GaN-based LEDs have been widely developed in many electronic industries related to full color displays, automobile lights, and other visible and non-visible lights due to a number of advantages such as low power consumption, long duration lifetime, and ecological-friendliness [1-6]. Although the LED technology has been remarkably evolved, there are still issues to be resolved for enhancing device performances, such as high joule heating and low light emission efficiency. Output power of LEDs is affected strongly by the wall-plug efficiency (η_total) that is determined from the product of internal efficiency (η_int), electrical efficiency (η_elec), and extraction efficiency (η_ext). η_int, mainly related with the material quality, is enhanced by low-defect epitaxial growth and optimized multiple quantum wells (MQWs). η_elec is improved by better ohmic contact and higher electron mobility. η_ext, more related with device geometry and surface /interface quality of the LED, can be enhanced by physical approaches including reduction of total internal reflection (TIR), patterning the substrate, giving textures to p-GaN anode, and novel device structures [7-9]. Conventional LEDs (CV-LEDs) generally are composed of asymmetric sturcture (in the radial direction), which results in low optical efficiency due to the high current crowding effect occurring at a certain localized active region between n- and p-electrodes [10-11].

In this paper, the optical performance of a rectangular type LED (RT-LED) with a centered island cathode is demonstrated by fabrication results and supporting simulation data. The optical and electrical characteristics of the RT-LED are enhanced by the reduction of current crowding near the n-electrode by the structural symmetries of the n- and p-electrodes [12]. Also, the identical current path between cathode and anode makes injection current uniform over the whole device. Therefore, η_elec increases as the effective area where electron-hole recombinations take place is enlarged by the help of uniform current injection. In addition to the optical and electrical performances, the device temperature of the RT-LED at the forward bias operation is dramatically reduced compared with that of CV-LED. Thus, heating-induced reliability degration is also substantially reduced.

Figure 1(a) shows the schematic diagram of RT-LED for a GaN-based 460-nm blue LED. The epitaxial multi-layers were grown on the patterned sapphire substrate by using metal-organic chemical vapor deposition (MOCVD). It consists of a GaN buffer layer for the epitaxy process, un-doped GaN layer, Si-doped n-GaN layer, InGaN/GaN multiple quantum wells, and Mg-doped p-GaN layer. The thicknesses of n- and p-type GaN layers were 4 μm and 300 nm, respectively, and the doping concentrations were Si 3×10¹⁸ cm^-3 and Mg 6×10¹⁷ cm^-3. The exact atom fractions in InGaN in the quantum wells were 23% In and 77% Ga (In_0.23 Ga_0.77N). Each pair was composed of 3-nm In_0.23Ga_0.77N and 10-nm GaN, which made up a 65-nm quantum-well region by employing 5 pairs. As the transparent metallic layer for effective current spreading, a Ni (50 A)/Au (50 A) multi-layer was deposited on a p-GaN layer and then annealed by a rapid thermal process (RTP) at 500℃ in the N₂/O₂ ambient to form stable ohmic contacts [13-14]. A Ti (300 A)/Au (4000 A) multi-layer for electrode metal was deposited by an electron beam (e-beam) evaporator. The n-type electrode was formed on the mesa etched n-GaN layer at the center of the LED as show in Fig. 1(b) and a p-type electrode was formed on the p-GaN layer with rectangular ring type. The CV- and RT-LED devices were fabricated on the same chip and went through the same process conditions. Also, the areas of p-GaN layer (1.62×10⁵ μm²), current spreading layer (1.39×10⁵ μm²) and electrodes (10⁴ μm²) of the RT-LED were designed to be the same as those of the CV-LED.

In designing an LED device, it is essential to extract the current spreading length from the material and process conditions and to utilize it as a design rule [15-16]. The distance between p- and n-electrodes of the RT-LED was also determined to be shorter than the current spreading length at the material conditions that we employed. The current spreading length is mathematically induced as follows [16]:

Here, ρ_c is the contact resistance between the transparent layer and the p-type GaN layer. ρ_p/n, and t_p/n are the resistivity and thickness of the p/n-GaN layer, respectively. In the similar fashion, ρ_t, and t_t are those of the transparent layer. For a well-made GaN Led, the contact resistance is known to be in the 10^-3-Ω· cm² order [17], and we assumed that ρ_c = 5×10^-3 Ω· cm² for our work. ρ_p of Mg-doped p-type GaN (ρ_p) at Mg 6×10¹⁷ cm^-3 is around 2 Ω·cm

[18], and t_p = 0.3×10^-4 cm as given above. ρ_n of Si-doped n-type GaN at Si 3×10¹⁸ cm^-3 is around 0.03 Ω·cm [19], and t_n was given as 4×10^-4 cm. Ni and Au thicknesses were commonly 50 A. ρ_t/tt = 25 Ω for the Ni/Au film with a 1:1 thickness ratio when the film thickness is 100 A in our case, according to the experimental data [16]. Substituting these values into the equation gives the current spreading length of 100.6 μm. The distance between the n-type island electrode and the surrounding p-type electrode is 93 μm and that between bonding pad is 98.6 μm, which confirms that the designed RT-LED meets the design rule with current spreading length.

Prior to the LED fabrication, we investigated the performances of CV- and RT-LED by an optical simulation tool, SpeCLED [20]. Fig. 2(a) shows the simulated current -voltage (I-V) and optical output power characteristics of the CV- and RT-LED. The total p-electrode metal areas of CV- and RT-LED devices in Figs. 1(b) and (c) were made

the same, which, in consequence, reduced the actual area of p-electrode bonding pad (the left upper area where probing in the measurements is made). By this design approach, we could make the areas covered by the metals as well as the areas of active regions the same in both devices to make fair comparisons. Additional simulations revealed that local changing the p-pad area of RT-LED has little effect on current drivability. As shown in Fig. 2(a), the RT-LED shows higher optical power and necessitates lower forward operation voltage at all current levels than the CV-LED. Based on the simulation results, we investigated the performances of the fabricated RT-LED compared with those of the CV-LED. Fig. 2(b) shows the measured I-V characteristic of CV-LED and RT-LED under the forward operation voltage. The measurements were performed by direct probing the p- and n-electrodes labeled in Figs. 1(b) and (c). In Fig. 2(b), the current reflects the total current injected into the diode when voltage is applied between anode and cathode of the LED. At an injection current of 100 mA, the forward voltage of the RT-LED (4.5 V) is lower than that of the CV-LED (4.9 V). It indicates that the power consumption of the RT-LED is substantially lower than that of the CV-LED at the identical injection current. Although CV- and RT-LEDs have the same surface areas, the p- and n-type electrodes are asymmetrically located in the device and most current flows along the shortest path, in the diagonal direction, from p- to n-type electrode. In this case, current crowding effect takes place near each electrode, which increases series resistance and self-heating. On the other hand, electrical characteristic of the RT-LED is enhanced by uniform current spreading and shorter distance between two electrodes. Fig. 2(b) shows the optical output power of CV- and RT-LEDs as a function of current applied to the LED. Output power of the RT-LED when the applied currents for measurement are 20 mA and 100 mA is more improved by about 43.5% and 64.7% as compared with those of CV-LED, respectively. The light emitting efficiency of the CV-LED is dominated by the diagonal current path due to the non-uniform current spreading and the light extraction along the edge is negligibly small. However, in the case of the RT-LED, the n-type electrode is surrounded by the p-type electrode in all directions. Thus, the current spreads more uniformly on the surface, and thus, electron-hole radiative recombinations are increased.

In order to confirm the directional uniformity of the injected currents, we observed the series resistance of fabricated LEDs. Fig. 3(a) shows the series resistance of CV- and RT-LEDs obtained by differentiations (dV/dI) from the I-V curve in Fig. 2(b). As a result, a series resistance at 20-mA current injection is 24 Ω for the RT-LED, which was a little bit lower than that of the CV-LED, 25 Ω. As the current injection increases, series resistances decreases and the difference between those of CV- and RT-LED devices becomes more prominent: at 100-mA current injection, resistances of CV-and RT-LEDs were 26 Ω and 15 Ω, respectively. It is

observed that that more current crowding in the CV-LED leads to higher series resistance due to interruption of current flow in the direction of the perimeter. The increase of series resistance due to non-uniform current also results in a rise in temperature of the LED [21-24]. As shown in the Fig. 3(b), the device temperature of the RT-LED predicted by simulation is about 343 K at 100 mA and it is 10.3% lower than 384 K of the CV-LED. Therefore, the RT-LED is operated with higher reliability in thermal perspective.

Figure 4 shows the luminescence efficiency of the RT-LED and the CV-LED. In this result, the RT-LED demonstrated improved luminescence efficiencies by 61.7% and 106.3% at two different current biases of 20 mA and 100 mA, respectively. The current flow in the RT-LED is distributed in every radial direction with the same distance between p- and n-electrodes, covering the whole device

surface and active region. Therefore, the electron-hole recombination extracting the light is drastically enhanced. Also, it is more probable that the light emission from the etched mesa sidewall is observed through both top and sidewall surfaces [3-4]. On the other hand, the local current -crowding in the small volume of region, for the case of the CV-LED, degrades the recombination rate.

In this work, we fabricated and demonstrated CV- and RT-LED devices. For more rigorous characterization of the designed RT-LED and its comparison with the CV-LED, the measurement analyses were accompanied by simulations. The electrode structures of the RT-LED led to uniform current spreading and reduced the series resistance. Through engineering the electrode geometry, RT-LED demonstrated higher electrical and optical performances. For wider commercialization of the RT-LED with centered island electrode, reliability issues such as short circuit-free wiring, degradation of external quantum efficiency, and failure by wire heating should be further studied.