# Improved Performance of High-Voltage Vertical GaN LEDs via Modification of Micro-Cell Geometry
## 3 Results and Discussion  
Figure 2a shows the I-V characteristics of the HV-LEDs (Samples A-F) after performing the epoxy package process. The injection current was increased from 20 to 350 mA. At injection currents of 20  
Figure 1: Schematic illustration of the fabrication for vertical high-voltage light emitting diodes (HV-LEDs): (**a**) transfer of the LED sample to a Cu metal substrate, (**b**) mesa process, (**c**) growth of the passivation layer, (**d**) connection of 2 \(\times\) 2 micro-cell LED array, and (**e**) formation of the n-pad. (**f**) The images of the HV-LEDs (Samples A–F) with various cell shapes and chip arrangements before operating. and 80 mA, the forward voltages of Samples A-F were 13.2 and 16.0 V, 12.7 and 15.1 V, 12.7 and 15.1 V, 12.6 and 15.0 V, 12.5 and 14.9 V, and 12.2 and 14.9 V, respectively. When the injection current was increased to 350 mA, the forward voltages of these six HV-LEDs increased to 19.3, 18.3, 18.2, 18.2, 18.4, and 18.1 V, respectively. The I-V characteristics of Samples B-F were similar to each other. It indicates that our fabrication processes for vertical HV-LEDs are highly stable. However, the forward voltage of Sample A was clearly higher than that of the other HV-LEDs. Except for the I-V characteristics, the light output powers for the epoxy-packaged HV-LEDs were also measured. Figure 2b shows the light output powers as a function of injection current from 0 to 350 mA for packaged Samples A-F. The surface morphology of the roughened n-type GaN layer taken by SEM is shown in the inset of Figure 2b. For Samples A-F, the output powers at 20 and 80 mA were 89.2 and 309.9 mW, 91.7 and 326.9 mW, 98.4 and 339.7 mW, 96.6 and 338.1 mW, 102.8 and 353.2 mW, and 90.6 and 321.5 mW, respectively. At an injection current of 350 mA, the output powers of these six HV-LEDs increased to 951.2, 991.1, 1029.3, 1021.1, 1070.2, and 966.2 mW, respectively. Obviously, Sample E possessed the optimal light emission performance. Moreover, when the injection current was increased from 20 to 350 mA, the lowest output powers almost occurred in Sample A. The spatial distribution images of the light output for Samples A-F are presented in Figure 3a-f, respectively, at an injection current of 20 mA. In these images, the red/yellow and green/blue colors indicate high and low brightness, respectively. As shown in these images, the performances of light emission were similar to each other. On the other hand, we observed that some obstructions to the emitted light all appeared in these six samples, which resulted from the electrodes. The obstruction of the emitted light near the electrodes was much more obvious in Sample A, likely resulting from the current-crowding phenomenon. In addition, Samples B-F had a favorable current spreading effect. Especially for Samples B, E, and F, the emitted lights of these three samples were more uniform than that of the other HV-LEDs. Actually, the current spreading in micro-cell is most dominantly affected by the distance between electrode and edge of chip. Thus, the shape of micro-cell has no significant influence on the current spreading behavior. On the contrary, the charge diffusion length between electrode and edge of micro-cell plays a more important role than the cell shape for the current spreading behavior. When the electrodes were close to the edges of micro-cells, the current spreading effect can be easily enhanced, as shown in Samples B, E, and F. However, in Sample A, the electrodes in these four micro-cells were all far away from the edges, leading to its severe current-crowding phenomenon. Moreover, the current densities of these six samples were also analyzed via the calculations (i.e., injection current divided by actual emission area). For Samples A-F, the current densities (@20 mA) were determined to be 9.86, 10.84, 10.41, 10.35, 10.71, and 10.77 A/cm\({}^{2}\)  
Figure 2: (**a**) Current-voltage characteristics and (**b**) light output powers as a function of injection current for Samples A–F.