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Wrinkle configurations can provide brittle Si ribbons with excellent stretchability via mechanical ..... black line with red solid circles represents the strain of the Si.
Soft Matter

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Controllable wrinkle configurations by soft micropatterns to enhance the stretchability of Si ribbons Yin Huang,ab Hang Chen,ab Jian Wuab and Xue Feng*ab Wrinkle configurations can provide brittle Si ribbons with excellent stretchability via mechanical buckling. We propose a strategy using micro-patterns to control the wrinkle configurations in ‘pop-up’ and ‘pop-

Received 18th November 2013 Accepted 5th December 2013

down’ styles, as well as the wrinkle's wavelength. After the wrinkle configuration is stretched flat, the micro-patterns will deform to buffer the Si ribbons, which enhances the additional stretchability of such structures. The experimental results show that the micro-patterns determine the wrinkle configurations

DOI: 10.1039/c3sm52906a

of Si ribbons and their stretchability can reach 51.2%. The analytical modeling and FEM simulation reveal

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the mechanism of such a phenomenon.

Introduction Mechanical instability can offer stretchability to rigid and brittle materials with buckling or wrinkling congurations. Stretchable inorganic electronics made by a transfer printing process,1,2 based on wavy structures with such a mechanism, are of high interest because of their potential application in many devices, such as ferroelectric ceramics,3 electronic eye cameras,4 and thermal management.5 These structures enable the production of high-performance stretchable systems and accommodate larger tensile and compressive strains through changes in the wave amplitudes and wavelength of wrinkles.6,7 However, previously reported wavy structures provide little chance to control the geometries of the wavy ribbons (e.g., the amplitude and wavelength) and the maximum strain that they can bear. Usually, the wavy structures will become at; in other words, the wave amplitude decreases to zero and the wavelength increases to innity when the applied strain approaches the prestrain. Aer this, the structures will be prone to failure if the applied strain exceeds the pre-strain and still increases. Therefore, the geometry of the wrinkles denes the maximum strain and the stretchability that ensure the structures’ safety. Sun8,9 reported an improved method which spatially controls the adhesion sites by using lithographically patterned surface chemistry and the elastic deformation of a supporting substrate to tune the geometry of wavy ribbons. However, the upper limit of stretchability is still lower than the pre-strain due to the adhesion sites. In addition, a lot of research has reported that bio-inspired micro- and nanostructure surfaces can reversibly control the adhesion and friction,10–14 such as the setae of geckos, which are

a

AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China. E-mail: [email protected]

b

Center for Mechanics and Materials, Tsinghua University, Beijing 100084, China

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capable of attaching and detaching their adhesive toes to vertical and inverted surfaces, however, there is relatively little work focused on tuning the wrinkles’ congurations through micro-patterns.15,16 Here, we report a strategy using micropatterns to not only enhance the surface adhesion, but also control the geometry as well as the wrinkle congurations of Si ribbons in ‘pop-up’ and ‘pop-down’ styles. Moreover, the micropatterns can deform to buffer the Si ribbons when the external strain is larger than the pre-strain. The Si ribbons do not fracture even the applied strain (51.2%) is much larger than prestrain (33.8%).

Fabrication of wavy Si ribbons on a micro-patterned substrate Fig. 1a schematically summarizes the key steps for fabrication of wavy Si ribbons on a PDMS substrate with micro-patterns. The rst step involves classical molding techniques using a silicon wafer with rectangle punches of 10 mm in height as a mold, which were fabricated with standard photolithography techniques (step i). To ease the next demolding step, the patterned silicon wafer was silanized with trimethylchlorosilane for 1 hour and baked on a hot plate at 80  C for 1 minute. PDMS elastomer (Sylgard 184, Dow Corning) with a thickness of 1 mm was cast into the silanized Si wafer and cured at 60  C for 4 hours and then peeled off from the Si wafer (step ii). Then the PDMS surface was patterned with negative punches of 10 mm in height. We denote the width and spacing of the rectangle punches on the PDMS surface as Wp and Wd, respectively, as shown in Fig. 1a. Dry etching with Reactive Ion Etching (RIE) through a photoresist mask dened the Si lm into dogbone-like ribbons with a thickness of 200 nm, widths of 100 mm and lengths of 5 mm as well as square pads (500  500 mm) at the ends of the ribbons. Then the structure was immersed in dilute

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(a) Process steps for the fabrication of wavy Si ribbons on a PDMS substrate with micro-patterns. (b) SEM images of ‘pop-up’ wrinkles on a patterned PDMS substrate with different punches under a large pre-strain. (c) SEM images of ‘pop-down’ wrinkles on a patterned PDMS substrate with different punches under a larger pre-strain.

Fig. 1

hydrouoric (HF) acid to completely etch off the SiO2 layer under the lengths of the ribbons, but only partially remove this layer under the pads.1,17 The Si ribbons were then transferred onto the patterned PDMS substrate under large and uniaxial pre-strain (3pre ¼ DL/L for length changed from L to L + DL) (step iii), which were partially brought into conformal contact with the rectangular punches of the PDMS. Finally, releasing the pre-strain in the PDMS led to wrinkle congurations of the Si ribbons corresponding to the welldened ‘pop-up’ and ‘pop-down’ styles, respectively (step iv). ‘Pop-up’ means the wrinkles are only in contact with the tops of the punches. In contrast, ‘pop-down’ means the wrinkles are in contact with the bottoms of the punches. The micro-patterns enhance the surface adhesion10,11 and trigger the Si ribbons’ buckling via the contact sites. Actually, all the geometry of the rectangular punches, the pre-strain and the adhesion strength of the patterned surface substantially determine the style, the wavelength and amplitude of the wrinkle congurations. Thus, we propose strategies for using micro-patterns to control wrinkle congurations leading to enhancement of the stretchability of wavy Si ribbons. Fig. 1b shows scanning electron microscopy (SEM) images of ‘pop-up’ wrinkles on a patterned PDMS substrate under a large pre-strain (>30%). The yellow lines schematically demonstrate

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the topography prole of the patterned PDMS substrate. The le images show a series of ‘pop-up’ wrinkles on patterned PDMS with different punches, which have relatively larger widthspacing ratios of Wp/Wd ¼ 10/3, Wp/Wd ¼ 10/5 and Wp/Wd ¼ 20/3 (from top to bottom), respectively. The ‘pop-up’ wrinkles stand on the top surface of the punches and their wavelengths are dened by the width and spacing of the punches. This observation suggests that the congurations of the wavy Si ribbons are totally determined by the geometry of the micro-pattern. In other words, the material property of Si and PDMS does not affect the wavelength. This phenomenon is signicantly different from other such cases of Si ribbons on a at PDMS substrate.7,18 We nd that the wavelength of the Si ribbons above on at PDMS should be about 23 mm as predicted by the ¯ f/(3E ¯ s)]1/3/(1 + 3pre)(1 + x)1/3,18 where E ¯ f, hf equation l ¼ 2phf[E ¯ s are the plane strain modulus, thickness of Si ribbons and and E the plane strain modulus of PDMS, respectively, and x ¼ 53pre(1 + 3pre)/32. However, the actual wavelengths in our experiment are 130 mm, 150 mm and 230 mm, respectively, which are totally decided by the geometry of the micro-patterns. The right image shows the top views of the ribbon array on patterned PDMS and they have uniform, periodic ‘pop-up’ wrinkles with almost the same wavelengths and amplitudes. The contact sites between the Si ribbons and the top surface of the punches constrain the

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deformation due to the interface adhesion, and then the noncontacting parts of the Si ribbons across the punches are prone to deect upward due to buckling aer releasing the pre-strain. More detailed analysis appears subsequently based on the minimum energy principle. Fig. 1c shows the ‘pop-down’ style of wavy Si ribbons on patterned PDMS aer releasing the pre-strain. The SEM images demonstrate a series of ‘pop-down’ wrinkles on a patterned PDMS substrate under a larger pre-strain (>20%). For the case of the ‘pop-down’ wrinkles, the rectangular punches of the PDMS have relatively small width-spacing ratios of Wp/Wd ¼ 5/3, Wp/Wd ¼ 3/5 and Wp/Wd ¼ 3/10 (le image, from top to bottom), respectively. The parts of the Si ribbons over the spacing of two adjacent punches deect downward and come into contact with the bottom of the punches aer releasing the pre-strain. The total energy, including the deformation energy of the Si ribbons and the adhesion energy between Si and PDMS, determines the buckling conguration of the Si ribbons. The Si ribbons buckle downward, debond from the punches’ top surface and create a new contact area on the spacing region to reach the optimal conguration due to minimizing the total energy. The right image shows that the wavelength of the wrinkles is almost equal to the total length of the spacing and punch width (e.g. Wd + Wp). Here, the actual wavelengths in our experiment are 80 mm, 80 mm and 130 mm, respectively, which are totally decided by the geometry of the micro-patterns but not affected by the materials’ modulus. Micro-patterns (e.g. punches) with different width-spacing ratios lead to different buckling congurations (Fig. 1b and c) due to the total energy of such congurations competing with each other. More detailed analysis appears subsequently. In this sense, the pattered PDMS with rectangular punches can not only control the wavelength of the wrinkles, but also decide the wrinkle congurations in ‘pop-up’ and ‘popdown’ styles.

Mechanical models Fig. 2(a) and (b) schematically show the ‘pop-up’ wrinkles and ‘pop-down’ wrinkles aer releasing the pre-strain in the PDMS

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substrate, respectively. For the upward buckling mode, the Si ribbons are only in contact with the tops of the punches, inducing the ‘pop-up’ wrinkles. For the downward buckling mode, the Si ribbons debond from the tops of the punches, adhere to the surface at the bottoms of the punches and create a new contact area on the spacing region, inducing the ‘popdown’ wrinkles. In this paper, a Si ribbon on a patterned substrate is modeled as an elastic nonlinear von Karman beam with out-of-plane displacement w and in-plane displacement u1.19 The energy method is adopted to determine the buckling mode and buckling geometry. The total energy involves the bending energy and membrane energy in the Si ribbons and the interface adhesion energy between the Si ribbons and patterned PDMS substrate, expressed by U ¼ Ub + Um + Us

(1)

where Ub, Um and Us represent the bending energy, the membrane energy and the interface adhesion energy, respectively. Further analysis is presented in the following sections to obtain the total energy for the ‘pop-up’ and ‘pop-down’ wrinkles, respectively. Analysis for the ‘pop-up’ wrinkles For “pop-up” wrinkles, the out-of-plane displacement can be characterized by 8   > < wup1 ¼ 1 A 1 þ cos px1 ; L1 \x1 \L1 2 L1 wup ¼ (2) > : wup2 ¼ 0; L1 \jx1 j\L2 where L1 ¼ L2  S/2 represents the half wavelength of the wrinkles, L2 ¼ (Wd + Wp)/2 represents the half overall length of the spacing and the width of punch. The wave amplitude A and contact region S are to be determined by the minimum energy principle. The bending energy for the “pop-up” wrinkles can be obtained by substituting eqn (2) into the following expression  2 ð L2 1 E f h3 d2 w h3 E f p4 A2 Ub1 ¼ dx ¼ (3) 1 dx1 2 96L1 3 L2 2 12 ¯ fh3/12 represents the bending stiffness.19 where E The membrane strain 311 is  2 du1 1 dw þ 311 ¼ dx 2 dx

(4)

The rst term of the right part of eqn (4) is the gradient of the in-plane and the second term of the right part of eqn (4) is the rotation caused by the deection. The membrane force N11 ¼ ¯ fh311 is obtained by Hooke's law, where E ¯ f represents the plane E strain modulus of the Si ribbons. Then the shear traction at the Si ribbon and PSMS substrate is given by T1 ¼ Fig. 2 Schematic diagram of the wrinkles’ configuration after releasing the pre-strain in the PDMS. (a) ‘Pop-up’ wrinkles. (b) ‘Popdown’ wrinkles.

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dN11 dx

(5)

The interface shear traction has very little effect on the wavelength and amplitude of the wrinkles,20 which requires that

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the membrane strain is constant. Then we can solve the membrane strain by 311 ¼

p2 A2  3pre 16L1 L2

C3 ¼

(6) C4 ¼

Furthermore, the membrane energy can be calculated by

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Um1 ¼ E¯ fhL2(1 + 3pre)3112.

(7)

Ð The interface adhesion energy is given by Us ¼ 2gdx, where g represents the surface energy density between the Si ribbons and the PDMS substrate. Therefore, the interface adhesion energy is given by Us1 ¼ g(Wp  S)

(8)

The buckling conguration of the Si ribbons can be obtained by minimizing the total energy with respect to the wave amplitude A and contact region S between the Si ribbons and the PDMS substrate as vUup ¼ 0; vA

vUup ¼0 vS

(9)

where Uup is the total energy of the ‘pop-up’ wrinkles. Then, the wave amplitude A and contact region S can be obtained by substituting eqn (3), (7) and (8) into (1) and (9) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi 2 3 E f p L2 3pre 4 p2 h2 A¼ ; L1 ¼ L1 L2 3pre  h (10) 2 p 6g 12L1

Analysis for ‘pop-down’ wrinkles Similarly, the ‘pop-down’ wrinkles can be analyzed using the same method for ‘pop-up’ wrinkles. Here, the Si ribbon debonds from the tops of the punches and creates a new contact area on the spacing region between two punches. In addition, the Si ribbon is still in contact with the corners of the punch walls. Therefore, the vertical displacement of the Si ribbon can be expressed segmentally as

wdown

cos kðL2  S=2Þ  cos kðL2  Wd =2Þ B1 cos kL2 ½cos kðWd  SÞ=2  1 ðWd  SÞsin kðL2  S=2Þ þ kB1 2 cos kL2 ½cos kðWd  SÞ=2  1

B2 ¼

B1 ¼

sin kL2 B1 cos kL2

cos kðL2 S=2Þ½cos kðWd SÞ=2  2 þ cos kðL2 Wd =2Þ H cos kL2 ½cos kðWd  SÞ=2  1 kðWd  SÞsin kðL2  Wd =2Þ H þ 2 cos kL2 ½cos kðWd  SÞ=2  1 (12)

where H is the height of the punches. Then, the bending energy can be obtained as "   1 3 S  Wd Ub2 ¼  EIk k C1 2 þ C2 2 2 2  2  C1  C2 2 ðsin kS  sin kWd Þ þ 2 # þ C1 C2 ðcos kWd  sin kSÞ   1 Wp  2  EIk3 k B1 þ B2 2 2 2  2  B1  B2 2 ðsin kWd  sin 2kL2 Þ þ 2  0 þ B1 B2 ðcos 2kL2  sin kWd Þ

cos kS=2 cos kðL2  Wd =2Þ  cos kL2 C1 ¼ B1 cos kL2 ½cos kðWd  SÞ=2  1

cos kS=2 cos kðL2  Wd =2Þ  sin kL2 B1 cos kL2 ½cos kðWd  SÞ=2  1

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(13)

The membrane energy for a thin lm/substrate system can be neglected,9 and the wave number k and contact region S can be obtained by minimizing the total energy as

8 < wdown1 ¼ 0;  S=2\x1 \S=2 ¼ wdown2 ¼ C1 cos kx1 þ C2 sin kx1 þ C3 x1 þ C4 ; S=2\jx   1 j\Wd =2 : wdown3 ¼ B1 cos kx1 þ B2 sin kx1 þ C4 ; Wd =2\jx1 j\ Wd þ Wp 2

where coefficients C1, C2, C3, C4, B1 and B2 can be determined by the boundary conditions as

C2 ¼

sin kðL2  S=2Þ kB1 cos kL2 ½cos kðWd  SÞ=2  1

vUdown ¼ 0; vk

vUdown ¼0 vS

(11)

(14)

where Udown represents the total energy for the downward buckling mode. It should be noted that the valley of the Si ribbon cannot reach the bottom of the punch if the pre-strain is small enough. In this case, the buckling prole should be replaced by

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Fig. 3 shows the critical strain 3cpre versus the width of the punches Wp with different spacing of the punches Wd when H ¼ 10 mm and h ¼ 200 nm. These curves show that the width and the spacing of the punches have a signicant inuence on the critical strain. The critical strain increases with the width of the punch but decreases with the spacing of the punch.

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Competition of the total energy

Fig. 3 The critical strain when the Si ribbon is just attached to the bottom of the punch.

wdown ¼ D cos

p p x1  D cos Wd L2 2L2

(15)

The minimization of the total energy as previously described gives the expression of parameter D as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2L2 p2 h2 3pre  (16) D¼ p 24L2 2 When the Si ribbon just attaches to the bottom of the punch but the contact force does not affect the buckling prole, the vertical displacement at x1 ¼ 0 should satisfy the following condition w|x¼0 ¼ H

(17)

When the buckling prole transforms from eqn (15) to (11), the critical strain can be obtain by substituting eqn (16) and (17) into (15) 3cpre ¼

p2 H 2 4L2 ð1  cosðpWd =2L2 ÞÞ 2

2

þ

p2 h2 24L2 2

(18)

Based on the energy method, the competition of the total energy of upward buckling and downward buckling determines the buckling mode. If Uup < Udown, upward buckling occurs; if Uup > Udown, downward buckling occurs. Therefore, we can obtain the criterion for buckling modes. The adhesion value in this paper is g ¼ 160 mJ m2 which has the correct order of magnitude for PDMS.21 Here, the material and geometry parameters of Si ribbons are Ef ¼ 130 GPa, nf ¼ 0.3, h ¼ 200 nm and the height of the punch is H ¼ 10 mm. The total energy of upward buckling Uup and downward buckling Udown with respect to the width of the punch Wp for Wd ¼ 50 mm and 3pre ¼ 35% are shown in Fig. 4a. There is an intersection point for the total energy of downward buckling and the total energy of upward buckling . Therefore, a critical value of the width of the punch, denoted as Wcp, can be obtained, below which downward buckling occurs as Uup > Udown and vice versa (Fig. 4a). Fig. 4b shows the critical width of the punch Wcp versus the spacing of the punch Wd for 3pre ¼ 35%. The curve theoretically predicts the buckling modes for different micro-patterns under a certain prestrain. We nd that the critical width of the punch Wcp increases with the spacing of the punch Wd, which means that it is easier to buckle upward for the punch with a larger width and smaller spacing and vice versa. These results provide the strategy to tune the buckling modes by selecting an appropriate geometry of the punches and pre-strain. In addition, in order to compare the experimental results to the analytical prediction, we conducted a series of tests selecting punches with different widths and spacings in our experiment. For different widths and spacings of the punches in our experiment, the blue solid triangles and the red solid inverted triangles represent the occurrence of the upward

Fig. 4 (a) The total energy of upward buckling Uup and downward buckling Udown versus the width of the punches Wp with respect to Wd ¼ 50 mm, 3pre z 35% and g ¼ 160 mJ m2. (b) The critical width of the punch versus the spacing of the punch.

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Table 1 Comparison of the buckling modes by theoretical prediction and experimental results for the punches with different width and spacing

Wd Wp 3pre Uup Udown Analytical (mm) (mm) (%) (106 J m2) (106 J m2) mode

Experimental mode

30

Downward Downward Downward Upward Upward Upward Downward Upward Upward Upward Upward Downward

50

100

30 50 50 100 100 200 30 50 100 100 200 30

35.1 36.4 34.5 33.8 44.8 37.1 46.1 36.4 15.4 31.1 34.7 20.9

18.5 20.1 19.7 24.1 26.6 27.6 17.2 17.8 15.4 20.4 27.6 6.99

13.5 18.4 18.5 29.7 29.1 45.8 6.90 11.7 19.4 22.6 45.8 1.93

Downward Downward Downward Upward Upward Upward Downward Downward Upward Upward Upward Downward

buckling mode and the downward buckling mode with a prestrain of 35%, respectively, as shown in Fig. 4b. We nd that the upward buckling mode occurs when the width of the punch Wp is larger than the critical width of the punch Wcp. In contrast, the

downward buckling mode occurs when the width of the punch Wp is smaller than the critical width of the punch Wcp. Therefore, the experimental results agree well with the analytical estimation. Table 1 summarizes the theoretical predictions and experimental results for the buckling modes for the punches with different width and spacing. As shown in Table 1, the buckling modes predicted analytically agree well with the experimental results except for when Wp ¼ 50 mm, Wd ¼ 50 mm and 3pre ¼ 36.4%. In addition, with the same spacing of the punch, we nd the that buckling mode transforms from downward to upward with increasing width of the punch, which is consistent with the analytical results. The consistency of the analytical results and experimental results effectively demonstrates that buckling modes can be tuned by selecting an appropriate geometry of the punches and pre-strain.

Stretchability of wavy Si ribbons on micro-patterns Si ribbons on a patterned PDMS substrate also exhibit considerable improvement in the stretchability of such a structure through the deformation of the micro-patterns isolating the

The stretchability of Si ribbons on a patterned PDMS substrate with a pre-strain of 33.8%. (a) SEM images of Si ribbons on a patterned PDMS substrate are stretched flat under an applied strain (33.8%). (b) Si ribbons on a patterned PDMS substrate under an applied strain (51.2%). The punches turn into an ‘arch’ configuration to absorb the applied strain. (c) The ‘pop-down’ wrinkles before stretching are stretched flat when the applied strain equals the pre-strain and switch to ‘pop-up’ wrinkles when the applied strain is totally released.

Fig. 5

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strain of the Si ribbons. Fig. 5a shows the at conguration when the applied tensile strain increases to the pre-strain of the patterned substrate (Wp ¼ 100 mm, Wd ¼ 30 mm). Before the applied strain approaches the pre-strain, the edges of the rectangular punches remain straight all the time. The wrinkles release the deformation by changing the wavelength and wave amplitude gradually when the external strain is smaller than the pre-strain, and they nally become at when the external strain reaches the pre-strain (3pre ¼ 33.8%), which is the upper limit of stretchability for wrinkles on a at substrate.7 However, the ribbons in our experiment can still be subject to the increasing applied strain by the deformation of the micro-patterns and do not fracture even the applied strain reaches 51.2%, as shown in Fig. 5b. The so punches bonded to the ribbons deform to isolate the ribbons’ deformation from the substrate when the external strain is larger than the pre-strain and the punches gradually turn into an ‘arch’ conguration to absorb the applied

FEM simulation of the stretchability of Si ribbons on patterned PDMS with Wp ¼ 100 mm and Wd ¼ 30 mm. (a) Schematic illustration of Si ribbons on patterned PDMS. (b) Deformation of micro-patterns under applied strain 3 ¼ 1%. (c) Enlarged view of deformation at the bottom of a punch wall. (d) Maximum logarithmic strain of Si ribbons and the PDMS substrate versus applied strain. The black line with red solid circles represents the strain of the Si ribbons and the black line with the blue solid circles represents the maximum strain of bottom of punch wall.

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strain. Thus, the micro-patterns can greatly enhance the stretchability of such structures though their deformation alone. This mechanism is very important for improving the stretchability of wavy structures in exible and stretchable electronics. We also observe a novel phenomenon that the type of buckling can transform when releasing the applied strain. Fig. 5c shows the ‘pop-down’ wrinkles switch to ‘pop-up’ wrinkles when the applied strain of 51.2% is totally released, which may be induced by local adhesion of micro-patterns and the initial stress of the Si ribbons.22 In order to further investigate the mechanism of extra stretchability aer the wavy ribbons are stretched at, the deformation of micro-patterns to buffer the Si ribbons is explored by the nite element method (FEM), which is based on Abaqus commercial soware. For the FEM simulation, the material and geometry parameters are the same as the parameters in the theoretical analysis. The plane strain model and beam model are selected to simulate the PDMS substrate and Si ribbon. The interface between the Si ribbon and PDMS punch is set to bond perfectly. The element size is 2 mm. Fig. 6a provides a schematic illustration of the Si ribbons on a patterned PDMS substrate with punches under tensile strain. Here we start FEM analysis when the external strain reaches the pre-strain, which means the Si ribbon is stretched at in the initial state. Fig. 6b shows the micro-patterns’ deformation by FEM, and we nd the punch walls bend and their bottoms deform largely due to the Young's modulus mismatch between Si (130 GPa) and PDMS (2 MPa). Fig. 6c shows the enlarged view of deformation at the bottom of a punch wall. Fig. 6d shows the logarithmic strain in the direction of the applied strain versus the applied strain. The black line with red solid circles represents the strain of the Si ribbons and the black line with the blue solid circles represents the maximum strain of bottom of punch wall. We nd the maximum logarithmic strain in the Si ribbons is about four orders of magnitude smaller than that in the PDMS substrate. Therefore, the punch wall deforms largely to isolate the Si ribbons from the applied strain. Furthermore, we explore the effects of the punch spacing on the stretchability by selecting

Fig. 6

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Fig. 7 Logarithmic strain versus the width of the punches. The black line with red solid circles and the black line with blue solid squares denote the maximum of the logarithmic strain of the Si nanoribbon and PDMS, respectively.

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punches of the same width with Wp ¼ 100 mm but varying Wd. Fig. 7 shows the logarithmic strain versus the width of the punches. The black line with red solid circles and the black line with blue solid squares denote the maximum of the logarithmic strain of the Si nanoribbon and PDMS, respectively. It can be seen from Fig. 7 that both the logarithmic strain of the Si nanoribbons and PDMS increase with an increasing spacing ratio of the punches.

Concluding remarks In conclusion, a so substrate with micro-patterns produced by classical molding techniques can be used as a tool to tune the wrinkle congurations in ‘pop-up’ and ‘pop-down’ styles as well as the wavelength of the wrinkles. Additionally, the micropatterns can deform to buffer the Si ribbons when the applied strain is larger than the pre-strain, which greatly enhances the extra stretchability of such structures. Both the experimental results and FEM simulation reveal the mechanism of such a phenomenon. The excellent stretchability and controllable wrinkle congurations of brittle ribbons provide a possibility for fabricating more stretchable and exible nano/microdevices.

Acknowledgements We gratefully acknowledge the support from National Natural Science Foundation of China (Grant Nos 11222220, 11227801, 11320101001, 11090331), Tsinghua University Initiative Scientic Research Program (No. 2011Z02173) and Tsinghua National Laboratory for Information Science and Technology (TNList).

References 1 M. A. Meitl, Z. T. Zhu, V. Kumar, K. J. Lee, X. Feng, Y. Y. Huang, I. Adesida, R. G. Nuzzo and J. A. Rogers, Nat. Mater., 2006, 5, 33. 2 X. Feng, M. A. Meitl, A. M. Bowen, Y. Huang, R. G. Nuzzo and J. A. Rogers, Langmuir, 2007, 23, 12555.

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