# Oblique Deposition of Ti/Pt/Au Electrode on Photonic Crystal for Vertical Current Injection +
## 3 Results and Discussion
### Transmission Line Method (TLM) Measurement for Specific Contact Resistance  
To achieve small resistance in the vertical current injection device, the resistance between the electrode and the GaAs contact layer with PhC holes needs to be small. Here, we used the transmission line method (TLM) for the resistance measurement [25].  
Figure 6 shows the electrodes on a PhC pattern for the TLM measurement. We performed a similar process as that shown in Figure 3 to draw the PhC pattern without a cavity or waveguide and obliquely deposited the rectangular electrodes. We designed the CBT structure to prevent the current from flowing through outside. The specific contact resistance \(\rho_{c}\) is determined by characterizing the current-voltage relationship. Rectangular electrodes are used in the TLM measurement, which measures the distance-resistance relationship between rectangular electrodes, to obtain the contact resistance. In this study, the distances between the electrodes are \(d\) = 4, 6, 8... 16 \(\upmu\)m (Figure 6a), the electrode length is \(L\) = 50 \(\upmu\)m, and the electrode width is \(w\) = 125 \(\upmu\)m. By assuming that the semiconductor layer is equivalent to the transmission line, the resistance \(R_{T}\) existing between the electrodes can be easily expressed by [25]  
\[R_{T}=2R_{c}+\frac{R_{SH}d}{w}, \tag{1}\]  
where \(R_{SH}\) is the sheet resistance of the semiconductor layer (GaAs) between the electrodes and \(R_{C}\) is the contact resistance defined by \(R_{c}=R_{SK}L_{T}/w\). \(R_{SK}\) is the sheet resistance of the semiconductor layer just below the electrode, and \(L_{T}\) is called the propagation length. It can be assumed that the current flows in the area with length \(L_{T}\) in the electrode, which means that only the resistance of the area of width \(L_{T}\) in the electrode is included in the contact resistance. The propagation length \(L_{T}\) is defined by \(L_{T}=\sqrt{\rho_{c}/R_{SK}}\) (here, \(R_{SK}\approx R_{SH}\)). Based on the above principles, the specific contact resistance \(\rho_{c}\) can be obtained from the slope of the approximate line of \(R_{T}\) and \(d\). First, the contact resistance of the GaAs contact layer was measured without a photonic crystal structure for comparison. The \(\rho_{c}\) without PhC was \(6.4\times 10^{-7}\)\(\Omega\cdot\)cm\({}^{2}\) after annealing the sample at 400 \({}^{\circ}\)C for 60 s. Then, we fabricated the sample with a PhC pattern and deposited the rectangular electrodes. Given the oblique direction shown by the arrows in Figure 6b, the stacked metal materials can be seen at the bottom of the electrode, not at the left or right side, which ensured accurate distances between the electrodes. Figure 7 shows the relationship between resistance and distance. Measurement results show that the specific contact resistance \(\rho_{c}\) was \(9.5\times 10^{-7}\)\(\Omega\cdot\)cm\({}^{2}\), which is 1.5 times higher than that of the structure without a PhC pattern under the same annealing conditions. The resistance increases slightly, due to the decrease in the conductive area, which indicates that the bonding between the electrode and the contact layer is as tight as that in the no-PhC sample, and there is no current leakage through other layers. This result means that the structure fabricated by the oblique deposition has an acceptable electrical conductivity.  
Figure 5: SEM images of top view (**a**) and cross-section view (**b**) of obliquely deposited electrode on the photonic crystal (PhC) structure.