supplementary information for - pnas · supplementary information for a mechanically driven form of...

Supplementary Information for

A mechanically driven form of Kirigami as a route to 3D mesostructures in micro/nanomembranes

Yihui Zhanga,1 , Zheng Yanb,1, Kewang Nanc, Dongqing Xiaod, Yuhao Liub, Haiwen Luane, Haoran Fue,f, Xizhu Wangb, Qinglin Yangb, Jiechen Wangb, Wen Reng, Hongzhi Sib, Fei Liua, Lihen Yangb, Hejun Lig, Juntong Wangc, Xuelin Guob, Hongying Luoe,h, Liang Wange,i, Yonggang Huange,2 , John A. Rogersb,d,j,2 aCenter for Mechanics and Materials, AML, Department of Engineering Mechanics, Tsinghua

University, Beijing 100084, P.R. China. bDepartment of Materials Science and Engineering and Frederick Seitz Materials Research

Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. cDepartment of Mechanical Science and Engineering, University of Illinois at Urbana-

Champaign, Urbana, IL 61801, USA. dDepartment of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. eDepartments of Civil and Environmental Engineering and Mechanical Engineering, Center for

Engineering and Health, and Skin Disease Research Center, Northwestern University, Evanston, IL 60208, USA.

fDepartment of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, P.R. China.

gDepartment of Chemical & Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.

hSchool of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P.R. China.

iInstitute of Chemical Machinery and Process Equipment, Zhejiang University, Hangzhou 310027, P.R. China.

jBeckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.

1These authors contributed equally to this work.

2To whom correspondence may be addressed. E-mail: [email protected] or [email protected]. This PDF file includes:

Figures S1 to S23

B. Multiple structures

Compress the Kirigami patterns; fix the structures by bonding to the pads

A. Single structure

No compression

Compressed by ~14%

Compressed by ~47%

Figure S1. Illustration of the Kirigami process applied to macroscale sheets of plastic. (A) A thin (~80 μm thick) plastic film in a freestanding state and in states of bi-axially compressed (14% and 47%) induced by manual application of force. (B) Four 2D plastic precursors with the same overall shape but different Kirigami cuts, and the corresponding 3D structures under compression (~ 47%). All scale bars are 20 mm.

x

y z

Design Kirigami patterns; Form 2D precursor structures; stretch the assembly platform

Transfer with selective bonding; release the assembly platform; Pop up to form 3D structures

0 90

εmax‐substrate (%)

0.0 1.3

εmax‐membrane (%)

0 80

εmax‐substrate (%)

0.0 1.3

εmax‐membrane (%)

Figure S2. Finite-element analysis (FEA) results that illustrate the formation of 3D structures from 2D silicon nanomebranes (Si NMs) bonded at selected regions (red dots) to a biaxially stretched silicone elastomer. Compressive forces induced by relaxing the strain in the elastomer lead to coordinated out-of-plane deformations and translational motions in the Si NMs, yielding 3D structures with geometries that depend highly on the geometries of the 2D precursors and the Kirigami cuts in them.

Figure S3. Images of the complex 3D membrane mesostructure in Fig. 1C, with three viewing angles that differ from the one in Fig. 1C. The scale bar is 200 μm.

Top view (FEA) Top view (SEM)

Front view (FEA) Side view (FEA)

Figure S4. Illustration of the reductions in strains that follow from the use of Kirigami. (A) Comparison of strain distributions in the silicon layers of 3D structures formed with two different 2D circular membranes (left: without any cuts; right: with cuts). (B) Comparison of strain distributions in the silicon layers of 3D structures formed with two different 2D square membranes (left: without any cuts; right: with cuts). All of these structures incorporate bilayers of silicon/polymer (each ~ 300 nm in thickness). The prestrain used in all cases is 80%. The color represents the magnitude of the strain.

A. 3D structures formed from two 2D circular membranes (one without and another with cuts)

B. 3D structures formed from two 2D square membranes (one without and another with cuts)

0.0

1.3 εmax (%)

2D precursor 3D structure 2D precursor 3D structure

0.0

5.0 εmax (%) Reduced

strain level

0.0

1.5 εmax (%)

2D precursor 3D structure 2D precursor 3D structure

0.0

4.8 εmax (%) Reduced

strain level

strain concentration

strain concentration

No cut With cuts

No cut With cuts

Figure S5. Effect of Kirigami design on the shapes of 3D structures. (A) Images with different viewing angles of a 3D structure formed from a 2D circular membrane without any Kirigami cuts and with a prestrain of 35%. (B) Images with different viewing angles of a 3D structure formed from a 2D circular membrane with both radial and circumferential cuts and with a prestrain of 90%. (C) Images with different viewing angles of a 3D structure formed from a 2D circular membrane with circumferential cuts and a prestrain of 64%. (D) Images with different viewing angles of a 3D structure formed from a 2D circular membrane with serpentine cuts and a prestrain of 64%. The design without any cuts yields a mesostructure with a basic, modest type of 3D configuration, as evidenced by the small aspect ratio (α = dout-of-plane / din-plane, where dout-of-plane and din-plane denote the maximum out-of-plane dimension and in-plane extent, respectively; α = 0.3 for the case shown here). This ratio is ~ 2.3 times smaller than that of the 3D structure formed with Kirigami cuts in (B). The scale bars in all SEM images are 200 μm.

A. 3D structure formed from a 2D circular membrane without any cuts

FEA (3D view) Experiment (3D view)

FEA (top view) FEA (front view)

εpre=35%, aspect ratio dout-of-plane / din-plane ≈ 0.30

din−plane

d out

-of-

plan

e

B. 3D structure formed from a 2D circular membrane with both radial and circumferential cuts




d out

-of-

plan

e

din−plane

C. 3D structure formed from a 2D circular membrane with circumferential cuts




din−plane

d out

-of-

plan

e

D. 3D structure formed from a 2D circular membrane with serpentine cuts




d out

-of-

plan

e

din−plane

Figure S6. 2D precursor patterns for the 3D structures shown in Fig. 1 A-G, where the bonding regions are highlighted in red.

A B

D E

C

G

F

ε max─

mat

eria

l (%

)

A FEA Model

0.8 0.6 0.4 0.2 0.0

0.6

0.4

0.0

0.2

ε max─

mat

eria

l (%

)

B FEA Model

0.8 0.6 0.4 0.2 0.0

1.2

0.8

0.0

0.4

ε max─

mat

eria

l (%

)

C FEA Model

0.8 0.6 0.4 0.2 0.0

εcompr=0% 25% 50%

1.2

0.8

0.0

0.4

εcompr=0% 25% 50% εcompr=0% 25% 50%

Figure S7. Maximum material strain as a function of the square root of the compressive strain, for various 3D structures formed using different Kirigami cuts: A) symmetric cuts along the radial direction (with t/L = 0.0011, wcut/L = 0.044, and lcut/L = 0.77); B) anti-symmetric cuts in a serpentine configuration (with t/L = 0.0011, wcut/L = 0.044, and lcut/L = 1.03); C) symmetric cuts partially along the radial direction and partially along the circumferential direction (with t/L = 0.0011, wcut/L = 0.044, and lcut/L = 0.72); D) symmetric cuts along the circumferential direction (with t/L = 0.0011, wcut/L = 0.044, and lcut/L = 0.77). The results show a proportional dependence of the maximum material strain on the square root of the compressive strain. For the Kirigami patterns in (C) and (D), the lengths (lcut) correspond to the circumferential cuts located at the outer region of the membrane.

ε max─

mat

eria

l (%

)

D FEA Model

0.8 0.6 0.4 0.2 0.0

1.2

0.8

0.0

0.4

εcompr=0% 25% 50%

compr compr

compr compr

0.00 0.54

εmax (%)

0.00 1.09

εmax (%)

0.00 1.16

εmax (%)

0.00 1.10

εmax (%)

A B FEA Model

C

t / L

0.012 0.009 0.006 0.003 0.000

6.0

4.0

0.0

2.0

8.0

10.0

FEA Model

t / L 0.012 0.009 0.006 0.003 0.000

6.0

4.0

0.0

2.0

FEA Model

t / L 0.012 0.009 0.006 0.003 0.000

0.0

6.0

4.0

2.0

8.0

10.0

Figure S8. Maximum material strain as a function of dimensionless thickness, for various 3D structures formed using 100% prestrain (i.e., corresponding to 50% compressive strain) and different Kirigami patterns: A) symmetric cuts along the radial direction (with wcut/L = 0.044 and lcut/L = 0.77); B) anti-symmetric cuts in the serpentine configuration (with wcut/L = 0.044 and lcut/L = 1.03); C) symmetric cuts partially along the radial direction and partially along the circumferential direction(with wcut/L = 0.044 and lcut/L = 0.72); D) symmetric cuts along the circumferential direction (with wcut/L = 0.044 and lcut/L = 0.77). The results show a proportional dependence of the maximum material strain on the normalized thickness. For cases in (C) and (D), the lengths (lcut) correspond to the circumferential cuts located at the outer region of the membrane.

D

FEA Model

t / L 0.012 0.009 0.006 0.003 0.000

0.0

6.0

4.0

2.0

8.0

10.0

0.0073 0.0127 t/L=0.0011

0.0073 0.0127 t/L=0.0011 0.0073 0.0127 t/L=0.0011

ε max─

mat

eria

l (%

)

ε max─

mat

eria

l (%

)

ε max─

mat

eria

l (%

)

ε max─

mat

eria

l (%

)

0.00 6.77

εmax (%)

0.00 8.82

εmax (%)

0.00 9.45

εmax (%)

0.00 9.79

εmax (%)

0.0073 0.0127 t/L=0.0011

Figure S9. Maximum material strain as a function of dimensionless cut width, for various 3D structures formed using 100% prestrain (i.e., corresponding to 50% compressive strain) and different Kirigami patterns: A) symmetric cuts along the radial direction (with t/L = 0.0011 and lcut/L = 0.77); B) anti-symmetric cuts in the serpentine configuration (with t/L = 0.0011 and lcut/L = 1.03); C) symmetric cuts partially along the radial direction and partially along the circumferential direction (with t/L = 0.0011 and lcut/L = 0.72); D) symmetric cuts along the circumferential direction (with t/L = 0.0011 and lcut/L = 0.77). The results show that the material strain decreases with increasing cut width. For the cases in (C) and (D), the lengths (lcut) correspond to the circumferential cuts located at the outer region of the membrane.

A B

C

1.0

1.5

0.5

0.0 0.12 0.09 0.03 0.00

wcut / L

0.4

0.2

0.0 0.16 0.08 0.04

wcut / L

0.8

0.00 0.12

1.6

0.8

1.2

0.4

0.0 0.16 0.08 0.04

wcut / L 0.00 0.12

0.6

wcut / L=0.0073 0.1455 0.0582

D

wcut / L

1.6

0.8

1.2

0.4

0.0 0.16 0.08 0.04 0.00 0.12

wcut / L=0.0073 0.1455 0.0582

wcut / L=0.0073 0.1018 0.0582 wcut / L=0.0073 0.1455 0.0582

0.06

ε max─

mat

eria

l (%

)

ε max─

mat

eria

l (%

)

ε max─

mat

eria

l (%

)

ε max─

mat

eria

l (%

)

0.00 1.36

εmax (%)

0.00 1.14

εmax (%)

0.00 0.69

εmax (%)

0.00 1.18

εmax (%)

Figure S10. Maximum material strains near the corners of the Kirigami cuts and near the bonding region as a function of the dimensionless cut length, for various 3D structures formed using 100% prestrain (i.e., corresponding to 50% compressive strain) and different Kirigami patterns: A) symmetric cuts along the radial direction (with t/L = 0.0011 and wcut/L = 0.044); B) anti-symmetric cuts in the serpentine configuration(with t/L = 0.0011 and wcut/L = 0.044); C) symmetric cuts partially along the radial direction and partially along the circumferential direction(with t/L = 0.0011 and wcut/L = 0.044); D) symmetric cuts along the circumferential direction(with t/L = 0.0011 and wcut/L = 0.044). For the cases in (C) and (D), the lengths (lcut) correspond to the circumferential cuts that are located at the outer region of the membrane. The lengths of the inner cuts scale with those of the outer cuts, with both reaching the corresponding limit (i.e., representing a throughout cut) simultaneously.

A B

C

0.45 0.30 0.15 0.00 0.60 0.75

2.0

1.0

0.0

2.5

lcut / L

0.6 0.4 0.2 0.0 0.8 1.0

0.4

0.2

0.0

0.8

lcut / L

0.9 0.6 0.3 0.0 1.2 1.5

4.0

2.0

0.0

5.0

lcut / L

Nearby bonding region

Nearby cut corners

0.6


Nearby cut corners

1.0

3.0


Nearby cut corners

0.90

0.5

1.5

D

0.3 0.0 0.9 1.2

1.2

0.0

1.8

0.89%

lcut / L


Nearby cut corners

0.6

0.3

1.5

0.9

0.6

ε max─

mat

eria

l (%

)

ε max─

mat

eria

l (%

)

ε max─

mat

eria

l (%

)

ε max─

mat

eria

l (%

)

0 εm

εmax

0 εm

εmax

0 εm

εmax

0 εm

εmax

lcut / L=0.090 0.538 0.852

εm=1.18% 1.05% 1.58%

lcut / L=0.109 0.547 1.040

εm=1.62% 1.05%

lcut / L=0.110 0.459 0.896

εm=0.59% 0.57% 0.68%

lcut / L=0.207 0.413 1.239

εm=5.01% 1.20% 0.96%

Figure S11. Four 3D structures (with hybrid configurations consisting of both membranes and ribbons) and their corresponding FEA results. The scale bars in all images are 200 μm.

2D precursor 3D structure (FEA) 3D structure (Experiment)

Figure S12. (A) 2D precursor for complex architecture with a geometry that resembles a ‘crown’, as shown in the top middle panel of Fig. 4B, where the bonding regions are highlighted in red. (B) Images of the 3D configurations with four different viewing angles.

Top view

Front view Side view

3D view

200 μm 200 μm

200 μm 200 μm

B. 3D configurations A. 2D precursor

Figure S13. 2D precursors for the four 3D structures shown in Fig. 5A (A) and in Fig. 5B (B), where the bonding sites are highlighted in red.

A

B

Figure S14. Comparison between experimental images and FEA predictions for various 3D structures made from polymer (SU8). The scale bars in all images are 200 μm.

B

C

2D precursor

3D structure (FEA) 3D structure (Experiment)

2D precursor

3D structure (FEA) 3D structure (Experiment)

A

Figure S15. Comparison between experimental images and FEA predictions for two 3D structures (made from Au). The scale bars in all images are 200 μm.

A B

Figure S16. Comparison between experimental images and FEA predictions for various 3D structures made from plastic films at macroscale. The scale bars in all images are 20 mm.

C. Patterns with anti‐symmetric cuts D. Patterns with asymmetric cuts

B. Patterns with symmetric cuts A. Patterns with no cut

Figure S17. Process steps for making silicon nanodisks on a silicon-on-insulator wafer (200 nm thicknesses of silicon) by soft lithography. The diameters of the nanodisks are 200 nm.

SU8

Si

SiO2

Si

PDMS stamp

Soft lithography

RIE etching to form SU8 masks

Bosch process to form Si nanodisks

RIE etching to remove SU8 masks

1 µm

Figure S18. Comparison between experimental images and FEA predictions for four hybrid 3D structures of polymer (SU8) and patterned Au. The scale bars in both images are 200 μm.

2D precursor

3D structure (FEA)

3D structure (experiment)

2D precursor

3D structure (FEA)


2D precursor

3D structure (FEA)


2D precursor

3D structure (FEA)


a b c d

Figure S19. Cyclic testing of an optical transmission window with engineered thickness variations, under uniaxial strain with an amplitude of ~ 65% at a frequency of ~ 0.04 Hz. The three images correspond to the initial state, and the states after 100 and 150 cycles.

Initial configuration After 100 cycles After 150 cycles

Si

SiO2

Si

1. Pattern AZ 5214

2. RIE etch Si

Si pattern Pattern SU8 on Si in a matching geometry

SU8 pattern

3. Use acetone to remove AZ 5214

Partially undercut in HF

AZ 5214 bonding sites

Fully undercut in HF

Pattern AZ 5214 on selective areas

Pick up 2D precursors using PDMS stamp

Pick up 2D precursors using PVA tape

UVO treatment

unstreched silicone

PDMS stamp

PVA tape

UVO treatment

Laminate PVA tape onto stretched silicone and bake

bonding sites

2. Use acetone to remove AZ5214 sacrificial layer

1. Use water to remove PVA tape

stretched silicone

Relax stretched silicone to form 3D Si NMs Kirigami

Figure S20. Schematic illustration of steps for fabricating 3D Kirigami structures of bilayers of Si NMs and layers of polymer (SU8).

Figure S21. Schematic illustration of steps for fabricating 3D Kirigami structures of polymer (SU8).

Si wafer

Thermal oxidation

SiO2 Pattern 2D SU8 precursors

SU8 pattern

Partially undercut in HF

AZ 5214 bonding sites

Fully undercut in HF

Pattern AZ 5214 on selective areas

Pick up 2D precursors using PDMS stamp

Pick up 2D precursors using PVA tape

UVO treatment

unstreched silicone

PDMS stamp

PVA tape

UVO treatment

Laminate PVA tape onto stretched silicone and bake

bonding sites

2. Use acetone to remove AZ5214 sacrificial layer

1. Use water to remove PVA tape

stretched silicone

Relax stretched silicone to form 3D SU8 Kirigami

Figure S22. (A) Schematic illustration of steps for fabricating 3D hybrid Kirigami structures of Si NMs and polymer (SU8), as shown in Fig. 5C. (B) Schematic illustration of steps for making 3D hybrid Kirigami structures of Si nanodisks on layers of polymer (SU8) as shown in Fig. 5D.

Si

SiO2

Si

1. Pattern AZ 5214

2. RIE etch Si

Si pattern

3. Use acetone to remove AZ 5214

Similar procedures with those of making 3D SU8 Kirigami

SU8 pattern

Pattern 2D SU8 precursors

A

Si

SiO2

Si

Soft lithography to Make Si nanodisks


Si nanodisks


B SU8 pattern

Figure S23. Schematic illustration of steps for fabricating 3D Kirigami structures of Au and polymer (SU8).

Si wafer

Thermal oxidation

SiO2 Au patterns


Photolithography, e-beam evaporation and lifting off to form Au patterns

Spin-casting Omni-coat layer

Omni-coat adhesive layer


RIE etching to remove exposed Omni-coat adhesive layer

SU8 patterns

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