The theoretical diffraction model for a crystalline multilayer system with inhomogeneous strain profile and randomly distributed defects has been created by using the statistical dynamical theory of X-ray diffraction in imperfect crystals. The dynamical scattering peculiarities in both coherent and diffuse scattering intensities have been taken into account for all the layers of the system by using derived recurrence relations between coherent scattering amplitudes.

The investigated yttrium-iron garnet films grown on gadolinium-gallium garnet substrate were implanted with different doses of 90 keV F+ ions. The rocking curves measured from the as-grown and implanted samples have been treated by using the proposed theoretical model. This model has allowed for the reliable self-consistent determination of strain profile parameters and structural defect characteristics in both implanted film and substrate of the investigated samples

Garpul’, O.Z.

Kotsyubynsky, V.O.

Kyslovs’kyy, Ye.M.

Lizunov, V.V.

Molodkin, V.B.

Olikhovskii, S.I.

Ostafiychuk, B.K.

Pylypiv, V.M.

Reshetnyk, O.V.

Skakunova, O.S.

Vladimirova, T.P.

Yaremiy, I.P.

SocioEconomic Challenges Journal (Sumy State University)

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  
NANOMATERIALS: APPLICATIONS AND PROPERTIES 
Vol. 3 No 1, 01PCSI10(4pp) (2014) 
 
 
2304-1862/2014/3(1)01PCSI10(4) 01PCSI10-1  2014 Sumy State University 
X-Ray Diffraction Characterization of Nanoscale Strains and Defects in Yttrium Iron Garnet 
Films Implanted with Fluorine Ions 
 
S.I. Olikhovskii1,*, O.S. Skakunova1, V.B. Molodkin1, V.V. Lizunov1, Ye.M. Kyslovs’kyy1, 
T.P.Vladimirova1, O.V. Reshetnyk1, V.M. Pylypiv2, V.O. Kotsyubynsky2, B.K. Ostafiychuk2, 
I.P. Yaremiy2, O.Z.Garpul’2 
 
1 G.V. Kurdyumov Institute for Metal Physics of NASU, 36, Vernadsky Blvd., 03680 Kyiv, Ukraine 
2 V. Stefanyk Precarphatian National University, 57, Shevchenko Str., 76025 Ivano-Frankivsk, Ukraine 
  
(Received 14 July 2014; published online 29 August 2014) 
 
The theoretical diffraction model for a crystalline multilayer system with inhomogeneous strain 
profile and randomly distributed defects has been created by using the statistical dynamical theory of 
X-ray diffraction in imperfect crystals. The dynamical scattering peculiarities in both coherent and dif-
fuse scattering intensities have been taken into account for all the layers of the system by using de-
rived recurrence relations between coherent scattering amplitudes.  
The investigated yttrium-iron garnet films grown on gadolinium-gallium garnet substrate were 
implanted with different doses of 90 keV F+ ions. The rocking curves measured from the as-grown and 
implanted samples have been treated by using the proposed theoretical model. This model has allowed 
for the reliable self-consistent determination of strain profile parameters and structural defect charac-
teristics in both implanted film and substrate of the investigated samples.   
 
Keywords: X-Ray diffraction theory, Yttrium iron garnet, Film, Ion implantation, Strain, Defects. 
 
 PACS numbers: 61.05.Cс, 61.05.Cp, 61.72.Dd, 
61.72.jd, 61.72.Nn, 61.72.Qq, 61.80.Jh, 61.82.Ms 
 
 
                                                          
* olikhovsky@meta.ua 
1.  INTRODUCTION 
 
Epitaxial single-crystalline yttrium iron garnet 
(YIG) Y3Fe5О12 films grown on gadolinium gallium 
garnet (GGG) Gd3Ga5O12 substrate are widely used in 
various scientific research and technical application 
fields. In particular, YIG films are used as sensors in 
magnetometers for the visual observation of the spatial 
distribution of inhomogeneous magnetic fields, in ener-
gy-independent magnetic memory devices, in magnetic 
microelectronics and integral magneto-optics, etc. (see, 
e.g., Refs. [1-3]).  
Ion implantation is the effective technique for pur-
poseful modifying the crystalline structure of subsur-
face layers in such films and, thus, for changing their 
physical properties, in particular, magnetic, optical, 
and magneto-optical ones [4-6]. However, despite the 
numerous experimental and theoretical investigations 
of ion-implanted garnets (see also Refs. [7-10]), some 
questions remain insufficiently elucidated, in particu-
lar, concerning processes of the formation of primary 
and secondary defects in YIG films after ion implanta-
tion and their relation with parameters of crystalline 
microstructure.  
To characterize structural defects and strains in the 
modified crystal layers, the X-ray diffraction methods 
are most widely used. Efficiency of application of these 
methods is dependent to large extent on the availabil-
ity of the analytical formulas which give the adequate 
description of measured diffraction intensity distribu-
tions. In particular, there exist various theoretical 
models to describe the rocking curves (RCs) which are 
measured from imperfect crystalline structures with 
inhomogeneous strain profiles [7-9, 11, 12] and addi-
tional structure imperfections  [13, 14-16].    
The aim of the present work consists in the 
demonstration of characterization possibilities of the 
generalized statistical dynamical theory of X-ray dif-
fraction, which has been extended to the case of imper-
fect crystals with randomly distributed defects and 
inhomogeneous strain profiles caused by ion implanta-
tion [16]. The proposed diffraction model will be ap-
plied to characterize nanometer-sized defects and 
strains in the epitaxial YIG films grown on GGG sub-
strate, which were implanted with 90 keV F+ ions at 
different doses, by using the RCs measured by the 
high-resolution double-crystal X-ray diffractometer 
(DCD).   
 
2. REFLECTIVITY OF INHOMOGENEOUS 
STRUCTURES WITH DEFECTS  
 
The multilayer system which consists of GGG sub-
strate covered on both sides by single-crystalline YIG 
films is characterized from the structural point of view 
by the presence of growth defects in the volumes of 
both substrate and films as well as inhomogeneous 
strain in subsurface and transition layers. Ion implan-
tation of this system results in the appearance of pri-
mary and secondary radiation defects which cause the 
additional strain in subsurface layers with constant 
and fluctuation components.   
To describe analytically X-ray diffraction in such a 
system we can subdivide it into M+1 laminae and con-
sider as a multilayer crystal system with constant av-
erage   strain in each lamina. Then, we can make use of 
the recurrence relations between coherent components 
of amplitude reflection coefficients of adjacent layers in 
 S.I. OLIKHOVSKII, O.S. SKAKUNOVA, ET.AL. PROC. NAP 3, 01PCSI10 (2014) 
 
 
01PCSI10-2 
the two-wave approximation for Bragg diffraction ge-
ometry [15, 16]:  
 
 
2 1 2 1
1
1
11
j j j j j j
j
j j j
r R t e r
R
r R
, (1) 
 
where 
jr  and jt  are the dynamical amplitude reflection 
and transmission coefficients of j th layer with random-
ly distributed defects, respectively, 
je  is the phase 
factor, the constant 1j , and the subscript 
0,1,...,j M
 
denotes the relation of corresponding 
quantity to jth layer . 
The coherent component of RC for the multilayered 
crystal system which consists of M+1 layers with ran-
domly distributed defects can be represented as follows: 
 
 
2
coh MR R , (2) 
 
where  is an angular deviation of the investigat-
ed sample from an exact Bragg position, and the ampli-
tude reflectivity of upper Мth layer MR  can be 
determined  by using the recurrence relation (1). The 
starting value in this relation, the dynamical ampli-
tude reflection coefficient of 0th layer corresponding to 
the thick substrate with defects, is calculated as fol-
lows: 
 
 
1 2 2
0 0 0r 0i 0sgn 1R y y y y
, (3) 
 
where quantities 0r 0Rey y  and  0i 0Imy y  
denote 
real and imaginary parts of the normalized angular 
deviation of the substrate 0y  
from an exact Bragg 
reflection position. 
The diffuse component of the RC for multilayered 
system, which is measured by DCD with widely open 
detector window and represents the differential diffuse 
scattering (DS) intensity integrated over exit angles, 
can be written as the sum of diffuse reflectivities of 
each layer with proper extinction and absorption fac-
tors [7]: 
 
 
diff abs ext diff
0
( )
M
j j j
j
R F F R
, (4) 
 
where 
ext
jF  and abs
jF  are extinction and absorption  
factors, respectively. 
Diffuse reflectivities of thick substrate ( j =0) and 
thin layers ( 1,j M ) in Eq. (4) are calculated as fol-
lows: 
 
 
ds
diff
0
( )
j
jj
d
R ,    
0
0 ds
diff 0
0
( )
(1 )
R
b
, (5)  
 
where 
0
j  and 
ds
j are photoelectric absorption coeffi-
cient and absorption coefficient due to DS in jth layer, 
respectively, jd   is the thickness of jth layer, 0  is the 
direction cosine of the incident X-ray, b is the diffrac-
tion asymmetry factor.  
It should be remarked here that the absorption coef-
ficients due to DS from several types of randomly dis-
tributed defects without correlations between them are 
summarized, similarly to exponents of corresponding 
static Debye-Waller factors. 
 
3. EXPERIMENTAL 
 
Epitaxial single-crystalline YIG films with 5.33 µm 
thickness were grown by Czochralsky method on both 
sides of 500 µm thick GGG substrates with [111] 
growth axis. The samples after lapping were polished 
mechanically, chemo-dynamically, and chemically. The 
investigated samples have been implanted with F+ ions 
at the energy of 90 keV and with doses 131 10D , 
13
6 10 , and 142 10  cm-2. 
Experimental RCs of the implanted samples were 
measured by using the high-resolution four-circle X-ray 
DCD with Cu tube (25 kV  25 mА) and two flat Ge 
(333) monochromators in the antiparallel setting. The 
symmetric (444) (see Fig. 1) and (888) reflections were 
used at the samples under investigation. 
 
-600 -300 0
10
-4
10
-3
10
-2
10
-1
, arcsec
R
444
 
 
Fig. 1 – Measured and calculated (solid line) RCs for 444 
reflection of CuK 1 radiation from YIG/GGG film system im-
planted with F+ ions (E = 90 keV) at doses D = 6 1012 cm2. 
Coherent and diffuse RC components are shown by dashed 
and dot-dashed lines, respectively  
 
4. THE STRUCTURE MODEL OF THE IM-
PLANTED YIG/GGG SYSTEM 
 
For realization of quantitative diagnostics of imper-
fect structure of a single-crystalline inhomogeneous 
system by X-ray diffraction methods it is necessary to 
use the adequate structural model. In garnet crystals, 
there always are present various point defects and 
growth microdefects, including new phase particles and 
dislocation loops (see, e.g., Ref. [18]. In garnet films, 
additionally to fluctuation strain fields from randomly 
distributed defects, the smooth inhomogeneous strain 
fields are created in transitional layers between film 
and substrate due to lattice mismatch [9].  
After ion implantation, the subsurface layer of a film 
is additionally saturated with primary and secondary 
radiation defects, which are distributed inhomogeneously 
in depth and cause the corresponding «in average» inho-
mogeneous strain. Separate isolated amorphous clusters 
that arise at bombardment of garnet films with light ions 
of intermediate energies are relatively stable [5, 6].   
 X-RAY DIFFRACTION CHARACTERIZATION OF NANOSCALE STRAINS… PROC. NAP 3, 01PCSI10 (2014) 
 
 
01PCSI10-3 
Thus, in the model of defect structure of the im-
planted epitaxial single-crystalline system of YIG films 
grown on GGG substrate the presence of two types of 
microdefects, namely, spherical clusters and circular 
prismatic dislocation loops was supposed.  The influ-
ence of point defects (antisite defects and anion vacan-
cies) and thermal DS was taken into account as well 
[18]. The film system in whole was considered as a 
multilayer system in each layer of which the strain was 
consisted of average and fluctuating components. The 
change of YIG and GGG cubic lattice constants due to 
point defects was calculated according to empiric ana-
lytical expression through concentrations of these de-
fects and effective radii of cations [18].  
When fitting theoretical RCs, the depth profiles of 
the strain caused by implantation were calculate 
through concentrations of the amorphous clusters 
formed by displaced matrix atoms in consequence of 
energy losses of the implanted ions [6]. The existence of 
two channels of energy losses for the implanted light 
ions was taken into account, namely, through excita-
tion of electronic subsystem and through elastic nucle-
ar collisions [10]. For electronic and nuclear channels 
channel this depth profile was set as a decreasing tail 
of Gaussian and asymmetric Gaussian, respectively.  
Such characteristics of clusters in implanted layer 
as radius and strain at the boundary with crystal ma-
trix were supposed to be equal for both channels. Re-
sulting strain profile in implanted layer was calculated 
as the sum of depth-depended strain profiles created by 
the two distributions of cluster concentrations along 
the normal to crystal surface.  
The depth profile of the so-called amorphization fac-
tor was described in our diffraction model by only the 
static Debye-Waller factor, exponent of which was cal-
culated through characteristics of clusters in implanted 
layer as well. Additionally, the attenuation of coherent 
component of diffraction intensity from the implanted 
layer was described by the coefficient of absorption due 
to DS 
ds
j , which was calculated similarly through 
characteristics of clusters in implanted layer. 
Thus, the chosen model of imperfect structure of the 
implanted YIG film on GGG substrate provides physi-
cally clear connection between defect characteristics 
and structurally sensitive diffraction parameters. Also, 
the self-consistent character of calculation of these 
parameters should be emphasized, what complements 
the self-consistency between coherent and diffuse com-
ponents of diffraction intensity in the present diffrac-
tion model.  
 
5. TREATMENT AND DISCUSSION  
 
The RC measured from a multilayer system like the 
implanted YIG film on GGG substrate is formed by a 
superposition of angular distributions of coherent and 
DS intensities from substrate, film, and implanted 
layer. Such superposition complicates the analysis of 
the RC for the assessment of strain and amorphization 
parameters in the implanted layer since the numerous 
additional fit parameters arise, which characterize 
defect structure of film and substrate.    
On the other hand, the account for influence of DS 
effects from dislocation loops and clusters in film and 
substrate on the form of diffraction peaks and tails has 
allowed for both the determination of as-grown defect 
characteristics (see Table 1) and correct description of 
X-ray intensity diffracted from the implanted layer. 
Also, such account has provided the possibility to avoid 
systematical errors when determining strain and defect 
characteristics in this layer. 
 
Table 1 – Characteristics of circular dislocation loops and 
spherical clusters in YIG film and GGG substrate  
 
Defects Characteristics GGG substrate 
YIG 
film 
 
Circular 
dislocation 
loops 
Radius, nm 90 5 5 
Density, cm-3 1,2×1012  1×1015 1×1015 
Spherical 
clusters 
Radius, nm 8 10 
Density, cm-3 1×1014 1×1014 
 
At modeling the strain distribution, the implanted 
layer was subdivided into 2 nm thick laminae, whereas 
the rest of film and substrate volume was subdivided 
into layers with thicknesses of order of few hundreds of 
nanometers. It was supposed that as a result of elec-
tronic and nuclear energy losses of implanted ions the 
spherical amorphous clusters were formed in the im-
planted layer. Their radii have been determined to be 
approximately 1.7 nm at the value of volume strain 
between cluster and crystal matrix ɛ  = 0.03. The corre-
sponding cluster concentrations found at various im-
plantation doses are given in Table 2.  
 
Table 2 – Maximal values of cluster concentrations and strain 
profiles in YIG film implanted with F+ ions (E = 90 keV) at 
various implantation doses 
 
D, cm–2 1 1013 6 1013 2 1014 
nucl,max
Cn , cm
–3 1.1 1019 6 1019 2 1020 
el,max
Cn , cm
–3 1.10 1019 6.00 1019 2.00 1020 
nucl,max
, % 0.10 0.54 1.79 
el,max
, % 0.04 0.22 0.73 
 
It should be emphasized that values of the parame-
ters that define the form of strain profile have been 
determined to be the same for all the implantation 
doses and both reflections measured (see Figs. 2 and 3).  
Thus, the complete set of defect characteristics and 
strain parameters of the implanted layers in YIG films 
on GGG substrates has been determined by the fully 
dynamical self-consistent treatment of diffraction pro-
files from the investigated samples simultaneously for 
two reflections. The self-consistentcy of the description 
of coherent and diffuse components of diffraction pat-
terns has been achieved due to the fully dynamical 
interpretation from such systems becomes possible 
with, which are connected analytically with strain and 
defect characteristics. 
Additionally, the strain distribution in the transi-
tion layer between film and substrate has been deter-
mined, which thickness approaches some hundreds of 
nanometers (see Fig. 3). 
 
 S.I. OLIKHOVSKII, O.S. SKAKUNOVA, ET.AL. PROC. NAP 3, 01PCSI10 (2014) 
 
 
01PCSI10-4 
0 25 50 75 100 125
0,00
0,25
0,50
 
3 2
1
, %
z, nm  
 
Fig. 2 – Strain profiles in implanted layer of YIG film, which 
are caused by electronic (1), nuclear (2), and total (3)  energy 
loses of implanted  F+ ions (E = 90 keV, D = 6 1013 cm2) 
 
10 100 1000 10000
10
-3
10
-2
10
-1
10
0
film substrate
1,2
3
1
2
3
+0.1, % 
z, nm  
 
Fig. 3 – Strain profiles in YIG/GGG film system implanted 
with F+ ions (E = 90 keV) at doses D = 1 1013 (1),   6 1013 (2), 
and 2 1014 cm2 (3), respectively.  
6.  RESUME AND CONCLUSIONS 
 
The theoretical diffraction model, based on the gen-
eralized statistical dynamical theory of X-ray scatter-
ing in imperfect crystals, has been proposed to describe 
RCs from imperfect film structures with randomly 
distributed defects and the inhomogeneous strain pro-
file caused by ion implantation. The dynamical charac-
ter of both coherent and diffuse components has been 
taken into account by means of recurrence relations 
between coherent scattering amplitudes of adjacent 
crystal layers. Thus, the fully dynamical interpretation 
of diffraction patterns from such systems becomes pos-
sible with self-consistent description of the coherent 
and diffuse components, which are connected analyti-
cally with strain and defect characteristics.  
The proposed diffraction model has been applied to 
characterize defects and strains in the epitaxial YIG 
films grown on GGG substrate, which were implanted 
with of 90 keV F+ ions at various doses. Simultaneous 
treatment of the RCs measured by the high-resolution 
DCD with widely open detector window for two reflec-
tions has provided the set of the parameters, which 
characterize both strain and defects in both implanted 
layer and YIG film on GGG substrate.   
 
AKNOWLEDGEMENTS 
 
This research was supported by the National Acad-
emy of Sciences of Ukraine under contract No. 3.6.3.13-
7/14-D.  
 
 
REFERENCES 
 
1. A.K. Zvezdin, V.A. Kotov, Modern Magnetooptics and 
Magnetooptical Materials (New York: Taylor & Francis 
Group: 1997). 
2. T. Aichele, A. Lorenz, R. Hergt, P. Görnert, Cryst. Res. 
Technol.  38, 575 (2003). 
3. T. Wehlus, T. Körner, S. Leitenmeier, A. Heinrich, 
B. Stritzker, phys. status solidi a 208, 252 (2011). 
4. V.S. Speriosu, C.H. Wilts, J. Appl. Phys.  54, 3325 (1983).   
5. B. Lagomarsino, A. Tucciarone, Thin Solid Films 114, 45 
(1984).  
6. P. Gerard, Nucl. Instrum. Meth. Phys. Res. B 19–20, 843 
(1987), 
7. V. S. Speriosu, J. Appl. Phys. 52, 6094 (1981). 
8. C. R. Wie, T. A. Tombrello, T. Vreeland, Jr., J. Appl. Phys. 
59, 3743 (1986). 
9. M. Dimer, E. Gerdau, R.  Rüffer, H. D.  Rüter, W. Sturhahn, 
J. Appl. Phys. 79, 9090 (1996). 
10. B.K. Ostafiychuk, V.D. Fedoriv, I.P. Yaremiy, O.Z., Garpul, 
V.V.  Kurovets, I.C. Yaremiy, phys. status solidi a 208, 2108 
(2011).  
11. R.N., Kyutt, P.V. Petrashen, L.M. Sorokin, phys. status 
solidi a 60, 381 (1980). 
12. Yu.N. Belyaev, A.V.  Kolpakov, phys. status solidi a 76, 
641 (1983). 
13. V.I. Punegov, phys. status solidi a 136, 9 (1993). 
14. P.K. Shreeman, R.J. Matyi, J. Appl. Cryst. 43, 550 (2010). 
15. V.B. Molodkin, S.I. Olikhovskii, Ye.M. Kyslovskyy, 
I.M. Fodchuk, E.S. Skakunova, E.V. Pervak, V.V. Molod-
kin, phys. status solidi a 204, 2606 (2007). 
16. V.M. Pylypiv, S.I. Olikhovskii, T.P. Vladimirova, 
O.S. Skakunova, V.B. Molodkin, B.K. Ostafiychuk, Ye.M. 
Kyslovskyy, O.V. Reshetnyk, S.V. Lizunova, O.Z. Garpul’, 
Metallofiz. Noveishie Tekhnol. 33, 1145 (2011). 
17. V.B. Molodkin, S.I. Olikhovskii, E.N. Kislovskii, TP. Vla-
dimirova, E.S. Skakunova, R.F. Seredenko, B.V. Shelud-
chenko, Phys. Rev. B 78, 224109 (2008). 
18. V.M. Pylypiv, T.P. Vladimirova, I.M. Fodchuk, B.K. Ostafi-
ychuk, Ye.M. Kyslovskyy, V.B. Molodkin, S.I. Olikhovskii, 
O.V. Reshetnyk, O.S. Skakunova, V.V. Lizunov, O.Z. Garpul’, 
phys. status solidi a 208, 2558 (2011). 
 


X-Ray Diffraction Characterization of Nanoscale Strains and Defects in Yttrium Iron Garnet  Films Implanted with Fluorine Ions

Electronic Sumy State University Institutional Repository

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  NANOMATERIALS: APPLICATIONS AND PROPERTIES Vol. 3 No 1, 01PCSI10(4pp) (2014)   2304-1862/2014/3(1)01PCSI10(4) 01PCSI10-1  2014 Sumy State University X-Ray Diffraction Characterization of Nanoscale Strains and Defects in Yttrium Iron Garnet Films Implanted with Fluorine Ions  S.I. Olikhovskii1,*, O.S. Skakunova1, V.B. Molodkin1, V.V. Lizunov1, Ye.M. Kyslovs’kyy1, T.P.Vladimirova1, O.V. Reshetnyk1, V.M. Pylypiv2, V.O. Kotsyubynsky2, B.K. Ostafiychuk2, I.P. Yaremiy2, O.Z.Garpul’2  1 G.V. Kurdyumov Institute for Metal Physics of NASU, 36, Vernadsky Blvd., 03680 Kyiv, Ukraine 2 V. Stefanyk Precarphatian National University, 57, Shevchenko Str., 76025 Ivano-Frankivsk, Ukraine   (Received 14 July 2014; published online 29 August 2014)  The theoretical diffraction model for a crystalline multilayer system with inhomogeneous strain profile and randomly distributed defects has been created by using the statistical dynamical theory of X-ray diffraction in imperfect crystals. The dynamical scattering peculiarities in both coherent and dif-fuse scattering intensities have been taken into account for all the layers of the system by using de-rived recurrence relations between coherent scattering amplitudes.  The investigated yttrium-iron garnet films grown on gadolinium-gallium garnet substrate were implanted with different doses of 90 keV F+ ions. The rocking curves measured from the as-grown and implanted samples have been treated by using the proposed theoretical model. This model has allowed for the reliable self-consistent determination of strain profile parameters and structural defect charac-teristics in both implanted film and substrate of the investigated samples.    Keywords: X-Ray diffraction theory, Yttrium iron garnet, Film, Ion implantation, Strain, Defects.   PACS numbers: 61.05.Cс, 61.05.Cp, 61.72.Dd, 61.72.jd, 61.72.Nn, 61.72.Qq, 61.80.Jh, 61.82.Ms                                                             * olikhovsky@meta.ua 1.  INTRODUCTION  Epitaxial single-crystalline yttrium iron garnet (YIG) Y3Fe5О12 films grown on gadolinium gallium garnet (GGG) Gd3Ga5O12 substrate are widely used in various scientific research and technical application fields. In particular, YIG films are used as sensors in magnetometers for the visual observation of the spatial distribution of inhomogeneous magnetic fields, in ener-gy-independent magnetic memory devices, in magnetic microelectronics and integral magneto-optics, etc. (see, e.g., Refs. [1-3]).  Ion implantation is the effective technique for pur-poseful modifying the crystalline structure of subsur-face layers in such films and, thus, for changing their physical properties, in particular, magnetic, optical, and magneto-optical ones [4-6]. However, despite the numerous experimental and theoretical investigations of ion-implanted garnets (see also Refs. [7-10]), some questions remain insufficiently elucidated, in particu-lar, concerning processes of the formation of primary and secondary defects in YIG films after ion implanta-tion and their relation with parameters of crystalline microstructure.  To characterize structural defects and strains in the modified crystal layers, the X-ray diffraction methods are most widely used. Efficiency of application of these methods is dependent to large extent on the availabil-ity of the analytical formulas which give the adequate description of measured diffraction intensity distribu-tions. In particular, there exist various theoretical models to describe the rocking curves (RCs) which are measured from imperfect crystalline structures with inhomogeneous strain profiles [7-9, 11, 12] and addi-tional structure imperfections  [13, 14-16].    The aim of the present work consists in the demonstration of characterization possibilities of the generalized statistical dynamical theory of X-ray dif-fraction, which has been extended to the case of imper-fect crystals with randomly distributed defects and inhomogeneous strain profiles caused by ion implanta-tion [16]. The proposed diffraction model will be ap-plied to characterize nanometer-sized defects and strains in the epitaxial YIG films grown on GGG sub-strate, which were implanted with 90 keV F+ ions at different doses, by using the RCs measured by the high-resolution double-crystal X-ray diffractometer (DCD).    2. REFLECTIVITY OF INHOMOGENEOUS STRUCTURES WITH DEFECTS   The multilayer system which consists of GGG sub-strate covered on both sides by single-crystalline YIG films is characterized from the structural point of view by the presence of growth defects in the volumes of both substrate and films as well as inhomogeneous strain in subsurface and transition layers. Ion implan-tation of this system results in the appearance of pri-mary and secondary radiation defects which cause the additional strain in subsurface layers with constant and fluctuation components.   To describe analytically X-ray diffraction in such a system we can subdivide it into M+1 laminae and con-sider as a multilayer crystal system with constant av-erage   strain in each lamina. Then, we can make use of the recurrence relations between coherent components of amplitude reflection coefficients of adjacent layers in  S.I. OLIKHOVSKII, O.S. SKAKUNOVA, ET.AL. PROC. NAP 3, 01PCSI10 (2014)   01PCSI10-2 the two-wave approximation for Bragg diffraction ge-ometry [15, 16]:    2 1 2 11111j j j j j jjj j jr R t e rRr R, (1)  where jr  and jt  are the dynamical amplitude reflection and transmission coefficients of j th layer with random-ly distributed defects, respectively, je  is the phase factor, the constant 1j , and the subscript 0,1,...,j M denotes the relation of corresponding quantity to jth layer . The coherent component of RC for the multilayered crystal system which consists of M+1 layers with ran-domly distributed defects can be represented as follows:   2coh MR R , (2)  where  is an angular deviation of the investigat-ed sample from an exact Bragg position, and the ampli-tude reflectivity of upper Мth layer MR  can be determined  by using the recurrence relation (1). The starting value in this relation, the dynamical ampli-tude reflection coefficient of 0th layer corresponding to the thick substrate with defects, is calculated as fol-lows:   1 2 20 0 0r 0i 0sgn 1R y y y y, (3)  where quantities 0r 0Rey y  and  0i 0Imy y  denote real and imaginary parts of the normalized angular deviation of the substrate 0y  from an exact Bragg reflection position. The diffuse component of the RC for multilayered system, which is measured by DCD with widely open detector window and represents the differential diffuse scattering (DS) intensity integrated over exit angles, can be written as the sum of diffuse reflectivities of each layer with proper extinction and absorption fac-tors [7]:   diff abs ext diff0( )Mj j jjR F F R, (4)  where extjF  and absjF  are extinction and absorption  factors, respectively. Diffuse reflectivities of thick substrate ( j =0) and thin layers ( 1,j M ) in Eq. (4) are calculated as fol-lows:   dsdiff0( )jjjdR ,    00 dsdiff 00( )(1 )Rb, (5)   where 0j  and dsj are photoelectric absorption coeffi-cient and absorption coefficient due to DS in jth layer, respectively, jd   is the thickness of jth layer, 0  is the direction cosine of the incident X-ray, b is the diffrac-tion asymmetry factor.  It should be remarked here that the absorption coef-ficients due to DS from several types of randomly dis-tributed defects without correlations between them are summarized, similarly to exponents of corresponding static Debye-Waller factors.  3. EXPERIMENTAL  Epitaxial single-crystalline YIG films with 5.33 µm thickness were grown by Czochralsky method on both sides of 500 µm thick GGG substrates with [111] growth axis. The samples after lapping were polished mechanically, chemo-dynamically, and chemically. The investigated samples have been implanted with F+ ions at the energy of 90 keV and with doses 131 10D , 136 10 , and 142 10  cm-2. Experimental RCs of the implanted samples were measured by using the high-resolution four-circle X-ray DCD with Cu tube (25 kV  25 mА) and two flat Ge (333) monochromators in the antiparallel setting. The symmetric (444) (see Fig. 1) and (888) reflections were used at the samples under investigation.  -600 -300 010-410-310-210-1, arcsecR444  Fig. 1 – Measured and calculated (solid line) RCs for 444 reflection of CuK 1 radiation from YIG/GGG film system im-planted with F+ ions (E = 90 keV) at doses D = 6 1012 cm2. Coherent and diffuse RC components are shown by dashed and dot-dashed lines, respectively   4. THE STRUCTURE MODEL OF THE IM-PLANTED YIG/GGG SYSTEM  For realization of quantitative diagnostics of imper-fect structure of a single-crystalline inhomogeneous system by X-ray diffraction methods it is necessary to use the adequate structural model. In garnet crystals, there always are present various point defects and growth microdefects, including new phase particles and dislocation loops (see, e.g., Ref. [18]. In garnet films, additionally to fluctuation strain fields from randomly distributed defects, the smooth inhomogeneous strain fields are created in transitional layers between film and substrate due to lattice mismatch [9].  After ion implantation, the subsurface layer of a film is additionally saturated with primary and secondary radiation defects, which are distributed inhomogeneously in depth and cause the corresponding «in average» inho-mogeneous strain. Separate isolated amorphous clusters that arise at bombardment of garnet films with light ions of intermediate energies are relatively stable [5, 6].    X-RAY DIFFRACTION CHARACTERIZATION OF NANOSCALE STRAINS… PROC. NAP 3, 01PCSI10 (2014)   01PCSI10-3 Thus, in the model of defect structure of the im-planted epitaxial single-crystalline system of YIG films grown on GGG substrate the presence of two types of microdefects, namely, spherical clusters and circular prismatic dislocation loops was supposed.  The influ-ence of point defects (antisite defects and anion vacan-cies) and thermal DS was taken into account as well [18]. The film system in whole was considered as a multilayer system in each layer of which the strain was consisted of average and fluctuating components. The change of YIG and GGG cubic lattice constants due to point defects was calculated according to empiric ana-lytical expression through concentrations of these de-fects and effective radii of cations [18].  When fitting theoretical RCs, the depth profiles of the strain caused by implantation were calculate through concentrations of the amorphous clusters formed by displaced matrix atoms in consequence of energy losses of the implanted ions [6]. The existence of two channels of energy losses for the implanted light ions was taken into account, namely, through excita-tion of electronic subsystem and through elastic nucle-ar collisions [10]. For electronic and nuclear channels channel this depth profile was set as a decreasing tail of Gaussian and asymmetric Gaussian, respectively.  Such characteristics of clusters in implanted layer as radius and strain at the boundary with crystal ma-trix were supposed to be equal for both channels. Re-sulting strain profile in implanted layer was calculated as the sum of depth-depended strain profiles created by the two distributions of cluster concentrations along the normal to crystal surface.  The depth profile of the so-called amorphization fac-tor was described in our diffraction model by only the static Debye-Waller factor, exponent of which was cal-culated through characteristics of clusters in implanted layer as well. Additionally, the attenuation of coherent component of diffraction intensity from the implanted layer was described by the coefficient of absorption due to DS dsj , which was calculated similarly through characteristics of clusters in implanted layer. Thus, the chosen model of imperfect structure of the implanted YIG film on GGG substrate provides physi-cally clear connection between defect characteristics and structurally sensitive diffraction parameters. Also, the self-consistent character of calculation of these parameters should be emphasized, what complements the self-consistency between coherent and diffuse com-ponents of diffraction intensity in the present diffrac-tion model.   5. TREATMENT AND DISCUSSION   The RC measured from a multilayer system like the implanted YIG film on GGG substrate is formed by a superposition of angular distributions of coherent and DS intensities from substrate, film, and implanted layer. Such superposition complicates the analysis of the RC for the assessment of strain and amorphization parameters in the implanted layer since the numerous additional fit parameters arise, which characterize defect structure of film and substrate.    On the other hand, the account for influence of DS effects from dislocation loops and clusters in film and substrate on the form of diffraction peaks and tails has allowed for both the determination of as-grown defect characteristics (see Table 1) and correct description of X-ray intensity diffracted from the implanted layer. Also, such account has provided the possibility to avoid systematical errors when determining strain and defect characteristics in this layer.  Table 1 – Characteristics of circular dislocation loops and spherical clusters in YIG film and GGG substrate   Defects Characteristics GGG substrate YIG film  Circular dislocation loops Radius, nm 90 5 5 Density, cm-3 1,2×1012  1×1015 1×1015 Spherical clusters Radius, nm 8 10 Density, cm-3 1×1014 1×1014  At modeling the strain distribution, the implanted layer was subdivided into 2 nm thick laminae, whereas the rest of film and substrate volume was subdivided into layers with thicknesses of order of few hundreds of nanometers. It was supposed that as a result of elec-tronic and nuclear energy losses of implanted ions the spherical amorphous clusters were formed in the im-planted layer. Their radii have been determined to be approximately 1.7 nm at the value of volume strain between cluster and crystal matrix ɛ  = 0.03. The corre-sponding cluster concentrations found at various im-plantation doses are given in Table 2.   Table 2 – Maximal values of cluster concentrations and strain profiles in YIG film implanted with F+ ions (E = 90 keV) at various implantation doses  D, cm–2 1 1013 6 1013 2 1014 nucl,maxCn , cm–3 1.1 1019 6 1019 2 1020 el,maxCn , cm–3 1.10 1019 6.00 1019 2.00 1020 nucl,max, % 0.10 0.54 1.79 el,max, % 0.04 0.22 0.73  It should be emphasized that values of the parame-ters that define the form of strain profile have been determined to be the same for all the implantation doses and both reflections measured (see Figs. 2 and 3).  Thus, the complete set of defect characteristics and strain parameters of the implanted layers in YIG films on GGG substrates has been determined by the fully dynamical self-consistent treatment of diffraction pro-files from the investigated samples simultaneously for two reflections. The self-consistentcy of the description of coherent and diffuse components of diffraction pat-terns has been achieved due to the fully dynamical interpretation from such systems becomes possible with, which are connected analytically with strain and defect characteristics. Additionally, the strain distribution in the transi-tion layer between film and substrate has been deter-mined, which thickness approaches some hundreds of nanometers (see Fig. 3).   S.I. OLIKHOVSKII, O.S. SKAKUNOVA, ET.AL. PROC. NAP 3, 01PCSI10 (2014)   01PCSI10-4 0 25 50 75 100 1250,000,250,50 3 21, %z, nm   Fig. 2 – Strain profiles in implanted layer of YIG film, which are caused by electronic (1), nuclear (2), and total (3)  energy loses of implanted  F+ ions (E = 90 keV, D = 6 1013 cm2)  10 100 1000 1000010-310-210-1100film substrate1,23123+0.1, % z, nm   Fig. 3 – Strain profiles in YIG/GGG film system implanted with F+ ions (E = 90 keV) at doses D = 1 1013 (1),   6 1013 (2), and 2 1014 cm2 (3), respectively.  6.  RESUME AND CONCLUSIONS  The theoretical diffraction model, based on the gen-eralized statistical dynamical theory of X-ray scatter-ing in imperfect crystals, has been proposed to describe RCs from imperfect film structures with randomly distributed defects and the inhomogeneous strain pro-file caused by ion implantation. The dynamical charac-ter of both coherent and diffuse components has been taken into account by means of recurrence relations between coherent scattering amplitudes of adjacent crystal layers. Thus, the fully dynamical interpretation of diffraction patterns from such systems becomes pos-sible with self-consistent description of the coherent and diffuse components, which are connected analyti-cally with strain and defect characteristics.  The proposed diffraction model has been applied to characterize defects and strains in the epitaxial YIG films grown on GGG substrate, which were implanted with of 90 keV F+ ions at various doses. Simultaneous treatment of the RCs measured by the high-resolution DCD with widely open detector window for two reflec-tions has provided the set of the parameters, which characterize both strain and defects in both implanted layer and YIG film on GGG substrate.    AKNOWLEDGEMENTS  This research was supported by the National Acad-emy of Sciences of Ukraine under contract No. 3.6.3.13-7/14-D.    REFERENCES  1. A.K. Zvezdin, V.A. Kotov, Modern Magnetooptics and Magnetooptical Materials (New York: Taylor & Francis Group: 1997). 2. T. Aichele, A. Lorenz, R. Hergt, P. Görnert, Cryst. Res. Technol.  38, 575 (2003). 3. T. Wehlus, T. Körner, S. Leitenmeier, A. Heinrich, B. Stritzker, phys. status solidi a 208, 252 (2011). 4. V.S. Speriosu, C.H. Wilts, J. Appl. Phys.  54, 3325 (1983).   5. B. Lagomarsino, A. Tucciarone, Thin Solid Films 114, 45 (1984).  6. P. Gerard, Nucl. Instrum. Meth. Phys. Res. B 19–20, 843 (1987), 7. V. S. Speriosu, J. Appl. Phys. 52, 6094 (1981). 8. C. R. Wie, T. A. Tombrello, T. Vreeland, Jr., J. Appl. Phys. 59, 3743 (1986). 9. M. Dimer, E. Gerdau, R.  Rüffer, H. D.  Rüter, W. Sturhahn, J. Appl. Phys. 79, 9090 (1996). 10. B.K. Ostafiychuk, V.D. Fedoriv, I.P. Yaremiy, O.Z., Garpul, V.V.  Kurovets, I.C. Yaremiy, phys. status solidi a 208, 2108 (2011).  11. R.N., Kyutt, P.V. Petrashen, L.M. Sorokin, phys. status solidi a 60, 381 (1980). 12. Yu.N. Belyaev, A.V.  Kolpakov, phys. status solidi a 76, 641 (1983). 13. V.I. Punegov, phys. status solidi a 136, 9 (1993). 14. P.K. Shreeman, R.J. Matyi, J. Appl. Cryst. 43, 550 (2010). 15. V.B. Molodkin, S.I. Olikhovskii, Ye.M. Kyslovskyy, I.M. Fodchuk, E.S. Skakunova, E.V. Pervak, V.V. Molod-kin, phys. status solidi a 204, 2606 (2007). 16. V.M. Pylypiv, S.I. Olikhovskii, T.P. Vladimirova, O.S. Skakunova, V.B. Molodkin, B.K. Ostafiychuk, Ye.M. Kyslovskyy, O.V. Reshetnyk, S.V. Lizunova, O.Z. Garpul’, Metallofiz. Noveishie Tekhnol. 33, 1145 (2011). 17. V.B. Molodkin, S.I. Olikhovskii, E.N. Kislovskii, TP. Vla-dimirova, E.S. Skakunova, R.F. Seredenko, B.V. Shelud-chenko, Phys. Rev. B 78, 224109 (2008). 18. V.M. Pylypiv, T.P. Vladimirova, I.M. Fodchuk, B.K. Ostafi-ychuk, Ye.M. Kyslovskyy, V.B. Molodkin, S.I. Olikhovskii, O.V. Reshetnyk, O.S. Skakunova, V.V. Lizunov, O.Z. Garpul’, phys. status solidi a 208, 2558 (2011).  

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X-Ray Diffraction Characterization of Nanoscale Strains and Defects in Yttrium Iron Garnet Films Implanted with Fluorine Ions

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