Nanostructures

Geometry-Induced Dislocations in Coaxial Heterostructural Nanotubes

Aram Yoon , Jun Young Park , Jong-Myeong Jeon , Yigil Cho , Jun Beom Park , Gyu-Chul Yi , Kyu Hwan Oh , Heung Nam Han , * and Miyoung Kim *

Crystallographic defects, inevitably encountered in mate-

rials science, have long been studied because of their critical

mechanical, electrical, and optical properties. Moreover,

defects and impurities have been intentionally incorporated

to engineer specifi c physical properties into a range of device

applications; the role of defects in advanced technology is

still evolving. [ 1–12 ] Dislocations in nanostructures in par-

ticular are of increasing interest because their contribution

to the material’s properties becomes more important as the

structure size decreases, despite the fact that the dislocation

density in a nanostructure is known to be very low because

of the larger elastic strain accommodation and easy strain

relaxation to the free side-surfaces. [ 13 , 14 ] Recently, hetero-

nanostructures, which may have substantial misfi t strain, have

been extensively studied because of a favorable architecture

for monolithic nanodevices. Consequently, a systematic study

of strain-induced dislocations in nanostructures is needed.

Creation of misfi t dislocations in a strained system could

be explained by a competition between elastic energies and

dislocation formation energies. For this reason, fi nite ele-

ment methods (FEMs) have been applied to calculate strain

fi elds in hetero-nanostructures, including axial or core-shell

heterostructures, in an attempt to fi nd the critical thickness

or height of dislocation-free nanostructures. [ 15–25 ] For device

applications of nanostructured materials, information on not

only the dislocation density but also the spatial location of

dislocations is essential, especially for optical devices in which

optically active areas should be defi ned. Herein, we inves-

tigated the effect of geometry on the formation of disloca-

tions in GaN, one of the leading materials for optoelectronics,

grown as a GaN/ZnO core-shell tube structure on a silicon

© 2013 Wiley-VCH Verlag Gmb

DOI: 10.1002/smll.201202051

A. Yoon, J. Y. Park, J.-M. Jeon, Y. Cho, Prof. K. H. Oh, Prof. H. N. Han, Prof. M. KimDepartment of Materials Science & Engineering and Research Institute of Advanced MaterialsSeoul National UniversityGwanak-ro 1, Gwanak-gu, Seoul 151-744, Korea E-mail: hnhan@snu.ac.kr; mkim@snu.ac.kr

J. B. Park, Prof. G.-C. YiDepartment of PhysicsSeoul National UniversityGwanak-ro 1, Gwanak-gu, Seoul 151-744, Korea

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dioxide (SiO 2 )/GaN buffer/sapphire substrate (see Figure 1 a

for a schematic diagram). The ZnO core structure was chosen

as a template for GaN because of the same crystallographic

structures and their similar lattice constants. Additionally,

ZnO/GaN core-shell structures of n-type ZnO and p-type

GaN are ideal for optoelectronic devices. [ 26–28 ] Interestingly,

in this nanostructure, misfi t dislocations are localized in spe-

cifi c areas and in specifi c directions, as shown in transmission

electron microscope (TEM) images (Figures 1 b,c). Locally

confi ned dislocations formed a shape having approximately

sixfold symmetry in the hexagonal GaN/ZnO nanotubes, and

all dislocation lines had equivalent crystallographic directions.

In general, dislocations in GaN thin fi lms, which often act as

recombination centers in optical devices, [ 29–31 ] are known to

be caused by lattice mismatches with the substrates; however,

the localized dislocations in Figure 1 cannot be explained by a

lattice mismatch between the ZnO core and GaN shell struc-

ture alone. In this work, we measured local strain fi elds by

electron diffraction and calculated the spatial distribution of

strain fi elds in nanostructures having different morphologies

by a 3D-FEM considering the thermoelastic anisotropy. This

approach successfully elucidated the origin of the geometry-

dependent dislocations in hetero-nanostructures.

To identify the cause of dislocations in this system, we

determined the dislocation types and their Burgers vec-

tors using large-angle convergent beam electron diffraction

(LACBED) and dark-fi eld images. The LACBED method

has the advantage of simultaneously providing both an image

of the specimen and the higher-order Laue zone (HOLZ)

lines. The samples were tilted from the zone axis [2̄113] . Burgers vectors were determined by the Cherns and Preston

rule. [ 32 ] Most dislocations had a dislocation line vector of

n = < 101̄0 > , and the resulting Burgers vectors were mainly

b = 1/3 < 112̄0 > , having edge-type characteristics (see details

in the Supporting Information). These dislocations of the

smallest Burgers vector, which typically appear in the wurtzite

lattice, are perfect and highly energetically stable. [ 33 ] Edge-

type dislocations are usually created to release strain fi elds

that arise from lattice mismatches in heterostructure systems.

In the present system, two interfaces can possibly generate

strain fi elds: one interface between the ZnO nanotube core

and n-doped GaN (vertical interface), and the other between

the substrate and the GaN/ZnO nanotubes (lateral interface).

Another source of strain fi elds could arise from the differ-

ences in thermal expansion coeffi cients or thermal gradients

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A. Yoon et al.

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Figure 1 . (a) Schematic structure of the nanotubes. (b,c) Bright-fi eld TEM images. TEM images show the axial direction of the nanotubes. Dislocations were found mostly in the center of the hexagonal facet with (b) a high density of dislocations and (c) a low density of dislocations. The cross-sectional samples were prepared using a focused ion beam at the top of each nanotube.

along the axial direction in the nanotubes when the experi-

mental growth condition is in a thermally nonsteady state.

Quantitatively, however, the inhomogeneous temperature

difference in the very small hetero-nanostructure calculated

by FEM was less than 1 ° C; thus, the strain fi elds induced by a

thermal gradient were neglected in this work.

The edge-type dislocations with b = 1/3 < 112̄0 > release

strain fi elds caused by a lattice mismatch between ZnO and

GaN; therefore, the interface could be a primary reason for

the generation of the dislocations shown in Figure 1 . In this

case, the dislocation lines in the hexagonal plane represent

threading dislocations to the side surfaces. The maximum

number of edge dislocations required to completely release

the strain fi elds between ZnO and GaN is, however, much

smaller than that shown in Figure 1 b. Fewer than 10 dislo-

Figure 2 . (a–c) Experimental CBED images of the bulk GaN, position 1 (corner) in Figure 1 c, and position 2 (center) in Figure 1 c. (d–f) CBED simulation patterns were obtained by Java-Electron Microscopy Software (JEMS) simulation. Yellow areas, red areas, and white arrows show the differences in each pattern. Differences were very clear despite small changes in the lattice constant.

cations can exist in each area, considering

a lattice misfi t of about 1.5% and a side

length of 100 nm for a hexagonal ZnO

nanotube. Consequently, an additional

major cause of dislocation generation

should exist. Indeed, these dislocations can

also release strain fi elds generated by the

lateral interface between the substrate and

GaN/ZnO nanotubes; this interface should

be responsible for the dislocations as well.

Although the lattice mismatches at

these interfaces may provide enough

stress to generate dislocations, this cannot

explain the spatial distribution of highly

localized dislocations. This intriguing

observation could be partly explained in

terms of the dislocation energy, which is

proportional to the dislocation length;

hence, the energy is lowest when its line is

shortest. When the dislocation line is gen-

erated at the center of the hexagonal facet

crossing the hole in the nanotube, the

dislocation energy is about half of that in

nanotubes with the connected dislocation

line crossing the corner. Localized dislo-

cations, however, were also observed in

nanotubes with very small holes, so a more

thorough explanation is needed. Con-

sidering that the position of dislocations

could be related to local strain fi elds in

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the nanotubes, we used convergent beam

electron diffraction (CBED) to examine

the local residual strain. The position of

HOLZ lines in CBED is very sensitive to

lattice constants, and we compared experi-

mental HOLZ lines with simulated ones

based on kinematic theory. A hexagonal

structure was maintained for the simula-

tion with a constant c parameter because

the edge dislocations with b = 1/3 < 112̄0 >

release strain in the ab hexagonal plane

only. Two kinds of GaN samples were

prepared for comparative TEM study:

one with a high density of dislocations

(Figure 1 b) and the other with only a few dislocations (Figure 1 c).

Figure 2 clearly shows the shift of HOLZ lines. Figure 2 a

was obtained from the bulk GaN sample as a reference, and

Figure 2 b,c were obtained at two different positions marked

by arrows in Figure 1 c in the GaN nanotube with a few dis-

locations. (In Figure 2 a, the six HOLZ lines most sensitive

to lattice parameters are indexed.) The ratios of the colored

areas of the triangles were compared with theoretical values.

From Figure 2 a to c, the ratio of the yellow areas of the upper

and lower triangles decreased, and the point at which the

two yellow triangles faced each other shifted upward. The

ratio of the red areas of the triangles varied as well. (See

raw and processed data and details in the Supporting Infor-

mation, Figure S2.) The corresponding simulation images

(Figure 2 d–f) indicated that the lattice constant a varied

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Geometry-Induced Dislocations in Nanotubes

Table 1. Material properties for dual-scaled FE analysis.

Materials Elastic constant [GPa] Coeffi cient of thermal expansion [ ° C − 1 ] Lattice parameter [Å]

C11 C12 C13 C33 C44 CTE ( a -axis) CTE ( c -axis) a c

ZnO [ 42 a–c ] 184 93 77 206 56 5.50 × 10 − 6 3.20 × 10 − 6 3.24 5.2

GaN [ 42 c,d ] 396 144 100 392 91 4.10 × 10 − 6 3.00 × 10 − 6 3.19 5.18

Al 2 O 3 [ 43 ] 497 163 117 498 147 8.17 × 10 − 6 9.06 × 10 − 6 4.76 13.0

Material Elastic modulus [GPa] Poisson’s ratio CTE Expected atom distance [Å]

SiO 2 [ 44 ] 73 0.16 5.00 × 10 − 7 5

Figure 3 . Calculated strain distribution of a representative GaN nanotube. (a) Tensile deformation is predicted at the bottom region (100 nm in height) of the nanotube. (b) Cross-sectional image of a position 2000 nm in height showing nearly uniform strain distribution. (c) Cross-sectional image of a position 100 nm in height showing accumulated tensile deformation at the center of the hexagonal facet. (d) Hoop directional strain profi le showing a strong strain gradient along the vertical direction. This strain gradient could act as a source of the GND.

from 3.190 to 3.196 Å. That is, a = b = 3.192 Å at the corner,

close to the reported experimental value of the bulk ( a = b =3.190 Å), while a = b = 3.196 Å in the center of hexagonal

facets. As expected, the highest strain was measured in the

center of the hexagonal facet, where most dislocations were

observed. This result supports the general consensus that

nanostructures are grown bearing high strain and/or stress

fi elds. It is worth noting that the lattice parameter a at the

corner was 3.193 Å for the sample with a high density of dis-

locations (not shown here), very similar to that at the corner

in the sample with a low density of dislocations.

The observed nonuniform strain fi elds in the GaN/ZnO

nanotube structures were interpreted using a dual-scale

FEM. This can effectively handle the 3D infi nite periodic

heterostructure (see details in the Supporting Information).

A thermoelastic constitutive relation considering thermoe-

lastic anisotropy ( Table 1 ) was used for the calculations. The

temperature of the system was set to decrease from 1000 ° C

to room temperature during crystal growth. With assistance

from the dual-scale scheme, the calculation considered one

nanotube as a representative volume element (RVE) for

the entire system. This approach enabled the prediction of

the spatial distribution of strain and stress in the GaN/ZnO

heterostructure considering both its thermal and lattice

mismatches.

First, we calculated strain fi elds in the hexagonal plane

generated by both interfaces, i.e., the interface between the

substrate and nanostructures and that between the ZnO core

tube and the GaN shell. The simulation revealed how a repre-

sentative nanotube deforms inhomogeneously during crystal

growth (see Figure 3 ) because of the lattice mismatches

between the GaN nanotube and the SiO 2 fi lm. [ 34 , 35 ] Interest-

ingly, the hoop strain was concentrated at the center of hex-

agonal facets on the cross-sectional plane in the nanotube

(Figure 3 c), consistent with the experimental CBED obser-

vations. In addition, the bottom of the nanotube, which was

attached to the fi lm, was strongly elongated along the hoop

direction of the tube, whereas the rest was under slight ten-

sion (Figure 3 a). This inhomogeneity generated a strong strain

gradient at the relatively small height along the vertical direc-

tion at the center of hexagonal facets (Figure 3 d). To release

the strong strain gradient along the vertical direction, several

sequential atomic planes can be accommodated by intro-

ducing dislocations, which have edge characteristics. Accord-

ingly, dislocations will be edge dislocations having Burgers

vector 1/3 < 112̄0 > and will be preferentially located at the

© 2013 Wiley-VCH Verlag Gmsmall 2013, 9, No. 13, 2255–2259

center site of hexagonal facets. Consequently, the concept

of a geometrically necessary dislocation (GND), [ 36 , 37 ] which

appears in strain gradient fi elds due to geometrical con-

straints, can successfully explain the presence of accumulated

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Figure 4 . Calculated hoop strain distributions in the cross-sectional image of the position 100 nm in height for the cases considering (a) only the interface between the ZnO core and GaN shell and (b) only the interface between SiO 2 substrates and GaN nanotubes (no ZnO layer).

dislocations at the center of hexagonal facets. The variation

in dislocation density observed for the various experimental

conditions could be explained by the growth conditions, such

as mobility of amorphous SiO 2 at the high temperature [ 38 ]

and the contact between the amorphous substrate and the

nanotubes.

Notable results were observed when the effect of each

interface was separated by including only one interface in the

simulations. Simulated strain fi elds generated by the interface

between the ZnO core and GaN shell structure ( Figure 4 a)

were similar to those in Figure 3 b, in the sense that strain is

highest in the center of hexagonal facets, although the range

is much broader. This is to be expected because the interface

is in the hexagonal plane, and the GaN radius is expanding.

Unexpectedly, the simulated strain fi elds generated with

only SiO 2 substrate and the GaN nanotube (with no ZnO

layer; Figure 4 b) showed much more localized fi elds, despite

the fact that the surface normal direction of this interface is

orthogonal to the hexagonal plane in this case. These results

led to the conclusion that the nonhomogeneous strain fi elds

are greatly enhanced in the presence of the interface between

the substrate and the nanostructures, contributing to the gen-

eration of highly localized dislocations, as shown in Figure 1 .

In conclusion, we investigated the relationship between

misfi t dislocations and crystal shape by examining highly

localized symmetric dislocations in the <101̄0> direction

for GaN/ZnO nanotubes. The dislocations were mostly

edge-type dislocations with Burgers vector 1/3 <112̄0> .

The highly localized nature of the dislocations is attribut-

able to the geometry of the nanostructure in the presence

of stress at the vertical and lateral interfaces due to the fol-

lowing two reasons. First, it is benefi cial for the system to

have dislocations with a shape and position that minimize

dislocation energy when the line is shortest in the nanotube

structure. More importantly, FEM revealed that the inter-

face between the substrate and nanotubes generates highly

localized strain fi elds in the hexagonal lateral plane. In the

hexagonal nanotube structure, the lattice was pulled out-

ward along the <112̄0> direction under tensile stress. The

strain evolved into strain fi elds and strain gradients in the

vertical direction, and the strain was effectively relaxed by

introducing dislocations at the position at which the strain

was the greatest.

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Experimental Section

Fabrication of GaN/ZnO Nanotubes : The GaN/ZnO heterostructure nanotubes were grown by metal organic chemical vapor depo-sition on sapphire substrates with a patterned SiO 2 mask for selective area growth. A GaN buffer layer was deposited on the sapphire substrate, followed by a SiO 2 masking layer. Subsequently, the masking layer was pat-terned by lithography with diameters of about 500 nm. ZnO nanotubes, with thicknesses estimated to be several nanometers based on scanning electron microscope images, were selectively grown in the holes of the masking layer. Then, n-doped GaN was layered on the

ZnO template. [ 39 ] The thicknesses of the n-doped GaN layers were between 100 and 200 nm, and the nanotubes were all about 3 μ m high.

Transmission Electron Microscopy : The cross-sectional speci-mens for TEM measurements were prepared using a focused ion beam at the top of each nanotube. Dislocations were examined by TEM (Technai F20) at 199.3 keV. For CBED measurements, the sample was tilted from [21̄1̄9] by 3.41 ° to an off-zone axis to avoid strong dynamic effects. Lattice parameters were determined by comparing quantitative electron diffraction simulations with CBED images. A Hough transformation was used to detect HOLZ lines [ 40 ] from the experimental patterns. The high tension of the micro-scope was determined fi rst and used for the refi nement of the lattice constant a .

Simulations : A dual-scaled FEM [ 41 ] was used for simulations. Periodic systems like GaN/ZnO heterostructure nanotubes are prob-lematic in simulations because of their infi nite periodic nature. A single-scaled analysis over the entire system is prohibitively expen-sive and impractical. A typical alternative approach to deal with this type of structure is to reduce the entire system into a RVE. When the character of the entire system is homogeneous during the process, this technique is successful. However, the presented GaN/ZnO het-erostructure undergoes inhomogeneous vertical spatial changes due to sequential stacking of fi lms, making the RVE approach inappropriate. The proposed dual-scaled scheme (Figure S3) is a suitable technique for periodic materials under an inhomoge-neous deformation (see details in the Supporting Information).

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgements

This work was supported by a grant from the National Research Foundation of Korea, funded by the Ministry of Education, Science and Technology (NRF 20120005637 and 20120006644). JYP and HNH acknowledge support from the Converging Research Center

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Geometry-Induced Dislocations in Nanotubes

[ 1 ] H. L. Tuller , Electrochim. Acta 2003 , 48 , 2879 . [ 2 ] A. Bera , D. Basak , Appl. Phys. Lett. 2009 , 94 , 163119 . [ 3 ] S. Dutta , S. Chattopadhyay , A. Sarkar , M. Chakrabarti , D. Sanyal ,

D. Jana , Prog. Mater. Sci. 2009 , 54 , 89 . [ 4 ] A. M. Smith , A. M. Mohs , S. Nie , Nat. Nanotechnol. 2009 , 4 , 56 . [ 5 ] T. C. Dinadayalane , J. S. Murray , M. C. Concha , P. Politzer ,

J. Leszczynski , J. Chem. Theory Comput. 2010 , 6 , 1351 . [ 6 ] M. Omari , A. Gupta , N. Kouklin , J. Appl. Phys. 2010 , 108 ,

024315 . [ 7 ] G. A. Beane , A. J. Morfa , A. M. Funston , P. Mulvaney , J. Phys.

Chem. C 2012 , 116 , 3305 . [ 8 ] D. Kabiraj , S. Ghosh , J. Appl. Phys. 2011 , 109 , 033701 . [ 9 ] N. J. Lawrence , J. R. Brewer , L. Wang , T. S. Wu , J. Wells-Kingsbury ,

M. M. Ihrig , G. Wang , Y. L. Soo , W. N. Mei , C. L. Cheung , Nano Lett. 2011 , 11 , 2666 .

[ 10 ] C. Sevik , H. Sevincli , G. Cuniberti , T. Cagin , Nano Lett. 2011 , 11 , 4971 .

[ 11 ] H. Gu , Y. Jiang , M. Yan , J. Alloys Compd. 2012 , 521 , 90 . [ 12 ] G. Jegert , D. Popescu , P. Lugli , M. J. Häufel , W. Weinreich ,

A. Kersch , Phys. Rev. B: Condens. Matter Mater. Phys. 2012 , 85 , 045303 .

[ 13 ] C. Y. Nam , P. Jaroenapibal , D. Tham , D. E. Luzzi , S. Evoy , J. E. Fischer , Nano Lett. 2006 , 6 , 153 .

[ 14 ] P. Khanikar , A. Kumar , A. Subramaniam , Adv. Mater. Res. 2009 , 67 , 33 .

[ 15 ] W. Ye , B. Paliwal , W. H. Goh , M. Cherkaoui , A. Ougazzaden , Int. J. Comput. Mater. Sci. 2012 , 58 , 154 .

[ 16 ] J. Oswald , E. Wintersberger , G. Bauer , T. Belytschko , Int. J. Numer. Meth. Eng. 2011 , 85 , 920 .

[ 17 ] Z. Liang , R. Colby , I. H. Wildeson , D. A. Ewoldt , T. D. Sands , E. A. Stach , R. E. García , J. Appl. Phys. 2010 , 108 , 074313 .

[ 18 ] P. Khanikar , A. Subramaniam , J. Nano Res. 2010 , 10 , 93 . [ 19 ] R. Colby , Z. Liang , I. H. Wildeson , D. A. Ewoldt , T. D. Sands ,

R. E. Garcia , E. A. Stach , Nano Lett. 2010 , 10 , 1568 . [ 20 ] J. Oswald , R. Gracie , R. Khare , T. Belytschko , Comput. Method

Appl. M. 2009 , 198 , 1872 . [ 21 ] H. Ye , P. F. Lu , Z. Y. Yu , L. H. Han , Semicond. Sci. Tech. 2009 , 24 ,

025029 . [ 22 ] E. Ertekin , P. A. Greaney , D. C. Chrzan , T. D. Sands , J. Appl. Phys.

2005 , 97 , 114325 .

Program (2012K001290) through the Ministry of Education, Sci-ence and Technology of the Korean government. JBP and GCY acknowledge support from the National Creative Research Initiative Project (R16-2004-004-01001-0) of the Korea Science and Engi-neering Foundations (KOSEF).

© 2013 Wiley-VCH Verlag Gmbsmall 2013, 9, No. 13, 2255–2259

[ 23 ] H. Ye , P. F. Lu , Z. Y. Yu , Y. X. Song , D. L. Wang , S. M. Wang , Nano Lett. 2009 , 9 , 1921 .

[ 24 ] W. Zhao , L. Wanga , J. Wang , Z. Hao , Y. Luo , J. Cryst. Growth 2011 , 327 , 3 .

[ 25 ] S. Raychaudhuri , E. T. Yu , J. Appl. Phys. 2006 , 99 , 114308 . [ 26 ] C. H. Lee , Y. J. Hong , Y. J. Kim , J. Yoo , H. Baek , S. R. Jeon , S. J. Lee ,

G. C. Yi , IEEE J. Sel. Top. Quant. 2011 , 17 , 966 . [ 27 ] S. B. Thapa , J. Hertkorn , T. Wunderer , F. Lipski , F. Scholz , A. Reiser ,

Y. Xie , M. Feneberg , K. Thonke , R. Sauer , M. Dürrschnabel , L. D. Yao , D. Gerthsen , H. Hochmuth , M. Lorenz , M. Grundmann , J. Cryst. Growth 2008 , 310 , 5139 .

[ 28 ] H. W. Kim , H. S. Kim , M. A. Kebede , H. G. Na , J. C. Yang , C. Lee , Cryst. Res. Technol. 2009 , 44 , 636 .

[ 29 ] S. Y. Karpov , Y. N. Makarov , Appl. Phys. Lett. 2002 , 81 , 4721 . [ 30 ] M. F. Schubert , S. Chhajed , J. K. Kim , E. F. Schubert , D. D. Koleske ,

M. H. Crawford , S. R. Lee , A. J. Fischer , G. Thaler , M. A. Banas , Appl. Phys. Lett. 2007 , 91 , 231114 .

[ 31 ] L. Sugiura , J. Appl. Phys. 1997 , 81 , 1633 . [ 32 ] D. Cherns , A. R. Preston , J. Electron. Microsc. Tech. 1989 , 13 ,

111 . [ 33 ] C. A. Flory , G. Hasnain , IEEE J. Quantum Elect. 2001 , 37 , 244 . [ 34 ] S. C. Jain , A. H. Harker , R. A. Cowley , Philos. Mag. A 1997 , 75 ,

1461 . [ 35 ] H. J. Gao , L. Zhang , S. P. Baker , J. Mech. Phys. Solids 2002 , 50 ,

2169 . [ 36 ] J. F. Nye , Acta Metall. Mater. 1953 , 1 , 153 . [ 37 ] M. F. Ashby , Philos. Mag. 1970 , 21 , 399 . [ 38 ] M. A. Lamkin , F. L. Riley , R. J. Fordham , J. Eur. Ceram. Soc. 1992 ,

10 , 347 . [ 39 ] Y. J. Hong , J. M. Jeon , M. Kim , S. R. Jeon , K. H. Park , G. C. Yi ,

New J. Phys. 2009 , 11 , 125021 . [ 40 ] J. M. Zuo , M. Kim , R. Holmestad , J. Electron Microsc. 1998 , 47 ,

121 . [ 41 ] B. Y. Kim , Y. Cho , M.-S. Jung , H.-A.-S. Shin , M.-W. Moon , H. N. Han ,

K. T. Nam , Y.-C. Joo , I.-S. Choi , Small 2012 , 8 , 3300 . [ 42 ] a) R. Chowdhury , S. Adhikari , F. Scarpa , Phys. E 2010 , 42 , 2036 ;

b) G. G. Gadzhiev , High Temp. 2002 , 40 , 778 ; c) H. Iwanaga , A. Kunishige , S. Takeuchiis , J. Mater. Sci. 2000 , 35 , 2451 ; d) V. I. Nikolaev , V. V. Shpeizman , B. I. Smirnov , Phys. Solid State 1999 , 42 , 437 .

[ 43 ] a) T. Vodenitcharova , L. C. Zhang , I. Zarudi , Y. Yin , H. Domyo , T. Ho , M. Sato , J. Mater. Process. Tech. 2007 , 194 , 52 ; b) W. M. Yim , R. J. Paff , J. Appl. Phys. 1974 , 45 , 1456 .

[ 44 ] a) S. M. Sze , K. K. Ng , Physics of Semiconductor Devices , John Wiley & Sons Inc. , New York, USA 2006 , Ch.2; b) H. A. Wrledt , J. Phase Equilib. Diff . 1990 , 11 , 43 .

Received: August 22, 2012 Revised: November 15, 2012Published online: February 11, 2013

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