Graphene for Flexible Electronic Devices
S.S. Jain Subodh P.G. (Autonomous) College
Flexible electronics [1,2] portray the combination of a thin passive wafer or substrate of, for example, metallic foil, textile or plastic, with active electrical components integrated over it so that the substrate turns conformally to highly curved surfaces on stretching along a direction [3,4]. Transparent electronics combine electronics of optically transparent materials (graphene or CNTs) with optically transparent substrate (glass) [5,6]. Similarly, the word “textile electronics” has been ascribed to integrated electronics fabricated on silk or other woven fabrics [7,8]. The various type of substrates for flexible electronics include polymers, thin substrates, paper, fabrics, and even thin metal foils as outlined above [9,10]. These substrates are cost- effective, good in thermal conduction, but resistant to electrical conduction, in addition to being flexible mechanically . Robustness is a mechanical property that makes them potentially attractive for flexible device applications (Figure 22.1). These substrates do not consist of structural defects, possess high resistive properties to mechanical deformations to creep, and can resist high temperatures before melting, as well as possess a high glass transition temperature (Tg) . The term “flexible” has a physical meaning that directly relates to the ability to suffer bending such that
the strain, =-, developed on the application of bending force should not exceed yield r
strain (7yield strain of the film [12-14]. Deposition of pm-thin layer is performed, patterned for device structuration, bonded, and integrated over flexible platforms such that the substrate retains its flexible nature. It is necessary that the intra-layers of the electronic material are strongly bonded such that the strain (ex) formed as a result of bending does not surpass yield strain <7у:еиstrain of the bilayer structure. In fact, durable flexible devices must possess the capability to withstand induced mechanical
FIGURE 22.1 Printed flexible device displays no effect on bending.
deformation caused by stretching, bending, twisting, folding, and compressing, and should maintain structural integrity along with electronic performance. In regard to flexible characteristics, the following points should be focused on:
i. Bending status of flexible devices is characterized by bending angle, bending radius, and distance between the two ends of the bend.
ii. Structural design include choice of suitable flexible substrates, optimized architectural design of devices on flexible platforms, as thin as possible by reduction in thickness, and a neutral plane platform.
iii. Mechanical modeling for analysis of strain and deformation distributive pattern in the entire flexible energy storage devices.
iv. Experimental methods for the determination of different bending parameters to analyze flexible materials and devices.
Different types of polymer substrates are /?o/v(tetrafluoroethylene) (PTFE) [15,16], kaptonz po/v(imide)  and /w/v(ethylene terephthalate) (PET) , /w/vfdimethylsiloxane) (PDMS) , and cellulose paper composite-based substrates [20,21], which are routinely used for flexible device technology. Nathan et al. has pointed out physical characteristics of many polymer substrates separately . Polyimide or Kapton, commonly called as thermal tape, is orange in color, possesses high thermal expansion coefficient, is costly, and chemically resistive along with a maximum deposition temperature of 250°C . PET possesses a moderate coefficient of thermal expansion, is cost-effective, chemically resistive in nature, with a maximum bearable deposition temperature of 160°C . Polyetherimide (PEI) is strong, brittle, and possesses a maximum tolerance of temperatures up to 180°C . Polyetheretherketone (PEEK) has good chemical resistive properties with the maximum tolerance of temperatures up to 240°C . These flexible substrates have been applied in a number of applications, including electronic skin, wearable electronic devices, portable devices for energy storage and harvesting, stretchable electronics technology, sensors fabricated on a flexible platform, high-end biotechnology devices, and logic devices.
Mechanical Properties of Flexible Systems
Flexible energy storage and harvesting devices are extremely important for biomedical applications, long-life battery systems, and low-cost solar cells [12-14]. Mechanical stability of electrodes is a significant challenge in these flexible devices requiring them to be sufficiently thin and flexible. Consequently, on applying bending force on flexible platforms, deformation mechanism occurs and is resisted by an intrinsically produced stress. Considering the case of a thin film deposited over flexible substrate equivalent to a mechanical beam of radius “r,” inner surface experiences compressive strain while outer surface sustains tensile strain [12-14]. In this device structure, a region devoid of uniaxial strain portrays a mechanically neutral plane. This mechanically neutral plane is placed in a position which is a function of thickness of each contributing layer and the Young’s modulus. A mechanically neutral plane is defined as the plane that passes through the printed flexible device when mechanical deformation with minimal radius curvature is applied that results in no uniaxial bending strain .
It is this mechanically neutral plane that forms the point of crux so that deposition of film at this location develops an ultra-flexible platform. In case of a device structure consisting of a stack of thin films and electrodes, bending mechanics become slightly complex leading to the development of stress factor due to the difference in mechanical properties, such as elastic modulus. Figure 22.2 displays the bending mechanism in a thin film on a flexible substrate. Strain generated in the upper part of the curved surface is expressed as follows:
FIGURE 22.2 Bending mechanics of a thin film on a flexible substrate for describing bending mechanism.
Here, x is the distance of the upper curved surface from the neutral plane and r is the cylindrical radius covered under the lower curved surface of the mechanical beam [12-14]. Equation (22.1) shows that the thin film endures minimum bending strain while sustaining its electrical performance at the threshold of bending radius. Mao et al. have given a mathematical expression for the distance of mechanically neutral plane to the upper curved convex surface as follows :
Here, rThinFilm and ?Substrale are the thicknesses of thin films and substrates, a = f 711,11F,lm
is the ratio of thickness of the thin film and substrate, and 8 = —Fllm expresses the
ratio of Young’s modulus of the thin film and substrate . Hence, the strain of the upper curved surface is expressed as:
In case of nearly similar Young’s modulus of the thin film and substrate ^Thin Rima Substrate s0 that ratio of these two quantities becomes 5 = 1. In this case, mechanically neutral plane lies along the same line coinciding with the line passing through the middle plane of the device structure. In that case, equations (22.2) and (22.4) are simplified as follows :
Extending the simplest case to a multi stacked structure, the constituent layers are theorized as a fused mechanical beam-type structure, then the length “x” of the top-surfaced bending curvature from the mechanically neutral plane is expressed as follows:
Here, n is the total number of constituent layers forming the multilayered structure, hj is the thickness of /th layer in case of narrow-structured devices, and Y, is Young’s modulus of each component layer.