a limited enclosure) and (4) excellent reliability (reliability of the cooling solution should be at least as good as that of LEDs). After selecting a suitable active cooling solution, the optimum design of LED-based recess downlights with either passive or active cooling is the use of minimum number of LED chips with an appropriate level of forward current, which meets the requirements of light output, cost and the lifetime (typically time for 70% lumen maintenance). Unlike luminaires with a passive cooling solution, however, the reliability of the luminaire with an active cooling device is dependent not only on the junction temperature but also on the reliability of the cooling method. This study suggest a novel, hierarchical physics-of-failure (PoF) based reliability model that can be used to assess the reliability of an actively cooled luminaire. The salient considerations for the design of the active cooling solution are offered first, followed by the discussion of the proposed reliability model. The model is implemented to predict the lifetime of a LED-based recess downlight with synthetic jet cooling. The effects of the time-dependent performance degradation mechanisms of the active cooling device on the lifetime of the luminaire are also discussed. ACKNOWLEDGEMENTS Authors would like to acknowledge General Electric for providing partial support for this research. This work was partially supported by the U.S. Department of Energy through contract# DEFC26-08NT01579. This work was also partially supported by the University of Maryland/Pusan National University Joint Doctoral Program funded in part by the BK21 Program in Korea.

RRFERENCES [1] [2]

Residential Recessed Downlights, in Energy Efficiency and Renewable Energy, LED Application Series, U.S. Department of Energy, 2008. M. Arik and S. Weaver, "Effect of chip and bonding defects on the junction temperatures of highbrightness light-emitting diodes," Optical Engineering 44(11), 111305-8 (2005).

Direct Determination of Interfacial Traction-Separation Relations in Chip-Package Systems Shravan Gowrishankar, Haixia Mei, Kenneth M. Liechti and Rui Huang Center for Mechanics of Solids, Structures, and Materials Aerospace Engineering and Engineering Mechanics The University of Texas at Austin 210 East 24th Street 1 University Station Austin, TX 78712-0235 [email protected]

ABSTRACT Microelectronic devices are multilayered structures with many different interfaces. Their mechanical reliability is of utmost importance when considering the implementation of new materials. The cohesive interface modeling approach has the capability of modeling crack nucleation and growth, provided interfacial parameters such as strength and toughness of the system are available. These parameters are obtained through the extraction of traction-separation relations, through indirect either hybrid numerical/experimental methods or direct experimental methods. The direct method promises to determine the parameters in an unambiguous manner. All methods of extracting traction-separation relations require some local feature of the crack-tip region to be measured. The focus in this work is on the use of the crack opening displacements measured using infrared crack opening interferometry (IR-COI), which are analyzed and incorporated into the cohesive interface modeling approach. A series of mode-I experiments that were performed on laminated silicon/epoxy/silicon interface specimens are described where crack growth and normal crack opening displacements (NCOD) were measured. Global measurements of load/displacement provide the J-integral as a function of the NCOD at the end of the cohesive zone. The path independence of the J-integral then allows the cohesive traction-separation relation for the interface to be extracted by differentiation. Results are compared with analytical and numerical models.

T. Proulx (ed.), MEMS and Nanotechnology, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series 999999, DOI 10.1007/978-1-4614-0210-7_28, © The Society for Experimental Mechanics, Inc. 2011

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