Materials Transactions, Vol. 43, No. 7 (2002) pp. 1464 to 1468 Special Issue on Grain Boundaries, Interfaces, Defects and Localized Quantum Structure in Ceramics c 2002 The Japan Institute of Metals Refinement of X-ray Fluorescence Holography for Determination of Local Atomic Environment Kouichi Hayashi 1, Yukio Takahashi 2 and Ei-ichiro Matsubara 1 1 Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan 2 Department of Materials Science, Tohoku University, Sendai 980-8579, Japan X-ray fluorescence holography (XFH) is a promising method for determination of a local environment around a particular element. Since the holographic signal is about 0.3% of the background isotropic fluorescent radiation, it takes a few months to record a set of complete XFH data using a conventional energy dispersive detector. In order to overcome this difficulty, we designed an XFH setup with a combination system of a cylindrical LiF analyzer and an avalanche photo diode (APD) for bulk samples, and with a multi-element SSD for impurity samples. The holography experiments of an Au single crystal and Zn atoms doped in a GaAs wafer performed with these systems at the synchrotron radiation facility SPring-8 enables us to obtain high quality hologram data within a practical measurement time. (Received February 12, 2002; Accepted March 15, 2002) Keywords: X-ray fluorescence holography, single crystal, impurity, structural analysis 1. Introduction X-ray fluorescence holography (XFH) is a new experimental tool for directly determining a 3D local atomic structure around a specified atom. In 1948, Gabor proposed and demonstrated the holography using electron wave. 1) Subsequently, the holography technique was rapidly developed by the invention of laser. The first holography experiment using X-rays was performed by Aoki et al. in 1974. 2) Szöke proposed the concept of the XFH that uses fluorescence emitted from atoms as coherent wave sources in 1986. 3) Tegze and Faigel succeeded in imaging atomic arrangements in a single crystal in 1996. 4) Recently, we also succeeded in observing a local atomic environment around dopants in semiconductor wafer. 5) The XFH method is not limited to systems with a long-range order, it is also possibly applied to clusters, surface adsorbates and impurities. There are two types of the XFH method, i.e. normal XFH 6, 7) and inverse XFH, 8 10) as shown in Figs. 1(a) and (b), respectively. In the normal XFH method, fluorescence from atoms in the sample directly coming into a detector constitutes the holographic reference beam, and fluorescence scattered by neighboring atoms acts as the object beam. A holographic pattern is recorded by scanning a detector around the sample. The inverse XFH is based on the idea of the optical reciprocity of the normal XFH and the application of X-ray standing wave. Fluorescence is used to detect an interference field originating from incident and scattered X-rays which correspond to reference and object beams, respectively. The holographic pattern is obtained by detecting the fluorescence while varying the sample orientation relative to the incident beam. Since the inverse XFH allows holograms to be recorded at any incident energy above the absorption edge of an emitter, the twin image effect is suppressed and the spatial resolution of an atomic image is improved. This method is called multiple energy X-ray holography (MEXH). The main difficulty of the XFH is weakness of the holographic undulation in the angular distribution, which is about 0.3% of X-ray fluorescence intensity. This requires that about Fig. 1 Illustration of XFH principle. (a) Normal and (b) inverse modes. ten thousand pixels are measured in one hologram and at least one million photons of fluorescence must be colleted in each pixel. Thus, with a conventional solid-state detector only accepting a low counting rate ( 5000 cps), it takes few months to record a complete hologram. In order to overcome this difficulty, energetically pure fluorescence has to be detected at high counting rate. We have designed fast XFH measuring systems for various samples. In this article, we will describe these systems and discuss the advantages. 2. Setup for Fast Recording XFH Most of our experiments have been done at the synchrotron radiation facilities of SPring8. Since the beam times at the fa-
Refinement of X-ray Fluorescence Holography for Determination of Local Atomic Environment 1465 Fig. 2 Experimental configuration for inverse XFH. cilities were limited to a few days, at least one million counts of the fluorescence should be collected for a few seconds. In order to overcome this difficulty, we adopted a system consisting of an avalanche photo diode (APD) and a cylindrical lithium fluoride (LiF) crystal as a fluorescence detector. 11) The APD can collect the X-rays at high counting rate of 10 8 cps, but its energy resolution is low. 12) Therefore, the fluorescence is analyzed and focused at the front surface of the detector by the cylindrical LiF crystal in order to collect with a larger solid angle. This system enables us to record holograms of single crystal samples within a few hours when a strong incident beam is available. However, this system is hardly applicable to the hologram measurements of impurity systems due to low counting rate even if we use the X-ray beam of the third generation synchrotron radiation. The reason is that the solid angle acceptance of cylindrical LiF crystal is small. The energy dispersive detector can enlarge the acceptance by approaching to the sample, though the counting rate limitation of the conventional type one is lower than 10000 cps in general. The multi-element SSD, which are mostly developed for X-ray absorption fine structure (XAFS) measurement, enables us high counting rate measurements proportional to the number of the elements. Thus, we have used the 19-element SSD for recording the holograms of impurities instead of the combination system of the cylindrical crystal and APD. Figure 2 shows the XFH setup using both systems. The samples are replaced on a two-axis (θ-φ) rotatable stage, where θ is a polar angle between the incident beam and the surface normal, and φ is an azimuthal angle. Motor of φ was continuously scanned in fast measurements, because the speed of the stepping scan was not high enough. 3. Data Analysis for Reconstructing Atomic Image The demonstration of the combined system was performed at BL39XU at SPring8 for a Au single crystal. The incident X-ray energy was controlled to be 12.5 kev by the double crystal Si (111) monochromator. The beam size was 1 1mm 2. The Au Lα X-ray fluorescence was measured as a function of φ and θ within the range of 0 φ 360 and 20 θ 70. The system rotates together with the polar angle θ using a fixed exit angle of 45. The total measurement time for one hologram was 5 hours, which is now Fig. 3 Holograms of Au at various stages. (a) Raw data. (b) Fully extended data. (c) Low-pass filtered data. improved to be 2.5 hours. Figure 3(a) shows the raw data of the hologram pattern. The sharp lines were observed in Fig. 3(a). These were due to the X-ray standing wave (XSW), which are related to the well-known Kossel line by the optical reciprocity theorem, and caused by the long range periodic order present in the sample. The hologram of single crystal with high S/N ratio
1466 K. Hayashi, Y, Takahashi and E. Matsubara Fig. 4 Reconstructed atomic images of Au. and angular resolution exhibits these standing wave lines or Kossel lines. Reconstruction of an atomic image from the hologram in Fig. 3(a). The reconstruction of the atomic image was done using the Barton algorithm. 13, 14) The atomic image was unclear and distorted. Thus, we symmetrized the hologram as shown in Fig. 3(b) by referring to the XSW lines which reflect the crystal symmetry. This symmetrization improves the S/N ratio of the hologram. Now, we can recognize a weak and broad holographic pattern created by the neighboring atoms in Fig. 3(b) as well as the XSW lines. Applying the low-pass filter we arrive at the hologram shown in Fig. 3(c). Figure 4 shows the 3D atomic image of Au reconstructed from the hologram in Fig. 3(c). The first and second Au neighbors can be clearly seen. 4. Application to Impurity System Until now, most of the papers about the XFH have reported demonstrations for structural determinations of the known single crystals. We carried out the holography experiment of Zn atoms in GaAs at two different energies using synchrotron radiation. 5) In this experiment, a multi element SSD was used for recording the hologram. The hologram measurement was carried out using synchrotron beam line BL10XU at SPring-8. The synchrotron radiation from an undulator was monochromatized by a Si (111) double-crystal monochromator. The Zn concentration in the wafer was determined to be 1.0 10 19 atoms cm 3 (0.02 mass%) by a Hall measurement. The diameter and thickness of the sample were 50.0 and 0.25 mm, respectively. The incident X-ray energy was 9.7 and 10.0 kev, which was between the Zn and Ga K absorption edges, so as to avoid excitation of the Ga and As X-ray fluorescence. The beam size was 1 1mm 2. The 19-element SSD was placed parallel to the incident X-ray electric field, as already shown in Fig. 2. The intensity of Zn Kα X-ray fluorescence was measured as a function of the φ and θ within the ranges of 0 φ 360 and 26 θ 60. The total integrated intensity of the Zn Kα X-ray fluorescence at each pixel was about two hundred thousand counts. Total measurement time for one hologram was about 10 hours. Figures 5(a) and (b) show two fold averaged and low-pass filtered holographic patterns at 9.7 and 10.0 kev, respectively. From these holograms, we reconstructed atomic images of planes parallel to the {001} plane including the Zn atom, and 0.141 nm ( = z/4) above and below the emitter Zn atom, which are termed here planes A, B and C. Figures 6(a), (b) Fig. 5 Holograms of Zn doped in GaAs wafer recorded at (a) 9.7 and (b) 10.0 kev. and (c) show the reconstructed images of planes A, B and C. From Fig. 6(a), 110, 110, 1 10 and 1 10 atoms are clearly seen and the distances between the intensity maxima of these atoms and the emitter are equally 0.402 nm. The crystal structure of GaAs is a ZnS-like structure with a = 0.565 nm; that is, it consists of two face-centered-cubic cells. The Ga and As layers stack alternately along the c-axis; they are separated by 0.141 nm. The atomic configuration of the Ga layer is the same as that of the As layer, and the nearest Ga Ga or As As distances are 0.400 nm. Thus, the Zn atoms are found to substitute for a Ga or As site. This result well agreed with the EXAFS one. 15) In Fig. 6(b), strong images of 1 1 1, 1 1 1, 3 3 1, 3 3 1 atoms
Refinement of X-ray Fluorescence Holography for Determination of Local Atomic Environment 1467 Fig. 7 Model of local environment around Zn atom. The atomic arrangement is obtained from the reconstructed images in Fig. 6. 1 and weak images of 1 1 1, 1 1, 3 3 1, 3 1 atoms are seen, revealing that Zn atoms substituted selectively for one site of Ga or As. The possibility of the As-site substitution may be negligible because of the charge neutrality. Figure 7 shows the possible model of the atomic arrangement around Zn atoms. Since the intensity of the X-rays scattered from the atoms lying on the plane B is stronger than those on the plane C, it is considered that the 1 1 1, 1 1 1, 3 3 1, 3 3 1 atoms are the real image and that the 1 1 1, 1 1 1, 3 3 1, 3 3 1 atom-like images are twin images of the 1 1 1, 1 1 1, 3 3 1, 3 3 1 atoms existing on plane C, respectively. Holographic twin images appear necessarily in the image reconstructed from the single energy hologram and are suppressed by reconstruction from the MEXH data. Twin image suppression becomes effective with an increase in the number of holograms recorded at different energies. 16) However, since we measured only two holograms in our experiment, this effect is little. The 1 1 1, 1 1 1, 3 3 1, 3 3 1 atomic images appearing in Fig. 6(c) are the twin images of 1 1 1, 1 1 1, 3 3 1, 3 3 1 atoms in Fig. 6(b), respectively. Since the intensity of each twin image is nearly equal to of the paired real image, the twin image suppression is not confirmed for these atoms. In contrast, the real images of 1 1 1 1 1 1, 3 3 1, 3 3 1 3, atoms in Fig. 6(c) are obviously in comparison with their twin images displayed in Fig. 6(b). This result revealed that the two energy MEXH data contribute to suppressing the twin image for 1 1 1, 1 1 1, 3 3 1, 3 3 1 atoms. 5. Conclusion Fig. 6 Holographic reconstruction of an environment around Zn. The planes parallel to the {001} lattice plane cutting through the fluorescence emitter atom, 0.141 nm above and below the emitter atom are displayed in (a), (b) and (c), respectively. The dashed lines the outline of the GaAs crystal cell. Solid and dotted circles show real and twin images, respectively. In the present report, we designed the setups using the fast fluorescence detection system composed of the cylindrical LiF crystal and APD for single crystal samples, and that using the 19-element SSD for impurity samples. Using these systems, the hologram measurements of the Au single crystal and the Zn doped in GaAs wafer were conducted at the SPring8, and clear atomic images were successfully obtained. These demonstrate that high quality hologram data are obtained within a reasonable measurement time by combining our XFH systems with the synchrotron radiation. We will be able to study structural phase transitions such as local lattice distortions of the superconductor or colossal magnetic resistance materials for a reasonable time, whose atomic arrange-
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