# Configurational Effects on Strain and Doping at Graphene-Silver Nanowire Interfaces
## 2 Results and Discussion  
The fabrication of the Gr/AgNW heterostructure (Figure 1) involves air-spraying of AgNW on ITO substrate and subsequent deposition of Poly(methyl methacrylate) (PMMA)/Gr composite by wet transfer technique [16]. The uppermost PMMA is then removed by immersion in acetone bath, resulting in sole coverage of monolayer graphene on the AgNW network. The other stacking arrangement of AgNW/Gr heterostructure is simply fabricated by spraying AgNW solution over graphene. After the deposition of AgNW and graphene, the light transmittance reduces up to 10% between wavelengths of 488 and 650 nm (Figure 1c), indicating the graphene and AgNW layer permit sufficient light transmission for the function of optoelectronic devices. In the Gr/AgNW system, conformation of graphene over the AgNW network (Figure 2a) is indicated by the morphology studies with atomic force microscopy. Substantial separation of two AgNWs (\(>\) 100 nm) allows graphene to follow the curvature and adhere to the ITO substrate between two nanowires, thanks to the low bending rigidity of single layer graphene (7.1 eV) [17]. However, closely spaced AgNWs reduce the tendency of graphene conformation and eventually result in snap-through transition, where graphene is suspended and fails to touch the substrate (indicated by yellow arrow in Figure 2b). This snap-through transition can also be confirmed by the adhesion force map in Figure 2c, which reveals the contrast in adhesion force between silica tip apex and Gr/ITO (\(3.7\pm 0.2\) nm), Gr/AgNW (\(1.3\pm 0.1\) nm), and graphene on constrained area indicated by the yellow arrow (\(3.1\pm 0.2\) nm). The adhesion force in 2D materials depends not only on the material surface chemistry, but also on the interfacial interaction between graphene and its subsurface, which regulates the contact area between tip apex and graphene. Compared to Gr/ITO, where the flat monolayer readily favours the contact, in Gr/AgNW, the conformed strain at the curvature of AgNW reduces the contact area in graphene, and hence its adhesion force is significantly lower than that of Gr/ITO. Given the adhesion force of graphene on constrained area is between that of Gr/ITO and Gr/AgNW, it is reasonable to suspect graphene is suspended between two AgNPs at that region. This snap-through transition occurs due to a balance between the surface adhesion energy and the conformed strain energy [18], which, according to our enlarged AFM image of intersection of two AgNPs (Figure 2b,c), takes place at the separation distance of \(50\pm 5\) nm. The surface potential of Gr/AgNW heterostructure is studied by Kelvin probe force microscopy (KPFM) as depicted in Figure 2d,e, which involves scanning of cantilever over the surface with an optimised height (lift height = 15 nm) to measure the contact potential difference (CPD) between the conductive tip and the hybrid surface. The work function \(\varphi\) can then be determined by Equation (1)  
\[e\cdot(CPD)=\varphi_{sample}-\varphi_{tip} \tag{1}\]  
where \(e\) represents the elementary charge. Highly oriented pyrolytic graphite (HOPG) (\(\varphi=4.66\)\(eV\)) serves as a reference for calibration of \(\varphi_{tip}\), which in turn permits the calculation of \(\varphi_{sample}\) at examined region. \(\varphi\) is defined as the electrostatic potential between near-surface vacuum energy and the Fermi level (E\({}_{\text{F}}\)). Hence, it can be regarded as the ability to bind the electron at the interface during contact, and electron charge will flow from lower \(\varphi\) material to higher \(\varphi\) material [9]. We observe a drop in \(\varphi\) of \(0.15\pm 0.03\) eV at the Gr/AgNW region compared to the surrounding Gr/ITO, which implies graphene gains electrons from AgNW and E\({}_{\text{F}}\) of graphene moves towards conduction band as illustrated in the schematic band diagram (Figure 2f).