1. ELSEVIER Thin SolidFilms289 (1996) 49-53
Synthesis and Characterization
New application of classical X-ray diffraction methods for epitaxial film
characterization
W.J.A.M. Peterse, P.M.L.O. Scholte, A.J. Steinfort, F. Tuinstra
Faculty of Applied Physics, Delft Universityof Technology, Loren~weg !. 2628CJDelft. The Netherlands
Received23 November1995;accepted9 April 1996
Abstract
The quality of an epilayer is characterized by its in-plane misfit and orientation with respect to the substrate, its out-of-plane cell parameter,
its orientation distribution and its in-plane and out-of-plane strains. We adapted the Weisscnbergequi-inclinationgeometry such that combined
with a powder diffractometer it provides all the information mentioned, in two single scans. The powder diffractometer data are used to
determine the out-of-plane texture of the film, while the photographic Weissenberg film provides a complete overview of the in-plane
characteristics. The method can be performed with starglard laboratory equipment in a simple and reliable way. The method is illustrated with
four different epilayer/substrate systems.
Keywords: Epitaxy;Interfaces:Surfacestructure;X-raydiffraction
1. Introduction explored. As with all scanning diffractometers, efficie~,g~"
demands that only limited areas in reciprocal space are
scanned. A complete overview of the intensity distribution in
One of the main activities in the field of thin film and reciprocal space can hardly be obtained.
surface technology is the controlled deposition of thin films A photographic X-ray technique gives the opportunity to
onto well chosen monocrystaUine substrate surfaces. The map out the intensity distribution from a slice in reciprocal
thickness of these films may vary from a few monatomic space. For this purpose different types of camera have been
layers to several micrometres. The crystalline quality of the developed [ 1,2 ]. In the three most common types, the Weis-
layer and its relation to the substrate is of crucial importance senberg camera, the retigraph and the precession camera, the
for further experiments or applications. mapping is one to one. The thickness of the slice in reciprocal
The essential structural features that characterize epitaxial space can be adjusted by the width of an insmm~ntal slit.
films are the following. Because of the experimental limitations the Weissenberg
The relation between the crystal lattices of the substrate and method is preferred as it operates mainly in the reflection
epilayer: mode rather than in transmission mode. In contrast to the
1. the crystalline orientation of the subs~ate surface (its retigraph and the precession camera, the Weissenbergcamera
miller indices and the in-plane azimuth); produces distorted pictures of reciprocal space.
2. the orientation of the epilayer with respect to the substrate; In combination with a powder diffraction diagram an
3. the in-plane lattice parameters of the epilayer in compar- almost complete set of diffraction data of epilayer and sub-
ison with those of the substrate (the mismatch). strate can be collected.
Crystalline quality of the epilayer: The power of the method is illustrated with a series of
1. the texture (orientation distribution of crystallites); examples ranging from metal film on a semiconductor sub-
2. the crystallite size (size distribution); strate to high Tc superconductor film on an insulator substrate.
3. strain in the epilayer (lattice distortion).
For all these features X-ray diffraction techniques can be
used successfully. For this purpose detailed intensity infor- 2. Powder diffractometry
mation from an appreciable volume in the reciprocal space is
needed. With an advanced computer-controlled four-circle A powder diffactometer operating in the standard Bragg-
diffractometer, in principle the whole reciprocal space can be Brentano geometry (0-20 geometry) scans along one line in
0040-6090/96/$15.00 © 1996ElsevierScienceS.A.All rightsreserved
P11S0040-6090(96)08883-9

2. 50 W.J.A.M. Peterseet al. / Thin Solid Films289 (1996) 49-53
reciprocal space. The recorded diagram only presents reflec-
tions from planes parallel to the sample surface.
~ 1 f IO
The presence of texture (i.e. preferred orientation) in the ! ¢ !
epilayer is indicated by the presence of reflections in the
V
diagram indexed as an integer multiple of (h',k',l') only,
where (h',k',l') are the Miller indices of the epilayer. The
extent of the texture cannot be deduced from a powder
~agram.
Statements about the structural features of the epilayer, as
listed in Section 1, can hardly be made with the limited
information which a standard powder diffraction diagram
provides. T/le d~.ffractometer is well suited to determine accu-
lately the d-spacing of those planes which happen to be ori-
ented parallel to the substrate surface.
Islll
3. The Weissenberg technique Fig. I. The geometryof the equi-inclinationmode. A reciprocalplane V
parallelto the samplesurfaceis imagedon a filmdependingon the angleof
incidenceand the slit position.
In order to obtain detailed information of the in -plane char-
acteristics of the epilayer/substrate system, we used a Weis- the primary or the diffracted beam during certain parts of the
senberg single-crystal X-ray camera. Like the powder exposure.
diffractometer, this instrument is sturdy and reliable. It If a crystalline epilayer is deposited onto the substrate
requires a standard laboratory X-ray facility with an addi- surface, additional diffraction intensity from that epilayer will
tional dark room facility for handling the exposed X-ray films. be present. In our method the slit is now used as a microtome
The Weissenberg camera records in one exposure a thin in reciprocal space, so the diffraction of the depositedepilayer
flat slice of reciprocal space. It has been used extensively as can be explored systematically. In the most simple case the
a tool for structure determinations by recording all reflections crystalline epilayer and the substrate both have a real lattice
in successive reciprocal lattice planes on a film, and subse- vector parallel to the camera axis so the reciprocal planes are
quently measuring one by one the integrated intensities of the perpendicular to the camera axis. In that ease a few situations
reflections. can be distinguished.
In the present setting we are not so much interested i n • Coinciding lattices: the reciprocal lattices of substrate and
precise intensity data of reflections but rather in the mutual epilayer are identical and coincide.
positions of the reflections of substxate and epilayer, their • Laterally coinciding lattices: the reciprocal planes perpen-
systematic absences and their widths and profiles. dicular to the camera axis are identical and coincide, out-
In the Weissenberg method the sample oscillates around of-plane the real lattice dimensions differ.
the axis of a cylindrical film. The rotation of the sample is • Laterally non-coinciding lattices: the reciprocal planes
coupled with an axial shift of the film in front of which a slit perpendicular to the camera axis differ, out-of-plane the
selects a specific slice in reciprocal space. Fig. 1 gives an real lattice dimensions are identical.
overview of the geometry of the equi-inclination mode which • Non-coinciding lattices: the reciprocal planes perpendic-
is most suited to the present purpose. For a detailed descrip- ular to the camera axis as well as the out-of-plane real
tion we refer to the literature [ 1]. lattice dimensions differ.
The crystal, mounted on the goniomcter head of the cam- Coinciding lattices will for instance occur in the case of
era, is oriented such that a real lattice vector [ uvw] coincides homoepitaxy, but also when the difference between the lattice
with the rotation axis of the camera. In that case two reciprocal parameters is smaller than the resolution of the camera. The
vectors exist lying in a plane perpendicular to the rotation reflections due to substrate and epilayer cannot be inspected
axis. Such a plane is called a reciprocal layer. Consecutive separately but comparison with an X-ray photograph of the
layers can be mapped out successively onto photographic bare substrate can reveal the contribution of the epilayer.
films. Their separation, being inversely proportional to the Additional diffuse scattering around the substrate Bragg spots
length of the real lattice vector [uvw] can be measured is an indication of non-ideal crystal quality of the epilayer.
directl) from a rotation photograph, i.e. an exposure taken A superstructure of the epilayer will show up in extra
without the slit and with stationary film. Since the primary reflections.
X-ray beam is reflected off the surface, only half of the recip- If in the case of laterally coinciding lattices the out-of-
rocal space can be mapped out, provided that the crystal plane lattice dimensions of the epilayer and the substrate
surface also is perpendicular to the rotation axis, which is differ sufficiently, depending on the value of the slit width,
nearly always the case. Otherwise the crystal will intercept separate equi-inclination exposures can be made for substrate

3. W.J.A.M.Peterseet al. I ThinSolid Films289 (1996)49-53 51
and epilayer. A comparison between the two reciprocal lat- lattice vector perpendicular to the substrate surface will these
tices on different photographs is not so easy to make. It is shadowing effects occur in the higher layers.
however possible to record both reciprocal layers on one
single film in two successive exposures, in between only
adjusting the equi-inclinationangle and the slit positions, not s. ApOieneo~
changing the orientation of either crystal or film. If the dis-
tance is too small to allow for separate exposures, the slit can
The described characterization technique was applied to a
be made wide enough to record both layers in one single film
variety of substrate/epilayer systems. In this section we
exposure. In this case the reciprocal lattices do not coincide
report a few illustrative examples of the four cases listed
because the reciprocal layers which differ in height intersect above. The layer thickness of all examples is between 100
the Ewald sphere in different planes. The radius of the inter-
and 200 nm.
secting circle is the magnification factor for the mapping of
the layer onto the Weissenberg film. Thus, although the in-
plan~,reciprocal lattices of substrate and epilayer are the same, 5.1. Coinciding lattices: YBa,Cu~OT_xfilm on a substrate
their reflections are recorded on different places on the film. of NdGaO~
The width of the epilayer reflections compared with the sub-
strate reflections gives an indication of the crystallineperfec- Crystal structure. The NdGaO3 substrate has an ortho-
tion of the epilayer. rhombic distorted perovskite structure with a--5.431 ~,
In the case of laterally non-coincidinglattices, diagrams of b=5.499 A and c--7.717 A [3].
reciprocal layers of the substrate and the thin epilayer can be With respect to the standard axes of the aristotype structure
recorded in one exposure since the out-of-plane parameters the axes should be taken along [110], [110] and [001]
are identical. As the reflections of the substrate and the thin respectively. This results in a monuelinic body-centred
epilayer do not coincide, the lattice mismatch and the relative pseudo cubic Bravais lattice with a ' = c ' = 7 . 7 2 9 1;,, b'=~
in-plane orientation of the two lattices can be found accurately 7.717 ~ and/3=90.70°. The unit cell contains eight original
from the relative positions of these reflections. perovskite cubes. The substrate is (100) oriented in the mow
In the case of non-coinciding lattices, both the reciprocal oclinic description.
layers of the substrate and the epilayer can he recorded on The modification of YBa2Cu307_x under considcratioR
one single film as described above. We have developed a is orthorhombic with a=3.325 A, b=3.886 ,~ and c=
computer program which can simulate the photographs for ll.C,~0 A.
different relative in-plane orientations taking into account the Results. From a rotational photograph the epilayer is found
instrumental distortions in these cases. Fitting the simulation to have (001) orientation, so the periodicity perpendicularto
to the observed photographs we can find both the relative in- the surface is 11.6 ]~ (approximately 3×3.88 A). Fox
plane orientation and the misfit of the lattices. NdGaO3 the periodicity is 7.729 ~ (approximately 2 × 3.86
A). so the reciprocal layers ( 2 n k l ) of lqdGaOs are super-
imposed on (h k 3m) of YBa2Cu30.:_x (n, m integers).
4. Experimental details Weissenherg photographs of the layers (3 k l) of NdGaO3
and ( h k 5 ) of YBa2Cu3OT_x on the conU'ary can be taken
We applied the equi-inclination geometry to a standard separately. However, the reflections in these layers are
Weissenberg camera, as it operates in the reflection mode. weak as they are due to the deviation of the cubic aristotype
The radiation was Cu Ka filtered with a graphite monochro- stracun'e.
mator. The beam was taken from a standard X-ray generator The results are taken from Weissenberg photographs of
fitted with a commercial tube and run at 40 kV and 20 mA. the superimposed layers of substrate and epilayer: I (2 k l)
The sample was a small slab of the substrate 1 x I cm?, +(hk3)}; {(4kt)+(hkt)} and { ( 6 k l ) + ( h k 9 ) } . A
mounted on a standard goniometer head and oriented perpen- perfect lattice match between the epilayer and the substrate
dicular to the camera axis. First a few rotation pictures are is found where the [ 100] direction of the epilayer is parallel
taken to adjust the orientation of the sample. From these to the [010] direction of the substrate. Reflections of
photographs the setting and width of the slit and the inclina- YBa2Cu30.t _x seem to be slightly less sharp than reflections
tion angle for each reciprocal layer can also be determined. of the substrate; however, they certainly cannot be regarded
We recorded first and higher reciprocal layers; the equator is as diffuse. The epilayer is close to monocrystalline.
just below the horizon. The exposure times ranged from a
few hours to 64 h, depending on the intensity of the diffraction 5.2. Laterally coinciding lattices: PbTiO3]ilm on a
effects to he observed. The exposures can run unattended. substrate of SrTiOj
With the equi-inclination setting all reflections can he
recorded unless the reflected beam is intercepted by the sam- Crystal description. SU'ontium titanatc substrate has the
ple, which mostly only occurs for the zeroth layer line (the cubic perovskite structure with a = 3.905 A. The substrate
equator). Only in cases where substrate and epilayer have no surface is (001) oriented. The )ead titanate epilayer is tetrag-

4. 52 W.J.A.M. Peterseet al. / ThinSolidFilms289 (1996) 49-53
×
x+ x+ a,.
x, ×
x+ x
+
~+ ~+ x+ x
x
-F
x
+ x
-I-
Fig.2. Reflectionsof a perfectreciprocalplaneofa layerof PbTiO3superimposedon a reciprocalplaneof a SrTiO3substrateshowntogetherwiththe simulation.
The + signcorrespondsto the subslrateand the × signcorrespondsto the perfectPbTiO3layer.
onal pseudo cubic with a = 3.905 A. and c = 4.156/~ [4 ] and Fig. 3. The Weissenberg photograph shows sharp reflections
the structure is of a distorted perovskite type. coming from the substrate and weak broadened reflections
Results. PbTiO3 film is known to grow perfectly on the from the epilayer. Reflections from two different orientations
(001) face of SrTiO~. Owing to the difference in the lengths of the epilayer are present, for one of which the cubic edges
of the c-axes, reciprocal layers perpendicular to the c*-axis (100) are parallel to the a-axis of MgO and the (i'10) direc-
intersect the Ewaid sphere at different heights. We have tion is parallel to the b-axis and for the other rotated 90 ° about
superimposed exposures of the ( h k 3 ) layers of the substrate (011 ). Moreover, with respect to the MgO lattice, the in-
and the epilayer on the same Weissenberg film by changing plane width of the diffuse reflections indicates an angular
the inclination angle and the position of the selecting slit spread of the crystallites in the epilayer of some 10°.
between subsequent exposures. Fig. 2 shows the Weissen-
berg picture together with a computer simulation of the reflec- 5.4. Incoherent lattices: aluminium on silicon
tion positions to be expected on such a film. The two equal
reciprocal two-dimensional nets appear at different positions Crystal description. A! has f.c.c, packing with a=4.049
on the film. The epilayer is found to be c oriented, i.e. the c- A., and Si has the diamond structure with a = 5.431 A [ 6] so
axis is oriented perpendicular to the substrate surface. From the lattices are laterally incoherent. The substrate surface is
the Weissenberg photograph shown in Fig. 2 it is seen that 111 ) oriented.
the sharpness of all the Bragg spots is of the same monocrys- Results. From a rotational photograph A! is found to grow
talline quality. The simulated image coincides perfectly with in the [ 11 ! ] orientation onto Si[ 111 ]. The layers in recip-
the photographic recording, so the relative positions of the rocal space parallel to the substrate surface contain reflections
spots indicate that there is no misfit and no misorientation. with h + k + l = c o n s t a n t and as the periodicity along the
[ 111 ] direction is different for Ai and Si, diffraction from
5.3. Laterally non-coinciding lattices: SmBazCu304film on epilayer and substrate can be recorded separately. A photo-
a substrate o f MgO graph was taken of tile layer h + k + l = 5 of Si superimposed
nn h + k + l = 4 of AI. This photograph shows perfect epitaxial
Crystal desc;iption. The substrate has the NaCi structure growth in the orientation as described above. Although the
with a=4.213 A, and the surface is (001) oriented. in-plane lattice parameters do not fit, the orientation of A1 is
SmBaCuO is orthorhombic with a = 3.91 A., b= 3.85 A, found to form a superceil in which the lattices coincide. In
c = 11.73 A (c = 3 × 3.91 A). Having a perovskite-like struc- this superceli the vector [303] of Si coincides with [404] of
ture, SmBaCuO on average can be considered to be cubic Al and [ 330] of Si coincides with [440] of Ai. The misfit of
[5]. The difference with the true lattice is revealed in the this superlattice is only 0.6%. The sharp reflections on the
presence of weak satellite r~flections which in this case were photograph coming from the thin Ai layer indicate a perfect
too weak to be observed. monocrystalline layer.
Results. The epihtyer is found to be (011 ) oriented, so the The examples show that the epilayer characteristics can be
reciprocal layers of SmBa2Cu304 perpendicular to the (0 ! 1) obtained in an easy fashion for all cases. In the cases where
contain reflections with k = - h . This reciprocal layer the lattices do coincide laterally, no relative rotation is found
(h h l) of the epilayer and the reciprocal layer 1=2 of between the principle axes of the two lattices, and the angular
MgO are superimposed on one Weissenberg photograph, see spread indicates perfect epitaxial growth. For the case of

5. W..I.A.M. Peterse el al. /Thin Sofid Films 289 (1996) 49-53
4~"
x÷ ++
x
× X ++ X
i
-+.
X+ X +X
+
×
+ + X
4g
+
+ ÷×
× ×
x + ÷ ×+
+
÷
+
x × -.,-
.p
Fig. 3. A recordingof the ( h/~ !) plane of a thin layer of SmBaCuOsul2eaimpo~tedo~ the (h k 2) plane of an MgO substratecompav~ wilh a conespondL¢g
simttlationof this system.The + siga correspondsto the s,lbstrateand the + and × signs correspondto the two independentorientationsof SmBaCuO.Note
the broadeningof the spots.
SmBa2Cu304 on a substrate of MgO where the lattices do not University o f Technology, The Netherlands for the alumin-
coincide laterally any more, two preferred orientations are ium on silicon sample, Philips Research, Laboratories for the
present which are both directed along the principle axis o f PbTiO3 on SrTiO3 sample, and the Supercotklucfivity Lab-
the substrate surface, ltowever, the two present directions oratory, 1C'I'P, Triest, Italy tbr the YBa2Cu3OT- ~ on NdGaO3
have a large angular spread which indicates epitaxial quality sample.
far from perfect. In the last case where the lattices of the AI
epilayer and the Si substrate do not coincide, a lattice match
is found in a (3vf2 × 3~'2)R45 superceli with a mismatch of References
only 0.6%, The epilayer is indeed found to he in this orien- [ I ] J. Buerger, X-RayCrystallography, Wiley, New York, 1966, 7th ada.
tation and from the width o f the reflections the epilayer is [2] MJ. Buerger,The Precession Method, Wiley, New York, 1964,
found to he perfect. 13] R.W.G.Wyckoff,Crystal Structures, Vol. II, Wiley, New York, 1965,
2nd adn.
[4] A.M.Glazer and S.A. Mabnd,Acta Crystallogr. B, 34 (1978) 1065.
[5] .I.M. Appelboonk V.C. Matijasevic, F. Mathu, G. Rier~eld, B.
Acknowledgements Anczykowski,W.J.A.M. Peterse,F. Tuinstra, J.E. Mooij, W.G. SIoof,
H. Rijken, S.S. Klein and LJ. van Yzcndoom,Physica C, 214 (1993)
323-334.
The samples used in this analysis originate from different [6] R.W.G. Wyckoff,Crystal Structures, Vol. I, Wiley, New York, 1965,
sources. We would like to thank the DIMES Institute, Delft 2nd adn.