## 3 Results and Discussion
### Electrical Characterization  
Recent studies on the graphene-silicon interface showed the Schottky junction is created when graphene or graphene derivatives are in contact with the silicon surface. Figure 4 shows the energy band diagram for graphene-silicon structure. When a graphene layer is in contact with a silicon surface, charge transfer occurs due to a difference in their work functions (\(\partial_{G}>\partial_{Si}\)) until the respective Fermi levels align at equilibrium condition. The energy diagram shows a discontinuity of the allowed energy states, which results in the formation of an energy barrier at the G/Si interface, known as the Schottky barrier. This energy barrier limits the electron flow from the graphene to the silicon. Schottky barrier height (\(\partial_{B}\)) can be described using the following equation:  
\[\partial_{B}=\partial_{\text{GN}W}-\chi_{Si} \tag{1}\]  
Figure 4: Energy band diagram of graphene on n-type silicon junction. Figure 3: (**a**) Low-resolution TEM image of GNW and (**b**) high-resolution TEM image of GNW of several layers of graphene with an interspace layer of 0.35 nm. \(dp_{B}\) is unaffected by voltage bias and doping level. It can be related to the work function of graphene, \(dp_{GNW}\) and electron affinity of silicon, \(\chi_{Si}\). A larger Schottky barrier height normallyshows a better rectifying behavior as reported by [PERSON] [11]. This also produces large built-in potential \(V_{bi}\). A two-point probe I-V test method was performed on the samples in which the first probe with the voltage applied was placed on the TMBS device and the second probe was grounded on the back of the sample. Both TiSi and GNW TMBS diodes were tested. Figure 5a shows the I-V characteristic of the GNW-TMBS diode exhibiting a rectifying behavior of a Schottky diode at different temperatures. The reverse leakage current at 5 V of the GNW-TMBS diode increased from 0.2 uA to 300 uA when temperature increased from 298 K to 473 K.  
Figure 5b shows the leakage current comparison of the GNW-TMBS and TiSi\({}_{2}\)-TMBS diodes at different temperatures. The I-V curve shows both the GNW-TMBS and TiSi\({}_{2}\)-TMBS diodes exhibited blocking voltage isabove 60 V at room temperature. The GNW-TMBS diode has a higher breakdown voltage by 5 V. At room temperature, both devices show comparable leakage current. However, at high temperature (>423 K) the TiSi\({}_{2}\)-TMBS diode shows thermal runaway effect, which the leakage current exponentially increased. On the other hand, the GNW-TMBS diode has low leakage current (<1 mA) when the temperature reaches above 423 K.  
Figure 5c shows the temperature effect on leakage current for both GNW and TiSi\({}_{2}\)-TMBS diodes. The leakage current of the TiSi\({}_{2}\)-TMBS diode reaches compliance limit (10 mA) once the temperature exceeds 423 K. The GNW-TMBS diode, on the other hand, shows stable leakage current below 1 mA for all the temperature settings. The low leakage current of the GNW-TMBS diode at high temperature could be due to micro heat sink effect resulted from the vertical structure of the GNW layer, as described in Section 3.1 above. As graphene has a high thermal conductivity characteristic, it also helps to reduce  
Figure 5: (a) Current versus voltage in semilog scale for GNW-TMBS. (b) I-V curves of GNW and TiSi\({}_{2}\) diodes showing breakdown voltage. (c) Leakage current versus temperature of GNW and TiSi\({}_{2}\)-TMBS diodes at 60 V.  
or eliminate the localized self-heating effect in the diode structure and effectively dissipate heat from the structure. In comparison to the TiSi\({}_{2}\)-silicon interface, the GNW-silicon interface has a more severe inhomogeneity issue, which results in multiple conduction paths through the non-uniform interface. The growth process of GNW on silicon is one of the primary sources of interfacial inhomogeneity, which includes the nucleation sites, patches of graphene nanowall, processing remnants, surface roughness, native oxide, an uneven doping profile, and crystal defects.