Structural Features of = 3 and 9, [110] GaAs Tilt Grain Boundaries

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1 Jpn. J. Appl. Phys. Vol. 40 (2001) pp Part 1, No. 7, July 2001 c 2001 The Japan Society of Applied Physics Structural Features of = 3 and 9, [110] GaAs Tilt Grain Boundaries Nam-Hee CHO and C. B. CARTER 1 Department of Materials Science and Engineering, Inha University, Inchon , Korea 1 Departmet of Chemical Engineering and Materials Science, University of Minnesota, MN , U.S.A. (Received March 2, 2001; accepted for publication April 10, 2001) The planar density of coincidence sites appears to be high along the observed boundary planes for the = 3 and 9, [110] GaAs tilt grain boundaries. The polarity in each grain on either side of the tilt grain boundaries has been confirmed by direct or indirect methods. The result indicates that a lower number of anti-site type bonds occur along the boundaries compared to when the polarity of one grain is reversed. Based on high-resolution transmission electron microscopy (HRTEM) analysis of several different symmetric and asymmetric = 3 and 9, [110] tilt grain boundaries in GaAs, models for the atomic structures of these boundaries have been made for the first time; particular atomic arrangements form the structural units of these boundaries. KEYWORDS: thin film; HRTEM; GaAs; grain boundary; structure 1. Introduction The presence of grain boundaries results in a discontinuity of the crystalline phase of each grain on either side of the boundaries. Consequently, materials exhibit different properties at their grain boundaries from those observed for the perfect crystal regions. Much attention has been focused on interfaces in semiconductors, because many interesting properties of these materials are greatly influenced by the presence of grain boundaries. For a given misorientation between two grains, a lattice consisting of sites common to each grain is referred to as a coincidence site lattice (CSL). The volume or the planar density of such coincidence lattice sites is assumed to be related to the energy of the system consisting of grain boundaries and crystals adjoining at the boundaries. 1 3) It has also been anticipated that the boundaries with a relatively low energy can consist of structural units with the mixture of those of lower energy boundaries. = 3, [110] tilt grain boundaries have the highest density of coincidence sites. With the rapid development of high-resolution transmission electron microscopy (HRTEM), the atomic structures of grain boundaries have been successfully imaged. In particular, for the last decade, much effort has been made to investigate the atomic structure of grain boundaries in elemental semiconductor materials such as Ge or Si. 4 7) This has been partly motivated by the technological importance of these materials in producing electronic devices. Such experimental investigations can be compared with the theoretical studies of the structure of tilt grain boundaries in Ge. 8, 9) Most of the samples for the studies of grain boundaries in elemental semiconductor materials have been made by Czochralski 5, 6, 10) or 4, 11, 12) hot pressing method. On the other hand, there have been few experimental studies concerning the structure of grain boundaries in compound semiconductors such as GaAs, even though GaAs has been regarded as an important semiconductor because of its high electron mobility and direct band gap. This has been mainly because it has been relatively difficult to make particular GaAs bicrystals compared to Ge or Si. Epitaxial growth of thin film has been applied to produce bicrystals in GaAs by reproducing the misorientation of substrates. 13, 14) The use of address: nhcho@inha.ac.kr Ge bicrystals as substrates allows more control over the interface plane. As is the case for diamond-structure materials discussed by Slawson, 15) a GaAs crystal has a strong tendency of twining. Microtwins were produced in GaAs epilayers when the epitaxial layers were grown on (110) Ge substrates. In addition to coherent twin boundaries, several different lateral twin boundaries were produced, and = 9, [110] tilt grain boundaries are also obtained due to interactions of = 3, [110] boundaries. There are two different kinds of atomic arrangements for grain boundaries of sphalerite-structure materials corresponding to each grain boundary of diamond-structure materials. 16) Such arrangements depend on the relative positions of higher and lower valence elements. For the determination of the atomic structure of grain boundaries in sphalerite-structure materials, it is necessary to identify the polarity of the grains in high-resolution transmission microscopy (HRTEM) images. The determination of polarity in GaAs crystals has been performed successfully by a convergent beam electron diffraction (CBED) technique, 17, 18) and this technique has been utilized in this study of grain boundaries in GaAs. The species of atoms at atomic sites near the grain boundaries has been identified from a determination of the polarities of the grains on either side of the boundaries. In this study, systematic investigation has been performed on the structure of = 3 and 9, [110] tilt grain boundaries in GaAs, which have been grown using the epitaxial thin film deposition techniques. Structural characteristics like periodic atomic arrangement, faceting behavior, atomic relaxation, lattice translation of the boundaries were investigated by TEM. 2. Experimental 2.1 Sample preparation Bicrystals of GaAs have been produced using epitaxial growth of GaAs on the substrates of Ge bicrystals. = 3 Ge bicrystals have been grown by the Czochralski technique using a double-seed holder with two single-crystal seeds of Ge. Substrates were then cut from the Ge bicrystal such that the cutting plane is perpendicular to the boundary in Ge. The surface was polished with diamond powder to a mirror finish and then cleaned by subsequent boiling in acetone and methanol for 6 min each, and then rinsing in de-ionized water for 2 min. The surface was chemically polished in a solution 4458

2 Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7 N.-H. CHO and C. B. CARTER 4459 of HF in water, and dried in N 2 gas. GaAs epilayers with a thickness of about 1.5 µm were then grown on the [110] Ge substrates by organometallic vapor phase epitaxy (OMVPE) methods. During the growth, the Ge substrate was held at 670 C, the growth rate was 60 nm/min, the chamber pressure was 76 Torr, and the As/Ga ratio was 120. Using this technique, = 3, [110] GaAs tilt grain boundaries have been successfully grown in GaAs thin films. In addition, microtwins have been produced in the epilayers. 2.2 TEM specimen preparation Disks with a diameter of 3 mm were cut from the samples such that the grain boundary passed through the center of the disc. These disks were mechanically polished from the Ge substrate side until the thickness was about 40 µm. Copper rings were glued to the top and the bottom sides of the thinned disks. They were then further thinned using 4 kev Ar + ions from the substrate side until a tiny hole appeared at the center of the disks. 2.3 TEM imaging condition A JEOL 200 CX operating at 200 kv was used to record the diffraction image of grain boundaries and selected area diffraction patterns (SADP) corresponding to boundary areas. A JEOL 4000 EX was used to record high-resolution images of tilt grain boundaries in GaAs. The spherical aberration contstant of this microscope (Cs) is 1.0 mm at 400 kv. The electron beam was aligned parallel to the misorientation axis of both grains, e.g., the [110] axis. Diffraction patterns were used to check the tilt condition of the specimens. The 111 diffraction spots from the grains on either side of the tilt grain boundaries must be of the same intensity for the [110] misorientation axis, when the electron beam is parallel to the [110] axis. 3. Results 3.1 Σ = 3, [110] boundaries Figure 1 shows a = 3, [110] tilt grain boundary in GaAs, which was grown on = 3, [110] Ge bicrystal surface by OMVPE methods. In the SADP shown in Fig. 1(b), a = 3-related misorientation is clearly seen to be present between two grains on either side of the boundary. A coherent twin bounary is observed in Fig. 1(a), and reflections from twin planes coincide with one another. Figure 2 illustrates a microtwin commonly observed in GaAs epilayers grown on {110} Ge substrates. When the boundary planes lie parallel to the beam direction, they appear to be lines in the corresponding diffraction images. The boundary between the microtwins indicated by T and the matrix indicated by M is observed to facet parallel to particular crystallographic planes. Coherent twin boundaries are shown at AB, CD, JK and NU, while ( 115) M /(1 11) T, ( 111) M /(1 15) T and ( 221) M /(001) T are observed at GH, SJ and KL. Coherent twin boundaries are seen along LD and NE; the area surrounded by these boundaries is = 3-related with the other microtwin. In the micrograph shown in Fig. 3, another microtwin is illustrated; the image was recorded using a beam scattered from the planes which are continuous across the boundary between the microtwin (T 1 ) and matrix (M). Faceting is clearly shown Fig. 1. Bright-field image (a) and associated diffraction pattern (b) of a = 3, [110] tilt grain boundary. Fig. 2. Bright-field image of a microtwin; = 3 coherent twin boundaries are seen at AB, CD, JK and NU. along particular crystallographic planes. (00 1) M /( 22 1) T is observed at EF, JK and HS, and (1 1 2) M /( 11 2) T are seen at AE and FG. Grain T 2 is = 3-twin related with microtwin

3 4460 Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7 N.-H. CHO and C. B. CARTER Fig. 3. Bright-field image of a microtwin; (00 1) M /( 22 1) T is observed at EF, JK and HS, and (1 1 2) M /( 11 2) T is shown at AF and FG. Grain T 2 is = 3-related to grain T 1, and = 9-related to grain M. (T 1 ) across boundary LN, while being = 9 related with the matrix (M). A high-resolution image is shown in Fig. 4(a); a mirror plane is seen along the line E and bright spots are arrayed symmetrically across this plane. The polarity of each grain was determined from the FOLZ lines in the {200} convergent beam disks as shown in Fig. 4(b). As shown in Fig. 5, a coherent twin boundary can have two alternative atomic structures without breaking the twin relation between two grains on either side of the boundary. Normal type bonds are present across the bounary in the model shown in Fig. 5(a), whereas anti-site type bonds are present across the boundary is Fig. 5(b). Each type can be geometrically produced from the other by rotating one grain 180 more about the common [110] axis, due to the operation of inversion symmetry. The atomic structure for the coherent twin boundary shown in Fig. 4 corresponds to the one shown in Fig. 5(a). A high-resolution image recorded from microtwins is shown in Fig. 6. Three grains A, B, and C, are observed and the {111} lattice images of each grain illustrate the misorientation relation of one grain to the other. Grain A is = 3 related to grain B and grain C, while grain B and grain C are = 9 related. The boundary planes seen in the micrograph appear to be parallel to particular crystallographic planes on the atomic scale. A short facet is shown along the segment MN. = 3 related boundaries are seen along SJ, JK, LM and MN in the schematic shown in Fig. 6. The boundary segments SJ, JK, LM and MN are of (1 11) A /(1 1 1) B, ( 112) A /(1 12) B, (1 12) A /( 112) C and ( 111) A /( 11 1) C planes respectively. A = 9, ( 111) B /(1 15) C is shown along PQ. Bright spots in grain A and grain B appear to be symmetric on either side of the coherent twin boundary SJ, and the bright spots are arrayed along the mirror plane SJ which is indicated by an arrow G. The lattice fringes of (1 1 1) A and ( 11 1) A are also observed to be symmetric with the lattice Fig. 4. (a) High-resolution image of a coherent twin boundary. A mirror plane is seen along the line E. Bright spots are arrayed along this plane. (b) FOLZ lines in 00 2 A and 002 B convergent beam disks in grain A and grain B. fringes of ( 11 1) B and ( 111) C across the ( 112) A /(1 12) B and the (1 12) A /( 112) B ; no translation of one grain with respect to the other is observed along the boundaries JK and LM. 3.2 Σ = 9, [110] boundaries Two = 3 coherent twin boundaries are seen along SK and JK in Fig. 7. The {111} lattice fringe images in grain B and grain C indicate that grain B is rotated with respect to grain C by 38.9 about an [110] rotation axis; this angle corresponds to the misorientation of two [110] fcc lattices which are = 9 related. Boundary KL is of a = 9, (2 2 1) B /( 22 1) C [110] plane. Bright spots are arrayed along the coherent twin bounaries JK and SK. The {111} lattice images in grain B and in grain C appear to be symmetric across boundary KL. A periodic arrangement of bright spots with a nearly symmetric triangular shape is observed along bound-

4 Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7 N.-H. CHO and C. B. CARTER 4461 Fig. 6. High-resolution image of microtwins in a [110] GaAs epilayer. A mirror plane is seen along the direction indicated by an arrow G. Fig. 5. Two different [110] projections of atomic arrangements corresponding to a coherent twin boundary in GaAs. Ga and As atoms are represented by open and closed circles respectively, and the two different sizes of circles indicate the two different heights in the [110] projection of a GaAs crystal. (a) One grain is rotated with respect to the other by (b) One grain is rotated with respect to the other by ary KL. In Fig. 8, the {111} lattice fringes in grain B and grain C indicate that grain B and grain C are = 9 related. Two = 3 coherent twin boundaries, SK and JK interact with one another to produce a third boundary at K; a short = 3 coherent twin boundary is also seen along QU and PQ; a short = 3, ( 112) B /(1 12) S boundary is observed along NU. The boundary KR is seen to facet parallel to particular planes such as the (1 15) B /(1 11) C along LM and QR. Bright spots form a symmetric arrangement across the coherent twin boundaries SK and JK and the mirror planes consist of the bright spots. Unlike the contrast near the coherent twin boundaries, the region near the = 9 boundary KR is blurred with a brighter contrast than a region far from the boundary. Fig. 7. High-resolution image of a = 9, [110] tilt grain boundary where two coherent = 3 twin boundaries combine to produce a = 9 boundary. Two coherent twin boundaries are seen at SK and JK. A = 9, (2 2 1) B /( 22 1) C boundary is observed at KL. 4. Discussion 4.1 Faceting behavior = 3-related boundaries between the observed microtwins and matrix are strongly faceted parallel to particular crystallographic planes. The boundary can be divided into

5 4462 Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7 N.-H. CHO and C. B. CARTER Fig. 8. High-resolution image of a = 9, [110] tilt grain boundary. Two coherent twin boundaries (SK and JK) interact with one another to produce a third boundary at K. The third boundary is shown to facet parallel to particular planes. A = 9, (1 15) B /(1 11) C [110] is seen at LM. two parts; coherent twin boundaries and lateral twin boundaries. As expected, coherent twin boundaries are parallel to {111} planes and the presence of relrods normal to the coherent twin boundary planes in the corresponding SADP indicates that these boundaries are very flat; 19) this can be seen from the high-resolution images of this boundary. Lateral twin boundaries are also seen to lie along particular planes. One of the common features seen in the facets is that the crystallographic planes of those facets contain relatively high densities of coincidence site lattice; (1 11)/(1 1 1), (1 1 2)/( 11 2), ( 111)/(1 15) and ( 221)/(001) are the planes with the first, second, third and fourth highest planar density of coincidence sites. The = 3-orientation relation between two grains of GaAs can be geometrically produced when one grain is reotated with respect to the other about the [110] axis by either or because [110] axis of GaAs has a two-fold symmetry element and a mirror symmetry is located perpendicular to the axis. The two different misorientations for a = 3, [110] boundary are relevant to the polarities of each grain on either side of the boundaries. The energy associated with the presence of grain boundaries in GaAs is believed to be influenced by the relative position of Ga and As in each grain on either side of the boundaries; i.e., geometrically depending on whether one grain is rotated by or The = 3 coherent twin boundary consists of the bonds of a normal type (Ga As) instead of an anti-site type (Ga Ga or As As), and as a result appears to have lower energy. 4.2 Atomic structural features In the analysis of high-resolution images of [110] tilt grain boundaries, it is essential to determine the correspondence of bright and dark spots in the images with atomic sites. Most of the high-resolution micrographs of the observed boundaries were recorded in an area with a thickness of within the first period of intensity oscillation of the forward scattered beam. According to image simulations for perfect GaAs crystals with a [110] orientation and a thickness less than 5 nm, the [110] channels appear as bright spots under the defocus values of nm. 18) Such imaging conditions seem to be very applicable for this study, from the fact that bright spots are arrayed along the mirror plane of coherent twin boundaries in the high-resolution images recorded in this study. In particular, the distance between Ga and As in the [110] orientation is 0.14 nm. These two atomic columns appear as one spot in the high-resolution images because the distance is too short to be resolved by the microscope. Therefore, the image of the mirror plane of the coherent twin boundaries can be used to obtain the information about the correspondence of image spots with atomic sites. The symmetric arrangement of bright spots across the boundary SJ in Fig. 6 indicates that the ( 11 1) atomic planes in grain A are continuous in grain B without any lattice translation. In Fig. 6, the boundaries JK and LM appear to be symmetric such that there is no lattice translation along the boundary plane normal to the beam direction. There have been several investigations of the structure of = 3, {112}/{112} tilt grain boundaries in Si or Ge. 6, 8, 9, 20) In particular, two atomic models for this boundary have been suggested based upon energy calculations in which no dangling bonds are present with certain bond reconstruction and with a particular lattice translation. 20) The translation of one grain with respect to the other was expected to be 0.54a[111] and 1/4a[011]. However, no such large translation component parallel to the boundary plane and normal to the beam direction is observed along boundaries JK and LM in Fig. 6. The observation of bright spots along the mirror plane SJ indicates that the [110] atomic columns and the [110] channels are imaged as dark spots and bright spots respectively in Fig. 6. The boundary JK in the high-resolution micrograph shown in Fig. 6 was enlarged, and in Fig. 9 a pair of Ga and As atomic columns were superimposed on each dark spot. The relative position of Ga and As in the microtwin was determined by assuming that the coherent twin boundary SJ in Fig. 6 does not have anti-site type bonds across the interface; geometrically the misorientation angle between grain A and B is about the common [110] axis. Using the determination of the atom sites in the high-resolution image of the boundary, the atom sites near the boundary are shown in Fig. 9(b). Open circles and closed circles correspond to Ga and As respectively, and the difference in size indicates the two levels of height of atoms in the [110] projection of GaAs (the convention of these notations will be used in the same way throughout this paper). A repeating unit is indicated by an arrow between two bars. This unit consists of 5-, 7- and two 6-member rings. A dangling bond is present at atom sites F and N because these atoms have 5- and 3-fold coordination. On the other hand, bond angles are little distorted from the tetrahedral bonddirection at atoms near the boundary compared to those in a good crystal region. The cross-boundary bond between atoms H and L is of a Ga Ga anti-site type bond. The measured length of this bond is about nm, while this length has a value of 0.23 nm if this boundary is geometrically symmetric and no reconstruction occurs. The equilibrium length be-

6 Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7 N.-H. CHO and C. B. CARTER 4463 Fig. 9. (a) Atomic sites are superimposed on dark spots near boundary JK in Fig. 6. Open and closed circles correspond to Ga and As atoms, respectively. (b) Atomic structure of the boundary shown in (a). tween atoms H and L appears to be different from the Ga Ga bond length in its bulk by about nm. 21) Considering the adjustment of grains adjoining at antiphase boundaries in GaAs, the presence of anti-site type bonds across the boundary is expected to increase the free energy of the system (two crystals containing a grain boundary). Such local relaxation is expected to reduce the energy associated with this boundary. If the Ga and As sides of the (111) atomic plane are interchanged in one grain, the cross-boundary bond between atoms F and G (or K), and the bonds between atoms N and J (or M) become anti-site type bonds. In this case, there will be three times as many anti-site type bonds as in the other case. This boundary is expected to be in a much higher energy state than the atomic structure suggested in Fig. 9(b). = 9, [110] tilt grain boundaries are produced when two microtwins with different orientations meet one another. In other words, two different = 3 twin boundaries interact with one another to produce a third boundary, which is a = 9 tilt grain boundary. Therefore, once the preferable type of bond across the coherent twin boundaries is found, the polarities in each grain one either side of = 9 boundaries can be determined easily by examining the Ga and the As side of (111) planes in the matrix. The atomic structure in Fig. 10(b) was made based on the high-resolution image of a = 9, (2 2 1) A /( 22 1) B boundary shown in Fig. 10(a). The mirror plane of the coherent twin boundary JK appears to be an array of bright spots in Fig. 7. And therefore the bright spots correspond to [110] channels. The boundary KL in Fig. 7 was enlarged, and atomic sites were superimposed on the dark spots in Fig. 10(a) under the assumption that there are no anti-site type bonds across the Fig. 10. (a) Atomic sites are superimposed on dark spots near boundary KL in Fig. 7. (b) 5- and 7-member rings are arrayed in a zig-zag fashion along the boundary. Anti-site bonds are seen between atoms F and K, and also between H and M. (c) Relation between the two lattices corresponding to grains B and C. coherent twin boundaries SK and JK in Fig. 7. This boundary plane has a high density of coincidence site lattice points when the two lattices are extended infinitely at the given misorientation. The repeating unit is shown in the area indicated by the arrow between two bars in Fig. 10(b). The observed boundary is seen to lie along the plane, such that this boundary contains a maximum number of coincidence site lattice points. The repeating unit consists of 7- and 5-member rings; the combination of the two rings appear to be similar to the atomic arrangement of the core of an a/2[110] edge dislocation. However, the atomic configuration shows that the bond length between atomic sites R and F is different from the length between atomic sites S and K. Several investigations have been carried out for the similar boundaries in Ge. 7 9) Kohn and Hornstra deduced the same atomic model for this boundary in Ge using an array of lattice dislocations along the boundaries. The arrangement of atoms in this boundary structure in GaAs appear to be similar to the atomic structure of the boundary in Ge. The misorientation between two grains is accommodated by the zig-zag arrangement of dislocation cores along the boundary. However, the presence of anti-site type bonds in the atomic structure of this boundary in GaAs presumably results in a particular local

7 4464 Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7 N.-H. CHO and C. B. CARTER strain field near the boundary plane, which does not exist in the same boundary structure in Ge. The relation between the two lattices corresponding to grain B and grain C is shown in Fig. 10(c). The boundary palne is indicated by arrow E. Coincidence lattice sites are seen along this boundary, which indicates that no rigid-body translation occurs across or along the boundary (normal to the electron beam direction); this displacement has been considered in a similar boundary in Ge. 7) On the other hand, a local relaxation near the boundary results in the contrast of a blurred ˆ shape in the high-resolution image shown in Fig. 10(a). The enlarged high-resolution image of the = 9, ( 115) A /(1 1 1) B boundary shown in Fig. 11(a) was obtained by Fourier-image filtering the image of the boundary LM shown in Fig. 8. The contrast of the mirror planes SK and JK in Fig. 8 indicates that a pair of Ga and As atomic columns are imaged as a dark spot in this high-resolution micrograph. Atomic sites are superimposed on each dark spot in Fig. 11(a) under the assumption that no anti-site type bonds exist along the coherent twin boundaries SK and JK in Fig. 8. The boundary plane appears clearly to be lying on the atomic scale between two atomic planes (111) and (115) of each grain adjoining at the boundary. This boundary plane contains a high-density of coincidence site lattice points. Half of the unit is translated with respect to the other by a/4[110] along the beam direction. When the two grains are arranged such that the coincidence sites are overlapped, the distance between the two atomic sites G and H is close to the normal bond length, as is shown in Fig. 11(b), and the direction of the bond between these two sites is distorted from a normal tetrahedral bond by about 15. Dangling bonds are present at atomic sites F and K. [110] GaAs tilt grain boundaries have structural units consisting of the units shown in Fig. 12. These units are believed to be formed at boundaries because of the strong directionality of tetrahedral bonds in GaAs and the tendency of the bonds to keep the equilibrium length across the boundaries. Presence of these units indicates that the structure of tilt grain Fig. 11. (a) Image processed figure of boundary LM in Fig. 8; atomic sites are superimposed. Definite (1 11) and (1 15) atomic planes are seen on either side of the boundary. (b) The structural unit in (a) is shown to consist of asymmetric 5-, 7-, and 6-member rings. An anti-site bond is seen between atomic sites G and H. Fig. 12. Units of atomic arrangement at [110] tilt grain boundaries in GaAs. Open and closed circles correspond to Ga and As atomic sites; the difference in size indicates two different heights along the [110] direction. (1) and (4) illustrates symmetric and asymmetric 6-member rings, respectively. (2) and (3) are symmetric configurations consisting of 5- and 7-member rings; (2) appears to be similar to the atomic arrangement of an a/2[110] edge dislocation core in GaAs. (5) is an asymmetric arrangement of atomic sites consisting of 5- and 7-member rings. boundaries in GaAs can hardly be described simply by particular dislocation arrangements or by a change of bond directions across the boundaries. The atomic planes adjoining at the boundaries, along with local atomic relaxation, are believed to play a crucial role in the shape of particular atomic configurations of tilt grain boundaries in GaAs. The occurrence of the 7-member rings and the relaxation process of this arrangement results in a relatively open atomic structure along the boundaries. The presence of anti-site type bonds between the 5- and the 7-member rings as well as dangling bonds is also expected to cause these tilt boundaries to have a more open atomic structure. 5. Conclusions The planar density of coincidence sites appears to be higher along the observed boundary planes for the = 3 and 9, [110] tilt grain boundaries. The energy associated with the presence of boundaries is believed to be reduced when the boundaries lie along planes which have a high density of coincidence sites; boundaries are considered to facet parallel to these planes in order to attain a lower energy state. The polarities in each grain on either side of the tilt grain boundaries have been confirmed by direct or indirect methods. The result indicates that a lower number of anti-site type bonds occur along the boundaries compared to when the polarity of one grain is reversed. Based on the experimental observation of several different symmetric and asymmetric tilt grain boundaries in GaAs, models for the atomic structures of these boundaries have been made for the first time. = 3- and = 9-related twin boundaries in GaAs appear to achieve their lower energy state primarily by a local atomic relaxation without rigidbody translation at the boundaries. Particular atomic arrangements form the structural units of these boundaries; dangling

8 Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7 N.-H. CHO and C. B. CARTER 4465 bonds are believed to be present in some of the units across the boundaries. The structural units include symmetric and asymmetric arrangements of 5- and 7-member rings, and normal and symmetric 6-member rings in the [110] projection of [110] tilt grain boundaries. 1) M. L. Kronberg and F. H. Wilson: Trans. AIME 185 (1949) ) D. G. Brandon: Acta Metall. 14 (1966) ) W. Bollmann: Surf. Sci. 31 (1972) 1. 4) C. B. Carter, H. Foll, D. G. Ast and S. L. Sass: Philos. Mag. A 43 (1981) ) C. D Anterroches and A. Bourret: Philos. Mag. A 49 (1984) ) Z. Elgat: Ph.D. thesis, Cornell University, ) O. L. Krivanek, S. Isoda and K. Kobayashi: Philos. Mag. 36 (1977) ) J. A. Kohn: Am. Miner. 43 (1958) ) J. Hornstra: Physica 25 (1959) ) A.-M. Papon, M. Petit and J.-J. Bacmann: Philos. Mag. A 49 (1984) ) H. Foll and D. G. Ast: Philos. Mag. A 40 (1979) ) C. B. Carter and Z. Elgat: Adv. Ceram. 6 (1983) ) J. P. Salerno, R. W. McClelland, P. Vohl and J. C. C. Fan: Mater. Res. Soc. Symp. Proc. 5 (1982) ) N.-H. Cho, C. B. Carter, Z. Elgat and D. K. Wagner: Appl. Phys. Lett. 49 (1986) ) C. B. Slawson: Am. Miner. 35 (1950) ) D. B. Holt: J. Phys. Chem. Solids 25 (1964) ) J. Tafto and J. C. Spence: J. Appl. Cryst. 15 (1982) ) B. C. DeCooman: Ph.D. thesis, Cornell University, ) C. B. Carter, A. M. Donald and S. L. Sass: Philos. Mag. A 39 (1979) ) R. C. Pond, D. J. Bacon and A. M. Bastaweesy: Inst. Phys. Conf. Ser. 67 (1983) ) J. C. Philips: Bonds and Bands in Semiconductors (Academic Press, New York, 1973).