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Experimental Section Crack junction-based sensor fabrication

10 µm thick UV-curable polyurethane acrylate (301RM, Minuta Tech. Co.) layer is fabricated

by dripping (20 µl) urethane acrylate precursors on a flexible polyethylene terephthalate film

(50 µm thick, SH40 SKC Inc.) and then covering the film with a flat silicon wafer followed by

350 nm ultraviolet (UV) flood exposure (approximately 360 mJ/cm2). A patterned 20- to 100-

nm-thick metal layer is formed by a shadow mask using sputtering (Muhan Vacuum Co.) (see

Fig. S24). This metallic film on PUA is mechanically bent with various radii of curvature (1, 2,

3 mm), and the cracks are formed in a highly controllable manner in terms of crack density

and direction, which in turn yields reproducible electrical signals. As observed in Figure S1,

the crack spacing (or density) can be controlled by bending the sample with different

curvatures. For example, the average spacing between cracks is approximately 10 µm when

the sample is bent with a curvature of 1 mm. The cracked Pt on PUA shown in Figure 1d has a

lateral dimension of 5 × 10 mm2 on 10-µm-thick PUA. The changes in resistance were

measured by a Lab View-based PXI-4071 system (National Instruments Inc.) at a high-

resolution sampling rate of 10,000 times/s. A thin crack junction based sensor was also made

on 6 µm thick PET film (Chemplex INDESTRIES Inc.) for flexibility test.

Multi-pixel array sample fabrication

To demonstrate the device’s scalability and ability for detecting mechanical vibrations and

pressure, a sensing network of 64 pixels (8×8 pixel array) with an area of 5×5 cm2 is presented

in Figure 2. The image and schematic view of the multi-pixel system are shown in Figure 2d-l

and Figures S9 and S10. Each pixel (2×2 mm2 islands) composed of 10-µm-thick PUA/20-nm-

thick Pt patterns on PET is formed by conventional photolithography and sputter deposition

using a shadow mask, followed by bending with a 1 mm radius of curvature to generate cracks.

The electrical connection between the cracked Pt and a Lab View-based PXI-4071 system (NI

instrument Inc.) is formed by evaporated gold (Au, 50 nm thick) lines on deposited dielectrics

(50-nm-thick SiO2 by a thermal evaporator; Selcos Inc.).

Strain sensitivity measurement of crack sensors

The crack sensor is clamped by all-electric test instrument (E3000, Instron Co.) and stretched

by exact strain and force. Resistance change is measured by a Lab View-based PXI-4071

system (NI instrument). Various percentages of strain (0.5 % to 2 %) are applied to the sensor

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with various speeds (0.1 mm/min, 1 mm/min, 10 mm/min). Multiple-cycle tests (<5,000

cycles) with repeated loading-unloading of strain in the range of 0-0.5 %, 0-2 % using a 1mm-

radius-curvature crack based sensor also use all-electric test instrument (E3000) with the speed

of 10mm/min.

Multi-pixel array measurement of the crack sensor

The flexible format of a multi-pixel array (Fig. 2g) enables the simultaneous measurement of

two different stimuli (pressure and vibration) using a simple analyzer scheme (Fig. 2h). The

results for static pressure with a PDMS piece (5 Pa in Fig. 2e) and a dynamic flapping ladybug

(5 Pa pressure and 200 Hz vibration with 14 µm amplitude in Fig. S11) are shown in Figure 2k

(with a PDMS piece) and Figure 2l (with a vibrator simulating ladybug flapping), respectively.

A piece of PDMS is placed on the red marked region in Figures 2d, e as a static pressure input,

and a piezoelectric vibrator as a vibration source similar to a ladybug’s flapping is placed onto

the blue marked region in Figures 2d, f. The applied pressure and their distributions from both

stimuli can be detected at both spots (Fig. 2i). However, the vibration signal is selectively

detected only at the spot where the vibration input is applied (Fig. 2j). Figures 2k and l

illustrate the dramatic changes in the in situ signals of these pixels placed at both locations.

The applied 200-Hz frequency vibration could be obtained by Fourier transform, as shown in

the inset of Figure 2l.

Flexibility test of the crack sensor

For flexibility test, the crack based sensor was bent with various radii (flat, 4 cm, 5 mm, 3 mm)

on vibration isolation table (SMTT-66; JINSUNG LASER Co.) that is stimulated by

piezoelectric vibration generator (E501.00; PI industrial Inc.) Force sensor system loaded on

the vibration generator has been used for measurement of physical stimulations like vibration.

The stimulation has been applied on 10 µm deep spot from sensor surface with 200 Hz

vibration (see also Fig. S12). All electrical measurement of the crack based sensor were done

by data acquisition system (PXI-4071, National Instruments Inc.).

Violin sound measurement

The crack-based sensor is attached to the surface of a violin (Fig. 3a). The sensor measures the

strings’ vibration on the right side of the instrument above the F-hole that transmits the

resonance of air to the outside. The measured G-D-A-E string sounds reveal peak signals at

different frequencies that correspond with the known frequencies, as shown in Figure 3b. Time


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dependent resistance variations were measured by our sensor attached on the violin while

‘Salut d’Amour’ is played and they were converted into digital signals (Supplementary video

file; ‘Salut d’Amour’). From those signals, the real-time peak spectrogram was retrieved

(shown in the bottom image of Figure 3c). The harmonic tone of each note is recorded

correctly and well matched.

Micro-fluidic flow measurement

Micro-fluidic channel is fabricated by chemical bonding using O2 plasma (18 W applied

power for 1 min; PDC-32G (Harrick Plasma Inc.)) and treated at 70 ̊C, 1 hour (Fig. 3i) with

demolded PDMS channel (100 µm width, 20 µm height, and 1.2 mm length) and PDMS sheet

(spacer, 500 µm thick). The sensor is attached under the spacer to measure the flow rate of

fluid (Fig. S16). The fluid flow is induced by a micro-fluidic controller (PHD2000, Havard

apparatus Inc.) and the electric signal of the sensor is measured by PXI-4071 system (NI

instruments). Resistance changes caused by various flow rates (5~9 ml/min) is measured (Fig.

3i).

Time-resolved response measurement with force sensor and water droplet

The crack-based sensor’s each end is clamped by a custom built clamper (stretcher), and the

rest of sensor’s body stands freely. Force sensing probe (FT-s10000, FemtoTools) is attached

at the middle of the sensor, applying and measuring the force. The sensor’s response is

measured simultaneously by PXI-4071 system (National Instrument Inc.) while applying force

by step function and sinusoidal function (Figs. S17b, c). The response of crack-based sensor

takes place within 100ms. A super-hydrophobic surface is attached on the crack-based sensor

and 5µl water droplet was dripped on. A high-speed camera takes snapshots of water droplet

bouncing (Fig. S17e) and the difference in the electrical resistance (!!"" − !!" ) was

measured for ~0.35s.

Speech recognition test

The sensor is attached to human speaker’s neck firmly with a commercialized transparent

medical dressing (Tegaderm film, 3M). Resistance changes of the sensor is measured by PXI-

4071 system and analyzed by real-time fast Fourier transform. Ten speakers are asked to

repeat four different words (“go”, “jump”, “shoot”, and “stop”) more than ten times with the

sensor attached to the subjects’ neck. The same process is repeated at silent and noisy



environment (approximately 92 dB, measured by Type 2250, B&K Inc.). The isolated word

recognition method was used to estimate accuracy of speech recognition based on the work1.

To compare the performance of the crack-based sensor, commercialized microphones are also

used for the same experiment. A standing microphone (KMC-3500, Kalron Co.) and an

electret microphone (CMP-756, CUI Inc.) attached on person’s neck are used.

Theory Section

We find an equation for !(!) using the argument that the small variations in the crack

asperity due to grain shifts are distributed in the same manner as the large variations due to

grain piling, which is conventional for the renormalization group2 with the only a “size”

parameter – the strain !! that corresponds to the grain size (!! = ! ∙ !!):

! ! !" =! !

!

!!!", (3*)

where ! = !/!!. The general solution satisfying Eq. (3*) is

! ! = ! !" !!

, (4*)

where ! ! is an even function of its arguments. The well-known log-normal distribution

function belonging to the class of a so-called skew distribution with long tails

! ! = exp − ln !!!

!/!! /(!" !) (3)

satisfies Eq. (4*).



Figure S1. Average spacing between two adjacent cracks fabricated by different bending

radius of curvatures, ranging from 1 mm to 3 mm. Average spacing between two adjacent

cracks are shown to be controlled by using different radius of curvature bending.



Figure S2. Atomic force microscopy (AFM) results on crack surface with applied various

strains. (a) 3D image of crack within 0 % strain. (b) Profile of red dashed line in (a). (c) 3D

image of crack within 1 % strain. (d) Profile of red dashed line of (c) indicating the crack

depth to be about 40-50 nm. (e) 3D image of non-crack surface. (f) Metal grain size

distribution obtained from (e)



Figure S3. Current (I)-voltage (V) characteristic comparison between samples with

cracks (fabricated by 1 mm bending) (a) and without crack (b). (a) I-V results applied

various strains on crack based sensor. Large variations of electrical resistance against applied

strains are found. (b) I-V results applied various strains on non-cracked metal film. Minor

variations of electrical resistance (all graphs are overlapped.) against applied strains are found.

Less than 0.5 % applied stains cannot induce electrical resistance change for this non-crack

bare Pt film case.



Figure S4. Reproducible results obtained from 30 crack junction based sensors

fabricated by 1 mm curvature bending (with 0.1mm/min speed).



Figure S5. Durability tests (<5,000 cycles) with repeated loading–unloading of strain

(with 10 mm/min speed). (a) In the range of 0 – 0.5 % using 1 mm radius of curvature crack

based sensor. (b) In the range of 0 – 2 % using 1 mm radius of curvature crack based sensor.

The durability was examined by doing 5000 cyclic strain tests and the sensor performance

would remain unchanged up to about 1000 loading and unloading cycles under 0-0.5% strain

and about 500 cycles under 0-2% strain



Figure S6. Sensitivity (resistance changes) comparison at applied 0.5 % strain using

sensors made with difference curvature bending. Sensitivity (resistance changes) is shown

to be controllable by changing crack density made by bending with different curvature.

Sensitivities of samples made by using different curvature bending (blue – 1mm; red – 2mm;

yellow – 3mm) are remarkably higher than the one without crack (black curve).

Figure S7. Comparison of the present sensor gauge factor with previous studies. Gauge

factors of sensors reported at 2 % applied strain are shown (red). The gauge factor of our

crack sensor is 2079 (blue).



Figure S8. Strain-dependent gauge factor comparison between our crack sensor and

graphene platelet case [8] of main reference by taking the derivative of !/!! with

respect to strain [Gauge Factor = (!"/!!)/!"]. Our case clearly shows much higher

gauge factors at 0-2% strain. Note also that there are inconsistencies among data

retrieved from [8].



Figure S9. Fabrication procedure and image for multiplexing array sensor. (a) Illustration

images of each processing steps. (b) Photograph image of the 8 × 8 multiplex sensor.



Figure S10. Shadow metal mask designs used for fabrication of multiplex sensor.



Figure S11. Resistance change with applied vibration and static pressure. Inset shows the

frequency, 200 Hz, obtained by Fourier transform with vibration result.

Figure S12. Flexibility test. (a) Scheme about flexibility test. (b) Sensitivity comparison of

the crack sensor made on 50 µm PET with 200 Hz vibration. (c) Sensitivity comparison of the

crack sensor made on 6 µm PET with 200 Hz vibration.



Figure S13. Vibration measurements from bent multi-pixel array crack sensor. (a) The

8×8 array of the crack sensor loaded on a curved PVC pipe (3 cm radius of curvature). The

overall dimension of the device is 5×5 cm, and the pixel is 2×2 mm. The red marked region is

the location where 100 Hz vibration is given by the piezoelectric vibrator (E501.00: PI

industrial Inc.) (b) Distribution of resistance changes due to the given vibration in 8x8 array

sensor. The resistance change at the spot where the vibration is given is the maximum (white

column) and pixels surrounding the vibration point show lower resistance changes decreasing

as the pixel is farther from the vibration spot which indicate damping behavior (blue columns).

Figure S14. Crack junction-based sensor applications for speech pattern recognition. (a)

An image of the Electret Condenser Microphone (ECM) attached on a neck for human speech

recording. (b) An image of the standing microphone for human speech recording. (c) The

sensing accuracy comparisons (over 400 speeches with one person) between the speech

pattern recognition results with a crack-based sensor, ECM and standing microphone are

shown. An accuracy of 97.5% is obtained from the crack sensor even with noise.



As shown in Fig. S14c, The accuracy of the standing microphone decreases by as much as

28.2%, whereas the crack sensor maintains its accuracy of approximately 97.5% (Fig. S13c)

which is slightly higher than the case of ECM for simple word recognition.

Figure S15. Crack junction-based sensor applications for human physiology monitoring.

Representative characteristic of the gray region from Figure 3h showing the typical

characteristics of the wrist pulse including percussion, tidal, and diastolic waves.



Figure S16. Crack junction-based sensor applications for flow rate indicators. (a)

Schematic of stack information in the sensing system. Inlet and outlet flow with various flow

rates (flow rate of 5-9 ml/min in the microfluidic channel with a width of 100 µm, height of

100 µm, and length of 10 mm) on a 500-µm-thick spacer (PDMS) to prevent electrical failure.

(b) Linear change in resistance as a function of flow rate.

The crack-based sensor is integrated into a microfluidic system to measure the input flow rate.

An image and scheme of the sensor embedded into a micro-fluidic system are presented in

Figures S16a. The pressure inside the micro-fluidic channel is higher than that outside, and it

varies depending on the flow rate, which can induce a spacer (500-µm-thick PDMS between

the channel and device) sagging down and touching the sensor such that the resistance can be

varied with the flow rate (Fig. S16b).



Figure S17. Time-resolved response test with force sensor and water droplet. (a) Scheme

about force sensor experiment13. (b) Resistance distribution of crack sensor in step functional

pressure. We can know that the sensor response within 100 ms. (c) Resistance distribution of

crack sensor in sinusoidal functional pressure. (d) The corresponding snapshots from a high-

speed camera are shown. (e) The difference in the electrical resistance (!!"" − !!") for the

duration of ∼0.35 s. Each dotted line relates the collision of a droplet to the peak position.



Figure S18. S (conductance) curve revealing fluctuations. The variation of ! = !!/! for

crack based sensor fabricated by 1 mm radius of curvature is shown as strain is applied. Inset

shows the enlarged view in red square revealing a large fluctuation of S.



Figure S19. An illustrative model conductance with disconnection/reconnection spikes at

lower strain that closely simulates the experimental derivative and averaged derivative

curves in Fig. 4a and b. (a) The real crack image is on the left. The schematic of creeping

motion of the crack lips given in the following boxes illustrates the corresponding

disconnection/reconnection events with spikes down and up in the model conductance curve,

shown in (b). (c) The negative derivative of the model curve from (b) (black) together with the

averaged one (red). All model curves in (c) closely mimic experimental Fig. 4a and b from the

main text, respectively. (d) The real crack image at larger strains is on the left. A maximim

simplified schematic of crack lips ignoring the creeping motion and reconnection events is

given in the following boxes. The model grasps the essence of the conductance stepwise

reduction with the increase of strain due to disconnection of the contacts. The orange ellipse



encompasses the small asperity “staircase” which is statistically scale invariant to the large

scale “staircase” on the right. (e) A simplified model conductance ignoring the spikes of

reconnection. (f) The negative derivative of (e) (black) together with the averaged one (red).

Figure S20. Dynamic motion test with the crack based sensor fabricated by 1 mm radius

of bending curvature. (a) Sensitivity change of crack sensor by increasing the sweep rate. (b)

Hysteresis test about loading and unloading (solid line - loading; dashed line - unloading).

Although the hysteresis remains negligible for very different sweep rates, the resistance curves,

normalized to the initial resistance grow somewhat lower at higher sweep rates. This behavior

is due to the stress relaxation time that should pass before the initial resistance diminishes to

its minimal value at the slowest sweep rate of 0.1 mm/min, therefore, being the resistance

divided by this minimal value, the normalized resistance for 0.1 mm/min becomes the highest.



Figure S21. Crack gap analysis in several applied strains via SEM results (with 30

samples). (a) Crack gap width variation vs. strain (black squares) and the fitting straight line

(red). Gap analysis is performed by imaging processing software, “Image J”. (b)

Representative SEM images used for the crack gap width determination. (c) The schematic of

the crack lip asperity for acquiring the statistics of the contact step heights. The heights are

defined as the distance between the nearest and extreme in the strain direction.



Figure S22. Additional tensile test of the crack sensor with 100 nm thickness Pt film. (a)

2 % cyclic tensile test at 0.1 mm/min. (b) Hysteresis test about loading and unloading (solid

line - loading; dashed line - unloading). (c) Gauge factor comparison with different Pt film

thickness.

Even at the slowest sweep rate of 0.1 mm/min the hysteresis persists because of participation

of mode 2 (in fracture mechanics mode 2 is characterized by a shear stress acting parallel to

the plane of the crack and perpendicular to the crack front)14 in sliding crack configuration

distortion that supports (via stronger mechanical stress for the thicker film) earlier snapping of

the contact (larger resistance) and sooner contact recovery (lower resistance) during unloading.

Therefore, for this film of 100 nm hysteresis loops are clockwise. Note that the magnitude of

the normalized resistance at 2% strain is nearly four times lower than for a 20 nm Pt film. This

fact indicates keeping a better contact between the thicker lips of the crack in a 100 nm

thickness Pt film as would be expected for stronger pressing forces in the thicker film.



Figure S23. SEM image of 20 nm gold film on PUA substrate. (a) before bending (b) after

1 mm curvature bending



Figure S24. Overall fabrication procedure for crack based sensor.



Table ST1. Gauge factor comparison of sensors made of gold and platinum. 20nm gold

film case does not show crack formation at 1 mm curvature bending.



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