E L S E V I E R Thin Solid Films 289 (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 University of Technology, Loren~weg !. 2628CJ Delft. The Netherlands

Received 23 November 1995; accepted 9 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 Weisscnberg equi-inclination geometry 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: Surface structure; X-ray diffraction

1. Introduct ion

One of the main activities in the field of thin film and surface technology is the controlled deposition of thin films onto well chosen monocrystaUine substrate surfaces. The thickness of these films may vary from a few monatomic layers to several micrometres. The crystalline quality of the layer and its relation to the substrate is of crucial importance for further experiments or applications.

The essential structural features that characterize epitaxial films are the following. The relation between the crystal lattices of the substrate and epilayer: 1. the crystalline orientation of the subs~ate surface (its

miller indices and the in-plane azimuth); 2. the orientation of the epilayer with respect to the substrate; 3. the in-plane lattice parameters of the epilayer in compar-

ison with those of the substrate (the mismatch). Crystalline quality of the epilayer: 1. the texture (orientation distribution of crystallites); 2. the crystallite size (size distribution); 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- mation from an appreciable volume in the reciprocal space is needed. With an advanced computer-controlled four-circle diffractometer, in principle the whole reciprocal space can be

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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 reciprocal space can hardly be obtained.

A photographic X-ray technique gives the opportunity to map out the intensity distribution from a slice in reciprocal space. For this purpose different types of camera have been developed [ 1,2 ]. In the three most common types, the Weis- senberg camera, the retigraph and the precession camera, the mapping is one to one. The thickness of the slice in reciprocal space can be adjusted by the width of an insmm~ntal slit. Because of the experimental limitations the Weissenberg method is preferred as it operates mainly in the reflection mode rather than in transmission mode. In contrast to the retigraph and the precession camera, the Weissenbergcamera produces distorted pictures of reciprocal space.

In combination with a powder diffraction diagram an almost complete set of diffraction data of epilayer and sub- strate can be collected.

The power of the method is illustrated with a series of examples ranging from metal film on a semiconductor sub- strate to high Tc superconductor film on an insulator substrate.

2. Powder diffractometry

A powder diffactometer operating in the standard Bragg- Brentano geometry (0-20 geometry) scans along one line in

50 W.J.A.M. Peterse et al. / Thin Solid Films 289 (1996) 49-53

reciprocal space. The recorded diagram only presents reflec- tions from planes parallel to the sample surface.

The presence of texture (i.e. preferred orientation) in the epilayer is indicated by the presence of reflections in the 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.

3. The Weissenberg technique

In order to obtain detailed information of the in -plane char- acteristics of the epilayer/substrate system, we used a Weis- senberg single-crystal X-ray camera. Like the powder diffractometer, this instrument is sturdy and reliable. It requires a standard laboratory X-ray facility with an addi- tional dark room facility for handling the exposed X-ray films.

The Weissenberg camera records in one exposure a thin flat slice of reciprocal space. It has been used extensively as a tool for structure determinations by recording all reflections in successive reciprocal lattice planes on a film, and subse- quently measuring one by one the integrated intensities of the reflections.

In the present setting we are not so much interested in precise intensity data of reflections but rather in the mutual positions of the reflections of substxate and epilayer, their systematic absences and their widths and profiles.

In the Weissenberg method the sample oscillates around the axis of a cylindrical film. The rotation of the sample is coupled with an axial shift of the film in front of which a slit selects a specific slice in reciprocal space. Fig. 1 gives an overview of the geometry of the equi-inclination mode which is most suited to the present purpose. For a detailed descrip- tion we refer to the literature [ 1 ].

The crystal, mounted on the goniomcter head of the cam- era, is oriented such that a real lattice vector [ uvw] coincides with the rotation axis of the camera. In that case two reciprocal vectors exist lying in a plane perpendicular to the rotation axis. Such a plane is called a reciprocal layer. Consecutive layers can be mapped out successively onto photographic films. Their separation, being inversely proportional to the length of the real lattice vector [uvw] can be measured directl) from a rotation photograph, i.e. an exposure taken without the slit and with stationary film. Since the primary X-ray beam is reflected off the surface, only half of the recip- rocal space can be mapped out, provided that the crystal surface also is perpendicular to the rotation axis, which is nearly always the case. Otherwise the crystal will intercept

~ 1 f IO ! ¢ !

V

Islll Fig. I. The geometry of the equi-inclination mode. A reciprocal plane V parallel to the sample surface is imaged on a film depending on the angle of incidence and the slit position.

the primary or the diffracted beam during certain parts of the exposure.

If a crystalline epilayer is deposited onto the substrate surface, additional diffraction intensity from that epilayer will be present. In our method the slit is now used as a microtome in reciprocal space, so the diffraction of the depositedepilayer can be explored systematically. In the most simple case the crystalline epilayer and the substrate both have a real lattice vector parallel to the camera axis so the reciprocal planes are perpendicular to the camera axis. In that ease a few situations can be distinguished. • Coinciding lattices: the reciprocal lattices of substrate and

epilayer are identical and coincide. • Laterally coinciding lattices: the reciprocal planes perpen-

dicular to the camera axis are identical and coincide, out- of-plane the real lattice dimensions differ.

• Laterally non-coinciding lattices: the reciprocal planes perpendicular to the camera axis differ, out-of-plane the real lattice dimensions are identical.

• Non-coinciding lattices: the reciprocal planes perpendic- ular to the camera axis as well as the out-of-plane real lattice dimensions differ. Coinciding lattices will for instance occur in the case of

homoepitaxy, but also when the difference between the lattice parameters is smaller than the resolution of the camera. The reflections due to substrate and epilayer cannot be inspected separately but comparison with an X-ray photograph of the bare substrate can reveal the contribution of the epilayer. Additional diffuse scattering around the substrate Bragg spots is an indication of non-ideal crystal quality of the epilayer. A superstructure of the epilayer will show up in extra reflections.

If in the case of laterally coinciding lattices the out-of- plane lattice dimensions of the epilayer and the substrate differ sufficiently, depending on the value of the slit width, separate equi-inclination exposures can be made for substrate

W.J.A.M. Peterse et al. I Thin Solid Films 289 (1996) 49-53 51

and epilayer. A comparison between the two reciprocal lat- tices on different photographs is not so easy to make. It is however possible to record both reciprocal layers on one single film in two successive exposures, in between only adjusting the equi-inclination angle and the slit positions, not changing the orientation of either crystal or film. If the dis- tance is too small to allow for separate exposures, the slit can be made wide enough to record both layers in one single film exposure. In this case the reciprocal lattices do not coincide because the reciprocal layers which differ in height intersect the Ewald sphere in different planes. The radius of the inter- 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, their reflections are recorded on different places on the film. The width of the epilayer reflections compared with the sub- strate reflections gives an indication of the crystalline perfec- tion of the epilayer.

In the case of laterally non-coinciding lattices, diagrams of reciprocal layers of the substrate and the thin epilayer can be recorded in one exposure since the out-of-plane parameters are identical. As the reflections of the substrate and the thin epilayer do not coincide, the lattice mismatch and the relative in-plane orientation of the two lattices can be found accurately from the relative positions of these reflections.

In the case of non-coinciding lattices, both the reciprocal layers of the substrate and the epilayer can he recorded on one single film as described above. We have developed a computer program which can simulate the photographs for different relative in-plane orientations taking into account the instrumental distortions in these cases. Fitting the simulation to the observed photographs we can find both the relative in- plane orientation and the misfit of the lattices.

4. Experimental details

We applied the equi-inclination geometry to a standard Weissenberg camera, as it operates in the reflection mode. The radiation was Cu Ka filtered with a graphite monochro- mator. The beam was taken from a standard X-ray generator fitted with a commercial tube and run at 40 kV and 20 mA. The sample was a small slab of the substrate 1 x I cm ?, mounted on a standard goniometer head and oriented perpen- dicular to the camera axis. First a few rotation pictures are taken to adjust the orientation of the sample. From these photographs the setting and width of the slit and the inclina- tion angle for each reciprocal layer can also be determined. We recorded first and higher reciprocal layers; the equator is just below the horizon. The exposure times ranged from a few hours to 64 h, depending on the intensity of the diffraction effects to he observed. The exposures can run unattended. With the equi-inclination setting all reflections can he recorded unless the reflected beam is intercepted by the sam- ple, which mostly only occurs for the zeroth layer line (the equator). Only in cases where substrate and epilayer have no

lattice vector perpendicular to the substrate surface will these shadowing effects occur in the higher layers.

s. ApOieneo~

The described characterization technique was applied to a variety of substrate/epilayer systems. In this section we report a few illustrative examples of the four cases listed above. The layer thickness of all examples is between 100 and 200 nm.

5.1. Coinciding lattices: YBa,Cu~OT_xfilm on a substrate of NdGaO~

Crystal structure. The NdGaO3 substrate has an ortho- rhombic distorted perovskite structure with a--5.431 ~, b=5.499 A and c--7.717 A [3].

With respect to the standard axes of the aristotype structure the axes should be taken along [110], [110] and [001] respectively. This results in a monuelinic body-centred pseudo cubic Bravais lattice with a '=c '=7.729 1;,, b'=~ 7.717 ~ and/3=90.70 °. The unit cell contains eight original perovskite cubes. The substrate is (100) oriented in the mow oclinic description.

The modification of YBa2Cu307_ x under considcratioR is orthorhombic with a=3.325 A, b=3.886 ,~ and c= ll.C,~0 A.

Results. From a rotational photograph the epilayer is found to have (001) orientation, so the periodicity perpendicular to the surface is 11.6 ]~ (approximately 3×3.88 A). Fox NdGaO3 the periodicity is 7.729 ~ (approximately 2 × 3.86 A). so the reciprocal layers (2nk l ) of lqdGaOs are super- imposed on (h k 3m) of YBa2Cu30.:_x (n, m integers). Weissenherg photographs of the layers (3 k l) of NdGaO3 and (hk5 ) of YBa2Cu3OT_ x on the conU'ary can be taken separately. However, the reflections in these layers are weak as they are due to the deviation of the cubic aristotype stracun'e.

The results are taken from Weissenberg photographs of the superimposed layers of substrate and epilayer: I (2 k l) + ( h k 3 ) } ; { ( 4 k t ) + ( h k t ) } and { ( 6 k l ) + ( h k 9 ) } . A perfect lattice match between the epilayer and the substrate is found where the [ 100] direction of the epilayer is parallel to the [010] direction of the substrate. Reflections of YBa2Cu30.t _x seem to be slightly less sharp than reflections of the substrate; however, they certainly cannot be regarded as diffuse. The epilayer is close to monocrystalline.

5.2. Laterally coinciding lattices: PbTiO3]ilm on a substrate of SrTiOj

Crystal description. SU'ontium titanatc substrate has the cubic perovskite structure with a = 3.905 A. The substrate surface is (001) oriented. The )ead titanate epilayer is tetrag-

52 W.J.A.M. Peterse et al. / Thin Solid Films 289 (1996) 49-53

× a,. x+ x+

x, × x+ x

+ ~+ ~+ x + x

x -F

x + x -I-

Fig. 2. Reflections of a perfect reciprocal plane of a layer of PbTiO3 superimposed on a reciprocal plane of a SrTiO3 substrate shown together with the simulation. The + sign corresponds to the subslrate and the × sign corresponds to the perfect PbTiO3 layer.

onal pseudo cubic with a = 3.905 A. and c = 4.156/~ [4 ] and the structure is of a distorted perovskite type.

Results. PbTiO3 film is known to grow perfectly on the (001) face of SrTiO~. Owing to the difference in the lengths of the c-axes, reciprocal layers perpendicular to the c*-axis intersect the Ewaid sphere at different heights. We have superimposed exposures of the ( h k 3 ) layers of the substrate and the epilayer on the same Weissenberg film by changing the inclination angle and the position of the selecting slit between subsequent exposures. Fig. 2 shows the Weissen- berg picture together with a computer simulation of the reflec- tion positions to be expected on such a film. The two equal reciprocal two-dimensional nets appear at different positions on the film. The epilayer is found to be c oriented, i.e. the c- axis is oriented perpendicular to the substrate surface. From the Weissenberg photograph shown in Fig. 2 it is seen that the sharpness of all the Bragg spots is of the same monocrys- talline quality. The simulated image coincides perfectly with the photographic recording, so the relative positions of the spots indicate that there is no misfit and no misorientation.

5.3. Laterally non-coinciding lattices: SmBazCu304film on a substrate o f MgO

Crystal desc;iption. The substrate has the NaCi structure with a=4.213 A, and the surface is (001) oriented. SmBaCuO is orthorhombic with a= 3.91 A., b= 3.85 A, c = 11.73 A (c = 3 × 3.91 A). Having a perovskite-like struc- ture, SmBaCuO on average can be considered to be cubic [5]. The difference with the true lattice is revealed in the presence of weak satellite r~flections which in this case were too weak to be observed.

Results. The epihtyer is found to be (011 ) oriented, so the reciprocal layers of SmBa2Cu304 perpendicular to the (0 ! 1 ) contain reflections with k = - h . This reciprocal layer (h h l) of the epilayer and the reciprocal layer 1=2 of MgO are superimposed on one Weissenberg photograph, see

Fig. 3. The Weissenberg photograph shows sharp reflections coming from the substrate and weak broadened reflections from the epilayer. Reflections from two different orientations of the epilayer are present, for one of which the cubic edges (100) are parallel to the a-axis of MgO and the (i'10) direc- tion is parallel to the b-axis and for the other rotated 90 ° about (011 ). Moreover, with respect to the MgO lattice, the in- plane width of the diffuse reflections indicates an angular spread of the crystallites in the epilayer of some 10 °.

5.4. Incoherent lattices: aluminium on silicon

Crystal description. A! has f.c.c, packing with a=4.049 A., and Si has the diamond structure with a = 5.431 A [ 6] so the lattices are laterally incoherent. The substrate surface is

111 ) oriented. Results. From a rotational photograph A! is found to grow

in the [ 11 ! ] orientation onto Si[ 111 ]. The layers in recip- rocal space parallel to the substrate surface contain reflections with h+k+l=cons tan t and as the periodicity along the [ 111 ] direction is different for Ai and Si, diffraction from epilayer and substrate can be recorded separately. A photo- 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 growth in the orientation as described above. Although the in-plane lattice parameters do not fit, the orientation of A1 is found to form a superceil in which the lattices coincide. In this superceli the vector [303] of Si coincides with [404] of Al and [ 330] of Si coincides with [440] of Ai. The misfit of this superlattice is only 0.6%. The sharp reflections on the photograph coming from the thin Ai layer indicate a perfect monocrystalline layer.

The examples show that the epilayer characteristics can be obtained in an easy fashion for all cases. In the cases where the lattices do coincide laterally, no relative rotation is found between the principle axes of the two lattices, and the angular spread indicates perfect epitaxial growth. For the case of

W..I.A.M. Peterse el al. /Thin Sofid Films 289 (1996) 49-53

4~"

×

-+.

× +

4g

x

+ x

. p

x÷ ++ x

X ++ X

i

X + X +X +

+ X

+ + ÷×

× × ÷ ×+ + + ÷

× -.,-

Fig. 3. A recording of the ( h/~ !) plane of a thin layer of SmBaCuO sul2eaimpo~ted o~ the (h k 2) plane of an MgO substrate compav~ wilh a conespondL¢g simttlation of this system. The + siga corresponds to the s,lbstrate and the + and × signs correspond to the two independent orientations of SmBaCuO. Note the broadening of the spots.

SmBa2Cu304 on a substrate of MgO where the lattices do not coincide laterally any more, two preferred orientations are present which are both directed along the principle axis o f the substrate surface, l towever, the two present directions have a large angular spread which indicates epitaxial quality 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 only 0.6%, The epilayer is indeed found to he in this orien- tation and from the width of the reflections the epilayer is found to he perfect.

Acknowledgements

The samples used in this analysis originate from different sources. We would like to thank the DIMES Institute, Delft

University of Technology, The Netherlands for the alumin- ium on silicon sample, Philips Research, Laboratories for the PbTiO3 on SrTiO3 sample, and the Supercotklucfivity Lab- oratory, 1C'I'P, Triest, Italy tbr the YBa2Cu3OT- ~ on NdGaO3 sample.

R e f e r e n c e s

[ I ] J. Buerger, X-Ray Crystallography, Wiley, New York, 1966, 7th ada. [2] MJ. Buerger, The Precession Method, Wiley, New York, 1964, 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.

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.

[6] R.W.G. Wyckoff, Crystal Structures, Vol. I, Wiley, New York, 1965, 2nd adn.