ONE-DIMENSIONAL CIRCULAR DIFFRACTION PATTERNS

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1 274 Surface Science 222 (1989) North-Holland, Amsterdam ONE-DIMENSIONAL CIRCULAR DIFFRACTION PATTERNS Hiroshi DAIMON and Shozo IN0 Department 5f Pkysics, Faculty of Science, University 5j Tokyo, Hongo, ~unkyo-k~ Tokyo ii3, Japan Received 23 February 1989; accepted for publication 5 June 1989 Circular diffraction patterns from a bulk crystal have been found in MEED patterns by using a newly developed two-dimensional spherical mirror analyzer. From the analysis of the energy dependence of their radii and from the fact that they are not associated with the tangential Kikuchi lines, the circles were interpreted by the concept of one-dimensional diffraction along the crystallographic axes. The hemi-circular patterns, which have been observed in RHEED patterns near superstructurat spots from a surface structure, were also explained by this concept. 1. Introduction The concept of diffraction from a one-dimensional atomic row was first discussed by Emslie [l]. He found a hemi-circle in the RHEED (reflection high energy electron diffraction) pattern and considered it a result of one-dimensional diffraction. Tillman [2] studied the hen&circle quantitatively and deduced that they were a one-dimensional Kikuchi pattern. After that, Shinohara [3] considered it as a Kikuchi envelope because the her&circles are always associated with many Kikuchi lines and often they look like a polygon. Because the radii of the circles of a one-dimensional Kikuchi pattern and those of a Kikuchi-envelope are equal, the concept of one-dimensional diffraction is not a definite one at present and usually the circles are considered as a Kikuchi envelope. Very recently, Peng et al. [4] re-examined the concept of one-dimensional diffraction using the idea of surface channeling of electrons along rows of atoms parallel to the crystal surface in the condition of surface wave resonance. In the present study, we found a full-circle diffraction pattern for the first time in a MEED (medium energy electron diffraction) pattern. Although it seems to be the result of one-dimensional diffraction, the concept of channeling of surface wave resonance is not readily applicable /89/$ Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

2 H. Daimon, S. ho / One-dimensional circular diffraction patterns Experiment The experiments were performed with a spherical mirror analyzer [5,6], which has been developed recently by ourselves. By using this analyzer, the pattern of a two-dimensional angular-distribution of charged particles emitted from a surface for a given kinetic energy can be directly observed. Fig. 1 shows a schematic diagram of the analyzer. It consists of a hemispherical grid G, a hemispherical electrode D, a small aperture A, six guard rings GR, and a two-dimensional detection system, which consists of a pair of microchannel plates M and a phosphorous screen P. The radius of D is twice as large as G. The centers 0 of the two hemispheres are common and their great circles are in the same plane, which is perpendicular to the paper in fig. 1, including 0, A, and S. The sample S and the aperture A in this plane, are symmetric with respect to 0. When particles of energy E (ev) are analyzed, the grid G is earthed and a potential E (V) is applied to the electrode D. Then all the particles emitted from the sample surface that have the same kinetic energy E converge at the exit aperture and pass through it, giving their angular distribution on the two-dimensional detector. The small electron gun e, used in the present experiment, was mounted inside the grid. 3. Results and discussion Figs. 2a and 2c show diffraction patterns taken from a clean Si(ll1) surface using the newly developed analyzer. The energies of the electrons in 2a and 2c are 3 kev and 1.5 kev, respectively. The energy resolution is about 1% in the whole display region except at the horizontal band AB just below the center of the screen. The resolution at the horizontal band AB is worse than 4% and the Fig. 1. A schematic diagram of a newly developed spherical mirror analyzer. G is a hemispherical grid, D a hemispherical electrode, A a smal aperture, M a pair of microchannel plates, and P a phosphorous screen. GR are guard rings. The small electron gun e, used in the present experiment, is mounted inside the grid.

3 signal to background ratio is poor. Although the method of measurement is peculiar, the patterns obtained are essentially the usual MEED patterns. The incidence angle of the electrons is 45 o and the screen is placed parallel to the Fig. 2. Circular diffraction patterns observed in the MEED pattern from clean Si(111)7 X 7, taken by using the newly developed spherical mirror analyzer. (a) and (c) are the patterns with electron energies of 3 kev and 1.5 kev, respectively. (b) and (d) are the calculated patterns using eq. (2) for the patterns (a) and (c). respectively.

4 H. Daimon, S. Ino / One-dimensional circdar ~iffrac~~o~ parterns Fig. 2. Continued. surface. The shadow of the electron gun is seen in the upper left part of the screen. In figs. 2a and 2c, many circles are observed around the zone axes together with three major Kikuchi bands. Their radii increase as the electron energy decreases. The centers of these circles always coincide with the zone axes.

5 278 H. Daimon, S. Inno / One-&men&ma1 circular diffraction patterns Fig. 3. Schematic representation of one-dimensional diffraction of a spherical wave I,!J emitted from an atom A. Hence, these circles are considered to be the result of diffraction from a one-dimensional atomic row along those axes. The me~urement was done below 3.3 kev, since the resistance voltage of the apparatus was not so high. The Kikuchi bands and the circular patterns were always observed for electron energies above 1 kev. The circular patterns and the Kikuchi bands became clear as the incident energy increased. The circular patterns sometimes looked like circles made of arc (fig. 2c) or sometimes looked like disks (fig. 2a). This difference is similar to that between Kikuchi lines and Kikuchi bands. The analysis was made in the following way. Consider an atom A in a linear regular row of spacing a as shown in fig. 3. A spherical wave 4 is created at the atom A by inelastic scattering of the incident electron. Part of the spherical wave that propagates toward atoms B, C, and D is elastically scattered by those atoms and creates scattered waves $J, I/J* etc. Interference occurs constructively in the cone whose angle from the axis is 8, when the path-length difference is an integral multiple of the wavelength of the electron: a(1 - cos 19) = nx, (1) where n is an integer and X is the wave length of the electron. When n = 1, eq. (1) becomes: cos 0= 1 --X/a. (2) Figs. 2b and 2d show the calculated patterns using eq. (2) for those energies which correspond to figs. 2a and 2c, respectively, where the innerpotential was set to 12 ev in the calculation of h. The value 12 ev was obtained by RHEED rod intensity analysis [7]. The Kikuchi bands are also calculated in the usual manner. The interatomic spacing a used in the one-dimensional diffraction (eq. (2)) and the interplanar spacing d used in the calculation of the Kikuchi bands are much different. The Kikuchi bands seen in the figure originate from (110) planes, etc., whose spacing is 1.92 A (= fia,/4). In the notation of reciprocal space, the bands originate from (220) reflections. The spacing al,,, in one-dimensional diffraction for the [IlO] axis is not 1.92 A for the inter-planar spacing but 3.84 A (= fia,/2) for the interatomic spacing in the [llo] direction as seen in fig. 4. Similarly, a,,1 and aill for the [112] and [ill]

6 H. Daimon, S. Ino / One-dimensional circular diffraction patterns 219 [loll Fig. 4. Structure of the silicon lattice. The long broken lines show the unit of one-dimensional diffraction, a in eqs. (1) and (2), for each axis. directions are 6.65 and 9.41 A, respectively. These spacings are also much different from those corresponding to the interplanar spacing of 1.11 and 3.14.& respectively. The calculated patterns using these spacings reproduced the observed patterns quantitatively well at all energies used in the measurement. In the following we discuss the difference between the Kikuchi envelope and the one-dimensional diffraction pattern. Her&circles have commonly been observed in RHEED experiments on flat surfaces. Fig. 5 [8,9] shows a RHEED pattern from a clean Si(111)7 X 7 surface. The circle denoted KE is Fig. 5. RHEED pattern from clean.%(111)7x7 with [llo] incidence at an electron energy of 20 kev.

7 280 H. Daimon, S. Ino / One-dimensionai circular diffraction patterns the same kind of circle that Emslie [l], Tillman [2], and Peng et al. [4] considered to be originating from a one-dimensional diffraction and for a long time we considered it as the Kikuchi envelope. This circle corresponds to the circular pattern for [110] in fig. 2. The distinction between the Kikuchi envelope and the circle from a one-dimensional diffraction is very difficult because the positions and the radii of both circles are the same, and the circle is always associated with many Kikuchi lines in the RHEED energy region unlike in the MEED region. Moreover, the circle sometimes looks like a polygon. Hence, the circle is sometimes really a Kikuchi envelope. It cannot be excluded, however, that the circle from a one-dimensional diffraction overlaps the Kikuchi envelope. In the MEED experiment in fig. 2, the Kikuchi lines cannot be seen. Hence, the circle in the MEED region is considered to be the circle from a one-dimensional diffraction. In fig. 5, additional circles R,-R, are observed. These circles cannot be explained by the three-dimensional Kikuchi envelope. Recently, researchers [9,10] noticed them but the origin has not been understood. These circles can also be explained by one-dimensional diffraction using the interatomic spacing in the linear chain in the superstructure lattice. The interatomic spacing u,~+, in this case should be the unit mesh size of the 7 X 7 reconstructed surface. The radius of the circle R, is explained by eq. (1) with IPI = n. For example the circle R, can be explained by eq. (1) with n = 2 and a = 7 X allo, where ul10 is the interatomic spacing along the [llo] axis, 3.84 A. These circles are not associated with Kikuchi lines. Hence, these are the circles from the one-dimensional diffraction by surface atomic rows. Although the origin of the circle near the fundament~ spots, for instance KE, in the RHEED pattern is not definite, the circles near the superstructural spots, for instance RI-R,, are explained as the circles from the one-dimensional diffraction. The circles R,-R, can be explained by the idea of surface axial channeling of Peng et al. [4] as well as KE. In the MEED energy region (< 3 kev), however, this concept is not readily applicable because the channeling of an electron is not likely to take place below 50 kev [ll]. The wave function of the channeling wave below about 50 kev is s like, the maximum density of which is on the atomic nuclei. The mean free path of the channeling wave near the nuclei is short because the probability of inelastic scattering is large. The fact that Kikuchi lines cannot be seen in the MEED pattern suggests that a mechanism exists which concentrates the wave within the atomic row and that the scattering along a one-dimensinal chain is stronger than other scattering. The intensity ratio between the circle and Kikuchi lines, which make the Kikuchi envelopes, is considered to be the ratio between the waves confined in the row and the waves outside the row. Although the reason is not clear at present, the experimental results suggest that the wave is likely to propagate along one-dimensional axes.

8 H. Daimon, S. Ino / One-dimensional circular diffraction patterns 281 Although it is only a supposition at present, the following idea may help to understand why the wave is likely to be confined along the axis. When an atom is located near the origin of the spherical wave, the wave field behind the atom increases because the forward scattering is strong. This effect collects the waves along the axis. Hence, the wave field along axes will be stronger than along other regions. This ratio is roughly estimated to be the ratio between the total elastic scattering cross section of the nearest neighbour atom at distance r in the row and all solid angles 4?rr *. This ratio increases as the kinetic energy decreases because the cross section increases as the kinetic energy decreases. Hence, the probability of the forward scattering and the probability of the wave field along the axis in the MEED energy region is considered to be higher than that in the RHEED energy region. 4. Summary So far the observation of circles has been limited in the RHEED patterns from flat surfaces, and the circles were hen&circles. The present work showed that: (1) one-dimensional diffraction can occur not only at surfaces but also in bulk, so surface wave resonance is not necessary, (2) one-dimensional diffraction can occur in the MEED energy region below 3 kev, and (3) the circles observed were full-circles. The reason why these patterns have not been observed so far may be that the energy resolution used during previous experiments of MEED was worse than the present one. The energy selection method in usual diffraction experiments is a retarding grid method. Hence, in the MEED or HEED energy region, it is difficult to supply a high retarding voltage to the grids, which are usually composed with narrow spacings. The spacing of the electrodes of the new analyzer used here is very large, and a high voltage is easily supplied to them. Acknowledgements The authors wish to thank Professor A. Ichimiya for stimulating discussions. This work was supported by a Grant in Aid for Special Distinguished Research Project ( ) from the Ministry of Education, Science and Culture. References [l] A.G. Emslie, Phys. Rev. 45 (1934) 43. [2] J.R. Tillman, Phil. Mag. S (1935) 485.

9 282 H. Daimon, S. Ino / One-dimensional circular diffraction patterns [3] K. Shinohara, Phys. Rev. 47 (1935) 730. [4] L.M. Peng, J.M. Cowley and Nan Yao, Ultramicroscopy 26 (1988) 189. [5] H. Daimon, Rev. Sci. Instr. 59 (1988) 545. [6] H. Daimon and S. Ino, J. Vacuum Sot. Japan 31 (1988) 954. [7] J.F. Menadue, Acta Cryst. A 28 (1972) 1. [8] S. Ino, Japan. J. Appl. Phys. 16 (1977) 891. [9] S. Ino, Japan. J. Appl. Phys. 17 (1978) [lo] Y. Gotoh and S. Ino, Japan. J. Appl. Phys. 17 (1978) [ll] K. Kambe, G. Lehmpfuhl and F. Fujimoto, Z. Naturforsch. 29a (1974) 1034.