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Mechanics Design of Flexible Sensors

Li Yuhang1, Zhao Zhao2, and Wu Wenbin1

1Beihang University (BUAA), Institute of Solid Mechanics, School of Aeronautic Science and Engineering, XueYuan Road, HaiDian District, Beijing 100191, P.R. China

2China Special Equipment Inspection and Research Institute, HePing Street, ChaoYang District, Beijing 100029, P.R. China

1.1 Design of Stretchable Flexible Device Structure

The physical synthesis of fragile inorganic semiconductor materials has been realized with the development of nanofabrication technology, which leads to explosive growth in the research of high-performance stretchable flexible devices [1-3]. Due to their excellent flexibility, ductility, and better mechanical properties, inorganic semiconductor materials can form three-dimensional (3D) structures through self-assembly or indirect guidance, including tubular, wrinkled, buckling, and other delicate structures [4, 5]. Inorganic semiconductor materials in lines, bands, films, sheets, and strips can be obtained [6]. These materials can be used for high-performance transistors and circuit components of flexible, stretchable electronic devices. Integrating these materials into flexible substrates to prepare high-performance flexible electronic devices has become an important research issue. Therefore, relevant scholars have proposed different mechanical structure guidance strategies based on the principles of mechanics, including the ripple method, island bridge connection method, etc., which meet the high-performance requirements of electronic devices for complex surfaces [7].

1.1.1 Ripple Method

Buckling means the instability and failure of the structure. However, the design method of controllable buckling can effectively improve the ability of flexible electronics to resist tensile and compressive failure. Based on the buckling principle, the ripple method can make the flexible substrate and the film attached to it produce large wavy deformation simultaneously through the pre-stretching and strain release of the flexible substrate to adapt to and withstand more significant deformation [8].

There are three main preparation methods for corrugated structure: substrate pre-strain releasing, closed colloidal solution expansion, and ultraviolet radiation method [9-11]. The substrate pre-strain release method mainly uses single-crystal etching to pattern the silicon film. The silicon film array is placed on the pre-stretched polydimethylsiloxane (PDMS) substrate based on the transfer printing. Then, the pre-stretched strain of the substrate is released to generate compressive stress, and a corrugated silicon film-PDMS double-layer structure is obtained, as shown in Figure 1.1.

Figure 1.1 (a) Scanning electron microscopy (SEM) images of wavy Si ribbons on PDMS substrates. (b) Optical microscopy images and atomic force microscopy images of wavy Si nanofilms.

Source: Song et al. [2]/with permission of AIP Publishing.

Yu et al. [10] from Arizona State University fabricated a novel stretchable temperature sensor using the substrate pre-strain release method. Figure 1.2 shows that the ultra-thin single-crystal silicon film was prepared by traditional lithography technology. The Cr-Au thin layer thermistor was prepared by the sputtering deposition method and patterned by the boosting method. Then, the single-crystal silicon band was prepared by reactive ion etching as the bonding layer between the thermistor and the rubber substrate. Based on the van der Waals force, the thermistor-monocrystalline silicon adhered to PDMS is peeled off from the silicon-on-insulator (SOI) film, and another PDMS substrate with pre-strain after radiation treatment is prepared. Finally, the pre-strain is released to obtain a corrugated flexible temperature sensor device.

Figure 1.2 Pre-strain preparation method of corrugated structure.

Source: Yu et al. [10]/with permission of AIP Publishing.

Yang et al. [9] used a closed colloidal solution expansion method to prepare a PDMS flexible double-layer structure with wavy wrinkled films and proposed a strategy to control wavy patterns and characteristic wavelengths to achieve various applications of corrugated structures, including adjustable adhesion, wetting, microfluidics, and microlens arrays. Figure 1.3 shows that the solvent or monomer solution is used to expand and seal the elastic-plastic polymer or hydrogel film. Because the bottom of the film is connected to the rigid substrate and cannot deform, an anisotropic osmotic pressure is generated along the thickness direction of the film. When the net pressure exceeds the critical pressure, the outer surface of the outer film will buckle and form a corrugated structure pattern (Figure 1.4).

Figure 1.3 (a-d) Schematic diagram of corrugated structure prepared by closed colloidal solution expansion method.

Source: Yang et al. [9]/with permission of John Wiley & Sons.

Figure 1.4 (a-d) Schematic diagram of film layer structure with modulus gradient prepared by photocrosslinking method.

Source: Yang et al. [9]/with permission of John Wiley & Sons.

Yu and Jiang [11] from Arizona State University processed the pre-stretched PDMS substrate by ultraviolet radiation to prepare an SIO2 film with a wavy structure. The effects of pre-strain, radiation duration, and modulus on the wavy profile were obtained, and the accuracy of the mechanical analysis was confirmed by experimental comparison. The researchers first prepared a pre-stretched PDMS substrate and placed it under the radiation of an ultraviolet lamp in the atmospheric environment. The chemical composition of PDMS can be changed by reacting with oxygen. After reaching a sufficient exposure time, the pre-strained PDMS surface will produce a wavy structure (Figure 1.5).

Figure 1.5 The steps of preparing corrugated structure by ultraviolet radiation.

Source: Yu and Jiang [11]/with permission of Elsevier.

To further study the buckling properties of corrugated structures in stretchable electronic devices, scholars have investigated through experiments, theories, and finite element methods and made a reasonable explanation for the formation and evolution mechanism of periodic buckling corrugated structures on macro- and microscales [8-10, 12-21]. Zhang and Yin [12] from Temple University carried out related research on the periodic delamination mechanism of spontaneous buckling of thin films on flexible substrates under significant compression. Firstly, the geometric evolution mechanical model of the periodic corrugated structure is established based on the energy method and verified by experiments and finite element simulation. According to the size of the compressive strain, the geometric deformation process of the corrugated structure can be divided into three stages: the generation of buckling delamination under minor compression conditions, the expansion of buckling delamination under medium compression conditions, and the post-buckling phenomenon of delamination stopping under extensive compression conditions. In the experimental study, a thin metal film Au (thickness of 40?nm) was deposited on a uniaxially pre-stretched PDMS (thickness of 2?mm) substrate. The delamination process of the buckling surface morphology was characterized by scanning electron microscopy to evaluate the evolution process of the microbuckling delamination release strain (Figure 1.6).

Figure 1.6 Geometric diagram of buckling delamination of corrugated structure.

Source: Zhang and Yin [12]/with permission of Elsevier.

Considering the large deformation of the silicone rubber substrate, it is assumed that the film is an elastic thin plate and the substrate is a semi-infinite solid that satisfies the Neo-Hookean constitutive law. The total energy Utol in the film-substrate system is composed of the tensile energy in the film Ustr, the bending energy Ubend, the elastic energy in the substrate Usub, and the adhesion energy between the film and the substrate Uadh, as shown in the following formula:

The tensile strain and bending energy of the film can be written as:

The approximate relationship between the shape of the corrugated structure and the applied strain is e?~?p2h2/4d2. So, the tensile strain energy in the film can be approximately ignored under the assumption of the nonexpandable film. The strain energy of nonlinear elastic substrate can be given as:

Since the strain energy in the substrate and the strain energy of the film delamination can be neglected, the effect of nonlinear buckling of the material in the elastic substrate...