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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

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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