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Wagner, Lacour, Jones, Hsu, Sturm, Li, Suo, Physica E 25 (2004), 326-334


Flexible electronics have a host of potential applications ranging from medicine (e.g. prosthetic skin) to flexible electronic devices. The materials traditionally used for the fabrication of circuits, such as silicon, are stiff. Flexible counterparts may be possible with the combination of an elastomer substrate on which conducting metal connections can be deposited; the system may then sustain considerable stress. The question the authors address is how subjecting a flexible substrate to strain affects the electrical properties of the deposited conductors.

Their initial approach to fabricating these systems was based on the creation of wavy metal films on elastomer substrates which could be stretched reversibly. The waviness of the films was caused by internal stresses within the metal-elastomer system, in a way that they have modelled in a previous publication [1]. Interestingly, such wavy films were not only stretchable, but they maintained their conductivity while stretched. In order to have more control over the orientation and lengthscale of features of the film, and thus over its stretchability, the authors have also deposited metal films on stretched PDMS substrates. When the substrates were let to relax, the superimposed films buckled in a way that correlated with the initial conditions of the substrate: peaks and troughs formed along the axis of initial expansion. Furthermore, the existence of a substrate on which the metal is bonded made the films more robust to deformations.

Main Experimental Details and Observations

As substrate the authors used a poly-dimethyl-siloxane (PDMS) membrane of 1mm thickness. The metal layers, ranging in thickness from 5nm to 500nm, were gold deposited in stripes using electron-beam evaporation and a mask with the inverse pattern on top of the substrate. Samples were prepared both on relaxed substrates and on stretched substrates which were subsequently released. Using relaxed substrates did not yield consistent results; sometimes the metal films buckled and sometimes they didn't (Fig.3). This difference, while it is not yet fully understood, is attributed to differences in the internal stresses of the film, as suggested by the different structural features of the two cases on the nanometer scale (Fig. 4). Films that buckled were smooth on that scale whereas films that did not buckle had randomly distributed micro-cracks - a difference that had direct correlation with electrical conductivity.

Microscope image of gold films.png

Figure 3

SEM image of gold films.png

Figure 4

Using pre-stretched substrates, however, always yielded wavy films (Fig. 6). The metal buckled in the direction along which the substrate was stretched during evaporation and cracked in the perpendicular direction (since, while expanded along one axis, PDMS contracted along the other one). The length scale of these cracks, on the order of ~50um, invites the expectation that metal stripes which are less wide than that would not crack.

3Drendering of buckled metal film.png

Figure 6

The structure of the films influenced directly their electrical resistivity, which is the main quantity of interest in this study (with relation to flexibility). Compared to continuous and straight gold films on glass slides, the wavy films had similar resistivity (~6μΩ cm) while the non-wavy but micro-cracked films had about 3-40 times higher resistivity. This makes buckled films a better candidate material for flexible circuits. The electrical properties of these samples under stress is also important; so the measurement of electrical resistivity was also performed as a function of strain. Different results were obtained for the three types of metal films. Those made on a relaxed substrate and which did not buckle had a resistance which increased continuously with increasing tensile strain; those which did buckle similarly showed increasing resistance with increasing tensile strain, up to a "failure strain" where the resistance had a discontinuous jump (Fig.7); those made on a pre-stretched substrate first showed the inverse behavior, i.e. decreasing resistance with increasing tensile strength, and then followed qualitatively the behavior of the other buckled samples, namely increase in resistivity up to a discontinuous jump (Fig.5). The latter samples have been shown to sustain their conductivity for strain up to 100%. For realistic applications, the robustness of flexible circuits to a sequence of multiple deformations is important; the authors have shown that their elastic electrical connections can remain functional after up to 200 cycles of stretching and relaxing.

File:R vs strain not prestretched.png

Figure 7.

R vs strain prestretched.png

Figure 5.


The authors have demonstrated a method for preparing gold metal connections on a flexible PDMS substrate which can be conducting during and after several cycles of stress. This is a promising step towards the realization of flexible electronics, an active area of current research. A lot remains to be understood about the fundamental physics behind their observations; but the result is, in my opinion, of great technological interest.

[1] S.P.Lacour, S.Wagner, Z.Huang, Z.Suo, Mater.Res.Soc.Proc. 736 (2002) D4.8.1