## 3 Results and Discussion  
### Material Characterization  
FESEM images of the top view and cross-sectional view of the as-grown GNW on the silicon trench structures are shown in Figure 2a,b. The SEM image shows a typical GNW film, with a leaf-like 2D wall structure vertically standing on silicon substrate indicating vertical graphene structure. It was grown directly on silicon surfaces without a metal catalyst. This non-catalytic growth of GNW is defined as self-assembled vertical graphene nanosheets with thicknesses in the range of a few to several nanometers. The height of the GNW in this study is approximately 50 nm to 60 nm, as shown in Figure 2b. The illustration diagram of the GNW structure is shown in Figure 2d, which illustrates the large surface area of freestanding few-layered graphene on silicon substrate. The fin-like protrusions of GNW increased the surface contact with the air, and help to increase the heat dissipation rate, hence eliminate localized self-heating effect in the diode structure. Beside this micro heat sink effect, the high thermal conductivity of the graphene layer also contributes to a high thermal dissipation rate, as reported by several studies on graphene heat spreader in thermal management of electronic devices [17; 18; 19].  
Figure 2c shows the Raman spectrum of the GNW grown on silicon substrates. The result shows typical graphite or nanostructured carbon characteristic of G, D, and 2D peaks. The existence of G and 2D peaks indicates the graphene layer was formed on the silicon substrate. The G peak at 1580 cm\({}^{-1}\) indicates the graphitized structures. The D peak at 1360 cm\({}^{-1}\) is associated with a defect in the material [12; 20] or disorder-induced phonon mode [16], which in this case may relates to a few types of defects, i.e., carbon materials that are not purely a single layer graphene, including amorphous carbon [6] and structural disorder and edges in the GNW layers [13]. The G peak has a shoulder peak on the right side indicating finite-size graphite crystals and graphene edges [21]. The intensity ratio of the G-band to the D-band (\(I_{\text{G}}\)/\(I_{\text{D}}\)) is generally related to the in-plane crystallite size of graphene. On the basis of the general Tuinstra\(-\)Koenig relation [22], an estimation of the average in-plane crystallite  
Figure 2: FESEM images of the (**a**) top view of graphene nanowall (GNW) on silicon trench, (**b**) cross-section of the GNW, (**c**) Raman spectrum of the GNW showing D, G and 2D peaks, and (**d**) illustration diagram of GNW on silicon substrate that have an ultra-large surface contact with the air.  
size was obtained using the following empirical formula: \(L_{\text{a}}=(2.4\times 10^{-10})\lambda^{4}(I_{\text{D}}/I_{\text{G}})^{-1}\), where \(\lambda\) is the laser excitation wavelength used for the Raman measurements. Here, the \(L_{\text{a}}\) value of the GNW was estimated to be \(\sim\)7.5 nm for the \(I_{\text{G}}/I_{\text{D}}\) ratio of 0.625 (or \(I_{\text{D}}/I_{\text{G}}\) ratio of 1.6), which is comparable to typical GNWs for thermal management [23]. An \(I_{\text{2D}}/I_{\text{G}}\) ratio of \(\sim\)1.0 indicates the existence of few layers of graphene sheets with random stacking order in agreement with previous work [24; 25]. This observation is also consistent with the high resolution transmission electron microscopy (HRTEM) image of GNWs, as shown in in Figure 3a,b. Several layers of graphene/graphite sheets with an interplanar spacing of 0.35 nm were observed, confirming the GNWs are made of several layers of graphene [12; 19; 20; 21].