Experimental investigation on the mechanical buckling of one-dimensional Si nanoribbons with a thickness contrast
Introduction
Stretchable electronics [1], [2], [3] can flex and stretch while in use, and therefore can fully conform to their surroundings. This important and emerging field is attracting considerable attention, from scientific and technological communities to the general public, due to its vast applications, such as an optoelectronics [4], [5], bioelectronics [6], sensors [7] and photovoltaics [8]. Many of the different approaches for stretchable electronics proposed in the literature can be classified into two different categories. One is the use of intrinsically stretchable materials, which are in general composites of conductor/semiconductor materials with an elastomeric matrix [3]. These composites are suitable for certain applications, although they suffer from poor performance.
An alternative strategy used to enable stretchable electronics is shape engineering. For this approach, well-developed high-performance materials are used, such as single-crystal Si. To overcome the brittle nature of the high performance (in)organic materials, a mechanical phenomenon is applied to make the brittle materials stretchable. In our previous work [9], we demonstrated stretchable electronic components (e.g. field-effect transistors) based on periodic, sinusoidal wavy-like single crystalline Si ribbons on an elastomeric substrate of poly(dimethylsiloxane) (PDMS). The crucial point was the use of mechanical buckling to make the inorganic-based devices stretchable. Once the device is in buckled, wavy configuration on an elastomer, the external tensile/compressive strain can be accommodated by the change in the wavy shape without any mechanical failure, such as cracks or fractures. Experiments and analytical analysis have shown that this buckled wavy-like silicon can sustain the stretchability up to 20% without failure. There have been many studies that have a similar approach to fabricate various devices in stretchable form following this [2], [10], [11].
One of the key concepts in this approach is the mechanical buckling of a stiff thin film (e.g. a silicon thin film) on compliant substrate (e.g. PDMS), which has attracted a great deal of attention in the mechanical community. A thorough understanding, or even control, of the buckling behavior and its geometry can be applied to many important fields besides stretchable electronics, for example, tunable diffraction and phase gratings [12], force spectroscopy in cells [13], biocompatible topographic matrices for cell alignment [14], modern metrology methods [15], and micro/nano-fibrication [16]. Several models have been proposed to understand the buckling mechanism of a stiff thin film/compliant substrate system. Some studies focus on the buckling behavior of one-dimensional ductile or elastic ribbons on an elastic or viscoelastic substrate [9], [17], [18], [19]. Alternative efforts have been devoted to the buckling of two-dimensional thin films [20], [21], [22], [23], [24]. Other analysis focused on thin film ribbons (1D) with a finite width effect [25] or a thin film plate (2D) with uniform thickness. However, the thickness is not uniform in many electronics components, such as field-effect transistors, due to device processes (doping, gate oxide, metal electrode deposition, etc.). Instead, real devices/components consist of multilayered stacks of different materials. An understanding of the buckling behavior of multilayered materials on compliant substrate is critical to provide design guidelines of electronic devices/circuits. Such fundamental studies of the thickness effect of thin film buckling on compliant substrate will also contribute to the other applications mentioned above.
In this work, we present an experimental investigation on the buckling of Si nanoribbons with varying thickness along their length. For rather small differences in thickness, each thin and thick section shows uniform buckling, with their own buckling characteristics, such as wavelength and amplitude, depending on their respective thicknesses. On the other hand, the Si nanoribbons with larger thickness differences show a different type of buckling behavior. While the thin parts buckle uniformly over the whole span, the thick parts show limited buckling waves within the central region only, with an almost flat shape for other areas. This nonuniform buckling on thick parts originates from the finite length effect, and thus traditional buckling analysis is not applicable to this system due to the common assumption of infinite length in conventional buckling mechanics. The results from this study can aid in designing functional electronic devices/circuits for various stretchable electronics, as such devices and circuits typically consist of different materials or thicknesses.
Section snippets
Experimental details
Fig. 1 shows presents the experimental steps. The silicon-on-insulator (SOI) wafers were made up of Si (thicknesses of 100 or 300 nm) placed onto SiO2 (thicknesses of 145 nm and 400 nm, respectively). Si substrates (Soitec, Inc.) were used. The top Si of these SOI wafers was patterned with photoresist (AZ 5214 photoresist, Karl Suss MJB-6 contact mask aligner) in order to open areas (pattern width of 0.5 mm or 1 mm) to be thinned. The exposed sample surface was then removed by reactive ion etching
Small thickness contrast
Fig. 2 shows the images and section profile of the buckled Si surface on the PDMS for small thickness differences. The thickness of the top Si layer is 100 nm, with parts etch-removed by RIE reducing the thickness to 80 nm. This led to the 20 μm-wide Si ribbons having alternating thick (100 nm) and thin (80 nm) portions along their length. The span of each thick/thin segment is 1 mm. As shown in Fig. 2a, the Si ribbons show uniform buckling on the both thick (yellowish color) and thin (bluish) parts.
Conclusions
In this work, we investigated the mechanical buckling of Si stripes with a thickness contrast along their length. This can be considered as a simplified model for real devices that consist of multilayered stacks of different materials. We found that the buckling follows the well-known mechanics in Si stripes for small thickness differences. On the other hand, traditional mechanics does not apply for the case of Si stripes with a large thickness contrast, although it can shed some light on the
Acknowledgements
D.-Y. Khang appreciates the financial support from the National Research Foundation of Korea (KRF) grant funded by the Korean government (MEST) (NRF-2010-C1AAA001-0029061). H. Jiang acknowledges the support from NSF CMMI-0700440.
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