X-ray diffraction is one of the most popular experimental methods employed for determination of dislocation densities, as it can recognize both the strain fields and the local lattice rotations produced by dislocations. The main challenge of the quantitative analysis of the dislocation density is the formulation of a suitable microstructure model, which describes the dislocation arrangement and the effect of the interactions between the strain fields from neighboring dislocations reliably in order to be able to determine the dislocation densities precisely. The aim of this study is to prove the capability of X-ray diffraction and two computational methods, which are frequently used for quantification of the threading dislocation densities from X-ray diffraction measurements, in the special case of partially bunched threading dislocations. The first method is based on the analysis of the dislocation-controlled crystal mosaicity, and the other one on the analysis of diffuse X-ray scattering from threading dislocations. The complementarity of both methods is discussed. Furthermore, it is shown how the complementarity of these methods can be used to improve the results of the quantitative analysis of bunched and thus inhomogeneously distributed threading dislocations and to get a better insight into the dislocation arrangement.

1.
A. Y.
Polyakov
,
N. B.
Smirnov
,
A. V.
Govorkov
,
H.
Amano
,
S. J.
Pearton
,
I.-H.
Lee
,
Q.
Sun
,
J.
Han
, and
S. Y.
Karpov
,
Appl. Phys. Lett.
98
,
072104
(
2011
).
2.
G.
Li
,
W.
Wang
,
W.
Yang
, and
H.
Wang
,
Surf. Sci. Rep.
70
,
380
423
(
2015
).
3.
G.
Li
,
W.
Wang
,
W.
Yang
,
Y.
Lin
,
H.
Wang
,
Zh.
Lin
, and
S.
Zhou
,
Rep. Prog. Phys.
79
,
056501
(
2016
).
4.
P.
Gay
,
P. B.
Hirsch
, and
A.
Kelly
,
Acta Metall.
1
,
315
(
1953
).
5.
C. O.
Dunn
and
E. F.
Koch
,
Acta Metall.
5
,
548
554
(
1957
).
6.
T.
Metzger
,
R.
Höpler
,
E.
Born
,
O.
Ambacher
,
M.
Stutzmann
,
R.
Stömmer
,
M.
Schuster
,
H.
Göbel
,
S.
Christiansen
,
M.
Albrecht
, and
H. P.
Strunk
,
Philos. Mag. A
77
,
1013
1025
(
1998
).
7.
R.
Chierchia
,
T.
Böttcher
,
H.
Heinke
,
S.
Einfeld
,
S.
Figge
, and
D.
Hommel
,
J. Appl. Phys.
93
,
8918
(
2003
).
8.
M. A.
Krivoglaz
,
X-Ray and Neutron Diffraction in Nonideal Crystals
(
Springer
,
Berlin
,
1996
).
9.
M.
Wilkens
,
Phys. Status Solidi A
2
,
359
370
(
1970
).
10.
R.
Kyutt
,
V.
Ratnikov
,
G.
Mosina
, and
M.
Shcheglov
,
Phys. Solid State
41
,
25
31
(
1999
).
11.
V.
Ratnikov
,
R.
Kyutt
,
T.
Shubina
,
T.
Pashkova
,
E.
Valcheva
, and
B.
Monemar
,
J. Appl. Phys.
88
,
6252
(
2000
).
12.
V. M.
Kaganer
,
O.
Brandt
,
A.
Trampert
, and
K. H.
Ploog
,
Phys. Rev. B
72
,
045423
(
2005
).
13.
V.
Holý
,
T.
Baumbach
,
D.
Lübbert
,
L.
Helfen
,
M.
Ellyan
,
P.
Mikulík
,
S.
Keller
,
S. P.
DenBaars
, and
J.
Speck
,
Phys. Rev. B
77
,
094102
(
2008
).
14.
V.
Srikant
,
J. S.
Speck
, and
D. R.
Clarke
,
J. Appl. Phys.
82
,
4286
(
1997
).
15.
N. V.
Safriuk
,
G. V.
Stanchu
,
A. V.
Kuchuk
,
V. P.
Kladko
,
A. E.
Belyaev
, and
V. F.
Machulin
,
Semicond. Phys. Quantum Electron. Optoelectron.
16
(
3
),
265
272
(
2013
).
16.
B. E.
Warren
,
Prog. Met. Phys.
8
,
147
202
(
1959
).
17.
A.
Sakai
,
H.
Sunakawa
,
A.
Kimura
, and
A.
Usui
,
Appl. Phys. Lett.
76
,
442
(
2000
).
18.
P.
Rudolph
,
Cryst. Res. Technol.
52
(
1
),
1600171
(
2017
).
19.
R.
Datta
,
M. J.
Kappers
,
M. E.
Vickers
,
J. S.
Barnard
, and
C. J.
Humphreys
,
Superlattices Microstruct.
36
,
393
401
(
2004
).
20.
F.
Kawamura
,
M.
Tanpo
,
N.
Miyoshi
,
M.
Imade
,
M.
Yoshimura
,
Y.
Mori
,
Y.
Kitaoka
, and
T.
Sasaki
,
J. Cryst. Growth
311
,
3019
3024
(
2009
).
21.
M.
Barchuk
,
V.
Holý
,
B.
Miljevic
,
B.
Krause
,
T.
Baumbach
,
J.
Hertkorn
, and
F.
Scholz
,
J. Appl. Phys.
108
,
43521
(
2010
).
22.
V. M.
Kaganer
,
O.
Brandt
,
H.
Riechert
, and
K. K.
Sabelfeld
,
Phys. Rev. B
80
,
033306
(
2009
).
23.
V. M.
Kaganer
and
K. K.
Sabelfeld
,
Acta Cryst. A
70
,
457
471
(
2014
).
24.
V. S.
Kopp
,
V. M.
Kaganer
,
M. V.
Baidakova
,
W. V.
Lundin
,
A. E.
Nikolaev
,
E. V.
Verkhovtceva
,
M. A.
Yagovkina
, and
N.
Cherkashin
,
J. Appl. Phys.
115
,
073507
(
2014
).
25.
V. S.
Kopp
,
V. M.
Kaganer
,
B.
Jenichen
, and
O.
Brandt
,
J. Appl. Cryst.
47
,
256
263
(
2014
).
26.
R. J.
Molnar
,
W.
Götz
,
L. T.
Romano
, and
N. M.
Johnson
,
J. Cryst. Growth
178
,
147
156
(
1997
).
27.
S.
Nakamura
,
S.
Pearton
, and
G.
Fasol
,
The Blue Laser Diode
(
Springer-Verlag
,
Berlin
,
2013
).
28.
J.
Hertkorn
,
F.
Lipski
,
P.
Brückner
,
T.
Wunderer
,
S. B.
Thapa
,
F.
Scholz
,
A.
Chuvilin
,
U.
Kaiser
,
M.
Beer
, and
J.
Zweck
,
J. Cryst. Growth
310
,
4867
4870
(
2008
).
29.
M.
Barchuk
,
C.
Röder
,
Y.
Shashev
,
G.
Lukin
,
M.
Motylenko
,
J.
Kortus
,
O.
Pätzold
, and
D.
Rafaja
,
J. Cryst. Growth
386
,
1
8
(
2014
).
30.
C.
Röder
,
F.
Lipski
,
F.
Habel
,
G.
Leibiger
,
M.
Abendroth
,
C.
Himcinschi
, and
J.
Kortus
,
J. Phys. D: Appl. Phys.
46
,
285302
(
2013
).
31.
K.
Yamane
,
T.
Matsubara
,
T.
Yamamoto
,
N.
Okada
,
A.
Wakahara
, and
K.
Tadatomo
,
J. Appl. Phys.
119
,
045707
(
2016
).
32.
P.
Brückner
,
F.
Habel
, and
F.
Scholz
,
Phys. Status Solidi C
3
,
1471
1474
(
2006
).
33.
M. J.
Hordon
and
B. L.
Averbach
,
Acta Met.
9
,
237
246
(
1961
).
34.
K.
Motoki
,
T.
Okahisa
,
S.
Nakahata
,
N.
Matsumoto
,
H.
Kimura
,
H.
Kasai
,
K.
Takemoto
,
K.
Uematsu
,
M.
Ueno
,
Y.
Kumagai
,
A.
Koukitu
, and
H.
Seki
,
Mater. Sci. Eng. B
93
,
123
130
(
2002
).
35.
Y. N.
Picard
,
M. E.
Twigg
,
J. D.
Caldwell
,
C. R.
Eddy
, Jr.
,
M. A.
Mastro
, and
R. T.
Holm
,
Scr. Mater.
61
,
773
776
(
2009
).
36.
M. M.
Hall
,
V. G.
Veeraraghavan
,
H.
Rubin
, and
P. G.
Winchell
,
J. Appl. Cryst.
10
,
66
68
(
1977
).
37.
Th. H.
de Keijser
,
E. J.
Mittemeijer
, and
H. C. F.
Rozendaal
,
J. Appl. Cryst.
16
,
309
316
(
1983
).
38.
M.
Barchuk
,
G.
Lukin
,
F.
Zimmermann
,
C.
Röder
,
M.
Motylenko
,
O.
Pätzold
,
J.
Heitmann
, and
D.
Rafaja
,
J. Electron. Mater.
46
(
3
),
1612
1619
(
2017
).
39.
M.
Barchuk
,
V.
Holý
,
B.
Miljevic
,
B.
Krause
, and
T.
Baumbach
,
Appl. Phys. Lett.
98
,
021912
(
2011
).
40.
G. K.
Williamson
and
W. H.
Hall
,
Acta Metall.
1
,
22
31
(
1953
).
41.
Y. J.
Sun
,
O.
Brandt
,
T. Yu
Liu
,
A.
Trampert
,
K. H.
Ploog
,
J.
Blaesing
, and
A.
Krost
,
Appl. Phys. Lett.
81
,
4928
(
2002
).
42.
M.
Barchuk
,
M.
Motylenko
,
G.
Lukin
,
O.
Pätzold
, and
D.
Rafaja
,
J. Appl. Cryst.
50
,
555
560
(
2017
).
43.
V.
Holý
,
U.
Pietsch
, and
T.
Baumbach
,
High-Resolution X-Ray Scattering from Thin Films and Multilayers
(
Springer-Verlag
,
Berlin, Heidelberg
,
1999
).
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