The Rigaku Journal Vol. 16/ number 1/ 1999 Technical Note DETERMINATION OF THE ORIENTATION OF AN EPITAXIAL THIN FILM BY A NEW COMPUTER PROGRAM CrystalGuide R. YOKOYAMA AND J. HARADA X-Ray Research Laboratory, Rigaku Corporation, Akishima-shi, Tokyo, 196-8666 Japan The technique to determine the crystallographic orientation matrix, which has been commonly used in the X-ray structure analysis of single crystal, has proved to be very powerful in the characterization of epitaxial thin films. This technique facilitates us to find out any reflection from the thin film mounted on a diffractometer. In particular, asymmetrical reflection conditions are helpfully found out by the present method. Moreover the diffractometer is directly set up to any scattering conditions such as the grazing incidence condition which is needed in the stress measurement of the films. 1. Introduction With the recent rapid growth of thin film technology in semiconductor devices, X-ray diffractometry has been focused on as an important technique to characterize the crystalline quality, because of its non-destructivity. In order to characterize the thin film, the following measurements have been implemented; the measurements of rocking curve, reflectivity and reciprocal mapping. It is required to set diffractometer in the condition of grazing incident X-ray diffraction (GIXD). Although there are many papers related to GIXD in thin film characterization since early 1980, only the following paper is sited here due to the limited space. B. L. Ballard and P. K. Predecki (1995) [1] showed that it is essential to study the biaxial stresses of thin film by using GIXD. In the structure analysis based on a single crystal mounted on a four-circle diffractometer it is well known that various Bragg conditions can be calculated by using a crystallographic orientation matrix. W. R. Busing and H. A. Levy (1967) [2] introduced the UB matrix, where U and B are the crystallographic orientation matrix and the reciprocal lattice matrix, respectively. These matrices can calculate the setting condition of a diffractometer for any Bragg reflections from a single crystal. This technique is so convenient that it has been widely utilized not only for the measurement of Bragg reflections but also for the measurement of diffuse scattering, when a four-circle diffractometer is used. Such an example is seen in the study by Harada, Iwata and Oshima (1984) [3]. Thus, once the crystallographic orientations of a thin film and its substrate are determined, it is expected to set easily a diffractometer for any special scattering condition such as the grazing incidence and to avoid non-measurable areas due to thd'geometry of a diffractometer as well. We recently programmed a computer software to control Rigaku diffractometers, ATX-series on the basis of this idea. This computer software 'CrystaIGuide' is programmed in such a way that it generates appropriate reflections from an epitaxial thin film to determine the crystallographic orientation of a thin film, then such reflections are searched to find out automatically and the reflections found out are finally assigned to their proper indices. On the basis of the orientation matrix determined by this process the control of the diffractometer was made easy to set any desired diffraction conditions. In this paper, the procedure of the determination of UB matrix of a thin film and the assignment of the reflections found out are presented. Finally the result obtained by applying this computer software to an epitaxial film specimen Mn 3 O 4 /MgO is presented and the accuracy of the results is discussed 2. Generation of Reference Reflections In order to determine the crystallographic orientation of a single crystal specimen it is required to measure precisely the peak positions of several Bragg reflections. In the case of thin films, however, not only the divergence but also the geometry of the 46 The Rigaku Journal
Fig. 1. Area exposed by the incident X-rays on a plate-like specimen. (a) the side view: projection along the χ-plane. (b) the top view; projection on the equatorial plane. incident beam to the thin film and that of the diffracted beam from it play a significant role in the determination of the peak positions. Fig. 1 illustrates such an example where the tilt angle a is defined as the angle between the surface normal of the specimen and a scattering vector. We see that the area exposed by the incident beam becomes wide for a large a. Consequently, the detector may happen to receive X-rays from the wide area of the specimen. We may lose the intensity in addition to getting a poor resolution in some cases. It is therefore recommended to select the Bragg reflections closer to in a symmetrical diffraction condition whose tilt angle is equal to zero degree. Moreover, the reflections with large structure factors are necessary to be used for this technique as shown in Fig. 2 since the X-ray diffraction intensities from thin films are usually fairly weak. Thus, the following two conditions are required to set in the determination of the crystallographic orientation of an epitaxial thin film. (i) Reflections with smaller tilt angles. (ii) Reflections with large structure factors. Fig. 2. The tilt angle α in the reciprocal lattice. It is defined as the angle between the surface normal and the reciprocal lattice vector of a Bragg reflection. Spots show the Bragg positoins with their structure factors. Vol. 16 No. 1 1999 47
In the software to control the Rigaku diffractometers, ATX-series, the generation of the Bragg reflections used to determine the crystallographic orientation of an epitaxial thin film has been so programmed as to fulfill above two conditions. 3. Search of Reflections A four-circle X-ray diffractometer sketched in Fig. 3 is conveniently utilized also in the characterization of a thin crystalline film, although any other diffractometer is available to use such as ATX-G of Rigaku that has been designed for the measurement of in-plane diffraction from a thin film. Before starting to find the reflections, the χ axis is set to 90 degrees and the surface normal of the specimen is aligned so as to be parallel to the φ axis. Then, one of the reflections which would be within the surface is also specified to be parallel to the incident beam, This alignment makes the coordinates of the specimen coincident with the coordinates of the instrument. By generating a reflection and setting ω (= θ ), 2θ and χ angles of the diffractometer to the appropriate positions to the reflection in the condition of symmetrical setting by the computer, the peak can be searched by rotating the φ axis. Once the peak is found, the peak tops are refined along the two axes, ω and χ. Repeating those procedures a couple of times it leads the setting to the peak top of a reflection. Here, the lattice constants are fixed to the reported values so that 2θ angle is fixed during the refinement. After all of the generated reflections are searched, the reciprocal positions of the reflections found are calculated from the measured angles. 4. Assignment of Reflections Acrystallographic orientation can be determined by indexing the reflections observed by comparing the generated and observed reflections. By this procedure the only U matrix is determined because the B matrix is fixed by given lattice constants. Finally UB matrix is used to express the crystallographic orientations of an epitaxial film and also of a substrate. The assignment is basically proceeded by the two-reflection method. A pair of reflections are arbitrarily selected from the generated reflections and also another pair of reflections are selected from the observed reflections, which have the same Bragg Fig. 3. A four-circle diffractometer in a symmetrical diffraction condition. The vertical half slit is used for aligning the diffracted beam in the vertical direction. Angular resolutions of 2θ, ω, χ, and φ are also shown. 48 The Rigaku Journal
Fig. 4. The reciprocal lattices projected on the plane of a* and b* for the Laue symmetries of 4/m, 6/m, 3 and 3 1m. Two kinds of reciprocal lattice points are indicated by the gray spots, group 1 (G 1 ), and the dark spots, group 2 (G 2 ), are shown. They are not equivalent to each other. angles as those of the first pair and also have the same angle between their scattering vectors as that of the first pair. The indices of the second pair are replaced by those of the first pair or their equivalent indices. However we found that it may happen to assign wrong indices to some reflections because their Bragg angles are equal to those of the expected reflections. Such cases are seen in Laue symmetries 4/m, 6/m, 3, 31m and 31m. Here the difference between the cases of 31m and 31m is the definition of the reciprocal lattice axes in which the a* and b* of 31m are rotated by thirty degrees from those positions of 31m along the c* axis in either directions. Thus, it is enough to take into account of the case of 31m. In Fig. 4, the projections of the reciprocal lattice on the a* and b* reciprocal lattice plane are shown for the cases of 4/m, 6/m, 3, and 31m. Both the gray spots, group 1, and the dark spots, group 2, indicate the reflections out from the a* and b* reciprocal lattice plane. They are not equivalent each other, while they are in the same Bragg angles. Thus, it may happen to index the reflections of group 1 to those of group 2 with a probability of 50%. As for the Laue symmetries 4/m and 6/m, however, the mistake is easily discovered because the rest of the observed reflections fail to be indexed. If the assignment of the reflections is proceeded with the higher Laue symmetries 4/mmm and 6/ mmm, respectively, for 4/m and 6/m, the failure of indexing disappears, as long as the axis perpendicular to the specimen surface is correctly kept. For the rest of the Laue symmetries such as 31m and 31m, there is no way to disclose the mistakes by a simple comparison of the reciprocal lattice. Even in this case, however, a correct assignment is found by comparing relative intensities; that is the comparison of intensity pattern observed with those calculated on the basis of the structure factors. Consequently, we may say that the observed reflections are correctly assigned provided that the comparison of the intensity distribution is made among the reciprocal lattice points. Included this procedure in the program, the correct UB matrix is calculated as well as the U matrix. 5. Application to Mn 3 O 4 /MgO In order to certify the effect of this technique, we examined to determine the crystallographic orientations of a specimen Mn 3 O 4 /MgO which consisted of an epitaxial thin film of Mn 3 O 4 with the thickness about 200 nm and a single crystal substrate of MgO. Vol. 16 No. 1 1999 49
Table la., lb-1 and lb-2. show generated Bragg reflections of the thin film and the substrate which are to be found. The tilt angles a and the structure factors F are also included in the tables. The square of the structure factors (F 2 ) are primarily regarded as Bragg intensities and the tilt angles (α ) are secondly taken into account. In Table 2a., the reflections found for the substrate MgO are shown. The item 'Measurement reflections' indicates that thirteen reflections of sixteen were found. Those reflections are successfully indexed with the UB matrix described at the bottom of the table. The errors of the indices calculated from the UB matrix are within 0.03. This fact ensures the accuracy of the crystallographic orientation matrix U determined for the substrate crystal. In addition the offset angles, are shown at the bottom of the table, showing some indication of the errors between the default and determined settings. 'Off angle' shows the offset angle of the axis determined as parallel to the surface normal, and 'Off angle from incident' shows the offset angleof the axis determined as parallel to the incident beam. As seen from the table both of the axes happen to be coincident with the default directions within less than 1.0 degree. In Table 2b., the results of the reflections found for the epitaxial thin film of Mn 3 O 4 are shown. Only fourteen of fifty reflections searched were found because of their weak intensities. However it should be noted that the errors of the indices calculated from UB matrix are fairly small, as they are within 0.04. Thus the crystallographic orientation matrix U of the eptaxial thin film has the same accuracy as that for the substrate. In Fig. 5, the difference between the observed and the calculated peak positions are shown. The difference between the calculations and the observations are less than 1.0 degree, not only for the grazing incidence but also for the symmetrical setting. Furthermore one can find out any other reflection within the same error. Table 1. Bragg reflections generated by the present method. The tilt angle α and the substrate factor F are tabulated in addition to the indices hkl and the Bragg angle 2θ. (a) for the substrate of MgO. (b) for the thin film of Mn 3 O 4. 50 The Rigaku Journal
Table 2. Bragg reflections obtained by peak search and indices calculated from the observed angles of ω, χ, and φ on the basis of the UB matrix determined. Specimen: the epitaxial thin film MgO/Mn 3 O 4. Vol. 16 No. 1 1999 51
Fig. 5. The Bragg profiles observed, showing the difference form the predicted point. (a) and (b) comparison of the 3, 1 and 1 profile obtained by the grazing incidence and that by the symmetrical setting. (c) and (d) for the reflection 2, 2, 4. 6. Conclusion By using the program 'CrystaIGuide', fully automatic determination system of the crystallographic orientation of thin films, all the reflections found for a Mn 3 O 4 /MgO epitaxial specimen can be successfully indexed within the error of 0.04. This program guides us to find out the scan along any direction and any trace in the reciprocal space with different diffraction conditions. A significant feature of this program is therefore in the fact that various possibilities are easily visualized, for the measurement of a given point in the reciprocal space with different diffraction conditions. We would like to show our great thanks to Prof. Yao and Mrs. L. W. Guo at IMR, Tohoku University, for growing thin films, 7. References [1] L. Ballard and P. K. Predecki, Advances in X-Ray Analysis, 39, 363, (1995). [2] W. R. Busing and H. A. Levy, (1967) Acta Cryst. 22, 457. [3] J. Harada, lwata and Oshima (1984) Colloque de Physique. 52 The Rigaku Journal