# Adhesion Behavior between Multilayer Graphene and Semiconductor Substrates
## 1 Introduction  
Numerous graphene-based Micro-Electro Mechanical Systems/Nano-Electro Mechanical Systems (MEMS/NEMS) devices have been reported, such as gas isolators [1], pressure sensors [2], graphene-silicon Schottky diodes [3, 4], photodiodes [5, 6], and so on, because of graphene's low mass in relation to the atomic thickness [7], high Young's modulus [8], and excellent thermal and electrical properties [9]. The bonding properties of graphene and silicon have a significant effect on the performance of these devices. Thus, it is essential to study the adhesion behavior and bonding strength between graphene and Si substrates. Graphene is ultrathin because it consists of layers with carbon with a six-membered ring structure. In order to study the adhesion phenomena of graphene on Si or SiO\({}_{2}\) substrates experimentally, researchers must turn to micro/nano-processing and high-precision instruments. [PERSON] et al. demonstrated that the adhesion properties are sensitive to the size of graphene oxide flakesand the deposition pressure on the polymer substrate, as revealed through tape tests and (Scanning Electron Microscope) SEM images [10]. By inserting nanoparticles into a graphene-SiO\({}_{2}\) interface to support axisymmetric blisters, the adhesion energy was measured to be 151 \(\pm\) 28 mJ/m\({}^{2}\)[11]. [PERSON] et al. designed an interfacial wedge crack test between graphene and native oxidized Si, then characterized the adhesion energy as 350 \(\pm\) 16 mJ/m\({}^{2}\)[12]. [PERSON] et al. measured the adhesion energy of graphene sheets with an Si substrate to be about 240 mJ/m\({}^{2}\) by a pressurized blister test [13; 14]. The experimental processes were elaborate and delicate, as well as easily influenced by external noise. In addition, the dynamic adhesive changes of the atomic structure could not be accessed. In addition to experimental methods, molecular dynamics (MD) simulations are widely used to study the interface mechanics of graphene on polymer and metal substrates [15; 16]. A more pronounced substrate-induced appreciation of the film glass-transition temperature (T\({}_{\mathrm{g}}\)) was discovered for polymers by MD simulations, in addition to weaker intermolecular interactions and low bulk T\({}_{\mathrm{g}}\) in ultrathin polymer films (18 nm thick) [17]. Nanoindentation and scratching of graphene-covered Pt (111) surfaces were studied in computer simulations, and it was found that graphene can substantially enhance the load-carrying capacity of Pt substrates with low friction. These results showed excellent agreement with experiment results [18]. However, only a few atomic calculation studies have looked at the adhesion behavior of graphene on Si substrates. [PERSON] and [PERSON] used molecular dynamics to apply normal strain to compress nanometer-sized graphite and drive top layer movement along the side length direction of the SiO\({}_{2}\) substrate. Graphene was exfoliated from graphite horizontally, which was called friction-induced exfoliation, and attributed to substrate roughness and graphite corrugation [19]. This study focused on a method to fabricate graphene, but it did not obtain the adhesion energy or vertical exfoliation force when the interlayer gap of graphene was in its natural state (3.35 A). [PERSON] et al. used a molecular dynamics method with a GraFF forcefield to examine graphene's unusual behavior in a superlubric state. Additionally, due to the lower level of friction, a peeling mechanism of exfoliation was predicted to exhibit less energy dissipation than shearing [20]. [PERSON] et al. reported a wedge-based mechanical exfoliation machining process to produce few-layer graphene by molecular simulation studies. The entry location of the wedge tip played a key role in the separation, folding, and shearing of graphene layers from graphite [21]. These previous works addressed the fabrication mechanism of graphene from graphite by friction-induced or wedge-based mechanical exfoliation.