In the present study, the effects of various types of strain and indium concentration on the total energy and optoelectronic properties of GaN nanowires (NWs) with embedded InxGa1−xN nanodisks (NDs) are examined. In particular, the bi-axial, hydrostatic, and uniaxial strain states of the embedded InxGa1−xN NDs are investigated for multiple In concentrations. Density functional theory is employed to calculate the band structure of the NWs. The theoretical analysis finds that the supercell-size-dependent characteristics calculated for our 972-atom NW models are very close to the infinite supercell-size limit. It is established that the embedded InxGa1−xN NDs do not induce deep states in the band gap of the NWs. A bowing parameter of 1.82 eV is derived from our analysis in the quadratic Vegard's formula for the band gaps at the various In concentrations of the investigated InxGa1−xN NDs in GaN NW structures. It is concluded that up to ∼10% of In, the hydrostatic strain state is competitive with the bi-axial due to the radial absorption of the strain on the surfaces. Above this value, the dominant strain state is the bi-axial one. Thus, hydrostatic and bi-axial strain components coexist in the embedded NDs, and they are of different physical origin. The bi-axial strain comes from growth on lattice mismatched substrates, while the hydrostatic strain originates from the lateral relaxation of the surfaces.

1.
M.
de la Mata
,
X.
Zhou
,
F.
Furtmayr
,
J.
Teubert
,
S.
Gradečak
,
M.
Eickhoff
,
A.
Fontcuberta i Morral
, and
J.
Arbiol
,
J. Mater. Chem. C
1
,
4300
(
2013
).
2.
V.
Consonni
,
Phys. Status Solidi RRL
7
,
699
(
2013
).
3.
Class for Physics of the Royal Swedish Academy of Sciences
, “
Scientific background on the nobel prize in physics 2014
,”
Technical Report
(Royal Swedish Academy of Sciences, Stockholm,
2014
).
4.
S.
Nakamura
,
T.
Mukai
,
M.
Senoh
,
S.
Nagahama
, and
N.
Iwasa
,
J. Appl. Phys.
74
,
3911
(
1993
).
5.
W.
Guo
,
M.
Zhang
,
A.
Banerjee
, and
P.
Bhattacharya
,
Nano Lett.
10
,
3355
(
2010
).
6.
H.
Lin
,
Y.
Lu
,
H.
Chen
,
H.
Lee
, and
S.
Gwo
,
Appl. Phys. Lett.
97
,
073101
(
2010
).
7.
H.
Kim
,
Y.
Cho
,
H.
Lee
,
S. I.
Kim
,
S. R.
Ryu
,
D. Y.
Kim
,
T. W.
Kang
, and
K. S.
Chung
,
Nano Lett.
4
,
1059
(
2004
).
8.
V.
Ramesh
,
A.
Kikuchi
,
K.
Kishino
,
M.
Funato
, and
Y.
Kawakami
,
J. Appl. Phys.
107
,
114303
(
2010
).
9.
Y.
Ra
,
R.
Navamathavan
,
H.
Yoo
, and
C.
Lee
,
Nano Lett.
14
,
1537
(
2014
).
10.
Y.
Kawakami
,
A.
Kaneta
,
L.
Su
,
Y.
Zhu
,
K.
Okamoto
,
M.
Funato
,
A.
Kikuchi
, and
K.
Kishino
,
J. Appl. Phys.
107
,
023522
(
2010
).
11.
S.
Keller
,
C.
Schaake
,
N. A.
Fichtenbaum
,
C. J.
Neufeld
,
Y.
Wu
,
K.
McGroddy
,
A.
David
,
S. P.
DenBaars
,
C.
Weisbuch
,
J. S.
Speck
, and
U. K.
Mishra
,
J. Appl. Phys.
100
,
054314
(
2006
).
12.
T.
Kehagias
,
G. P.
Dimitrakopulos
,
P.
Becker
,
J.
Kioseoglou
,
F.
Furtmayr
,
T.
Koukoula
,
I.
Häusler
,
A.
Chernikov
,
S.
Chatterjee
,
T.
Karakostas
,
H.
Solowan
,
U. T.
Schwarz
,
M.
Eickhoff
, and
P.
Komninou
,
Nanotechnology
24
,
435702
(
2013
).
13.
W.
Guo
,
A.
Banerjee
,
P.
Bhattacharya
, and
B. S.
Ooi
,
Appl. Phys. Lett.
98
,
193102
(
2011
).
14.
G.
Tourbot
,
C.
Bougerol
,
F.
Glas
,
L. F.
Zagonel
,
Z.
Mahfoud
,
S.
Meuret
,
P.
Gilet
,
M.
Kociak
,
B.
Gayral
, and
B.
Daudin
,
Nanotechnology
23
,
135703
(
2012
).
15.
Y.-J.
Lu
,
H.-W.
Lin
,
H.-Y.
Chen
,
Y.-C.
Yang
, and
S.
Gwo
,
Appl. Phys. Lett.
98
,
233101
(
2011
).
16.
A.
Rosenauer
,
T.
Mehrtens
,
K.
Müller
,
K.
Gries
,
M.
Schowalter
,
P. V.
Satyam
,
S.
Bley
,
C.
Tessarek
,
D.
Hommel
,
K.
Sebald
,
M.
Seyfried
,
J.
Gutowski
,
A.
Avramescu
,
K.
Engl
, and
S.
Lutgen
,
Ultramicroscopy
111
,
1316
(
2011
).
17.
Y. M.
Niquet
,
Phys. Rev. B
74
,
155304
(
2006
).
18.
E.
Sarigiannidou
,
E.
Monroy
,
B.
Daudin
,
J. L.
Rouviére
, and
A. D.
Andreev
,
Appl. Phys. Lett.
87
,
203112
(
2005
).
19.
G. P.
Dimitrakopulos
,
E.
Kalesaki
,
J.
Kioseoglou
,
T.
Kehagias
,
A.
Lotsari
,
L.
Lahourcade
,
E.
Monroy
,
I.
Häusler
,
H.
Kirmse
,
W.
Neumann
,
G.
Jurczak
,
T. D.
Young
,
P.
Dłużewski
,
P.
Komninou
, and
T.
Karakostas
,
J. Appl. Phys.
108
,
104304
(
2010
).
20.
A.
Trampert
,
O.
Brandt
, and
K. H.
Ploog
, in
Gallium Nitride (GaN) I
, Semiconductors and Semimetals Vol. 50, edited by
J. I.
Pankove
and
T. D.
Moustakas
(
Academic Press
,
New York
,
1997
), Chap. 7, pp.
167
192
.
21.
V. Y.
Davydov
,
A. A.
Klochikhin
,
V. V.
Emtsev
,
S. V.
Ivanov
,
V. V.
Vekshin
,
F.
Bechstedt
,
J.
Furthmüller
,
H.
Harima
,
A. V.
Mudryi
,
A.
Hashimoto
,
A.
Yamamoto
,
J.
Aderhold
,
J.
Graul
, and
E. E.
Haller
,
Phys. Status Solidi B
230
,
R4
(
2002
).
22.
23.
J. P.
Goss
,
M. J.
Shaw
, and
P. R.
Briddon
, in
Theory of Defects in Semiconductors
, Topics in Applied Physics Vol. 104, edited by
D. A.
Drabold
and
S. K.
Estreicher
(
Springer-Verlag
, Berlin
Heidelberg
,
2007
), Chap.
3
, pp.
69
94
.
24.
M. J.
Rayson
and
P. R.
Briddon
,
Comput. Phys. Commun.
178
,
128
(
2008
).
25.
H. J.
Monkhorst
and
J. D.
Pack
,
Phys. Rev. B
13
,
5188
(
1976
).
26.
M.
Methfessel
and
A. T.
Paxton
,
Phys. Rev. B
40
,
3616
(
1989
).
27.
C. D.
Latham
,
M.
Alatalo
,
R. M.
Nieminen
,
R.
Jones
,
S.
Öberg
, and
P. R.
Briddon
,
Phys. Rev. B
72
,
235205
(
2005
).
28.
N. A.
Modine
,
A. F.
Wright
, and
S. R.
Lee
,
Comput. Mater. Sci.
92
,
431
(
2014
).
29.
S.
Plimpton
,
J. Comput. Phys.
117
,
1
(
1995
).
30.
31.
32.
J.
Nord
,
K.
Albe
,
P.
Erhart
, and
K.
Nordlund
,
J. Phys.: Condens. Matter
15
,
5649
(
2003
).
33.
J.
Kioseoglou
,
P.
Komninou
, and
T.
Karakostas
,
Phys. Status Solidi B
245
,
1118
(
2008
).
34.
K.
Nordlund
,
J.
Nord
,
J.
Frantz
, and
J.
Keinonen
,
Comput. Mater. Sci.
18
,
283
(
2000
).
35.
J. E.
Northrup
and
J.
Neugebauer
,
Phys. Rev. B
53
,
R10477
(
1996
).
36.
A.
Filippetti
,
V.
Fiorentini
,
G.
Cappellini
, and
A.
Bosin
,
Phys. Rev. B
59
,
8026
(
1999
).
37.
E. C.
Do
,
Y.-H.
Shin
, and
B.-J.
Lee
,
J. Phys.: Condens. Matter
21
,
325801
(
2009
).
38.
M. J.
Hýtch
,
E.
Snoeck
, and
R.
Kilaas
,
Ultramicroscopy
74
,
131
(
1998
).
39.
Gatan Inc., Digitalmicrograph scripting resources.
40.
M. J.
Hýtch
and
T.
Plamann
,
Ultramicroscopy
87
,
199
(
2001
).
41.
C.
Stampfl
and
C. G.
Van de Walle
,
Phys. Rev. B
59
,
5521
(
1999
).
42.
M.
Fuchs
,
J. L. F.
Da Silva
,
C.
Stampfl
,
J.
Neugebauer
, and
M.
Scheffler
,
Phys. Rev. B
65
,
245212
(
2002
).
43.
J.
Neugebauer
and
C. G.
Van De Walle
,
Phys. Rev. B
51
,
10568
(
1995
).
44.
K. S. A.
Butcher
,
A. J.
Fernandes
,
P. P.-T.
Chen
,
M.
Wintrebert-Fouquet
,
H.
Timmers
,
S. K.
Shrestha
,
H.
Hirshy
,
R. M.
Perks
, and
B. F.
Usher
,
J. Appl. Phys.
101
,
123702
(
2007
).
45.
D.
Segev
and
C. G.
Van De Walle
,
Europhys. Lett.
76
,
305
(
2006
).
46.
L.
Lymperakis
,
P. H.
Weidlich
,
H.
Eisele
,
M.
Schnedler
,
J.-P.
Nys
,
B.
Grandidier
,
D.
Stiévenard
,
R. E.
Dunin-Borkowski
,
J.
Neugebauer
, and
P.
Ebert
,
Appl. Phys. Lett.
103
,
152101
(
2013
).
47.
M.
Bertelli
,
P.
Löptien
,
M.
Wenderoth
,
A.
Rizzi
,
R. G.
Ulbrich
,
M. C.
Righi
,
A.
Ferretti
,
L.
Martin-Samos
,
C. M.
Bertoni
, and
A.
Catellani
,
Phys. Rev. B
80
,
115324
(
2009
).
48.
K.
Termentzidis
,
T.
Barreteau
,
Y.
Ni
,
S.
Merabia
,
X.
Zianni
,
Y.
Chalopin
,
P.
Chantrenne
, and
S.
Volz
,
Phys. Rev. B
87
,
125410
(
2013
).
49.
Z.
Dridi
,
B.
Bouhafs
, and
P.
Ruterana
,
Semicond. Sci. Technol.
18
,
850
(
2003
).
50.
B.-T.
Liou
,
C.-Y.
Lin
,
S.-H.
Yen
, and
Y.-K.
Kuo
,
Opt. Commun.
249
,
217
(
2005
).
51.
P. G.
Moses
and
C. G.
Van de Walle
,
Appl. Phys. Lett.
96
,
021908
(
2010
).
52.
C.
Hartwigsen
,
S.
Goedecker
, and
J.
Hutter
,
Phys. Rev. B
58
,
3641
(
1998
).
53.
J. P.
Perdew
and
Y.
Wang
,
Phys. Rev. B
45
,
13244
(
1992
).
54.
R. M.
Nieminen
, in
Theory of Defects in Semiconductors
, Topics in Applied Physics Vol. 104, edited by
D. A.
Drabold
and
S. K.
Estreicher
(
Springer-Verlag
,
Berlin Heidelberg
,
2007
), Chap.
2
, pp.
29
68
.
55.
S. G.
Louie
,
S.
Froyen
, and
M. L.
Cohen
,
Phys. Rev. B
26
,
1738
(
1982
).
56.
C. G.
Van de Walle
,
Phys. Rev. B
56
,
R10020
(
1997
).
57.
C. G.
Van de Walle
,
S.
Limpijumnong
, and
J.
Neugebauer
,
Phys. Rev. B
63
,
245205
(
2001
).
58.
C. D.
Latham
,
R. M.
Nieminen
,
C. J.
Fall
,
R.
Jones
,
S.
Öberg
, and
P. R.
Briddon
,
Phys. Rev. B
67
,
205206
(
2003
).
59.
C. D.
Latham
,
R.
Jones
,
S.
Öberg
,
R. M.
Nieminen
, and
P. R.
Briddon
,
Phys. Rev. B
68
,
205209
(
2003
).
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