metal waves flat and straining thin flat metal lines. We begin by discussing the mechanisms of buckling and wave formation of gold (Au) thin films evaporated ...
Deformable interconnects for conformal integrated circuits Stéphanie Périchon Lacour1, Zhenyu Huang2, Zhigang Suo2, Sigurd Wagner1 1 Department of Electrical Engineering, Princeton University, Princeton NJ 08544 2 Department of Mechanical & Aerospace Engineering and Princeton Material Institute, Princeton University, Princeton NJ 08544 ABSTRACT The electro-mechanical response of thin gold layers evaporated onto silicone substrates is reported. Gold layers are prepared either thin and flat or thin and wavy on the compliant substrate. The electrical resistance of gold/silicone stripes is measured and analyzed during tensile deformation. For a 100-nm thick gold layer evaporated on a 1-mm thick silicone membrane, we have observed electrical continuity up to ~ 22 % strain. This maximum strain decreases when the gold layer thickness is raised. INTRODUCTION The inherent flexibility of thin-film electronics could be used in a variety of applications. One approach to making flexible and deformable structures is to use polymer substrates. The flexibility of the polymer substrate offers application opportunities that utilize curved and/or deformable surfaces. Retina-shaped photosensor arrays [1], electro-active polymer actuators [2], or stretchable sensitive skin [3] are electronic systems that combine electronic functions with the flexibility of plastic substrates. Once circuits are fabricated onto a deformable substrate, stretchable metallic interconnects must be made [1]. Thin film metallization typically has low critical strain and fractures easily. Here we demonstrate two approaches to make stretchable interconnects: stretching thin-film metal waves flat and straining thin flat metal lines. We begin by discussing the mechanisms of buckling and wave formation of gold (Au) thin films evaporated onto silicone (polydimethylsiloxane PDMS) substrates. Then we describe the preparation of samples, and their electromechanical properties. Surprisingly, we find that the Au layers remain electrically conducting up to large tensile deformation (~ 22%). THEORY Complex wave structures of thin films on compliant substrates have been studied recently [4-6]. Figure 1 shows a cross section of a thin metal wave/substrate structure. The layer thickness is h, its wavelength and amplitude are λ and A. L0 is the net length of the metal and N is the number of periods in the pattern. The gross length Lmax of the film is longer than L0, and can be calculated from equation 1: π
L max = 2 N × ∫ 1 + 0
2πA λ
2
2πx cos dx λ
(1)
When we pull on the structure, the waves flatten until the film is stretched flat. The strain in the film is then the ratio of its elongation (L1 – L0) over L0. The flattening introduces bending not
D4.8.2
tensile strain to the film. We simply denote the net elongation of the sample as strain. The theoretical maximum strain, reached when the thin film is flat (L1 = Lmax) depends on the initial wave parameters λ and A. L1 λ
Au
A L0
PDMS
PDMS
PDMS
Lmax Figure 1. Schematic illustration of thin film deformation under uniaxial tensile strain. L0 and L1 are the initial and final length of the film. We made wavy layers of 100-nm thick Au on PDMS substrates. Compressive stress is induced in the Au film by evaporation. Because the metal film is much thinner than the substrate, the compressive stress in the film is higher than the tensile stress in the substrate, and it causes the film to buckle. The following equations relate the stress within the thin metal film/PDMS structure to the wave pattern [6]. 2πh = λ A = h
2 3
4
13
(1 − ν1 ) 2 E 2 E1
(2)
ε0 −1 εc
(3)
The wavelength λ depends on the Au film thickness h, the Young’s moduli E1 and E2 and the Poisson ratios ν1 and ν2 = 0.5 of gold and PDMS. The amplitude A depends on the initial built-in strain ε0 and the critical buckling strain of the film εc. ε0 is produced by the built-in stress, which depends on film deposition. εc is the buckling threshold. When ε0
