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Research Papers

Band Gap Formation and Tunability in Stretchable Serpentine Interconnects

[+] Author and Article Information
Pu Zhang

School of Mathematics,
University of Manchester,
Oxford Road,
Manchester M13 9PL, UK
e-mail: puz1@pitt.edu

William J. Parnell

School of Mathematics,
University of Manchester,
Oxford Road,
Manchester M13 9PL, UK
e-mail: William.Parnell@manchester.ac.uk

Manuscript received May 18, 2017; final manuscript received July 17, 2017; published online July 26, 2017. Assoc. Editor: Yihui Zhang.

J. Appl. Mech 84(9), 091007 (Jul 26, 2017) (7 pages) Paper No: JAM-17-1263; doi: 10.1115/1.4037314 History: Received May 18, 2017; Revised July 17, 2017

Serpentine interconnects are highly stretchable and frequently used in flexible electronic systems. In this work, we show that the undulating geometry of the serpentine interconnects will generate phononic band gaps to manipulate elastic wave propagation. The interesting effect of “bands-sticking-together” is observed. We further illustrate that the band structures of the serpentine interconnects can be tuned by applying prestretch deformation. The discovery offers a way to design stretchable and tunable phononic crystals by using metallic interconnects instead of the conventional design with soft rubbers and unfavorable damping.

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Figures

Grahic Jump Location
Fig. 1

Schematic illustration of two forms of stretchable serpentine interconnects. The relaxed configurations are described by Eqs. (1) and (2).

Grahic Jump Location
Fig. 2

Schematic illustration of the relaxed and stretched configurations of the serpentine interconnects.

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Fig. 3

Comparison of the dispersion curves obtained from the current elastica model and the undulated beam model [16]. The geometric parameters are chosen as H0/L0=0.05,β=0, and the thickness of the beam is 0.07L0.

Grahic Jump Location
Fig. 4

Phononic band structures of serpentine interconnects in the relaxed state. The dispersion curves are indicated by dotted curves, while the band gaps are represented by shaded areas. (a) H0/L0=2, β=0, (b) H0/L0=1, β=0, (c) H0/L0=0.5, β=0, (d) H0/L0=2, β=0.2, (e) H0/L0=1, β=0.2, and (f) H0/L0=0.5, β=0.2.

Grahic Jump Location
Fig. 5

Phononic band structures of prestretched serpentine interconnects with β = 0: (a) Λ = 2, (b) Λ = 5, (c) Λ = 7, and (d) band gaps for different stretch ratio Λ

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Fig. 6

Phononic band structures of prestretched serpentine interconnects with β=0.2: (a) Λ = 3, (b) Λ = 5, (c) Λ = 8, and (d) band gaps for different stretch ratio Λ

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Fig. 7

Bloch wave modes for relaxed ((a) and (c)) and prestretched ((b) and (d)) serpentine interconnects. The stationary configurations are indicated by dashed–doted curves, while the Bloch wave modes are represented by solid curves. The wave number is chosen as k¯=π/2, and the eigenfrequencies ω¯1 and ω¯2 indicate the first and second bands, respectively. The geometric parameters are chosen as H0/L0=2 and β = 0 for all cases: (a) ω¯1  = 8.73, Λ = 1, (b) ω¯1  = 8.92, Λ = 2, (c) ω¯2  = 9.79, Λ = 1, and (d) ω¯2  = 10.28, Λ = 2.

Grahic Jump Location
Fig. 8

Phononic band structures of prestretched serpentine interconnects when internal forces are neglected. The aspect ratio is H0/L0=2 for all cases. (a) β=0, Λ=2; (b) β=0, Λ=7; (c) β=0.2, Λ=3; (d) β=0.2, Λ=8.

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