Supplementary Information s67

Supplementary Information

Less strained and more efficient GaN light-emitting diodes with embedded silica hollow nanospheres

Jonghak Kim1, Heeje Woo2, Kisu Joo3, Sungwon Tae4, Jinsub Park5, Daeyoung Moon4, Sung Hyun Park1, Junghwan Jang4, Yigil Cho6, Jucheol Park1, Hwankuk Yuh1, Gun-Do Lee1, In- Suk Choi6, Yasushi Nanishi4,7, Heung Nam Han1, Kookheon Char2,8*, and Euijoon Yoon1,4,9**

1. Department of Materials Science and Engineering, Seoul National University, Seoul 151- 744, Korea 2. School of Chemical and Biological Engineering, Seoul National University, Seoul 151- 744, Korea 3. Nano Science and Technology Program, Graduate School Convergence Science and Technology, Seoul National University, Suwon, 443-270, Korea 4. WCU Hybrid Materials Program, Department of Materials Science and Engineering, Seoul National University, Seoul 151-744, Korea 5. Department of Electronic Engineering, Hanyang University, Seoul, 133-791, Korea 6. High Temperature Energy Materials Research Center, Korea Institute of Science and Technology, Seoul, 136-791, Korea 7. Department of Photonics, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan 8. The National Creative Research Center for Intelligent Hybrids and The WCU Program of Chemical Convergence for Energy & Environment, Seoul National University, Seoul 151- 744, Korea 9. Energy Semiconductor Research Center, Advanced Institutes of Convergence Technology, Seoul National University, Suwon, 443-270, Korea

Correspondence should be addressed to and K.C.* email: [email protected], and E.Y. ** email: [email protected]

1 S1. Material properties of sapphire and III-nitrides

-6 -1 -6 -1 a(Å) c(Å) aa (10 K ) ac (10 K ) Refractive index

Al2O3 4.758 12.99 7.5 8.5 1.78 GaN 3.189 5.185 5.59 3.17 2.4 InN 3.545 5.703 5.7 3.7 2.9

AlN 3.111 4.98 5.3 4.2 2.03

Table S1: Material properties of sapphire and III-nitrides Differences in thermal expansion coefficient and lattice constant between GaN and sapphire are over 30 % and 17%, respectively. Significant wafer bowing and high density threading dislocations are two major drawbacks from this combination.

S2. Synthesis and deposition of polystyrene/silica (PS/SiO2) core-shell nanospheres

Monodisperse PS/SiO2 core-shell nanospheres with uniform shell thickness were prepared by the synthesis technique based on the traditional dispersion polymerization combined with sol-gel

1 reaction(Figs S1 and S2). To prepare the PS/SiO2 core-shell nanospheres, polystyrene (PS) nanosphere templates were first synthesized and silica shells were coated onto the PS surface. 1 The size of PS/SiO2 nanospheres was readily controlled by varying the diameter of PS templates as well as

2-4 the SiO2 shell thickness. The size of PS nanospheres were controlled from 130 nm to 450 nm by varying the concentration of reactants.2 As the concentration of azobis-isobutyramidine dihydrochloride (AIBA), initiator, was increased, the average size of PS nanosphere was increased. With higher initiator concentration, the growth of PS nuclei was facilitated and larger PS nanospheres were finally formed.3 As the concentration of styrene monomer was increased or the concentration of polyvinylpyrrolidone (PVP), stabilizer, was decreased, the average size of PS nanospheres was increased. The SiO2 shell thickness was also controlled by varying the concentration of TEOS and

4 ammonium hydroxide (NH4OH). As the concentrations of TEOS and NH4OH were increased, the

SiO2 shell thickness was also increased (Fig. S1).

To realize the uniform coverage of monolayered PS/SiO2 nanosphere arrays on sapphire substrates, a novel deposition strategy combining a conventional dipping method and the layer-by-layer (LbL)

5 deposition method was developed. To make uniformly arranged PS/SiO2 nanospheres, surface charge of the sapphire substrates was first varied by the deposition of polyelectroyte multilayered films on

6 the sapphire substrates based on the spin-assisted LbL deposition method , and the PS/SiO2

2 nanospheres were then adsorbed on the surface-modified sapphire substrates by the dipping method.

To characterize the influence of surface charge on the morphology of PS/SiO2 nanospheres, three different sapphire substrates, non-charged, positively-charged, and negatively-charged, were used for dip coating. While the massive aggregates of PS/SiO2 nanospheres were formed with non-charged and negatively-charged substrates, the uniform and monolayered PS/SiO2 array was prepared with positively-charged substrates (Fig. S2). We assume that the negatively-charged PS/SiO2 nanospheres should be effectively adsorbed on positively-charged surface only. The uniform particle arrays with various nanosphere size, 250, 350, and 450 nm, were successfully obtained with the dip coating method and the surface coverage of PS/SiO2 could be controlled by varying the dipping time and number of dipping (Fig. S3). The surface coverage of nanospheres adsorbed on the sapphire substrates was easily increased above 50 % by simply varying the dipping time and number. Furthermore, uniformly arrayed PS/SiO2 nanospheres could be also obtained with large-area (2 inch wafer) substrates (Fig. S4). With this novel deposition strategy, we easily secured reproducibility on the highly uniform nanosphere monolayer arrays on large-area, 2 inch, sapphire substrates with simple all solution processes. Despite the increased demand on the usefulness and productivity in mass production of substrates with uniform and tunable surface coverage of nanomaterials, this deposition strategy has not thoroughly been explored. The substrates containing S-HNSs were finally obtained by the selective removal of organic PS cores within PS/SiO2 nanospheres by the thermal treatment above 800 °C.

Fig. S1. Synthesis of PS/SiO2 core-shell nanospheres. a-c, The average size of PS nanospheres prepared with different concentration of AIBA (a), PVP (b), and styrene (c). d-f, The SiO2 shell thickness of PS/SiO2 nanospheres prepared with different concentration of TEOS (d), NH4OH (e) and reaction time (f). 3 Fig. S2. Morphology of S-HNS and PS/SiO2 arrays. a, FE-SEM image of S-HNS with 240 nm outer diameter and 20 nm shell thickness. (scale bar: 400 nm) Inset shows the TEM image of a S-

HNS. b-d, FE-SEM images of PS/SiO2 arrays coated on bare, non-charged, (b), positively-charged (c), negatively-charged (d) sapphire substrates (scale bars: 6 m). In the case of the positively- charged substrate, the PS/SiO2 nanospheres were uniformly coated. However, in the case of the non- charged and the negatively-charged substrates, the PS/SiO2 nanospheres were massively aggregated and formed in isolated clusters.

Fig. S3. Changes in surface coverage of PS/SiO2 monolayers.

4 a-e, FE-SEM image of the 450 nm-sized PS/SiO2 nanospheres coated on positively-charged sapphire substrates with different dipping times (scale bars: 10 m). The concentration of PS/SiO2 dispersion was 10 mg/ml. The surface coverage of PS/SiO2 was increased with dipping time and finally saturated. The surface coverages of PS/SiO2 nanospheres with dipping time of 20 (a), 40 (b), 60 (c), 180 (d), and 300 s (e) were 7.7, 15.8, 22.0, 32.9, and 35.0 %, respectively. f, FE-SEM image of 450 nm-sized PS/SiO2 nanospheres coated on positively-charged sapphire substrates with double dipping and drying (scale bars: 6 m). The concentration of PS/SiO2 dispersion was 10 mg/ml and the dipping time was 180 s each. The surface coverage of PS/SiO2 nanospheres was 48.0 %.

Fig. S4. Uniformity of PS/SiO2 monolayer coated on 2 inch sapphire substrate. To confirm the uniformity of surface coverage in 2 inch substrate, the surface coverages at five different locations in 2 inch substrate were compared. a, A schematic of 2 inch sapphire substrate marked with numbers from 1 to 5 indicating the points where the surface coverage was measured. b-f, The SEM images taken from point 1 (b), 2 (c), 3 (d), 4 (e), and 5 (f) (scale bars: 3 m). The surfaces coverages of point 1, 2, 3, 4, and 5 were 42.5 %, 41.5 %, 42.6 %, 43.0 %, and 42.0 %, respectively. The difference of surface coverage among the 5 points was less than 2 %.

5 Fig. S5. Calculation of surface coverage.

To calculate the surface coverage of the PS/SiO2 nanospheres coated on sapphire substrates, Image J program was used. By adjusting the contrast of FE-SEM images, the PS/SiO2 nanospheres coated surface and uncovered surface are converted white and black regions, respectively. And the surface coverage was calculated by dividing the area of white region with the total area. Fig. S5a is the original FE-SEM image and Fig. S5b is the converted image by Image J program. (scale bar 4 m)

S3. X-ray rocking curve measurement To measure the crystal quality of GaN epitaxial layers, full width at half maximum (FWHM) values of XRD rocking curve were measured. The GaN epitaxial layer containing S-HNS shows large reduction in FWHM value of (102) plane from 483 to 343 arcsec. However, the XRD FWHM values of (002) planes are 283 and 270 arcsec for the GaN thin film with and without the presence of S-HNSs, respectively.

Fig. S6. XRC of GaN thin film. X-ray diffraction peaks of ω scan from (002) of reference GaN thin film (a) and GaN thin film grown on S-HNS coated substrate (b). And (102) plane reflections of reference GaN thin film (a) and GaN thin film grown on S-HNS coated substrate (b).

6 S4. Calculation of compressive stress in GaN epitaxial layers Because of the mismatch in thermal expansion coefficient and high growth temperature of GaN, huge compressive stress is generated in GaN after cooling to room temperature. To calculate the stress, correct elastic constants are necessary. However, values of Poisson ratio and Young’s modulus vary from 0.14 to 0.37 and from 148 to 324 GPa, respectively. The elastic constants used in this study are from the reference.7

Young’s Thermal expansion Biaxial modulus modulus Possion ratio coefficient (GPa) (GPa) (a-axis, 10-6/K)

Al2O3 425 0.3 607 7.5 GaN 297 0.25 396 5.59

Table S2: Elastic constants of sapphire and GaN.

To confirm the stress reduction in GaN with S-HNS, 3 m thick GaN epitaxial layers were grown by MOCVD using 2 inch sapphire substrates with 30 % and 50 % S-HNS surface coverage. The substrate thickness was 430 m. To calculate stress in GaN from the measured wafer bowing, Stoney’s equation was used.8 Stoney’s equation evaluates the stress of a thin film from the curvature of the substrate with the film. Stoney equation is expressed as follows;

2  E f   Es  ts  th   ( s   f )(TL  TI )    (S.3.1) 1  f  1  s  6t f R where v is the Poisson ratio and ts, tf are the thickness of substrate and thin film. R is the radius of curvature and fs are the thermal expansion coefficient of thin film and substrate. T L is the growth temperature and TI is the initial temperature. However, Stoney’s equation can be applied only for the case when the thickness of thin film is much thinner than that of substrate. Hsueh developed the equation which can be applied for thick film by including higher order terms in their solutions to obtain better accuracy.9 The modified stress equation is expressed as follows;

3  1   E f  th   2 4 3 2  ( s  f )(TL  TI ) (S.3.2) 1    2 (2  2  3 )1 f

3 2 1   Es  ts      (S.3.3)  1  1  s  6t f R

7 where   t f t f ,   M f /M s , M  E /(1 v). The compressive stress was calculated using Stoney’s equation and Hsueh’s equation. S5. Finite element (FE) simulation To evaluate the stress evolution in GaN with S-HNSs accurately, detailed geometry which consists of sapphire substrate, S-HNS’s, and GaN should be considered. However, this is impossible due to extremely large number of S-HNS’s (over 1010 in the considered system). Here, we conducted a unit structure whose dimension is 0.4 × 0.4 × 3.5 μm3 (Fig. 5a), and adopted a periodic boundary condition along the in-plane axes under assumption of uniform stress in the inside part of wafer. FE simulation of a full scale wafer confirmed that the stress evolution in GaN was nearly uniform in the inside of wafer, and only small part of edge region showed inhomogeneous stress distribution due to boundary effect (Fig. S7). In addition to the periodic boundary condition, we also considered effective Young's modulus of the substrate. Contrary to the GaN epitaxial layer, the substrate, which is relatively very thick, has significant inhomogeneity along the thickness direction due to its bowing. This inhomogeneity leads an undesirable out-of-plane periodicity as well as in-plane periodicity. However, because the in-plane axial stiffness is in linear proportion to the cross-sectional area as k=AE/L, where k is axial stiffness, A is cross-sectional area, E is the Young's modulus, and L is length, identical stiffness of the substrate can be derived from reduced area A' and corresponding E' which satisfy a relationship AE=A'E'. Note that what is interesting here is the stress evolution in the GaN epitaxial layer, not the stress in the substrate. Therefore, one can reduce the considered thickness of substrate to e.g. 0.5 μm from its original (430 μm) in order to avoid the undesirable out-of-plane periodicity. The corresponding effective Young's modulus would be 860 times larger.

Fig. S7. FE simulation of a full-scale wafer. FE simulation of a full-scale 2 inch wafer confirmed: (a) wafer bowing due to thermal mismatch between GaN thin film and sapphire substrate, and (b) nearly uniform stress distribution along in-plane axes in the inside part.

S6. Finite-difference time-domain (FDTD) simulation To evaluate the extraction efficiency of GaN containing S-HNS’s, FDTD simulations were conducted. The simulation structures used in this study are in Fig. S8. The thickness of GaN epitaxial layer is 2.3 m, and the length and width of a simulation structure is 6.76 and 3.9 m, respectively. In this study, a reference and a sapphire substrate with S-HNS were used. The surface coverage of S-HNS used in this simulation were 33, 46.9 and 62.5%. Because of the finite domain size for simulation, periodic boundary condition was used at each side of the simulation structure and absorbing boundary condition was used above the GaN layer to measure the light extraction efficiency.

Fig. S8. FDTD simulation structure LED structure with S-HNS used in FDTD simulation. Upper and lower parts are plan-view and 3-

9 dimensional view of the simulation structure. a, LED structure with 33.5 % S-HNS surface coverage. b, LED structure with 45.6% S-HNS surface coverage. c, LED structure with 62.5% S-HNS surface coverage. Arrangement in square lattice was assumed for simplification.

The extraction efficiency varied slightly according to the location of the electromagnetic dipole. To obtain accurate results, simulation was done until extraction efficiency was saturated. The simulation structures are in Fig. S9. The electromagnetic dipole locations are indicated by sky-blue dots.

Fig. S9. Location of electromagnetic dipoles in FDTD simulation Plan-view of electromagnetic dipole location in FDTD simulation. Location of electromagnetic dipole is indicated as a sky-blue dot in each image. Simulation structure when the number of electromagnetic dipoles is 1(a) , 5(b) , 9(c) and 13(d).

10 Supplementary references

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