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Research Papers

A Viscoelastic Model for the Rate Effect in Transfer Printing

[+] Author and Article Information
H. Cheng

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208;
Department of Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60208

M. Li, Z. Kang

State Key Laboratory of Structural Analysis for Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China

J. Wu

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China
e-mail: wujian@tsinghua.edu.cn

A. Carlson

Department of Materials Science and Engineering,
University of Illinois,
Urbana, Il 61801;
Materials Research Laboratory,
University of Illinois,
Urbana, Il 61801; and
Beckman Institute,
University of Illinois,
Urbana, Il 61801

S. Kim

Department of Mechanical Science and Engineering,
University of Illinois,
Urbana, IL 61801

Y. Huang

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208;
Department of Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60208

K.-C. Hwang

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China

J. A. Rogers

Department of Materials Science and Engineering,
University of Illinois, Urbana, Il 61801;
Materials Research Laboratory,
University of Illinois,
Urbana, Il 61801; and
Beckman Institute,
University of Illinois,
Urbana, Il 61801
e-mail: jrogers@illinois.edu

1H.C. and M.L. contributed equally to this work.

2Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received August 4, 2012; final manuscript received October 13, 2012; accepted manuscript posted May 16, 2013; published online May 16, 2013. Assoc. Editor: Huajian Gao.

J. Appl. Mech 80(4), 041019 (May 16, 2013) (5 pages) Paper No: JAM-12-1369; doi: 10.1115/1.4007851 History: Received August 04, 2012; Revised October 13, 2012; Accepted May 16, 2013

Transfer printing is a volatile tool to retract micro devices from a donor substrate via elastomeric stamps, from which the devices are grown or fabricated, followed by printing to a receiver substrate where the device is assembled to an array for integration in various applications. Among the five approaches of transfer printing summarized in the paper, the viscoelastic property of stamps is widely adopted to modulate the interfacial adhesion between the stamp and devices by applying different pulling speeds. A viscoelastic model for transfer printing is analytically established. It shows that the interfacial adhesion increases with pulling speed, which is verified by the experiments and numerical simulations.

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References

Meitl, M. A., Zhu, Z. T., Kumar, V., Lee, K. J., Feng, X., Huang, Y. Y., Adesida, I., Nuzzo, R. G., and Rogers, J. A., 2006, “Transfer Printing by Kinetic Control of Adhesion to an Elastomeric Stamp,” Nature Mater., 5(1), pp. 33–38. [CrossRef]
Feng, X., Meitl, M. A., Bowen, A. M., Huang, Y., Nuzzo, R. G., and Rogers, J. A., 2007, “Competing Fracture in Kinetically Controlled Transfer Printing,” Langmuir, 23, pp. 12555–12560. [CrossRef] [PubMed]
Kim, S., Carlson, A., Cheng, H., Lee, S., Park, J.-K., Huang, Y., and Rogers, J. A., 2012, “Enhanced Adhesion With Pedestal—Shaped Elastomeric Stamps for Transfer Printing,” Appl.Phys. Lett., 100(17), p. 171909. [CrossRef]
Kim, S., Wu, J. A., Carlson, A., Jin, S. H., Kovalsky, A., Glass, P., Liu, Z. J., Ahmed, N., Elgan, S. L., Chen, W. Q., Ferreira, P. M., Sitti, M., Huang, Y. G., and Rogers, J. A., 2010, “Microstructured Elastomeric Surfaces With Reversible Adhesion and Examples of Their Use in Deterministic Assembly by Transfer Printing,” Proc. Natl. Acad. Sci. U.S.A., 107(40), pp. 17095–17100. [CrossRef] [PubMed]
Yang, S. Y., Carlson, A., Cheng, H., Yu, Q., Ahmed, N., Wu, J., Kim, S., Sitti, M., Ferreira, P. M., Huang, Y., and Rogers, J. A., 2012, “Elastomer Surfaces With Directionally Dependent Adhesion Strength and Their Use in Transfer Printing With Continuous Roll-to-Roll Applications,” Adv. Mater., 24(16), pp. 2117–2222. [CrossRef] [PubMed]
Wu, J., Kim, S., Chen, W., Carlson, A., Hwang, K.-C., Huang, Y., and Rogers, J. A., 2011, “Mechanics of Reversible Adhesion,” Soft Matter, 7(18), pp. 8657–8662. [CrossRef]
Carlson, A., Kim-Lee, H.-J., Wu, J., Elvikis, P., Cheng, H., Kovalsky, A., Elgan, S., Yu, Q., Ferreira, P. M., Huang, Y., Turner, K. T., and Rogers, J. A., 2011, “Shear-Enhanced Adhesiveless Transfer Printing for Use in Deterministic Materials Assembly,” Appl. Phys. Lett., 98(26), p. 264104. [CrossRef]
Cheng, H., Wu, J., Yu, Q., Kim-Lee, H.-J., Carlson, A., Turner, K. T., Hwang, K.-C., Huang, Y., and Rogers, J. A., 2012, “An Analytical Model for Shear-Enhanced Adhesiveless Transfer Printing,” Mech. Res. Commun., 43, pp. 46–49. [CrossRef]
Kim, T. H., Carlson, A., Ahn, J. H., Won, S. M., Wang, S. D., Huang, Y. G., and Rogers, J. A., 2009, “Kinetically Controlled, Adhesiveless Transfer Printing Using Microstructured Stamps,” Appl. Phys. Lett., 94(11), p. 113502. [CrossRef]
Childs, W. R., and Nuzzo, R. G., 2002, “Decal Transfer Microlithography: A New Soft-Lithographic Patterning Method,” J. Am. Chem. Soc., 124(45), pp. 13583–13596. [CrossRef] [PubMed]
Childs, W. R., and Nuzzo, R. G., 2004, “Patterning of Thin-Film Microstructures on Non-Planar Substrate Surfaces Using Decal Transfer Lithography,” Adv. Mater., 16(15), pp. 1323–1327. [CrossRef]
Childs, W. R., Motala, M. J., Lee, K. J., and Nuzzo, R. G., 2005, “Masterless Soft Lithography: Patterning UV/Ozone-Induced Adhesion on Poly(Dimethylsiloxane) Surfaces,” Langmuir, 21(22), pp. 10096–10105. [CrossRef] [PubMed]
Childs, W. R., and Nuzzo, R. G., 2005, “Large-Area Patterning of Coinage-Metal Thin Films Using Decal Transfer Lithography,” Langmuir, 21(1), pp. 195–202. [CrossRef] [PubMed]
Hines, D. R., Mezhenny, S., Breban, M., Williams, E. D., Ballarotto, V. W., Esen, G., Southard, A., and Fuhrer, M. S., 2005, “Nanotransfer Printing of Organic and Carbon Nanotube Thin-Film Transistors on Plastic Substrates,” Appl. Phys. Lett., 86(16), p. 163101. [CrossRef]
Saeidpourazar, R., Li, R., Li, Y. H., Sangid, M. D., Lu, C. F., Huang, Y., Rogers, J. A., and Ferreira, P. M., 2012, “Laser-Driven Micro Transfer Placement of Prefabricated Microstructures,” J. Microelectromech. Syst., 21(5), pp. 1049–1058. [CrossRef]
Li, R., Li, Y., Lü, C., Song, J., Saeidpourazar, R., Fang, B., Zhong, Y., Ferreira, P. M., Rogers, J. A., and Huang, Y., 2012, “Thermo-Mechanical Modeling of Laser-Driven Non-Contact Transfer Printing: Two-Dimensional Analysis,” Soft Matter, 8, pp. 3122–3127. [CrossRef]
Suh, D., Choi, S. J., and Lee, H. H., 2005, “Rigiflex Lithography for Nanostructure Transfer,” Adv. Mater., 17(12), pp. 1554–1560. [CrossRef]
Yang, W., Yang, H., Qin, G., Ma, Z., Berggren, J., Hammar, M., Soref, R., and Zhou, W., 2010, “Large-Area INP-Based Crystalline Nanomembrane Flexible Photodetectors,” Appl.Phys. Lett., 96(12), p. 121107. [CrossRef]
Varenberg, M., and Gorb, S., 2007, “Shearing of Fibrillar Adhesive Microstructure: Friction and Shear-Related Change in Pull-Off Force,” J. R. Soc. Interfaces, 4, p. 721. [CrossRef]
Aksak, B., Murphy, M. P., and Sitti, M., 2008, “Gecko Inspired Micro-Fibrillar Adhesives for Wall Climbing Robots on Micro/Nanoscale Rough Surfaces,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA2008), Pasadena, CA, May 19–23. [CrossRef]
Jeong, H. E., Lee, J.-K., Kim, H. N., Moon, S. H., and Suh, K. Y., 2009, “A Nontransferring Dry Adhesive With Hierarchical Polymer Nanohairs,” Proc. Natl. Acad. Sci. U.S.A., 106(14), pp. 5639–5644. [CrossRef] [PubMed]
Murphy, M., Aksak, B., and Sitti, M., 2009, “Gecko Inspired Directional and Controllable Adhesion,” Small, 5, p. 170. [CrossRef] [PubMed]
Kramer, R. K., Majidi, C., and Wood, R. J., 2010, “Shear-Mode Contact Splitting for a Microtextured Elastomer Film,” Adv. Mater., 22, p. 3700. [CrossRef] [PubMed]
Carlson, A., Wang, S., Elvikis, P., Ferreira, P. M., Huang, Y., and Rogers, J. A., 2012, “Active, Programmable Elastomeric Surfaces With Tunable Adhesion for Deterministic Assembly by Transfer Printing,” Adv. Funct. Mater., 22(21), pp. 4476–4484. [CrossRef]
Nguyen, T. D., Govindjee, S., Klein, P. A., and Gao, H., 2004, “A Rate-Dependent Cohesive Continuum Model for the Study of Crack Dynamics,” Comput. Methods Appl. Mech. Eng., 193(30-32), pp. 3239–3265. [CrossRef]
Nguyen, T. D., Govindjee, S., Klein, P. A., and Gao, H., 2005, “A Material Force Method for Inelastic Fracture Mechanics,” J. Mech. Phys. Solids, 53(1), pp. 91–121. [CrossRef]
Schapery, R. A., 1975, “A Theory of Crack Initiation and Growth in Viscoelastic Media. I. Theoretical Development,” Int. J. Fract., 11(1), pp. 141–159. [CrossRef]
Schapery, R. A., 1975, “A Theory of Crack Initiation and Growth in Viscoelastic Media. II. Approximate Methods of Analysis,” Int. J. Fract., 11(3), pp. 369–388. [CrossRef]
Gent, A. N., and Petrich, R. P., 1969, “Adhesion of Viscoelastic Materials to Rigid Substrates,” Proc. R. Soc. London, Ser. A, 310(1502), pp. 433–448. [CrossRef]
Hui, C.-Y., Xu, D.-B., and Kramer, E. J., 1992, “A Fracture Model for a Weak Interface in a Viscoelastic Material (Small Scale Yielding Analysis),” J. Appl. Phys., 72(8), p. 3294. [CrossRef]
Nguyen, T. D., and Govindjee, S., 2006, “Numerical Study of Geometric Constraint and Cohesive Parameters in Steady-State Viscoelastic Crack Growth,” Int. J. Fract., 141(1-2), pp. 255–268. [CrossRef]
Rahulkumar, P., Jagota, A., Bennison, S. J., and Saigal, S., 2000, “Cohesive Element Modeling of Viscoelastic Fracture: Application to Peel Testing of Polymers,” Int. J. Solids Struct., 37(13), pp. 1873–1897. [CrossRef]
Slanik, M. L., Nemes, J. A., Potvin, M. J., and Piedboeuf, J. C., 2000, “Time Domain Finite Element Simulations of Damped Multilayered Beams Using a Prony Series Representation,” Mech. Time-Depend. Mater., 4(3), pp. 211–230. [CrossRef]
Tada, H., Paris, P. C., and Irwin, G. R., 2000, The Stress Analysis of Cracks Handbook, American Society of Mechanical Engineers, New York.
Huang, Y. G. Y., Zhou, W. X., Hsia, K. J., Menard, E., Park, J. U., Rogers, J. A., and Alleyne, A. G., 2005, “Stamp Collapse in Soft Lithography,” Langmuir, 21(17), pp. 8058–8068. [CrossRef] [PubMed]
Abaqus Analysis User's Manual V6.9, 2009, Dassault Systemes, Pawtucket, RI.
Chaudhury, M. K., and Whitesides, G. M., 1991, “Direct Measurement of Interfacial Interactions Between Semispherical Lenses and Flat Sheets of Poly(Dimethylsiloxane) and Their Chemical Derivatives,” Langmuir, 7(5), pp. 1013–1025. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

An illustration of the stamp/ink system (left) and the stamp geometry consisting of a post and a backing layer (right)

Grahic Jump Location
Fig. 2

The storage modulus of PDMS versus the frequency at room temperature. The theory is based on a 2nd order Prony series (N = 2) with Young's modulus E = 1.32 MPa and the parameters in the Prony series g1 = 0.102, g2 = 0.209, τ1 = 0.426 s and τ2 = 0.0167 s.

Grahic Jump Location
Fig. 3

The crack tip energy release rate versus time for the crack length a = 2.5 μm, post width L = 100 μm, and the applied stress rate σ·=5.86×105Pa/s

Grahic Jump Location
Fig. 4

The normalized critical time tc/τ1 versus the nondimensional combination of the applied stress rate, crack length, Young's modulus, and interfacial toughness (σ·τ1)2a/(E∞Γ0)

Grahic Jump Location
Fig. 5

The pull-off force used to delaminate a PDMS stamp from a silicon ink versus the pulling speed

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