Articles
https://doi.org/10.1038/s41563-021-00921-8

Highly stretchable multilayer electronic circuits
using biphasic gallium-indium
Shanliangzi Liu, Dylan S. Shah

1,2

1

and Rebecca Kramer-Bottiglio

1✉Stretchable electronic circuits are critical for soft robots, wearable technologies and biomedical applications. Developmentof sophisticated stretchable circuits requires new materials with stable conductivity over large strains, and low-resistanceinterfaces between soft and conventional (rigid) electronic components. To address this need, we introduce biphasic Ga–In, a
printable conductor with high conductivity (2.06 × 106 S m−1), extreme stretchability (>1,000%), negligible resistance change
when strained, cyclic stability (consistent performance over 1,500 cycles) and a reliable interface with rigid electronics. We
employ a scalable transfer-printing process to create various stretchable circuit board assemblies that maintain their performance when stretched, including a multilayer light-emitting diode display, an amplifier circuit and a signal conditioning board
for wearable sensing applications. The compatibility of biphasic Ga–In with scalable manufacturing methods, robust interfaces
with off-the-shelf electronic components and electrical/mechanical cyclic stability enable direct conversion of establishedcircuit board assemblies to soft and stretchable forms.

S

oft and stretchable electronics are being integrated intonext-generation electronic devices in a broad range of emerging fields, including soft robotics1, wearable electronics2,
biomedical devices3 and human–machine interfaces4,5. Encouraging
progress has been made in developing novel materials andarchitectures for stretchable sensors6, displays7, heaters8, energy
storage devices9 and integrated circuits (ICs)10. However, the fieldstill lacks highly stretchable, multilayer electronic circuits withintegrated computation, efficient data transmission and minimal electrical losses. Commercial electronics can provide a wide
range of unobtrusive, inexpensive, high-performance ICs, ranging from microcontrollers to amplifiers, but creating stretchable
circuits with these ICs requires a robust interface between eachcircuit element. In this work, we present stretchable versions of conventional printed circuit board (PCB) assemblies by employing abiphasic gallium-indium alloy (bGaIn) to create highly stretchable
conductive traces and robust interfaces between soft and rigid
electronic components.
Three main strategies are being actively researched to enable
stretchable electronics: structure-based stretchable conductors,
intrinsically stretchable conductors and conductive composites.
Highly conductive, inextensible thin metal films can be geometricallypatterned to gain out-of-plane deformability and linear stretchability10–13. Although they interface well with traditional electronic components, their stretchability and component areal density are often
limited. Intrinsically stretchable conductors—such as room temperature liquid metals (eutectic gallium-indium, eGaIn14), ionic conductors15 and conducting polymers16,17—do not require sophisticatedpatterning, but each suffers from several drawbacks, including leaking, dehydration, embrittlement and low conductivity. Conductive
inclusion polymer composites are also stretchable without complex
patterning, but usually suffer from low maximum strains and highresistance18,19. Further, there are relatively few reports on stretchable
conductors that exhibit minimal resistance change during strain20,21.
Much effort has been devoted to making reliable junctions between
stretchable parts and commercially available, high-performance ICs.
One popular approach, placing conventional electronic components

onto strain-isolating (rigid) islands10,22, reduces both the stretchability and durablilty of the resulting circuits. Another approach uses liquid metal droplets or solder paste to make temporary connections,but the stretchability of these solutions is usually limited to less than
100%, without consistent cyclic performance23–27. Taken together, afacile and scalable process to attain both strain-insensitive stretchable conductors and reliable conductor–component interfaces underlarge repetitive strain is still missing.
Here, we introduce biphasic Ga–In (bGaIn), a printable, solid–
liquid biphasic material that maintains a near-constant resistanceunder extreme strains; maintains direct, consistent and stretchable
electrical connections with conventional electronic components;
and is mechanically stable when applied onto numerous soft materials. bGaIn is produced by thermally treating eGaIn nanoparticles
to create a mixture of liquid and crystalline solids. It shows a highinitial conductivity of 2.06 × 106 S m−1 and near-constant resistanceat strains over 1,000%. We employ bGaIn as a stretchable interconnect to interface with commercial electronic components, including resistors, capacitors, light-emitting diodes (LEDs), operational
amplifiers and microcontrollers, by simply pressing the electronics into the bGaIn trace. We demonstrate this facile and scalable
approach with a highly stretchable amplifier circuit (Fig. 1a) anda ‘YALE’ LED array (Fig. 1b). Using bGaIn vertical interconnect
accesses (VIAs) to connect traces on the top and bottom layers, weconvert conventional multilayer PCB designs into stretchable circuit board assemblies (SCBAs) that maintain performance while
experiencing large strains. We demonstrate the utility of these VIAs
with a multilayer LED display (Fig. 1c) and a smart sensing garment (Fig. 1d,e). bGaIn is a simple, non-toxic, single-material solution for making stretchable conductors with robust interfaces toconventional electronic components, opening up opportunities tomass-manufacture stretchable circuits for a wide range of industrial
applications, including soft displays and smart garments.

Material characteristics

eGaIn has emerged as a favourable material for stretchable electronics
due to its high conductivity, intrinsic stretchability and printability14.

School of Engineering and Applied Science, Yale University, New Haven, CT, USA. 2School of Mechanical Engineering, Purdue University, West Lafayette,
IN, USA. ✉e-mail: rebecca.kramer@yale.edu
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a

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Stretchable multilayer
signal conditioning
circuit board

Stretchable
capacitive sensoreEncapsulation layer

Resistors

Microcontroller

Top bGaIn circuit

Top substrate layer
VIAs

Resistors
Bottom bGaIn circuit

Capacitor

Bottom substrate layer

Fig. 1 | bGaIn for SCBAs. a, Amplifier circuit before and after stretching to 400% strain. b, ‘Yale’ LED array before and after stretching to 250% strain.
c, Multilayer LED display before and after diagonal stretching. d, Multilayer signal conditioning circuit board integrated with a stretchable capacitive sensor
attached to the surface of a user’s shirt sleeve. e, Illustration of the circuit board in d. The encapsulation and substrate layers are 3M VHB tape. Scale bars,
1 cm (a–c).

When exposed to oxygen, eGaIn develops a near-instantaneous gallium oxide layer composed primarily of Ga2O3 (ref. 28), which allows
liquid metal to adhere to surfaces and adopt stable non-sphericalshapes29, but also imparts high surface tension (~624 mN m−1)30,
making the material challenging to process. To overcome the limitations posed by the large surface tension of liquid metal, we previously created liquid metal nanoparticle inks by sonicating bulk
eGaIn in ethanol, and then printed those inks into thin films31. The
electrically insulating oxide layer prevents spontaneous particle
coalescence and makes the film non-conductive. To reactivate theliquid metal in micrometre-scale traces, we used a laser31 to rupture
the oxide skins of the nanoparticles and coalesce them into conductive paths. However, we discovered that, due to severe oxidation andphase segregation, high-temperature thermal sintering (anothercommon sintering approach) often depletes the liquid cores of thenanoparticles, creating a pure solid film32,33. Fortunately, this technique paved the way for the creation of bGaIn via a general thermal
treatment of the nanoparticles (Fig. 2a).
We made bGaIn by spray-printing a thick layer of eGaIn
nanoparticles onto silicon (Fig. 2a,i), heating the deposited film

in an enclosed furnace for 30 min at 900 °C (Supplementary
Note 1) and then cooling the film in ambient conditions. This thermal sintering transforms the eGaIn nanoparticles into a thin solid
film on top (~500 nm, invariant with respect to the original layer
thickness) and a thick biphasic portion (~24 μm) with solid particles embedded in liquid eGaIn. During heating, the particles at the
top surface transform into heterogeneously structured crystalline
solids due to oxidation and phase segregation33 (Fig. 2a(ii),b(i–iii)
and Supplementary Fig. 1). The dense oxide layer largely prevents
further oxygen penetration into the particles that lie deeper in thefilm, hence the consistent thickness. Meanwhile, the liquid particles underneath this solid layer experience large internal thermal
stresses, owing to a larger thermal expansion of the liquid cores
relative to the oxide shells33, rupturing the oxide skins and coalescing the particles (Fig. 2a(iii),b(iv)). Once the bGaIn film was made,we transferred it to stretchable substrates (such as acrylic-basedtape (VHB, 3M) or silicone elastomer (Dragon Skin, Smooth-On))by pressing the silicon wafer onto the substrate. The solid film
adheres to the substrate, and the biphasic portion remains
on the surface (Fig. 2a(iv)). Although the bGaIn film initially conNature Materials | www.nature.com/naturematerials

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(i)

(ii)

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Crystalline solid
Silicon
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Fig. 2 | Material characteristics of bGaIn. a, Illustration of the process used to create and print bGaIn: eGaIn nanoparticles are spray printed onto a siliconwafer (i); during thermal sintering, particles at the top surface form heterogeneously structured crystalline solids (ii); below the solid film, a small numberof particles are oxidized into solids (primarily Ga2O3), while the majority of the eGaIn particles coalesce into a conductive liquid (iii); the resulting bGaIn
is transferred to a stretchable substrate (VHB/silicone; iv). b, Scanning electron microscopy images showing the cross-section of a bGaIn film, including
the top solid film at various length scales (i–iii) and the biphasic portion (iv). c, Scanning electron microscopy image of the top surface of a bGaIn film
after transferral to VHB tape. d, Energy dispersive spectroscopy mappings of the top surface of the bGaIn film after transfer, indicating higher oxygen
concentrations in the areas with solid particles. e, X-ray diffraction patterns of the bGaIn film on a silicon wafer (before transferring to a soft substrate) andon VHB (after transfer).

tained some solids, this transfer process embeds additional solid
particles into the biphasic portion (Fig. 2c and Supplementary
Fig. 2). These solid particles exhibit higher oxygen concentrations than the liquid in the energy dispersive spectroscopy mappings (Fig. 2d and Supplementary Figs. 3–6), indicating a higher
extent of oxidation. X-ray diffraction analysis shows that thesesolids are primarily monoclinic β-Ga2O3 crystals (Fig. 2e andSupplementary Note 2).

Electromechanical response

To establish a baseline of the electromechanical performance ofbGaIn, we measured the relative resistance change (R/R0) of bGaIn
traces undergoing uniaxial tensile strain on multiple stretchable substrates. The traces had exceptionally stable electrical performance,experiencing negligible resistance change at both 100% strain on
silicone elastomer (polydimethylsiloxane (PDMS); R/R0 ≈ 1.06;
Fig. 3a) and 500% strain on VHB (R/R0 ≈ 1.81; Fig. 3b). These values are notably smaller than the theoretical prediction for a classicalincompressible, constant-conductivity bulk liquid metal conductor
using Pouillet’s law, which exhibits large increases in resistance evenat moderate strains (R/R0 = (1 + ϵ)2, where ϵ is the applied strain;
Fig. 3a,b, black; R/R0 = 4 at 100% strain on PDMS, 36 at 500%
strain on VHB; experimental validation in Supplementary Fig. 7).
At strains over 1,000%, the resistance increased less than five times(Supplementary Fig. 8), but strains of ~1,200% typically resulted inmechanical failure of the VHB substrate. Furthermore, we subjectedbGaIn traces to cyclic strains of 100% (Fig. 3c) on PDMS and 500%
on VHB (Fig. 3d). After moderate settling during the initial cycles,
the bGaIn attained stable electromechanical behaviour over 1,500loading cycles. We hypothesize this is due to rearrangement of thesolid particles, from a random or non-uniform distribution caused
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by the transfer process, into a more uniform distribution induced
by stretching. Compared to state-of-the-art stretchable conductors,
bGaIn has outstanding performance in its high initial conductivity(2.06 × 106 S m−1), extreme stretchability (>1,000%) and negligible
resistance change over strains (Fig. 3e,f).
Due to the scattered solid oxide particles being primarily semiconductive Ga2O3, the initial conductivity of bGaIn (2.06 × 106 S m−1)
is lower than that of bulk eGaIn (3.40 × 106 S m−1). As a bGaIn trace
is stretched on a substrate, the liquid portion of it decreases in thickness to compensate for the increase in trace length. We hypothesizethat the thickness of the embedded solid particles quickly exceeds
the thickness of the liquid during strain, and therefore the solid
particles begin to emerge from the liquid. Thus, the volume of thesolid particles completely immersed in the liquid decreases withincreasing strain. When the system is relaxed, the solid particles
are resubmerged in the liquid. This mechanism results in increasing conductivity of the bGaIn trace with increasing strain, which isoffset by the decreasing cross-sectional area of the trace and resultsin stable trace conductance during strain (Supplementary Note 3).
The unique electromechanical behaviour of bGaIn also relies
upon the wettability of the liquid metal to the solid oxide particles.
A previous approach to fabricating similar biphasic alloys involves
mixing solid particles with liquid eGaIn, which typically resultsin poor adhesion between the liquid and solid components andconsequently large resistance increases under strain34–36. Here,the thermal sintering process generates solid particles fromwithin the liquid metal, allowing the liquid to wet the solid particles and encouraging it to percolate through their interstices(Supplementary Fig. 9). This superior wettability reduces separation between solid and liquid in the biphasic material, and therefore promotes continuous, high conductivity. The solid particles

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Fig. 3 | Electromechanical characteristics of bGaIn. a,b, Relative change in resistance as a function of uniaxial tensile strain of the bGaIn traces on
PDMS (blue, a, R/R0 ≈ 1.06 ± 0.016, four samples) and VHB (pink, b, R/R0 ≈ 1.81 ± 0.26, six samples), and theoretical prediction based on bulk conductor
assumptions (black). The insets illustrate top views of the samples. c,d, Relative resistance change of the bGaIn traces subjected to uniaxial tensile
cyclic loading to 100% on PDMS (blue, c) and 500% on VHB (pink, d) up to 1,500 cycles. The insets show detailed electrical resistances as a response
to uniaxial strains. e,f, Comparison of initial conductivity (0% strain) and stretchability (e), as well as relative resistance change at maximum strain (f)with other stretchable conductors: Ag flakes in fluorine rubber (Ag flakes)18, Ag nanoparticles in fluorine rubber (AgNPs)44, Ag nanoparticles in poly(styrene-block-butadieneblock-styrene) rubber fibres (AgNPs-SBS)45, Ag nanowires (AgNWs)46, poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate)(PEDOT:PSS)16, liquid metal fibre (LM fibre)47, liquid metal Ag flakes in ethylene-vinyl acetate (EVA) (LM-Ag flakes)20, single-walled carbon nanotubes(SWCNTs)48, polyaniline (PANI)17, polymerized liquid metal networks (Poly-LMNs)21, multi-walled carbon nanotubes and Ag flakes in polyvinylidenefluoride
copolymer (MWCNTs-Ag flakes)49 and polyacrylamide hydrogel (Hydrogel)15.

adhere to the substrate throughout stretching, while maintaining adhesion to the liquid metal and preventing the formationof electrically isolated liquid droplets (Supplementary Fig. 10).
Supplementary Video 1 shows the solid side of the bGaIn film
breaking into flakes when stretched, while the biphasic portion
fills in the cracks, maintaining connection between the solid particles, which allows the bGaIn film to remain thin and continuous
on the substrate during stretching.

Integration with rigid electronic components

With the baseline behaviour of bGaIn characterized, we now showthat it creates robust electrical connections with rigid electronics.
Reliably interfacing liquid metal with rigid electronics is challenging, and the few existing examples of liquid metal based SCBAs
require cumbersome fabrication processes that are not compatible with current scalable manufacturing methods23,24,26. Further,state-of-the-art stretchable conductors have not been shown to
directly interface with rigid electronics21,37. Here, we employ bGaIn
as a stretchable interconnect to achieve reliable interfaces with rigid
electronic components.
First, we used the transmission line method38 to measure the contact resistance between bGaIn and (equivalently)
zero-ohm-resistance, tinned copper contacts. By varying the lengthof the bGaIn traces (the space between adjacent tinned copper
contacts), measuring the total resistance between bars and fitting aline to the data (Fig. 4a; coefficient of determination, R2= 0.9986),
we calculated the contact resistance (half of the y intercept) to be

0.06 Ω, an order of magnitude lower than other liquid metal based
contacts previously reported39 (Supplementary Note 4).
After measuring the contact resistance, we interfaced a zero-ohm
surface mount resistor with a bGaIn trace on various stretchable
substrates, and measured the resistance change during strain. At
100% strain on PDMS (Fig. 4b), the R/R0 value was approximately
1.40, and at 500% strain on VHB (Fig. 4c) the relative resistance wasapproximately 4.47. When pressing an electrical component onto
patterned bGaIn traces, the oxide layers of the liquid metal break,and the bGaIn flows and encompasses the rigid pins, increasing
contact area and reducing the contact resistance. The solid particles
aid in securing the liquid to the rigid pin due to their natural inextensibility, their propensity to adhere to solid surfaces and the strong
wettability to them by the liquid (Fig. 4d, Supplementary Fig. 11 andSupplementary Video 1), resulting in stable electrical connections
during and after stretching. This electromechanical sensitivity tostrain is low compared to the prediction based on bulk conductor
assumptions (Fig. 4e black) and other liquid metal based interfacing approaches (Fig. 4e). Furthermore, the bGaIn traces with anembedded zero-ohm resistor subjected to a repetitive strain of 100%
(Fig. 4f) on PDMS and 500% on VHB (Fig. 4g) remained functional
over 1,500 loading cycles. Additional strain tests on bGaIn traces
with and without embedded zero-ohm resistors on both PDMS andVHB substrates verified their stable performance at various strain
rates (150 mm min–1, 225 mm min–1 and 300 mm min–1) for 1,000
loading cycles (Supplementary Fig. 12). Further, traces aged forover six months in standard laboratory conditions (23 °C and 50%
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Measured resistance

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CyclesFig. 4 | Integration with rigid electronic components. a, Contact resistance measurement for a bGaIn–component interface using the transmission line
method (Rc = 0.06 Ω, R2 = 0.9986). The inset shows the schematic of the samples for the contact resistance measurement. b,c, Relative change in resistanceas a function of uniaxial tensile strain of the bGaIn traces with embedded zero-ohm resistor on PDMS (blue, b, R/R0 ≈ 1.40 ± 0.1, five samples) and VHB(pink, c, R/R0 ≈ 4.47 ± 0.77, seven samples), and theoretical prediction based on bulk conductor assumptions (black). The insets illustrate top and sideviews of the samples. d, Scanning electron microscopy images showing microstructure of a bGaIn–component interface at different stretching states(unstretched, stretched to 30% and released). The leftmost image of the electronic pin is included as a comparison. Scale bar, 200 μm. e, Comparison ofrelative resistance change over strains with other liquid metal based interfacing approaches: AgNP–Ga–In (ref. 50), HCl-vapour treatment24 and VIA-based
interface26. f,g, Relative resistance change of the bGaIn traces with embedded zero-ohm resistor subjected to uniaxial tensile cyclic loading to 100% on
PDMS (blue, f) and 500% on VHB (pink, g), up to 1,500 cycles. The insets show detailed electrical resistances as a response to uniaxial strains.

humidity) exhibited no evidence of long-term electromechanicaldegradation (Supplementary Fig. 13).

Printable patterns and stretchable VIAs

Patterning thin films of bulk eGaIn is challenging since its high surface tension causes the liquid metal to bead up and deviate fromthe desired deposition pattern40. By contrast, the solid particles inbGaIn spread evenly over the printed area, and then strong wetting between the liquid metal and the crystalline particles stabilizes
the liquid, preventing unwanted beading. This mechanical stability helps bGaIn to work well with a variety of trace manufacturing
processes. The main fabrication process that we use istransfer-printing by simply pressing a silicon wafer, on which bGaIn
was made, onto a masked, stretchable substrate. Alternatively, we
turned bGaIn into a conductive, printable paste by scraping bGaIn
off the silicon wafer and mechanically mixing the top oxide into thebiphasic portion. We used the paste to stencil-print and hand-write
stretchable patterns on a variety of substrates, including VHB tapeNature Materials | www.nature.com/naturematerials(Fig. 5a), paper (Fig. 5b), high-porosity foam (Fig. 5c) and latex balloon (Fig. 5d). Through these two techniques, we show facile printing of thin (<20 μm) bGaIn films.
The bGaIn paste can be filled into laser-cut cavities to easily create stretchable VIAs. The bGaIn strongly wets and adheres to thecavity, bridging the top and bottom traces (Supplementary Fig. 14),even when stretched (Supplementary Fig. 15). We measured theelectrical resistance of circuits with a single VIA connecting two
bGaIn traces at high strains (Fig. 5e). The relative resistance at 500%
strain on VHB was 2.03, which remains notably lower than the theoretical prediction based on bulk conductor assumptions (Fig. 3a
black; R/R0 = 36 at 500%). The electromechanical response of a VIA
strained cyclically to 500% on VHB also remained consistent over
1,500 loading cycles (Fig. 5f).

SCBAs

We made various SCBAs that demonstrate the near-universal utilityof bGaIn to create stretchable soft robotic and wearable electronics.

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CyclesFig. 5 | Printable patterns and stretchable VIAs. a,b, Stencil-printed bGaIn circuits on VHB tape (a; scale bar, 5 mm) and paper (b; scale bar, 2 cm). c,d,
Hand-written bGaIn circuits on high-porosity foam (c) and a latex balloon (d); scale bar, 2 cm. e, Relative change in resistance as a function of uniaxial tensile
strain of two bGaIn traces connected by a single VIA on VHB (pink, R/R0 ≈ 2.03 ± 0.32, six samples) and theoretical prediction based on bulk conductor
assumptions (black). The inset illustrates top and side views of the samples. f, Relative resistance change of two bGaIn traces connected by a single VIA
subjected to uniaxial tensile cyclic loading to 500% on VHB up to 1,500 cycles. The inset shows detailed electrical resistances as a response to uniaxial strains.

We first stretched a ‘YALE’ LED array (bGaIn electrical interconnects, 33 LEDs pick-and-place assembled) on VHB tape to 250%
strain (Fig. 1b and Supplementary Video 2), with no perceptible
diminishing of the LED brightness. We then made an SCBA witha non-inverting summing amplifier circiuit (Figs. 1a and 6a, andSupplementary Fig. 16). The output voltage (Vout) of the representative summing circuit is proportional to the sum of the input
voltages (Vin1 and Vin2), as V out ¼ ðR23 ´þRR34 Þ ´ ðV in1 þ V in2 Þ, andis therefore highly sensitive toI large resistance changes in the circuit. Initially, when supplied with a 100 mV peak-to-peak voltage(100 mVpp) sinusoidal signal with a 100 mV offset on both Vin1 and
Vin2, the circuit produced the expected output voltage (1.1 Vpp; Fig.
6b), closely matching the results obtained with the same circuit
built on a rigid PCB. Furthermore, stretching the circuit to different strains had a negligible impact on the output signal (Fig. 6band Supplementary Video 3). Finally, the measured amplitude andphase shift at different strains were approximately the same as thetheoretical values (0.55 V; 0 rad).
To further clarify the utility of bGaIn in resistance-sensitive
circuits, we also demonstrated a first-order resistor–capacitor
low-pass filter circuit using bGaIn as electrical interconnects andcompared it to an identical circuit manufactured using bulk eGaIn(Supplementary Fig. 17). The bGaIn circuit exhibited similar outputs and cut-off frequencies (~936 Hz) at various strain levels up to
400% strain, while the eGaIn circuit failed at less than 100% strain.
The stable performance during these collective experiments proves
the capability of bGaIn to enable SCBAs that retain their electricalperformance over large strains.
After demonstrating single-layer bGaIn circuits, we used bGaIn
VIAs to create multilayer, high-performance stretchable circuits.

First, we made a stretchable LED display with 25 LEDs and 25 corresponding bGaIn VIAs arranged in a 5 × 5 grid (Fig. 1c). We built
this circuit in silicone elastomer to demonstrate the transferrability of our manufacturing methods to non-adhesive substrates. The
LEDs in the display could be controlled individually by an external
microcontroller (Arduino Uno) to create a scrolling message, while
being stretched along all in-plane strain directions (Supplementary
Video 4).
Lastly, we made a multilayer signal conditioning circuit, withintegrated sensing and computation, for wearable sensing applications. Typical wearable capacitive stretch sensors require acolocated, rigid signal conditioning circuit board for capacitancemeasurement41, moderately constraining the movement of the
body. We rebuilt this board as an SCBA on VHB tape, integrating a
microcontroller, a capacitor and five resistors with transfer-printedbGaIn interconnects and bGaIn-filled VIAs (Fig. 1d,e, Fig. 6d,e andSupplementary Fig. 18).
We held the signal conditioning circuit board at a series of strains(0%, 50%, 100%, 150%, 200%), while subjecting the capacitive sensor to ten cycles of 50% strain (Fig. 6f). As expected, the signal conditioning board maintained a linear response when stretched up to
200%, with any deviations simply the result of sensor noise. We thendirectly integrated the stretchable capacitive sensor with the signal
conditioning board and attached the sensor–circuit assembly to thesurface of a shirt sleeve (Fig. 1d and Fig. 6g). The sensor and the circuit deformed simultaneously during elbow flexion, and the signal
conditioning circuit measured the motion of the user’s arm (Fig. 6g
and Supplementary Video 5). In contrast to previous works where
the sensing circuit was often placed outside the active region42,43,
here we were able to colocate the circuit and sensor directly over
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1.25
1.00
0.75
0.50

Vout

Vss

0.25
0

1 kΩ R4 10 kΩ

0.1

0

0.2

0.3

ii Transfer-printing
bottom layereResistors

Resistors
Microcontroller

bGaInfilled VIAs

Normalized sensor
readingf
Capacitor

0.5Time (ms)di Maskingbottom layer

0.4

iii

Masking
top layer

1

2

0.8

1

0.6

0

0.4

–1

0.2

–2

100

0

Laser-cut
cavitybGaIn-filled
VIA

iv Transfer-printing top
layer and laser-cutting
cavitiesv Filling cavities
with bGaIn

200
Strain (%)

0
400

300

vi Interfacing withelectronics andexternal wiresg

1.0

Signal conditioning board strain
0.8 0%
50%
100%
0.6
150%
200%
0.4
0.2
0

3

Sensor reading

Operational
amplifier

Voltage (V)1.75

Phase shift (rad)2.00

Amplitude (V)Input 1
Input 2
Output 0% ε
Output 400% ε
Output copper PCB

0

10

20

30

Sensor strain (%)

40

50

0

10

20

Time (s)30

Fig. 6 | Applications of SCBAs. a, Top view and circuit diagram of the summing amplifier circuit. Vdd and Vss are the drain and sink power voltage,
respectively. R1 and R2 are the input resistors, R3 is the grounded input resistor and R4 is the feedback resistor. Scale bar, 1 mm. b, Input sinusoidal voltage
signals (100 mVpp, 100 mVpp offset), along with output signals after amplification when the amplifier circuit is at 0% and 400% strain, as well as the same
circuit built with copper traces as a control group. c, Phase shift and amplitude of the amplifier circuit output signals as a function of applied strain. The
dash–dot line (red) and dashed line (black) represent the theoretical amplitude value (0.55 V) and phase shift (0 rad), respectively. d, Fabrication processof the multilayer signal conditioning circuit board. Scale bar, 1 cm. e, Top view of the signal conditioning circuit board. Scale bar, 5 mm. f, Normalized sensor
reading as a function of the capacitive sensor strain up 50% for ten cycles at different strains of the signal conditioning circuit board (0%, 50%, 100%,150%, 200%). Each shaded region represents ± 1 s.d. about the mean (solid line). g, A stretch sensor and signal conditioning circuit board were attached
to a spandex sleeve and stretched together during normal bending motions of a user’s arm. The insets show this sensory sleeve while the user’s arm isstraight (left inset) and bent (right inset).

the user’s elbow. This presents a key advance towards unobtrusive
wearable electronics.

OutlookIn this work, we have introduced a material and fabrication method
to rapidly produce SCBAs with excellent electrical performance andreliability. The bGaIn developed herein incorporates high initialconductivity (2.06 × 106 S m−1), extreme stretchability past 1,000%,
cyclic stability up to at least 1,500 cycles and negligible resistancechange over strains. This material can directly interface with conventional electronic components to attain robust and stretchable
electrical connections. The combination of these unique traits
enables facile and direct conversion of sophisticated PCB assemblies
into their corresponding SCBAs.
Resolution of the SCBAs fabricated using this approach is currently limited by the laser-cut masks (~25 μm). Appropriately
tailoring the solid-to-liquid ratio of bGaIn could potentially create inks with improved physical properties for higher resolution,
Nature Materials | www.nature.com/naturematerials

extrusion-based printing. Further research in optimizing bGaIn
ink properties would enable scalable manufacturing of stretchable circuits with high integration densities. The potential applications and impact of this material are wide, including wearable
health-monitoring devices for next-generation healthcare; intuitive,
soft human–machine interfaces; and circuits with integrated sensing, actuation and distributed computation, for soft robotics.

Online content

Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of
author contributions and competing interests; and statements ofdata and code availability are available at https://doi.org/10.1038/
s41563-021-00921-8.
Received: 28 May 2020; Accepted: 6 January 2021;
Published: xx xx xxxx

Articles
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Nature Materials
Methods

Material fabrication. The liquid metal nanoparticle ink was made by adding
362 ± 5 mg of eGaIn alloy (75.5% Ga, 24.5% In; 495425, Sigma Aldrich) into 4 ml ofethanol (V1001, Koptec) and then sonicating at an amplitude of 36 μm (30% setting)for 120 min using a tip sonicator (1/16 inch microtip probe, QSonica Q700). Prior tospray-printing, the ink was mixed vigorously using a vortex mixer (VortexGenie) for
3 min to ensure uniform dispersion. The nanoparticle ink was then sprayed onto asilicon wafer substrate using a customized spray printer. Compressed air (20 psi) was
blown over a syringe needle while ink was dispensed at a fixed rate (0.3 ml min−1),with the printer stage translating underneath at 5 mm s−1. A 3 ml syringe of ink
made a single layer of film, with the process being repeated ten times to create films
thick enough for bGaIn to form. After spray deposition, the printed liquid metal
nanoparticle film was heated in a furnace (Lindberg/Blue M BF51766A-1, Thermo
Fisher Scientific) at 900 °C for 30 min and then cooled in ambient conditions.
After the thermal sintering, stretchable substrates such as VHB tape (4905,
3M) or silicone elastomer (Sylgard 184 PDMS, Dow Corning) were brought into
conformal contact with the silicon wafer. Pressure was manually applied, and thesubstrate was lifted to complete the transfer-printing. In other experiments(Fig. 5), the bGaIn was scraped off the silicon wafer and thoroughly hand-mixed.
It was then patterned onto VHB tape (Fig. 5a) and paper (Fig. 5b) using a thin film
applicator (Elcometer 3540), and directly written onto a piece of foam (Fig. 5c) anda latex balloon (Fig. 5d). Surface mounted LEDs (0603 package size, Kingbright)
were adhered to the foam using cyanoacrylate (Loctite Instant-Bonding Adhesive
414, McMaster-Carr).
Electrical and mechanical characterization. The bGaIn resistance was measured
using a four-point probe with a digital multimeter (5492B, BK Precision), after
being transferred to a VHB substrate in a dog-bone pattern. The resistance values(0.16 ± 0.02 Ω) were averaged from twelve measurements. The dog-bone patterns
had an aspect ratio (length/width) of 5:1 (7.5 × 1.5 mm). Thicknesses of thesepatterns were measured using a three-dimensional optical profiler (Zygo Nexview),
and averaged from twelve measurements (15.51 ± 1.55 μm). Initial conductivity ofthe biphasic material was calculated as σ = l/Rwt = (2.06 ± 0.29) × 106 S m−1,
where l, w, t and R are the length, width, thickness and resistance of the bGaIn
patterns, respectively.
Contact resistance between bGaIn and electrical pins was measured using
the transmission line method. An array of tinned copper contacts with various
spacings was attached to a single bGaIn trace. Resistance values between eachpair of contacts were measured. The measured contact resistance is half of the yintercept value of the linearly fitted line.
For electromechanical characterization, rectangular samples (length, 20 mm;
width, 0.8 mm) were fabricated by transfer-printing bGaIn onto VHB or PDMS
substrates. To eliminate the resistance changes at the interfaces between bGaInand external wires, electrical connections were made by adhering copper tapeon each end of the bGaIn traces, secured using silver conductive epoxy (Part no.
8331-14G, MG Chemicals). For the samples on PDMS substrates, fabric strips wereplaced at the interfaces to prevent stretching. The films were then encapsulatedwith another layer of VHB or PDMS. To test the circuits with bGaIn–component
interfaces, zero-ohm resistors (1/10 W, 0603 package size, Yageo) were placed
between two bGaIn traces. For VHB substrates, the resistors were held for 3 min
to encourage bonding. For PDMS substrates, the resistors were placed when thesilicone was only partially cured, and still ‘tacky,’ to enhance bonding. The two endsof the samples were clamped on three-dimensional printed parts and assembled
on a customized tensile stage. The resistance values were measured using a
Wheatstone bridge and corrected based on the clamped portion of the samples.
The bGaIn samples were then subjected to uniaixal tensile loading at 15 mm min−1,
150 mm min−1, 225 mm min−1 or 300 mm min−1.
Material characterization. Scanning electron microscopy images were taken by
a Hitachi SU8230 ultra-high-resolution cold-field-emission scanning electron
microscope. Samples for cross-section imaging were made by cleaving in liquid
nitrogen. Elemental composition and mappings were obtained using energy
dispersive X-ray spectroscopy (Flat-Quad, Bruker) at 5 kV. Optical imaging was
performed using Zeiss Smartzoom 5. X-ray diffraction patterns were collected usinga Rigaku Smartlab X-Ray diffractometer with CuKα radiation (8.04 keV, 1.5406 Å).
SCBA demonstration. The SCBAs shown in this work were fabricated bytransfer-printing bGaIn onto VHB or silicone substrates with patterned masks. The
masks were created by laser cutting liners of white matte sticker papers (Online
Labels) using an ultraviolet laser micromachining system (Protolaser U4, LPKF)
with 355 nm wavelength and 15 μm beam diameter. The glossy side of each liner
was placed onto the VHB adhesive or silicone substrate, and easily peeled off after
patterning. To provide electrical leads, tinned copper wires were flattened using aroller mill (Feiuruhf) and pressed onto the bGaIn contact pads. The VHB substrates
were reinforced with double-sided tape, and the silicone substrates were reinforced
with inextensible fabrics. Electrical wires were then soldered onto the flattened wires.
For the ‘YALE’ LED array, 33 LEDs (Kingbright, 0603) were pressed onto the
VHB substrate at the designated positions and held for 3 min to encourage adhesion.
The circuit was sealed with a layer of VHB on top. With voltage held constant at
2.7 V, the LED array was stretched to 250% strain by hand and then released.
Nature Materials | www.nature.com/naturematerials

The operational amplifier circuit consisted of a 14-pin rail-to-rail output
operational amplifier (LMV 324, Texas Instruments). We supplied a 100 mVpp
sinusoidal signal with a 100 mVpp offset and measured the output signals withan oscilloscope. The circuit was incrementally stretched, and the outputs wererecorded at increments of 25% strain, up to 400%. As a control, the same circuit
was built on a rigid copper-clad PCB board (G10/FR4, Pulsar) patterned by the
LPKF laser, and tested with the same inputs at 0% strain.
The first-order resistor–capacitor low-pass filter circuit consisted of a resistor, acapacitor and bGaIn as electrical interconnects. We supplied a 500 mVpp sinusoidal
signal (Vin) at various frequencies and measured the output signals (Vout) withan oscilloscope. The circuit was incrementally stretched, and the outputs wererecorded at increments of 100% strain, up to 400%. The magnitude in decibels (dB)
Þ. As a comparison, we created an identical circuit using
was calculated as 20logðVVout
ineGaIn as electrical Iinterconnects. The bGaIn was patterned as interfacial contacts
for the eGaIn circuit to ensure stable connections with rigid electronic components.
The stretchable LED display was fabricated by first rod-coating a layer ofsilicone elastomer (Dragon Skin 10 Slow, Smooth-On) onto a polyethylene
terephthalate (PET) substrate. Once the silicone cured, bGaIn was transfer-printed
onto it to create the bottom circuit. Next, another layer of silicone elastomer was
rod-coated on top and, after curing, another layer of bGaIn was printed. Once the
top layer patterning was complete, 25 VIAs were created between the two layers
by cutting cavities with an infrared laser (Universal Laser Systems VLS 2.30, 30 W,
10.6 μm CO2 laser) and filling them with bGaIn. Then, 25 surface mounted LEDs
(0603 package size, Kingbright) were bonded to the silicone elastomer layer using
a silicone adhesive (Sil-Poxy, Smooth-On). Finally, the circuit was encapsulated by
rod-coating another layer of silicone elastomer on top. The LEDs were controlledindividually by an external microcontroller (Arduino Uno).
For the signal conditioning circuit board, an alignment fixture was built on an
acrylic plate to achieve rapid and precise assembly of the top and bottom layers.
VIA fabrication and transfer-printing methods were the same as in the otherexperiments. The circuit board included resistors, capacitors, a microcontroller(PIC16F1825, Microchip Technologies) and flattened tinned copper wires forinterfacing with the stretch sensor and sending data to an external microcontroller(Arduino Uno). For characterization experiments, the signal conditioning circuitboard was stretched and held at a certain strain using a customized tensile stage,
while the capacitive sensor (1 cm wide with 105 mm gauge length) was subjected
to ten cycles of repetitive strain from 0% to 50% using a materials tester (Instron3345) at a strain rate of 150 mm min–1. The sensor was secured to the materials
tester via acrylic plates that had been sewn onto the ends of the sensor. The sensor
was installed in a slack position, and the crosshead of the materials tester was
raised until the sensors were not slack; no further pre-tension was applied to thesensors. For the sensory sleeve demonstration, the capacitive sensor was sewn onto
a user’s shirt sleeve and the signal conditioning circuit board was placed on the topof the sensor.

Data availability

Source data are provided with this paper. Other data supporting the findings of thisstudy are available upon request from the corresponding author.

Acknowledgements

We acknowledge R. A. Bilodeau, M. C. Yuen and S. Y. Kim for their valuable commentson the manuscript; S. Wang for drawing the illustrations in Fig. 1e and Fig. 2a; L. Wang foraccess to the Zygo Nexview 3D Optical Profiler at the Yale West Campus Cleanroom; andM. Li for access to the scanning electron microscopy, energy dispersive spectroscopy and
X-ray diffraction instruments at the Yale West Campus Materials Characterization Coreand his advice on data analysis. S.L. was supported by the National Science Foundation(CAREER Award 1454284). D.S.S. was supported by a NASA (US National Aeronautics
and Space Administration) Space Technology Research Fellowship (80NSSC17K0164).

Author contributions

S.L., D.S.S. and R.K.-B. conceived the project and planned the experiments. S.L.
conducted all the experiments. D.S.S. programmed the PIC microcontroller for thesignal conditioning circuit board demonstration. All authors participated in drafting andediting the manuscript. All authors contributed to, and agree with, the content of the
final version of the manuscript.

Competing interests

The authors declare no competing interests.

Additional information

Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s41563-021-00921-8.
Correspondence and requests for materials should be addressed to R.K.-B.
Peer review information Nature Materials thanks Jaehong Lee, Tsuyoshi Sekitani andthe other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Reprints and permissions information is available at www.nature.com/reprints.