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# A Stretchable Form of Single-Crystal Silicon for High-Performance Electronics on Rubber Substrates

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Science  13 Jan 2006:
Vol. 311, Issue 5758, pp. 208-212
DOI: 10.1126/science.1121401

## Abstract

We have produced a stretchable form of silicon that consists of submicrometer single-crystal elements structured into shapes with microscale, periodic, wavelike geometries. When supported by an elastomeric substrate, this “wavy” silicon can be reversibly stretched and compressed to large levels of strain without damaging the silicon. The amplitudes and periods of the waves change to accommodate these deformations, thereby avoiding substantial strains in the silicon itself. Dielectrics, patterns of dopants, electrodes, and other elements directly integrated with the silicon yield fully formed, high-performance “wavy” metal oxide semiconductor field-effect transistors, p-n diodes, and other devices for electronic circuits that can be stretched or compressed to similarly large levels of strain.

Progress in electronics is driven mainly by efforts to increase circuit operating speeds and integration densities, to reduce the power consumption of circuits, and, for display systems, to enable large area coverage. A more recent direction seeks to develop methods and materials that enable high-performance circuits to be formed on un-conventional substrates with unusual form factors (1, 2), such as flexible plastic substrates for paperlike displays and optical scanners (37), spherically curved supports for focal plane arrays (8, 9), and conformable skins for integrated robotic sensors (10, 11). Many electronic materials can provide good bendability when prepared in thin-film form and placed on thin substrate sheets (1217) or near neutral mechanical planes in substrate laminates (18, 19). In these cases, the strains experienced by the active materials during bending can remain well below the typical levels required to induce fracture (∼1%). Full stretchability, a much more challenging characteristic, is required for devices that can flex, stretch, or reach extreme levels of bending as they are operated or for those that can be conformally wrapped around supports with complex curvi-linear shapes. In these systems, strains at the circuit level can exceed the fracture limits of nearly all known electronic materials, especially those that are well developed for established applications. This problem can be circumvented, to some extent, with circuits that use stretchable conducting wires to interconnect electronic components (such as transistors) supported by rigid isolated islands (2025). Promising results can be obtained with this strategy, although it is best suited to applications that can be achieved with active electronics at relatively low coverages. We report a different approach, in which stretchability is achieved directly in thin films of high-quality, single-crystal Si that have micrometer-scale, periodic, “wave”-like geometries. These structures accommodate large compressive and tensile strains through changes in the wave amplitudes and wavelengths rather than through potentially destructive strains in the materials themselves. Integrating such stretchable wavy Si elements with dielectrics, patterns of dopants, and thin metal films leads to high-performance, stretchable electronic devices.

Figure 1 presents a fabrication sequence for wavy, single-crystal Si ribbons on elastomeric (rubber) substrates. The first step (top panel) involves photolithography to define a resist layer on a Si-on-insulator (SOI) wafer, followed by etching to remove the exposed parts of the top Si. Removing the resist with acetone and then etching the buried SiO2 layer with concentrated hydrofluoric acid releases the ribbons from the underlying Si substrate. The ends of the ribbons connect to the wafer to prevent them from washing away in the etchant. The widths (5 to 50 μm) and lengths (∼15mm) of the resist lines define the dimensions of the ribbons. The thickness of the top Si (20 to 320 nm) on the SOI wafers defines the ribbon thicknesses. In the next step (middle panel), a flat elastomeric substrate [poly(dimethylsiloxane) (PDMS), 1 to 3 mm thick] is elastically stretched and then brought into conformal contact with the ribbons. Peeling the PDMS away lifts the ribbons off of the wafer and leaves them adhered to the PDMS surface. Releasing the strain in the PDMS (that is, the prestrain) leads to surface deformations that cause well-defined waves to form in the Si and the PDMS surface (Fig. 2, A and B). The relief profiles are sinusoidal (top panel, Fig. 2C), with periodicities between 5 and 50 μm and amplitudes between 100 nm and 1.5 μm, depending on the thickness of the Si and the level of prestrain in the PDMS. For a given system, the periods and amplitudes of the waves are uniform to within ∼5% over large areas (several square centimeters). The flat morphology of the PDMS between the ribbons and the absence of correlated phases in waves of adjacent ribbons suggest that the ribbons are not strongly coupled mechanically. Figure 2C (bottom panel) shows micro-Raman measurements of the Si peak, measured as a function of distance along one of the wavy ribbons. The results provide insights into the stress distributions.

The behavior in this static wavy configuration is consistent with nonlinear analysis of the initial buckled geometry in a uniform, thin, high-modulus layer on a semi-infinite low-modulus support (26, 27) $Math$(1) where $Math$ is the critical strain for buckling, ϵpre is the level of prestrain, λ0 is the wavelength, and A0 is the amplitude. The Poisson ratio is ν, the Young's modulus is E, and the subscripts refer to properties of the Si or PDMS. The thickness of the Si is h. This treatment captures many features of the as-fabricated wavy structures. Figure 2D shows, for example, that when the prestrain value is fixed (∼0.9% for these data), the wavelengths and amplitudes both depend linearly on the Si thickness. The wavelengths do not depend on the level of prestrain (fig. S1). Furthermore, calculations that use literature values (28, 29) for the mechanical properties of the Si and PDMS (ESi = 130 GPa, EPDMS = 2 MPa, νSi = 0.27, νPDMS = 0.48) yield amplitudes and wavelengths that are within ∼10% (maximum deviation) of the measured values. The strains computed from the ratio of the effective lengths of the ribbons (as determined from the wavelength) to their actual lengths [as determined from surface distances measured by atomic force microscopy (AFM)], which we refer to as ribbon strains, yield values that are approximately equal to the prestrain in the PDMS, for prestrains up to ∼3.5%. The peak (that is, the maximum) strains in the Si itself, which we refer to as Si strains, can be estimated from the ribbon thicknesses and radii of curvature at the extrema of the waves according to κh/2, where κ is the curvature, in regimes of strain where the waves exist and where the critical strain (∼0.03% for the cases examined here) is small as compared to the peak strains associated with bending. For the data of Fig. 2, the peak Si strains are ∼0.36 (±0.08)%, which is more than a factor of 2 smaller than the ribbon strains. This Si strain is the same for all ribbon thicknesses, for a given prestrain (fig. S2). The resulting mechanical advantage, in which the peak Si strain is substantially less than the ribbon strain, is critically important for achieving stretchability. Buckled thin films have also been observed in metals and dielectrics evaporated or spin-cast onto PDMS (in contrast to preformed, transferred, single-crystal elements and devices, as described here) (3032).

The dynamic response of the wavy structures to compressive and tensile strains applied to the elastomeric substrate after fabrication is of primary importance for stretchable electronic devices. To reveal the mechanics of this process, we measured the geometries of wavy Si ribbons by AFM as force was applied to the PDMS to compress or stretch it parallel to the long dimension of the ribbons. This force creates strains both along the ribbons and perpendicular to them, due to the Poisson effect. The perpendicular strains lead primarily to deformations of the PDMS in the regions between the ribbons. The strains along the ribbons, on the other hand, are accommodated by changes in the structure of the waves. The three-dimensional height images and surface profiles in Fig. 3A present representative compressed, unperturbed, and stretched states (collected from slightly different locations on the sample). In these and other cases, the ribbons maintain their sinusoidal (lines in the right-hand panels of Fig.3A) shapes during deformation, in which approximately half of the wave structure lies beneath the unperturbed position of the PDMS surface, as defined by the regions between the ribbons (fig. S3). Figure 3B shows the wavelength and amplitude for compressive (negative) and tensile (positive) applied strains relative to the unperturbed state (zero). The data correspond to averaged AFM measurements collected from a large number (>50) of ribbons per point. The applied strains were determined from the measured end-to-end dimensional changes of the PDMS substrate. Direct surface measurements by AFM, as well as contour integrals evaluated from the sinusoidal wave shapes, show that the applied strains are equal to the ribbons strains (fig. S4) for the cases examined here. [The small-amplitude (<5 nm) waves that persist at tensile strains larger than the prestrain minus the critical strain might result from slight slippage of the Si during the initial buckling process. The computed peak Si strains and ribbon strains in this small- (or zero-) amplitude regime underestimate the actual values.] The results indicate two physically different responses of the wavy ribbons to applied strain. In tension, the waves evolve in a non-intuitive way: The wavelength does not change appreciably with applied strain, which is consistent with post-buckling mechanics. Instead, changes in amplitude accommodate the strain. In this regime, the Si strain decreases as the PDMS is stretched; it reaches ∼0% when the applied strain equals the prestrain. By contrast, in compression, the wavelengths decrease and amplitudes increase with increasing applied strain. This mechanical response is similar to that of an accordion bellows, which is qualitatively different than the behavior in tension. During compression, the Si strain increases with the applied strain, due to the decreasing radii of curvature at the wave peaks and troughs. The rates of increase and magnitudes of the Si strains are, however, both much lower than the ribbon strains, as shown in Fig. 3B. These mechanics enable stretchability.

The full response in regimes of strain consistent with the wavy geometries can be quantitatively described by equations that give the dependence of the wavelength λ on its value in the initial buckled state, λ0, and the applied strain εapplied according to $Math$(2) This tension/compression asymmetry can arise, for example, from slight reversible separations between the PDMS and the raised regions of Si, formed during compression. For this case, as well as for systems that do not exhibit this asymmetric behavior, the wave amplitude A, for both tension and compression, is given by a single expression, valid for modest strains (<10 to 15%) (33) $Math$(3) where A0 is the value corresponding to the initial buckled state. These expressions yield quantitative agreement with the experiments without any parameter fitting, as shown in Fig. 3A. When the waviness, which accommodates the tensile/compressive strains, remains, the peak Si strain is dominated by the bending term and is given by (33) $Math$(4) which agrees well with the strain measured from curvature in Fig. 3B (see also fig. S5). Such an analytic expression is useful to define the range of applied strain that the system can sustain without fracturing the Si. For a prestrain of 0.9%, this range is –27% to 2.9% if we assume that the Si failure strain is ∼2% (for either compression or tension). Controlling the level of prestrain allows this range of strains (that is, nearly 30%) to balance desired degrees of compressive and tensile deformability. For example, a prestrain of 3.5% (the maximum that we examined) yields a range of –24% to 5.5%. Such calculations assume that the applied strain equals the ribbon strain, even at extreme levels of deformation. Experimentally, we find that these estimates are often exceeded because of the ability of the PDMS beyond the ends of the ribbons and between the ribbons to accommodate strains, so that the applied strain is not completely transferred to the ribbons.

We have created functional, stretchable devices by including at the beginning of the fabrication sequence (Fig. 1, top panel) additional steps to define patterns of dopants in the Si, thin metal contacts, and dielectric layers using conventional processing techniques (33). Two- and three-terminal devices, diodes, and transistors, respectively, fabricated in this manner provide basic building blocks for circuits with advanced functionality. A dual transfer process in which the integrated ribbon devices were first lifted off of the SOI onto an undeformed PDMS slab, and then to a prestrained PDMS substrate, created wavy devices with metal contacts exposed for probing. Figure 4, A and B, show optical images and electrical responses of a stretchable p-n–junction diode for various levels of strain applied to the PDMS. We observed no systematic variation in the electrical properties of the devices when stretched or compressed, to within the scatter of the data. (The deviation in the curves is due mainly to variations in the quality of probe contacts.) As expected, these p-n–junction diodes can be used as photo-detectors (at reverse-biased state) or as photo-voltaic devices, in addition to their use as normal rectifying devices. The photocurrent density was ∼35 mA/cm2 at a reverse bias voltage of ∼–1V. At forward bias, the short-circuit current density and open-circuit voltage were ∼17 mA/cm2 and 0.2 V, respectively, which yields a fill factor of 0.3. The shape of the response is consistent with modeling (solid curves in Fig. 4B). The device properties do not change substantially, even after ∼100 cycles of compressing, stretching, and releasing (fig. S6). Figure 4C shows current-voltage characteristics of a stretchable, wavy, Si, Schottky-barrier metal oxide semiconductor field-effect transistor (MOSFET) formed with procedures similar to those used for the p-n diode, and with an integrated thin layer (40 nm) of thermal SiO2 as a gate dielectric (33). The device parameters extracted from electrical measurements of this wavy transistor [linear regime mobility ∼100 cm2/Vs (likely contact-limited), threshold voltage ∼–3 V] are comparable to those of devices formed on the SOI wafers under the same processing conditions (figs. S7 and S8). As with the p-n diodes, these wavy transistors can be reversibly stretched and compressed to large levels of strain without damaging the devices or substantially altering their electrical properties. In both the diodes and the transistors, deformations in the PDMS beyond the ends of the devices lead to device (ribbon) strains that are smaller than the applied strains. The overall stretchability results from the combined effects of device stretchability and these types of PDMS deformations. At compressive strains larger than those examined here, the PDMS tended to bend in ways that made probing difficult. At larger tensile strains, the ribbons either fractured, or slipped and remained intact, depending on the Si thickness, the ribbon lengths, and the strength of bonding between the Si and PDMS.

These stretchable Si MOSFETs and p-n diodes represent only two of the many classes of wavy electronic devices that can be formed. Completed circuit sheets or thin Si plates can also be structured into uniaxial or biaxial stretchable wavy geometries. Besides the unique mechanical characteristics of wavy devices, the coupling of strain to electronic properties, which occurs in many semiconductors, might provide opportunities to design device structures that exploit mechanically tunable periodic variations in strain to achieve unusual electronic responses. These and other areas appear promising for future research.

Supporting Online Material

Materials and Methods

Figs. S1 to S8