## 3 Results and Discussions
The specific contact resistances of these ITO-ZnO/Ti/_n_-GaN contact systems as well as the Ti/Al ohmic contact to the _n_-GaN epilayer are summarized in Table 2. A specific contact resistance of \(2.5\times 10^{-3}\)\(\Omega\cdot\)cm\({}^{2}\) was obtainable from the cosputtered ITO-ZnO film's contact to the _n_-GaN epilayer with an additional 2-nm-thick Ti interlayer inset between the interface of ITO-ZnO and _n_-GaN. As the thickness of the Ti interlayer reached 8 nm, the specific contact resistance was optimized further to \(4.8\times 10^{-5}\)\(\Omega\cdot\)cm\({}^{2}\), a value that was a little better than that of the metallic Ti/Al contact to the _n_-GaN epilayer. The optical transmittances of these Ti/ITO-ZnO systems with various Ti interlayered thicknesses are given in Figure 6 (the optical transmittance of the cosputtered ITO-ZnO film also is shown for comparison). The thin Ti interlayer did not change the onset absorption of the cosputtered ITO-ZnO film at the near-UV wavelength. However, the optical transparency of the Ti/ITO-ZnO systems was reduced gradually as the thickness of the Ti interlayer increased. The average transmittances at the visible wavelengths of these Ti/ITO-ZnO systems are listed in Table 2. It can be found that the average transmittances of these Ti/ITO-ZnO systems decreased monotonously from 83.2% to 48.8% as the thickness of the Ti interlayer was increased from 2 to 10 nm. Accordingly, although the cosputtered ITO-ZnO film's ohmic contact to the _n_-GaN epilayer can be optimized when an 8-nm-thick Ti interlayer is inset between the ITO-ZnO/_n_-GaN interface, the structural transmittance at the visible wavelengths apparently decreased to 63.2% as compared to the cosputtered ITO-ZnO film (\(\sim\)84.6%). Herein, we proposed the figure of merit (FOM), \(\Phi\), to quantitatively determine the performance of these  
Figure 4: (**a**) _I-V_ curve of the as-deposited metallic Ti/Al system’s contact to _n_-GaN epilayer and (**b**) the elemental distribution of the Al/Ti/_n_-GaN contact system conducted from AES depth profile measurement. transparent electrodes' ohmic contact to the \(n\)-GaN epilayer. This value is calculated according to the following expression which takes into consideration both the specific contact resistance, \(\rho_{c}\), and the average optical transmittance, \(T_{ave}\)[19,20]:  
\[\Phi=\frac{T^{10}}{\rho_{c}} \tag{1}\]  
The higher the FOM of the Ti/ITO-ZnO system obtained, the better the quality of the transparent electrode contacted to the \(n\)-GaN epilayer. Table 2 gives the FOM of the Ti/ITO-ZnO systems as a \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Thickness of Ti Interlayer** & \(\rho_{c}\) (\(\Omega\cdot\)**cm\({}^{2}\))** & \(T_{ave}\) (\%) & **FOM (\(\Omega^{-1}\cdot\)**cm\({}^{-2}\))** \\ \hline Ti/Al & \(5.1\times 10^{-5}\) & - & - \\
0 nm & - & 84.6 & - \\
2 nm & \(2.5\times 10^{-3}\) & 83.2 & 49 \\
5 nm & \(3.8\times 10^{-4}\) & 75.1 & 144 \\
8 nm & \(4.8\times 10^{-5}\) & 63.2 & 203 \\
10 nm & \(7.8\times 10^{-4}\) & 48.8 & \textless{}1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specific contact resistance, optical average transmittance, and FOM of the Ti/ITO-ZnO systems as a function of the thickness of the Ti interlayer (the specific contact resistance of the Ti/Al contact to the \(n\)-GaN epilayer also is given for comparison). Figure 5: (**a**) _I-V_ characteristics of the ITO-ZnO/Ti/_n_-GaN contact system as a function of the Ti interlayered thickness, measured from the contact spacing of 15 \(\upmu\)m (the _I-V_ curve of the Al/Ti/_n_-GaN contact system also is shown for comparison) and (**b**) the corresponding specific contact resistance as a function of the Ti layered thickness. Figure 6: Optical transmittance of the Ti/ITO-ZnO systems as a function of the Ti interlayered thickness (the optical transmittance of the pure ITO-ZnO also is shown for comparison). function of the thickness of the Ti interlayer.