Copyright WILEY‐VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2012. Supporting Information for Adv. Mater., DOI: 10.1002/adma. 201104648 Design Rule of Nanostructures in Light-Emitting Diodes for
Complete Elimination of Total Internal Reflection
Jun Ho Son, Jong Uk Kim, Yang Hee Song, Buem Joon Kim,
Chul Jong Ryu, and Jong-Lam Lee *
Submitted to
Supporting Information
Design rule of nanostructure in light-emitting diodes for complete
elimination of total internal reflection**
Jun Ho Son, Jong Uk Kim, Yang Hee Song, Buem Joon Kim, Chul Jong Ryu, and JongLam Lee*
Figure S1. Schematic of total internal reflection and light escape cone at GaN-air interface.
Due to the large difference in refractive indices between GaN (n=2.52) and air (n=1), the
critical angle for total internal reflection is about 23.4o.
Figure S1 shows the schematic of total internal reflection and light escape cone at GaN-air
interface. Considering the refractive indices of GaN (n=2.52) and air (n=1) at 450 nm
wavelength, the critical angle, given by following equation, α c = sin −1
nair
, is only about
nGaN
23.4o. Therefore, a flat n-GaN surface in vertical LEDs results in waveguided modes that
photons cannot escape, and subsequently will be absorbed by the metal electrode or active
layer.
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Figure S2. SEM images of n-face n-GaN roughened by photochemical etching (PCE) as a
function of NaOH concentration and etching time. As a NaOH concentration and etching time
increase, the size of hexagonal pyramids was also increased.
Figure S2 shows the SEM images of n-face n-GaN in vertical LEDs roughened by
photochemical etching (PCE) with various NaOH concentration and etching time. PCE was
carried out by dipping the vertical LEDs in a NaOH : H2O2 = 1 : 1 solution for various time
under UV illumination from a Xe halogen lamp, leading to formation of hexagonal pyramids
on the n-face n-GaN. The experimental results clearly show that the size of hexagonal
pyramids was increased with NaOH concentration and etching time.
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Figure S3. Changes of side wall angle of hexagonal pyramids formed by photochemical
etching (PCE) of n-face n-GaN with various NaOH concentrations as a function of etching
time. The angles of pyramids for 5 and 15 min in 1 M and 2 M NaOH solution were not
plotted, because the sizes of pyramid nanostructures were too small to measure the side wall
angle.
Figure S3 shows the changes of side wall angle for the hexagonal pyramids structures
formed by photochemical etching (PCE) as a function of etching time. The side wall angles
for all etching conditions were not changed significantly with etching condition, distributed
from 30 to 32o. This could be attributed to the selective etching of GaN {10-1-1} surface
during PCE due to the lowest surface energy and small number of bonds of GaN {10-1-1}.
Therefore, it is impossible to control the side wall angle of hexagonal pyramids structures to
maximize the light extraction efficiency of GaN-based vertical LEDs, which has critical angle
of 23.4o.
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Figure S4. Calculated light output power of V-LEDs with flat n-GaN, cone-shaped
nanostructured n-GaN, and nanorods structured n-GaN. Compared to V-LEDs with coneshaped nanostructures, V-LEDs with nanorods shows clearly low light output power. The
diameter and height of nanorods were same with cone-shaped nanostructures.
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Figure S5. SEM images of SiO2 nanospheres-coated GaN substrate with various surface
treatments. (a) no treatment, (b) O2-plasma treatment and (c) UV-O treatment. Inset shows the
water contact angle. The large-area SiO2 monolayer was successfully formed on the UV-O
treated GaN substrate with hydrophilic surface.
Large-area single-layer coating of SiO2 nanospheres is required for the application to
vertical LEDs. For conformal coating of single-layer SiO2 nanospheres on large-area GaN
substrate, surface energy of the substrate has to be increased by surface treatment, so the SiO2
nanosphere suspension can be easily spread over the entire substrate. Typically, hydrophilic
surface result in the lower contact angle. Ultraviolet-ozone (UV-O) treated surface shows the
lowest measured contact angle of ~11° compared to untreated and O2 plasma treated surfaces,
76 and 55.6° respectively (Figure S5 a-c inset). As the water contact angle decreases, the area
of hexagonally closed packed single-layer SiO2 nanospheres was increased as shown in
Figure S5. The large-area single-layer of SiO2 nanospheres was successfully fabricated on the
UV-O treated GaN substrate.
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Figure S6. Cross-sectional SEM image of n-face n-GaN after ICP etching for 2 min 30 sec.
Figure S6 shows the cross-sectional SEM image of n-face n-GaN aftter ICP etching for 2
min 30 sec, showing the side-wall angle of about 23.1o, which is further closed to critical
angle, but the top surface was a little flat. However, after ICP etching for 3 min, the coneshape nanostructure with side-wall angle of 24.1o was formed on n-GaN. (Figure 2c)
Therefore, we fabricated the V-LEDs with ICP etching varied from 3 min to 5 min.
Figure S7. Changes of light output power in vertical LEDs roughened by photochemical
etching (PCE) with NaOH concentration and etching time.
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Figure S7 shows the changes of light output power in vertical LEDs roughened by
photochemical etching (PCE) with NaOH concentration and etching time. For 1 and 2M
NaOH solution, the light output power was increased with increase of etching time due to the
increased size of hexagonal pyramids structures as shown in Fig. S2. However, for the 4 and
8M NaOH solution, the light output power was saturated after 15 min etching. The V-LEDs
etched at 8 M for 15 min showing highest light output power was used as a reference vertical
LEDs.
Figure S8. Calculated light output power of V-LEDs as a function of n-GaN thickness. The
side-wall angle of cone-shaped nanostructures was fixed at 23.4o. The light output power was
normalized to that of V-LEDs with 2-µm-thick n-GaN.
We performed additional FDTD simulations to show the changes of light extraction efficiency in
V-LEDs with changes of n-type GaN thickness as shown in Figure S8. The calculated light output
power was increased as the thickness of n-type GaN layer was decreased. This could be due to the
decreased absorption of photons at n-GaN layer and small number of guided modes inside thin GaN
layer.[1] Therefore, the light output power could be further increased by using thin n-GaN layer in V-
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LEDs. However, the decrease of light output power by current crowding at high injection current and
mechanical stability in thin-GaN V-LEDs are still challenging.
[1] S.-K. Kim, J. W. Lee, H.-S. Ee, Y.-T. Moon, S.-H. Kwon, H. Kwon, and H.-G. Park, Opt. Express
2010, 18, 11025.
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