Flaw-Containing Alumina Hollow Nanostructures Have Ultrahigh

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Flaw-containing Alumina hollow nanostructures have ultrahigh fracture strength to be incorporated into high-efficiency GaN LEDs Sung Gyu Kang, Dae-Young Moon, Jeonghwan Jang, Ju-Young Kim, Jin-Yoo Suh, Euijoon Yoon, Heung Nam Han, and In-Suk Choi Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b05009 • Publication Date (Web): 23 Jan 2018 Downloaded from http://pubs.acs.org on January 23, 2018

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Nano Letters

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Flaw-containing Alumina hollow nanostructures

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have ultrahigh fracture strength to be incorporated

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into high-efficiency GaN LEDs

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Sung-gyu Kang, †, ‡ Daeyoung Moon, † Jeonghwan Jang, † Ju-Young Kim, § Jin-Yoo Suh, ‡ Euijoon

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Yoon, † and Heung Nam Han,*, † In-suk Choi,*, ‡

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†

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08826, Republic of Korea

Department of Materials Science and Engineering, RIAM, Seoul National University, Seoul

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‡

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Technology, Seoul 02792, Republic of Korea

High Temperature Energy Materials Research Center, Korea Institute of Science and

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§

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Technology, Ulsan 44919, Republic of Korea

School of Materials Science and Engineering, Ulsan National Institute of Science and

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ACS Paragon Plus Environment

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ABSTRACT

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In the present study, we found that α-alumina hollow nanoshell structure can exhibit an ultrahigh

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fracture strength even though it contains a significant number of nanopores. By systematically

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performing in-situ mechanical testing and finite element simulations, we could measure that the

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fracture strength of an α-alumina hollow nanoshell structure is about four times higher than that

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of the conventional bulk size α-alumina. The high fracture strength of the α-alumina hollow

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nanoshell structure can be explained in terms of conventional fracture mechanics, in that the

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position and size of the nanopores are the most critical factors determining the fracture strength,

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even at the nanoscales. More importantly, by deriving a fundamental understanding, we would

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be able to provide guidelines for the design of reliable ceramic nanostructures for advanced GaN

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LEDs. To that end, we demonstrated how our ultra-strong α-alumina hollow nanoshell structures

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could be successfully incorporated into GaN LEDs, thereby greatly improving the luminous

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efficiency and output power of the LEDs by 2.2 times higher than that of conventional GaN

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LEDs.

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KEYWORDS: Ceramic nanostructures, Nanopores, Fracture strength, Size effect, Hollow

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nanostructures, Light-emitting diodes

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Strength of nanostructured ceramic materials has always been questioned because of inherent

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flaws inside. Flaws in the body or on the surface of bulk ceramic structural materials are

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regarded as being possible causes of fatal failures because the local stresses around those flaws

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can be concentrated and dramatically extenuated to a level where a catastrophic failure can occur

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without any warning. However, when fabricating bulk ceramic structural materials, the formation

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of flaws, with sizes in the order of tens of micrometers, is inevitable. Hence, the fracture strength

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of conventional structural ceramic materials is only about 1/200 of their theoretical strength.1-3

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The present study addresses the aforementioned conventional fracture issue at the nanoscale

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regime, thus raising the issue of whether ceramic nanostructures with internal flaws are strong

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enough to use as the components of advanced electronic and optical devices. We provide the

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theoretical foundation, simulation results, and experimental confirmation that show alumina

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nanostructures can have ultra-high fracture strength even with internal flaws. Moreover, these

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fundamental findings enable us to successfully design and fabricate reliable hollow

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nanostructures that can dramatically enhance efficiency of GaN LEDs. Our result effectively

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broadens the practical design space for engineered nanoceramic materials for applications

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ranging from flexible/stretchable devices and photonic materials to bioscaffolds.

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Ceramics are widely used as the core functional materials of many electronic and optical

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devices. With the tendency towards higher levels of integration and improvements in the

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performance of devices, many research groups are trying to introduce 3-dimensional ceramic

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nanostructures to the design of electronic and optical device.4-14 Particularly, the field of GaN

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light-emitting diodes (LEDs) has recently seen attempts to incorporate hollow nanostructures

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into LEDs to achieve high-efficiency LEDs for solid-state lighting.15-20 In GaN-based LEDs, the

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different material properties of the GaN and sapphire lead to several problems such as a high


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defect density in the GaN, serious wafer bowing in large-area wafers, and poor light extraction in

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devices.21-23 These problems can be resolved by introducing a few different types of hollow

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oxide nanostructures (silica, alumina, etc.) into the interface between the GaN thin film and the

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sapphire substrate.15,

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GaN/sapphire interface can help scatter light effectively to attain improved light extraction.16, 18

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However, the formation of internal flaws, especially nanopores, can hardly be avoided during the

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fabrication or post-treatment process which would be a serious reliability issue because structural

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failure can occur due to the thermal stress that arises during the fabrication process. Therefore,

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when applying ceramic nanostructures to novel electronic and optical devices, it is essential to

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accurately estimate the fracture strength of nanoceramics with internal flaws, which also

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constitutes a fundamental scientific challenge in the field of nanomechanics.

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Moreover, well-defined hollow nanostructures embedded at the

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Recently, the size-related phenomenon of “smaller is stronger,” whereby there is an increase in

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the strength of metallic materials at the nanoscale,24-31 has also been identified in ceramic

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materials.32-39 However, the reason for the phenomenon occurring in nanoceramics has yet to be

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elucidated. One of the most plausible explanations is that the fracture strength ( ) in the

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nanoceramic material still depends on the size of the flaw (), which can be roughly estimated to

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be ~

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strength drastically increases because the size of the flaws decreases to the nanoscale regime as

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the size of the specimen reaches the nanoscale level. Nonetheless, it has not yet been clarified

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whether the fracture strength at the nanoscale level increases and whether this can be predicted

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by conventional bulk-scale fracture mechanics. Furthermore, a systematic analysis of the

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correlation between the fracture strength and the internal flaws, especially the nanopores inside

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the nanostructure, is still lacking.

√

, according to continuum-based fracture mechanics. In other words, the fracture


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Nano Letters

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In the present study, we set out to show that a ceramic nanostructure can exhibit an ultrahigh

2

fracture strength even though it contains a significant number of nanopores. By systematically

3

performing in-situ mechanical testing and finite element simulations, the high fracture strength

4

of an α-alumina hollow nanoshell structure can be explained in terms of conventional fracture

5

mechanics, in that the position and size of the nanopores are the most critical factors determining

6

the fracture strength, even at the nanoscales. More importantly, by deriving a fundamental

7

understanding, we would be able to lay down predictions and guidelines for the design of reliable

8

ceramic nanostructures for advanced GaN LEDs. To that end, we demonstrated how our ultra-

9

strong α-alumina hollow nanoshell structures could be successfully incorporated into GaN LEDs,

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thereby greatly improving the luminous efficiency and output power of the LEDs.16

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Among the various α-alumina hollow nanoshell structures of GaN LEDs, we chose a cylinder-

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shaped hollow nanoshell structure (henceforth, referred to as “CSH nanoshell structure”) as our

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model structure because the cylindrical shape is better suited to mechanical testing and analysis

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than other shapes, while it is also a candidate for application to new GaN LEDs through a

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conventional fabrication process.16 To investigate the thickness-dependent size effect on the

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mechanical properties, α-alumina CSH nanostructures with the same cavity size (a diameter of 2

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µm and a height of 2 µm) but different shell thicknesses (63 nm, 73 nm, and 115 nm) were

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fabricated on (0001) sapphire wafers by a series of processes using photolithography, atomic

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layer deposition (ALD), and appropriate heat treatment, as illustrated in Supporting Information

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S1 and Figure S1. The thickness of the α-alumina CSH nanoshell structure was controlled by

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modulating the number of ALD process cycles, such as 800 cycles for 63 nm, 1000 cycles for 73

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nm, and 1500 cycles for 115 nm. Figure 1 presents the structural characterizations of the CSH

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nanoshell structures. Figure 1a shows a representative array of CSH nanostructures with a shell


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thickness of 73 nm on a sapphire wafer. The cross-sectional TEM image of the CSH nanoshell

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structure in Figure 1b clearly indicates that the CSH nanoshell structures retained a hollow

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alumina wall while the residual photoresist inside the nanoshell was burned away during the heat

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treatment. (Note that the space inside of the CSH nanoshell structure is partly filled with Ga

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residue from focused ion beam sampling.). The TEM analysis shown in Figure 1c, d confirms

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that the as-deposited alumina, which was originally amorphous, crystallized to the α phase as a

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result of the heat treatment. This phase is the same as that of the sapphire wafer. Moreover,

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diffraction patterns in Figure 1c and 1d show that the α-alumina nanoshell is a single crystalline

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solid having the same crystallographic orientation with the (0001) sapphire substrate. More

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importantly, we found that the fabricated CSH nanoshell structures contained multiple spherical

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nanopores with internal diameters of 20–32 nm and exhibited a porosity of about 5 % regardless

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of the nanoshell thickness, as shown in Figure 1e and Figure S3. (The detailed method for

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characterizing the nanopores in the nanoshell is described in the Supporting Information S2) The

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formation of the nanopores is attributed to the volume reduction of the alumina during the phase

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transformation from amorphous to α-alumina.40, 41

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From the viewpoint of conventional fracture mechanics, the nanopores inside the nanoshell

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will act as critical stress concentration sites, while the fracture strength of the material is

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inversely proportional to the flaw size. The Griffith equation can provide us with a first-order

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approximation of the fracture strength ( ) for flaw-containing brittle nanostructures. This is

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expressed as,

/

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=

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where is the elastic modulus, is the surface energy, is the Poisson’s ratio, and is the

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flaw size. For α-alumina, is 425 GPa, is 4.83 J-m2 for the (0001) surface, and is 0.27.42

,

(1)


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Assuming that the bulk α-alumina incorporates a flaw of the same size as the critical nanopore

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initiating crack failure in this study (Figure 1e and Table S1), the fracture strength can be

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estimated to be about 13 GPa which is about four times greater than the fracture strength of bulk

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alumina with micropores. This prompts us to ask whether this high fracture strength, estimated

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from conventional fracture mechanics, is reasonable for nanoceramic materials with nanopores.

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By performing in-situ indentation with a cono-spherical indenter (Supporting Information S3)

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and computational analysis, we set out to quantitatively reveal how these nanopores affect

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mechanical properties, including the elastic modulus and the fracture strength, of α-alumina CSH

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nanoshell structures. Figure 2 presents a series of in-situ SEM images (Figure 2a–e and Movie

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S1) and the corresponding load–displacement curve (Figure 2f). Together, these describe the

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deformation and fracture behavior of the CSH nanoshell structure with a shell thickness of 73 nm

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for an indentation displacement of 300 nm. Most deformation and fracture occurs at the top

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surface of the CSH nanostructure (Figure 2a–c) until a catastrophic failure occurs (Figure 2d).

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The load–displacement curve (Figure 2f) indicates three notable pop-in discontinuities (denoted

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by the red, green, and blue dotted circles). The largest load drop at a displacement of 253 nm

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(blue dotted circle in Figure 2f) is associated with the catastrophic failure of the top surface

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(Figure 2d). Before the catastrophic failure, a small load drop near at the indenter displacement

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of 100 nm (red dotted circle in Figure 2f) and another pop-in discontinuity (green dotted circle in

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Figure 2f) are observed. A series of additional indentation tests provided more detailed

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information for the critical stages which helped us to understand the overall deformation and

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failure process of the CSH nanoshell structure. As shown in the load–displacement in Figure 2g,

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the indentation test with a displacement of 100 nm reveals that the unloading path is identical to

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the loading path. This indicates that the initial deformation before the first load drop is elastic


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without any structural failure at the top surface, as shown in Figure 2b. Another indentation test

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explains that the first load drop was caused by radial crack initiation underneath the indenter tip.

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The top-view SEM image of the CSH nanoshell structure (Figure 2h), captured immediately after

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the first load drop, clearly shows newly generated radial cracks emanating from the center of the

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top surface of the structure. After radial crack initiation, the top surface of the CSH nanoshell

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structure was continuously deformed (Figure 2c) until the second pop-in occurs at around 190

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nm. A SEM image (Figure 2i) of the top surface of the CSH nanoshell structure, captured

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immediately after the second pop-in event, shows circumferential crack formation in addition to

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radial crack propagation emanating from the center. Hence, the deformation behavior of the CSH

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nanoshell structure during the cono-spherical indentation can be summarized as initial elastic

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bending of the top surface followed by radial and circumferential crack formation at the center of

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the top surface before completely collapsing. (Figure S3)

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Since the occurrence of a fracture relieves the elastically stored energy resulting from external

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loading, we can estimate the fracture strength of the α-alumina in the CSH nanoshell structure by

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analyzing the stress evolution underneath the indenter at the first load drop which was caused by

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the initial radial crack formation. Figure 3 shows a finite element analysis of the in-situ

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indentation tests of each α-alumina CSH nanoshell structure with different thicknesses (63, 73,

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and 115 nm). Based on the actual geometric information and experimental conditions, we

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constructed computational models in which a CSH nanoshell structure containing nanopores is

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assumed to be a body with an elastic solid continuum and an effective modulus that considers the

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effects of nanopores on the elastic properties of the α-alumina nanostructure (Supporting

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Information S4 and Figure S4). Pabst et al.43, 44 suggested that the effective elastic modulus of

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porous ceramics is inversely proportional to the porosity and can be expressed as,


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Nano Letters

!

%

= 1 − $ 1 − % ,

(2)

&

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where '()*'('+ is the intrinsic elastic modulus, $ is the porosity and $, is the critical porosity

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at which a porous ceramic loses its integrity and collapses. By substituting the porosity of the α-

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alumina nanoshell structures (0.05), as obtained by SEM analysis, and the parameter for the

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critical porosity (0.684) into Equation (2),43 the effective elastic modulus is found to be about

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360 GPa which is 14 % smaller than the intrinsic elastic modulus of the α-alumina phase (425

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GPa). This estimated value of the effective modulus was also confirmed by our indentation

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experiment and simulation. The effective elastic modulus could be extracted from the initial

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elastic region of the load–displacement curves, as shown in Figure 3a-c. By iteratively

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optimizing the elastic modulus of the CSH nanoshell structures in the computational model, we

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found that the load–displacement curves of the computational analysis were in good agreement

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with those of the experimental results when the elastic moduli inputs were optimized to 360 GPa,

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370 GPa, and 350 GPa for the 63-, 73-, and 115-nm thicknesses of the α-alumina CSH nanoshell

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structures, respectively. These optimized modulus values are consistent with the effective

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modulus obtained from the above Equation (2) which confirms that the nanopores formed inside

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the nanoshells significantly affect the elastic deformation behavior of the α-alumina CSH

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nanostructures. Hence, we used these effective modulus values as our computational inputs to

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reflect the effect of the nanopores during elastic deformation. We then evaluated the failure

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stress developed underneath the indenter before the first load drop occurs as a result of radial

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crack formation. As shown in Figure 3d, the tensile stresses were developed at the lower part of

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the top surface area of the CSH nanoshell structure. We found that the maximum principal

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tensile stresses reach 15.29 (±1.89), 16.65 (±0.72), and 18.05 (±0.83) GPa (standard deviation in

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parentheses) for the CSH nanoshell structures with shell thickness of 63, 73, and 115 nm,


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respectively, when the indentation depth is reached before the first load drops in Figure 3a-c. If

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we choose to use the maximum principal stress theory as our fracture criterion among the

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different failure criteria, the above maximum principal tensile strength values become the

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fracture strengths of the α-alumina CSH structures, which are an order of magnitude higher than

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that of the microscale α-alumina, for which the values are in the order of a few gigapascals.45, 46

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When the external load reaches the fracture strength, the maximum principal stress around the

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critical flaw initiating failure should exceed the theoretical strength. To confirm that our nano

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ceramic structures with nanopores also conform to the same failure mechanism, we constructed a

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model CSH nanoshell structure including the critical nanopore located at the bottom-center of

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the top surface area, as shown in Figure 3e. (Supporting Information S5, Figure S8 and Movie

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S2) Figure 3e shows the maximum principal stress distribution around the critical nanopore in

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the CSH nanoshell structures with thicknesses of 63, 73, and 115 nm. The highly concentrated

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maximum tensile principal stresses were developed at the bottom of the critical nanopores. Their

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values were 32.30 (±4.72), 31.05 (±1.40), and 34.89 (±1.77) GPa, respectively. In general, the

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theoretical tensile strength of a perfect ceramic is about E/10, while that of α-alumina is between

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31 GPa and 38 GPa.47, 48 Therefore, we confirmed that the fracture of the alumina in the CSH

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nanoshell structures occurs when the maximum principal tensile stress reaches the theoretical

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strength at the critical nanopore before the first pop-in. Note that, even with this critical nanopore

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in the model structure, the overall stress distribution and values around the bottom part of the top

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surface area are identical to those of the elastic continuum models with the effective modulus

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shown in Figure 3d. Hence, the fracture strength of the α-alumina in the CSH nanoshell structure

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containing multiple nanopores is estimated to be around 16 GPa. Interestingly, this remarkably

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high fracture strength is also in good agreement with the first-order approximation obtained with


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the Griffith equation (around 13 GPa) with the flaw size of the critical nanopore, implying that

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the value of the high fracture strength as estimated using conventional fracture mechanics, is

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reasonable for nanoceramic materials containing nanopores. In addition, the size effect

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phenomenon of “smaller is stronger” in ceramic materials at the nanoscale level can also be

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explained not by the shell thickness but by the size of the flaws, implying that the fracture

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strength increases drastically because the size of the nanopores decreases to the nanoscale regime

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as the size of the specimen reaches the nanoscale level. Therefore, it is possible to easily obtain a

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fracture strength at the gigapascal scale. Furthermore, unlike bulk ceramic materials, the ceramic

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nanostructures exhibit a narrower distribution of flaw sizes and shapes because of the effect of an

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upper bound, such as the nanoshell thickness in the present study. This implies that the fracture

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strength can be more accurately predicted for a ceramic nanostructure than for a bulk ceramic.

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When the ceramic nanostructure is utilized as a structural material, it is possible not only to

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secure an ultrahigh fracture strength, but also to precisely predict the fracture strength, so that the

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mechanical reliability can be greatly improved.

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Next, we will demonstrate how this ultra-strong nanoceramic can be utilized in an actual GaN

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LED application. Up to this point, we have used a CSH nanoshell structure as our model hollow

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nanoshell structure to determine the mechanical properties of α-alumina with nanopores at the

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nanoscale. However, we chose a hemisphere-shaped hollow nanoshell structure (henceforth

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referred to as the HSH nanoshell structure) for an actual GaN LED application, as shown in

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Figure 4a. We selected this structure because, according to the results of previous studies, it

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offers a better light-extraction efficiency and output power than the CSH nanoshell.18 A new

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GaN LED design with an HSH nanoshell structure is expected to resolve the following key

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mechanical issues: (a) whether the newly incorporated alumina nanoshell structures can


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effectively generate a stress gradient in the GaN film, allowing us to reduce the number of

2

threading dislocations and defect sites and thus mitigate the residual stress in the thin film to

3

prevent serious wafer bowing and (b) whether the nanoshell structures are strong enough to

4

survive under the thermal stress produced by the conventional GaN LED fabrication process. To

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address the above mechanical issues before the actual fabrication stage, we constructed

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computational models of the GaN LEDs with and without the HSH nanostructures, as shown in

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Supporting Information S6 and Figure S9.49-51 The conventional GaN LED model consists of a

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GaN thin film with a thickness of 3.2 µm on a sapphire wafer. In contrast, in the nanostructured

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GaN LED model, the HSH hollow nanoshell structure was located between the GaN thin film

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and the sapphire wafer. The fabrication of a GaN LED typically starts with the deposition of a

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GaN thin film on a sapphire wafer at a temperature of 1040 °C, after which it is cooled to room

12

temperature. This is reflected in the simulations. As shown in Figure 4b, a residual compressive

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stress of about 800 MPa was homogeneously distributed in the conventional GaN LED model

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after the cooling process. On the other hand, in the GaN film with the HSH nanoshell structure,

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stress gradients are generated around its periphery and significantly reduce the residual stress.

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This reduction in the residual compressive stress in the GaN thin film is significant enough to

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alleviate wafer bowing in a conventional GaN LED.15 In addition, the shape and amount of the

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stress gradient field formed around the nanoshells is similar to those reported previously, which

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is required to reduce the density of the threading dislocations in the GaN thin film.15 Figure 4c

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presents the maximum principal stress distribution within the HSH nanoshell structure after the

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cooling process, which was induced by the residual compressive stress in the GaN thin film.

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While a small compressive stress was observed in the top surface of the hollow nanoshell

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structure, a high tensile stress of 1.4 GPa along the y-axis was developed in the circumferential


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part of the structure. However, because the α-alumina nanoshell structure has an ultrahigh

2

fracture strength of around 16 GPa with a factor of safety of about 10, the α-alumina HSH

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nanoshell structures will not fracture through the conventional GaN LED fabrication process.

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Since the suggested design of the α-alumina HSH nanoshell structures in the GaN LEDs is

5

mechanically reliable, we finally fabricated actual GaN LEDs with α-alumina HSH nanoshell

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structures. As shown in Figure 4d, GaN LEDs with the α-alumina HSH nanostructure provide a

7

significantly improved light-extraction efficiency with an improved output power that is 2.2

8

times higher than that of conventional GaN LEDs.16 (The detailed methods for fabrication and

9

output power analysis are described in the Supporting Information S7)

10

In summary, we demonstrated that the α-alumina hollow nanoshell structure can exhibit an

11

ultrahigh fracture strength even though it contains a significant number of nanopores. Our

12

experimental and computational analyses revealed that the ultrahigh fracture strength of the α-

13

alumina hollow nanoshell structure can be explained from the perspective of conventional

14

fracture mechanics, in that the fracture strength drastically increases because the size of the flaws

15

decreases to the nano-scale regime. Furthermore, we could state with confidence that the hollow

16

nanoshell structure successfully maintains its shape as an interlayer even after the fabrication

17

process has ended, as predicted by the computational analysis, and thus improves the light-

18

extraction efficiency and output power of a GaN LED. We believe that the fundamental

19

understanding of the size effect of fracture strength gained through this study will provide an

20

invaluable baseline for the design of 3D nanostructures in advanced devices.

21


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Figure 1. Cylinder-shaped α-alumina hollow nanoshell structures. (a) Tilted-view SEM image of

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73-nm thickness hollow nanoshell structure. (b) Cross-sectional TEM image of 73-nm thickness

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hollow nanoshell structure. (c, d) Magnified TEM images of area indicated with red and orange

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squares in b. Insets show SAED patterns of the area marked with white circles in each figure. (e)

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Distribution of radius of nanopores inside each nanoshell: 63-nm thickness nanoshell (top), 73-

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nm thickness nanoshell (middle), and 115-nm thickness nanoshell (bottom).

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Figure 2. In-situ indentation test of 73-nm thickness CSH nanoshell structure. (a-e) Series of

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SEM images of in-situ indentation. (f) Load-displacement (L-D) curve of 300-nm indentation.

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(g) L-D curve of 100-nm indentation. Inset indicates load function. (h, i) Top-view SEM images

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of 73-nm thickness CSH nanoshell structure. The yellow circle and white arrows represent the

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contact area of the indenter tip and the deformation-induced cracks, respectively. SEM images

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with colored frames (b-d), (h-i) represent the tilted- and top-view SEM images of 73-nm

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thickness CSH nanoshell structures at each point marked with circles of the same color on the

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300-nm indentation L-D curve (f). The scale bars are 1 um.

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Figure 3. Finite element analysis of in-situ indentation tests for CSH nanoshell structures. (a-c)

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Representative experimental L-D curves of 63-nm thickness (a), 73-nm thickness (b), and 115-

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nm thickness (c) CSH nanoshell structures and corresponding FE simulations (red line). The

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black and gray points represent the material response before and after the crack initiation,

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respectively. (d-left) Cut-view of meshes used in FE simulation. The green, orange, and gray

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elements indicate the α-alumina hollow nanoshell structures, sapphire substrate, and indenter tip,

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respectively. (d-right) Maximum principal stress distribution within each CSH nanoshell

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structure. The nanoshell is assumed to be solid. (e) Maximum principal stress distribution around

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critical nanopore for each CSH nanoshell structure.

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Figure 4. Introduction of hemisphere-shaped α-alumina hollow nanoshell structures to GaN

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LEDs. (a) Tilted-view SEM image of HSH nanoshell structure (top) and cross-sectional SEM

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image of HSH nanoshell structure (bottom) after GaN thin film deposition. Scale bar is 1 µm. (b)

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Residual stress distribution within GaN thin film and sapphire substrate of conventional (left)

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and HSH nanoshell structure-incorporated (right) GaN LEDs when cooling from 1040 °C to 25

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°C ends. (c) Maximum principal stress evolution of inner nanoshell structure (top) and outer

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nanoshell structure (bottom) when cooling from 1040 °C to 25 °C ends. (d) Schematic diagrams

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and turn-on images of conventional (left) and HSH nanoshell structures-incorporated (right) GaN

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LEDs.

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ASSOCIATED CONTENT Supporting Information.

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This Supporting information material is available free of charge on the ACS Publications

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website. Section 1: Fabrication of the α-alumina hollow nanoshell structures (Figure S1) with

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thermal gravimetric analysis of photoresist (Figure S2). Section 2: Analysis of nanopore

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distribution in each CSH nanoshell with thickness of 63 nm, 73 nm and 115 nm (Figure S3).

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Section 3: In-situ indentation tests for every CSH nanoshell structure up to structural collapse.

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Load-displacement curves of in-situ indentation tests for every hollow nanoshell structure

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(Figure S4). Section 4: Finite element analysis for in-situ indentation test (Figure S5). Load-

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displacement curves of the finite element simulation considering the anisotropy of the alpha

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alumina (Figure S6). Average indentation depth where crack initiates for each nanoshell

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structure (Figure S7). Section 5: Finite element analysis for crack initiation. Computational

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model for evaluating stress evolution around nanopore (Figure S8). Parameters for the chosen-

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nanopores and the critical nanopore of each nanoshell (Table S1). Section 6: Finite element

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analysis for applying the nanoshell structures into GaN LEDs (Figure S9). Section 7: Fabrication

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of the conventional- and the nanoshell introduced-GaN LEDs and light output power analysis of

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LED chips. Average light output power of the LED chips with- and without- HSH nanoshell

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(Figure S10).

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In-situ indentation test for 73 nm thickness CSH nanoshell structure and description of the stress

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evolution around nanopore are also provided as movies (Movie S1, S2).

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AUTHOR INFORMATION

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Corresponding Author

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*E-mail: (H.N.H.) [email protected]

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*E-mail: (I.S.C.) [email protected]

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Author Contributions

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S.G.K., I.-S.C. and H.N.H. conceived the concept. D.M., J.J. and E.Y. fabricated the materials

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and devices. J.-Y.S. characterized the material through TEM analysis. S.G.K. and J.-Y.K.

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conducted the in-situ experiments and collected the data. S.G.K., I-S.C. and H.N.H. analyzed the

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data with computational method. I.-S.C. and H.N.H. supervised the project. All the authors

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discussed the results and commented on the manuscript.

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Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENT

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This research is funded by Engineering Research Center (ERC) program of National Research

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Foundation of Korea (NRF) grant funded by the Ministry of Science, ICT & Future Planning

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(MSIP) (NO. NRF-2015R1A5A1037627). I.-S.C. acknowledges the financial support through a

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NRF of Korea (2015R1A2A2A04006933).

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Flaw-Containing Alumina Hollow Nanostructures Have Ultrahigh

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