Large-sized out-of-plane stretchable electrodes
Large-sized out-of-plane stretchable electrodes based on
polydimethylsiloxane (PDMS) substrate
Design of the electrode
To improve the flexibility and stretchability of the electrode, various designs such as serpentine, horseshoe, arch, wavy shapes of the electrode pads and traces were developed previously. In the present study, the
electrode pads and traces were designed in out-of-plane structure with serpentine traces. The out-of-plane
structures were attached to the PDMS substrate using parylene posts that were located nearby the traces and
under the pads.
The detailed design of the out-of-plane electrode with serpentine trace is illustrated in Fig. S1 and is
described in Table S1. The serpentine trace was defined by the radius r and the bending angle θ as shown in Fig.
S1(a). The trace was designed to suspend above the substrate except the area where the parylene posts held the
trace together with the substrate. The dimensions of the cross-sectional area of the trace without and with
parylene post are described by the width of insulated parylene trace wt, metal wm, and post wp, thickness t of
electrode trace, and height h of suspended trace from the substrate (Fig. S1(c) A-A′ and B-B′, respectively). The
suspended electrode pad was attached to the PDMS substrate using an array of parylene posts (Fig. S1(b)).
These parylene posts of same shape and diameter (wp) were arranged at equal interval (i). The array size was
controlled by the number of lows and columns, diameter of the post, and interval between posts.
Fig. S1. Schematics of the proposed electrode trace and pad with cross-sectional areas.
Table S1. Dimensions of the proposed mono- and bi-layer electrodes.
Numerical analysis of strain distribution using finite element method (FEM)
A three-dimensional electrode model consisting of PDMS substrate and parylene trace with the
dimensions listed in the previous section was constructed in a finite element analysis software (ANSYS
Workbench, ANSYS Inc., PA, USA) to analyze the strain distribution in the stretched structure (Fig. S2). For
comparison, the in-plane electrode with the same dimensions without posts was also constructed and simulated.
The model was simplified to include only portion of the electrode trace due to the repetitive trace pattern.
A linear elastic model was used for the parylene trace and a hyper-elastic model was used for PDMS
substrate. Tetrahedral and hexahedral elements were used for the PDMS substrate and tetrahedral elements were
used for parylene trace. The density of mesh around the trace was increased and refined for accuracy in the
stress distribution at the contact interfaces. The parylene trace and metal line was stretched under an axial strain
applied to one side of the PDMS substrate in longitudinal direction (Z-direction in Fig. S2), with the opposite
side fixed in the same direction. The structure could move in the X- and Y-directions freely. Axial strain of 30%
was used to simulate the strain distributions in the out-of-plane electrode structure at around electrical
disconnection, which was found to be 33% from experiments.
Fig. S2. FEM model of the electrode trace with posts.
The strain distribution in the serpentine trace and the substrate when subjected to 30% strain in
longitudinal direction is shown in Fig. S3 and Fig. S4. The magnitude of equivalent strain in the PDMS
substrate was about 37% in the regions around the parylene posts arranged in the direction perpendicular to the
applied strain (X-direction) while it was about 60% in the PDMS regions nearby the parylene posts arranged in
longitudinal direction to the applied strain (Z-direction) (Fig. S3(a-1)). On the other hand, the peak value of the
strain in the parylene trace was around 2.6%, which was found in the joining area of parylene posts and trace as
shown in Fig. S3(a-2). The strain distribution in the in-plane electrode is shown in the Fig. S3(b). The maximum
magnitude of equivalent strain in the PDMS substrate was about 106%, which was observed nearby the parylene
trace as shown in Fig. S3(b-1). In Fig. S3(b-2), the strain distribution in the parylene trace of the in-plane
electrode shows that the maximum strain in the parylene trace was 4.5%, which occurred in the inner region of
the serpentine structure. To analyze the strain distribution depending on directions, different shear strain
components in the parylene trace are displayed in Fig. S4. The peak values of shear strain in the serpentine trace
of the in-plane electrode were about twice than those of the out-of-plane electrode, in all directions. Also, the
shear strain in the parylene trace of the out-of-plane structure was concentrated in the joining area of posts and
serpentine trace as shown in Fig. S4(a-1, a-2, a-3) whereas the shear strain in the in-plane structure occurred
over a larger area as marked by the red dot arrows in Fig. S4(b-1, b-2, b-3).
Although PDMS can be stretched more than 130% under uniaxial strain, it is known that metals break
easily at about 2% strain1,2, and parylene is plastically deformed at over 4% strain and stretched without break
until about 18% 3. From the simulated results, the maximum magnitude of the equivalent strain in the parylene
trace of the out-of-plane structure was smaller than that of the in-plane structure, about 60% of the latter. Also,
the strain of the out-of-plane structure was concentrated only in the regions where the parylene posts are joined
with the trace whereas the strain of the in-plane structure was distributed over a larger area in the parylene trace.
Thus, the metal inside the parylene trace of the out-of-plane electrode remains intact under higher strain applied
to the PDMS substrate than that of in-plane electrode structure.
In Table S2, the measured and simulated strains between posts of the out-of-plane electrode are
summarized, showing that both are in good agreement. Also, the simulated strain distribution in the out-of-plane
electrode at higher strain was in agreement with the observations during measurement as shown in Fig. S5,
which shows the location of disconnection when 35% stretch was applied.
Fig. S3. Equivalent strain distribution of (a) out-of-plane and (b) in-plane electrodes when subjected to 30%
strain. The strain distribution of out-of-plane electrode is shown (a-1) in the entire structure including PDMS
substrate and (a-2) in the parylene trace only. The strain distribution of in-plane electrode is shown (b-1) in the
entire structure and (b-2) in the parylene trace only. Small red boxes show zoomed-in images.
Fig. S4. Shear strain distribution in the parylene trace of (a) out-of-plane and (b) in-plane electrodes, in XY, YZ,
XZ planes, when 30% strain was applied. Small red boxes show zoomed-in images. Dotted red arrows indicate
the locations of highest strains.
Table S2. Simulated and measured strains between the posts in different directions. For directions, see FIG. S2.
Length in A
Strain in A
Length in B
Strain in B
Fig. S5. SEM images of the electrode trace and posts after 35% stretch. The sites of electrode disconnection
were found nearby the parylene posts, indicated by red arrows.
N. Chou, J. Jeong, S. Kim, J. Micromech. Microeng. 23, 125035 (2013).
J. H. Kim, A. Nizami, Y. Hwangbo, B. Jang, H. J. Lee, C. S. Woo, S. Hyun, T. S. Kim, Nature communications
4, 2520 (2013).
R. P. Von Metzen, T. Stieglitz, Biomed. Microdevices 15, 727 (2013).