A curvy, stretchy future for electronicsJohn A. Rogersa,1 and Yonggang Huangb

aDepartment of Materials Science and Engineering, University of Illinois at Urbana–Champaign, Champaign, IL 61801;and bDepartment of Mechanical Engineering and Department of Civil and Environmental Engineering, Northwestern University,Evanston, IL 60208

Electronics of the future will besoft and rubbery. Devices basedon this new technology will bestretchable, twistable, and de-

formable into curvilinear shapes,thereby enabling applications that wouldbe impossible to achieve by using thehard, rigid electronics of today. Exam-ples range from ultrathin, conformablehealth-monitoring tapes that seamlesslymount on the skin, ‘‘electronic skin,’’ toadvanced imaging devices that use hemi-spherical detector layouts, ‘‘electroniceyeball cameras.’’ In these and othersystems, mechanical design will be asimportant as circuit design. Vella et al.(1) in this issue of PNAS introduce sim-ple schemes to measure the mechanicalproperties of structures for stretchableelectronics and they describe powerfulanalytical approaches that capture theunderlying physics.

Historically, progress in electronicshas been dominated by a developmentpath first noted by Gordon Moore in1965 (2): the number of transistors insilicon microprocessors tends to doubleevery 18–24 months, mainly throughreductions in the sizes of the transistors.This trend, known as Moore’s Law, isnow so well established that it is self-fulfilling, via roadmaps that guide theefforts of the entire industry. Modernprocessors incorporate more than a bil-lion transistors each with critical dimen-sions of tens of nanometers. Continueddownscaling represents an importantfuture for electronics, but not the onlyone. In the early 1990s, a completelydifferent class of electronics emerged tomeet a need that was impossible to ad-dress with silicon wafer technology: ac-tive matrix circuits for switching pixelsin liquid crystal displays. Progress in thiskind of electronics is most definitely notdictated by Moore’s Law. Here, the pri-mary scaling metric is overall size: big-ger is better, because large area cover-age means large video screens. The totalnumber of transistors, beyond a few mil-lion, and their sizes are both compara-tively unimportant. The most advancedfabrication facilities produce circuits thatcover areas of nearly 10 m2, with totaloutputs that exceed a thousand acres ofelectronics per year. This ‘‘macroelec-tronics’’ (3) technology began its growthnearly 40 years after the birth of mod-ern microelectronics, yet it captures arapidly growing market that now repre-

sents a sizable fraction of the entirebroader industry.

Many believe that the ‘‘next big thing’’in electronics is with systems that avoidthe rigid, brittle, and planar nature ofmicro/macroelectronics, to enable new

modes of use. Research in this directionbegan �15 years ago (4), initially drivenby interest in flexible, paperlike displays(5, 6). More recently, the scope has ex-panded to include more compelling, andmore technically challenging, opportuni-ties in biomedical devices that intimatelyintegrate with the human body and inproduct designs that exploit curvilinear,ergonomic, or biologically inspired lay-outs. One approach to such technologyrelies on the development of new elec-tronic materials, e.g., organic semicon-ductors that can flex (4) and compositeelastomer conductors that can stretch(7). Different strategies use optimizedstructural configurations (8) of estab-lished inorganic materials for stretchableinterconnects (8–13) and/or active de-vices (8, 14–16). The concepts that en-able stretchy properties from these brit-tle materials are simple. For example,ultrathin sheets of silicon are flexible,for the same reason that any material inthin film form is flexible: bendingstrains are inversely proportional tothickness. Such sheets, formed in buck-led ‘‘wavy’’ shapes and integrated withrubber substrates, yield composite sys-tems that provide fully elastic responsesto applied strains, with an underlyingphysics similar to that of an accordionbellows. These and related ideas provideroutes to high-performance electronicswith the mechanical properties of a rub-ber band. Fig. 1A shows a wavy siliconintegrated circuit that has these charac-teristics (14). In parallel with fundamen-tal research on the materials and me-chanics, advanced development work isincreasing in areas of biomedicine suchas intracardial and neural monitoring.As applied to digital imaging, this tech-nology enables hemispherical electroniceyeball cameras that provide enhancedoperating characteristics compared withdevices with conventional planar layouts(17).

Mechanical design plays a criticallyimportant role in this type of stretchableelectronics technology. Experimental

Author contributions: J.A.R. and Y.H. wrote the paper.

The authors declare no conflict of interest.

See companion article on page 10901.

1To whom correspondence should be addressed at: Depart-ment of Materials Science and Engineering, University ofIllinois at Urbana/Champaign, 1304 West Green Street,Urbana, IL 61801. E-mail: jrogers@illinois.edu.

Fig. 1. Buckled ultrathin silicon circuit sheetsbonded to elastomeric substrates represent a form ofelectronics that responds elastically to appliedstrains. (A) Optical image of a silicon CMOS (comple-mentary metal–oxide semiconductor) integrated cir-cuit of this type, pressed downward in the centralregion with a glass rod. The wavelengths and ampli-tudes of the buckled structures, visible here as colorand contrast variations, change to accommodate thedeformation. This physics provides a useful degree ofcircuit-level stretchability that avoids any significantstrains in the electronic materials themselves. (B)Scanning electron micrograph of buckled nanorib-bons of single crystalline silicon bonded to an elas-tomer substrate. This composite system provides anelastic response to applied strains, with a physics thatis conceptually similar to that of an accordion bel-lows. The ribbon in the center of this image had adefect that caused it to delaminate locally from thesubstrate to form an isolated bridge structure, fur-ther highlighting certain aspects of the mechanics.This stretchable form of silicon embodies, in a simplesystem, the key physics associated with the full inte-grated circuit shown in A.

www.pnas.org�cgi�doi�10.1073�pnas.0905723106 PNAS � July 7, 2009 � vol. 106 � no. 27 � 10875–10876

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work involves characterizing the micro-scopic behavior of the material struc-tures, the devices, circuits, and systems,where the length scales for the relevantdeformations range from millimeters tonanometers (8, 10, 12, 14–16). Fig. 1Bpresents a scanning electron micrographof an array of wavy silicon nonoribbonson an elastomer substrate (16). Analyti-cal and computational modeling canquantitatively capture the physics (18) ofthis basic subunit of stretchable inte-grated circuits (Fig. 1 A). Although suchstudies of the mechanics are criticallyimportant, they require sophisticatedcapabilities in device fabrication andtest. Vella et al. (1) show that the essen-tial physics can be explored by usingmacroscopic analogs, consisting of plas-tic sheets on rubber supports, manipu-lated with clamps and translation stages.This approach greatly simplifies the ex-periments, thereby opening up the fieldto researchers who do not have accessto cleanroom fabrication facilities oradvanced microscope systems. Vella et

al. exploit their setups to study the non-linear processes that lead to buckledstructures. Their mathematical treat-ment uses established methods of en-ergy minimization (16, 18, 19), but witha unique linking of the release of total

system energy to the interfacial fracturetoughness. The result provides a usefulway to determine not only the onset butalso the evolution of buckling with ap-plied strain. They use macroscopicallymeasurable interfacial toughness to de-termine microscopic parameters such as

buckling and wavelength and amplitude.One outcome of this analysis is the rec-ognition of a critical film thicknessneeded to avoid damage or plastic de-formation, thereby providing an impor-tant design rule for devices. Explicitlyaccounting for the loading and geometrydependence of the interfacial fracturetoughness in the theory will further im-prove the accuracy of the results.

This and other recent research instretchable electronics indicate thatprogress requires multidisciplinary pro-grams, incorporating nearly every fieldof traditional study, from chemistry, ma-terials science, mathematics, and physicsto mechanical and electrical engineer-ing. Successful efforts will transform theway that we think about electronics,from rigid semiconductor chips for con-sumer electronics to soft biocompatiblesheets for devices that address impor-tant problems in human health. The richrange of scientific aspects together withthe strong potential for societal benefitscreates an exciting future for this field.

1. Vella D, Bicoa J, Boudaoudb A, Romana B, Reis PM(2009) The macroscopic delamination of thin films fromelastic substrates. Proc Natl Acad Sci USA 106:10901–10906.

2. Moore GE (1965) Cramming more components ontointegrated circuits. Electronics 38:114–117.

3. Reuss R, et al. (2005) Macroelectronics: Perspectives ontechnology and applications. Proc IEEE 93:1239–1256.

4. Garnier F, Hajlaoui R, Yassar A, Srivastava P (1994)All-polymer field-effect transistor realized by printingtechniques. Science 265:1684–1686.

5. Rogers JA (2001) Toward paperlike displays. Science291:1502–1503.

6. Rogers JA, et al. (2001) Paper-like electronic displays:Large-area, rubber-stamped plastic sheets of electron-ics and electrophoretic inks. Proc Natl Acad Sci USA98:4835–4840.

7. Sekitani T, et al. (2008) A rubberlike stretchable activematrix using elastic conductors. Science 321:1468–1472.

8. Kim D.-H., Rogers JA (2008) Stretchable electronics:Materials strategies and devices. Adv Mater 20:4887–4892.

9. Lacour SP, Jones J, Wagner S, Li T, Suo Z (2005) Stretch-able interconnects for elastic electronic surfaces. ProcIEEE 93:1459–1467.

10. Kim D-H, et al. (2008) Materials and noncoplanar meshdesigns for integrated circuits with linear elastic re-sponses to extreme mechanical deformations. ProcNatl Acad Sci USA 105:18675–18680.

11. Someya T, et al. (2005) Conformable, flexible, large-area networks of pressure and thermal sensors withorganic transistor active matrixes. Proc Natl Acad SciUSA 102:12321–12325.

12. Kim DH, et al. (2008) Complementary metal oxide sili-con integrated circuits incorporating monolithically in-tegrated stretchable wavy interconnects. Appl PhysLett 93:044102.

13. Brosteaux D, Axisa F, Gonzalez M, Vanfleteren J (2007)Design and fabrication of elastic interconnections for

stretchable electronic circuits. IEEE Electron Device Lett28:552–554.

14. Kim D-H, et al. (2008) Stretchable and foldable siliconintegrated circuits. Science 320:507–511.

15. Sun Y, Jiang H, Huang YY, Sun Y, Rogers JA (2006)Controlled buckling of semiconductor nanoribbonsfor stretchable electronics. Nat Nanotechnol 1:201–207.

16. Khang DY, Jiang H, Huang Y, Rogers JA (2006) Astretchable form of single-crystal silicon for high-performance electronics on rubber substrates. Science311:208–212.

17. Ko HC, et al. (2008) A hemispherical electronic eyecamera based on compressible silicon optoelectronics.Nature 454:748–753.

18. Jiang H, et al. (2007) Finite deformation mechanics inbuckled thin films on compliant supports. Proc NatlAcad Sci USA 104:15607–15612.

19. Huang ZY, Hong W, Suo Z (2005) Nonlinear analyses ofwrinkles in a film bonded to a compliant substrate. JMech Phys Solids 53:2101–2118.

Vella et al. exploit theirsetups to study the

nonlinear processes thatlead to buckled

structures.

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Corrections

STATISTICSCorrection for ‘‘Sequential Monte Carlo without likelihoods,’’ byS. A. Sisson, Y. Fan, and Mark M. Tanaka, which appeared inissue 6, February 6, 2007, of Proc Natl Acad Sci USA (104:1760–1765; first published January 30, 2007; 10.1073/pnas.0607208104).

The authors note the following: It has been brought to ourattention that the algorithm introduced in our paper (ABC-PRC) can produce a biased posterior sample, most noticeablythrough underestimation in distributional tails. This result

occurs as the likelihood ratio in the sequential Monte Carloincremental weights is approximated by using two unbiasedMonte Carlo estimates. One way to avoid a biased posteriorsample in the ABC-PRC algorithm is to directly evaluate theimportance sampling distribution using a near-optimal back-wards kernel. Hence the need for the Monte Carlo estimate inthe denominator of the likelihood ratio is circumvented, and anunbiased sampler is obtained. As such, a corrected ABC-PRCalgorithm would be:

ACKNOWLEDGMENT. The authors thank C. Robert and G. W. Peters for constructive discussion.

www.pnas.org/cgi/doi/10.1073/pnas.0908847106

COMMENTARYCorrection for ‘‘A curvy, stretchy future for electronics,’’ by JohnA. Rogers and Yonggang Huang, which appeared in issue 27,July 7, 2009, of Proc Natl Acad Sci USA (106:10875–10876; firstpublished June 30, 2009; 10.1073/pnas.0905723106).

The authors note that on page 10875, right column, thesentence beginning on line 22, ‘‘For example, ultrathin sheets ofsilicon are flexible, for the same reason that any material in thinfilm form is flexible: bending strains are inversely proportionalto thickness’’ should instead appear as ‘‘For example, ultrathinsheets of silicon are flexible, for the same reason that anymaterial in thin film form is flexible: bending strains are directlyproportional to thickness.’’

www.pnas.org/cgi/doi/10.1073/pnas.0908993106

ENVIRONMENTAL SCIENCES, CHEMISTRYCorrection for ‘‘Chlorine activation indoors and outdoors viasurface-mediated reactions of nitrogen oxides with hydrogenchloride,’’ by Jonathan D. Raff, Bosiljka Njegic, Wayne L.Chang, Mark S. Gordon, Donald Dabdub, R. Benny Gerber, andBarbara J. Finlayson-Pitts, which appeared in issue 33, August18, 2009, of Proc Natl Acad Sci USA (106:13647–13654; firstpublished July 20, 2009; 10.1073/pnas.0904195106).

The authors note that on page 13648, Equation 5 appearedincorrectly. Further, in Equation 6 on page 13649, the formulafor nitryl chloride should have read: ClNO2. These errors do notaffect the conclusions of the article. The corrected equationsappear below.

NO�NO3� � HCl3 ClNO � HNO3 [5]

NO2�NO3

� � HCl3 ClNO2 � HNO3 [6]

www.pnas.org/cgi/doi/10.1073/pnas.0909721106

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