Stacking faults in β-Ga2O3 crystals observed by X-ray topography

X-ray topography analysis reveals the presence of stacking faults in β-Ga2O3 wafers grown by the edge-defined film-fed growth method. These stacking faults are found to be associated with a Shockley-type partial dislocation loop on the basis of the contrast extinction rules determined by varying the value of the diffraction vector.


Introduction
The monoclinic modification of gallium oxide (-Ga 2 O 3 ) is a promising material for power electronics applications owing to its superior physical properties, such as a wide electron energy band gap (Tippins, 1965) and high electric breakdown field (Higashiwaki et al., 2012). -Ga 2 O 3 is the most thermally stable of the several polymorphs of Ga 2 O 3 and high rates of crystal growth can be achieved using the melt growth technique. Recently, wafers cut from ingots grown by the edgedefined film-fed growth (EFG) method have become commercially available as substrates for electronic devices , encouraging the further development of this material for electronic device applications. The first Ga 2 O 3 metal-semiconductor field-effect transistors based on single-crystal -Ga 2 O 3 substrates were demonstrated by Higashiwaki et al. (2012).
Crystallographic defects such as dislocations and stacking faults (SFs) play a crucial role in device performance and reliability. The electrical properties of -Ga 2 O 3 diodes have been investigated using etch pit observations to study the relationship between defects and current leakage Kasu et al., 2017). Furthermore, the dislocations and hollow defects in -Ga 2 O 3 single crystals have been examined by X-ray topography (Nakai et al., 2015), and the dislocations and twin structures have been analyzed by transmission electron microscopy (Ueda et al., 2016). However, the detailed crystal structure of -Ga 2 O 3 containing defects has not yet been reported, and therefore the nature of these defects remains unclear. In our previous paper, we proposed a hypothetical slip system based on the crystal structure ISSN 1600-5767 (Yamaguchi et al., 2016). We also analyzed the dislocations using X-ray topography and identified the Burgers vectors and slip planes for some typical dislocations.
In this paper, we analyze planar defects on the ð201Þ plane. The ð201Þ plane is the unique plane on which GaO 4 tetrahedra and GaO 6 octahedra are separately stacked, which enables partial dislocation by slip on the plane. The planar defects were found to be stacking faults enclosed by a partial dislocation loop.

Dislocations
The crystal structure of -Ga 2 O 3 is monoclinic (space group C2=m) with the lattice parameters a = 12.23, b = 3.04, c = 5.80 Å , = 103.7 , as depicted in Fig. 1 (Geller, 1960). The unit cell contains two different Ga-O structural units: GaO 4 tetrahedra and GaO 6 octahedra. As Geller described, 'the oxygen ions are arranged in a 'distorted cubic' close-packed array'. The close-packed planes in -Ga 2 O 3 , corresponding to the {111} planes of the face-centered cubic structure, create a distorted tetrahedron with faces formed by the ð201Þ, (101), ð310Þ and ð310Þ planes (Yamaguchi et al., 2016). Among these planes, the ð201Þ plane is unique in terms of its atomic arrangement; the tetrahedral GaO 4 and octahedral GaO 6 units are alternately stacked and are completely separated in a layer-by-layer manner (Fig. 2a). As depicted in the figure, the stacking sequence of the O ions is . . . abcabc . . ., where a, b and c are the indices denoting in-plane positions. The possible Burgers vectors, which are the shortest and second shortest translation vectors in the ð201Þ plane, are b 1 ¼ h010i and b 2 ¼ 1 2 h112i in both the tetrahedral and octahedral units. Fig. 2(b) shows an atomic model of the translational vector in the octahedral unit.

Dissociation
If the total self-energy of a dislocation is reduced by decomposition of the original Burgers vector into a combination of shorter Burgers vectors, dissociation occurs. In the tetrahedral units, slip between widely spread layers, that is, the Ga-O units of the -a, -b and -c pairs in Fig. 2(a), is difficult to directly dissociate into partials, which is similar to the 'shuffle set' in a diamond cubic lattice (Hirth & Lothe, 1982). On the other hand, in the octahedral Ga units, the Ga ions are positioned in a close-packed arrangement between the O layers; that is, the Ga ions at the c positions are located between the O ions at the a and b positions on the underlayer and overlayer of the Ga layer, respectively, the Ga ions at the b positions are located between the O ions at the c and a positions, and so on. 'Glide-set' dislocations as in the diamond cubic lattice are, therefore, expected in the GaO 6 units on the ð201Þ plane in -Ga 2 O 3 . As shown in Fig. 2(c), the Burgers vector b 1 ¼ AB (displacement between the c positions) dissociates into AE þ EB, where displacement occurs via a b position, that is, ½010 ! 1 18 ½192 þ 1 18 ½192. We refer to this type of dissociation as 'Shockley partials' after the case of the diamond cubic lattice.
We next consider another type of dissociation, b 2 ¼ 1 2 ½112 ¼ AC, the norm of which is larger than that between the neighboring c positions. This displacement can be composed of the three shortest c ! c displacements, for example, . This type of dissociation is analogous to the model proposed by Kronberg (1957) for basal slip in sapphire (-Al 2 O 3 ). As the longer period of the Ga ions arises from a superlattice with regularly aligned empty sites on the Ga layer, we refer to this type of dissociation as 'superlattice partials'.

Experiments
The samples used in this study were ð201Þ-oriented wafers with a diameter of two inches and a thickness of 680 mm cut from ingots grown by the EFG method in 2015. X-ray topography experiments using synchrotron radiation from a bending magnet were performed at beamlines BL-3C and BL-20B at the Photon Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization (Tsukuba, Japan), and beamlines BL09 and BL15 at the SAGA Light Source (SAGA-LS), Kyushu Synchrotron Light Research Center (Tosu, Japan). The diffraction geometry was Braggcase asymmetric diffraction with a low incident angle. The X-ray wavelength was selected using the double-crystal Si 111 monochromator such that the incident angle was optimized for each diffraction vector (g). The X-ray topographs were recorded on nuclear emulsion plates (Ilford L4).

Results
In the X-ray topographs of the ð201Þ wafers, rectangular defects were observed at appropriate values of g, in addition to several dislocations, as shown in Fig. 3; the rectangular defects were observed in the X-ray topograph measured with the 12 0 1 reflection but not in that measured with the 623 reflection. These defects are widely scattered throughout the wafer, although their density varies with the location. The finding that the rectangular defects were visible or invisible depending on g indicates that they are crystallographic defects in the crystal. As the aspect ratios of the rectangles measured with different g values were almost unchanged, the defects are presumed to lie parallel to the wafer surface ð201Þ.
Another feature of the planar defects is that they are isolated, with no connections to any dislocations. The planar defects are therefore considered to be SFs enclosed by a single partial dislocation loop on the ð201Þ plane, indicating that the fault vector of the SF should be identical to the Burgers vector of the partial dislocation loop.
The contrast of SFs in X-ray topography is associated with the relative change in the structural factors between the matrix and SF regions (Whelan & Hirsch, 1957;Kohra & Yoshimatsu, 1962). We cut a crystal along a particular plane, and shifted the upper part parallel to the plane with a vector f, the magnitude of which was smaller than the unit lattice vector, relative to the lower part. We set the structural factor for the reflection g in the lower part (matrix) as F g , such that the factor in the upper part (SF) was F g expð2if Á gÞ. When g Á f 6 ¼ (integer), the structural factors in the two parts separated by the SF were different, and the SF exhibited contrast in the diffraction intensity. To examine the nature of each SF, that is, whether they were Shockley or superlattice partials, we compared the appearances of the SFs in the X-ray topographs obtained for several values of g. The conditions under which the SFs appeared are summarized in Table 1. The results from the X-ray topographs measured with 12 0 1 and 623 reflections (Fig. 3) were found to be consistent with the contrast extinction rules regardless of the type of dissociation, that is, Shockley or superlattice partials. The ð201Þ pole figure indicating the diffraction indices with which X-ray topographs were acquired in this study is presented in Fig. 4. The experimental results relating to the g dependence of the SF appearance are summarized in Table 1(a), and some representative X-ray topographs are presented in Fig. 5. Almost all of the observed SFs exhibited the same g dependence and no obvious exceptions were found. The contrast of the SFs in the X-ray topographs was sensitive to the diffraction conditions. The existence and shape of each SF were confirmed by comparing a series of X-ray topographs acquired with small X-ray topographs of a ð201Þ-oriented wafer obtained with (a) 12 0 1 and (b) 623 reflections. Some apparent SFs are schematically depicted on the right-hand side of (a). The scale bars correspond to 100 mm.

Table 1
Conditions for the appearance of SFs in (a) ð201Þ and (b) ð001Þ wafers, jg Á f 1 j and jg Á f 2 j, for several reflections g used in this study.
The fault vectors f 1 and f 2 correspond to the Shockley and superlattice partials, respectively. The Appearance column shows whether the SFs were observed (Yes) or not observed (No). The column shows the X-ray wavelengths used for the topography, and the B and columns show the Bragg angles and the angles between the Bragg plane and the crystal surface, respectively. (up to 30 00 ) stepwise variation of the X-ray incident angle. Fig. 5 shows single shots selected from a series of X-ray topographs for each g, and therefore not all of the SFs depicted in Fig. 5(c) are readily apparent in Figs. 5(d)-5( f ). Thus the SFs observed in this study were determined to be those associated with Shockley partials. As shown in Fig. 5, six SFs were detected in a 1 mm square, meaning that the SF density in this area can be roughly estimated as 600 cm À2 . The characteristics of the SFs can be summarized as follows: (1) They are rectangular and observed parallel to the surface ð201Þ plane.
(2) One pair of sides elongates in the h010i direction, and the other pair of sides is in the perpendicular direction, h102i.
(3) They are isolated SFs associated with Shockley partials. We briefly comment about some typical dislocations found in Fig. 5. The arrays of points with bright contrast in (a), (d) and ( f ) are dislocations running through the wafer surface although their Burgers vectors are unidentified yet. We also find some lines running in the vertical direction in (b) and (e). They can be identified as screw dislocations with the Burgers vector b ¼ h010i from the g Á b relation.

Discussion
As explained in x2, the close-packed stacking structure of the ð201Þ plane enables slip between the glide-set planes. During the analysis of the SFs, we considered the possibility of the superlattice partials because they can be derived from the close-packed structure. The superlattice partials were, however, disproved experimentally by the contrast extinction rules depending on g. The other plausible possibility for the SFs is that they are associated with prismatic dislocation loops by the insertion or extraction of partial atomic layers. In this   The arrows indicate the direction of X-ray incidence. The X-ray wavelength for each topograph is listed in Table 1.  case, the fault vector would contain a component perpendicular to the ð201Þ plane, resulting in different appearance rules from those observed.
Note the vacancy arrays running along the b axis in the octahedral Ga layers (Fig. 2). If a glide-set slip between the octahedral Ga and O layers occurred with the boundary along the vacancy array, it would reduce the self-energy of dislocation along the b axis. This is because the elastic compressive or tensile stress of the edge component is reduced by the gap and no dangling bonds occur at the partial dislocation. The Ga-O bonds exhibit rotation by 60 and no polarization. The proposed SF model based on this consideration is illustrated in Fig. 6. When the highlighted region in the original structure (Fig. 6a) slips in the octahedral Ga layer, the Ga ions at the c positions slip with the boundary along the vacancy arrays parallel to the b axis over the underlying O ions at the a positions. The possible destination sites of the Ga ions after the slip are the b positions. As they slip c ! b, the resulting SF is as depicted in Fig. 6(b).
The wafers were cut from ingots grown using the EFG method with the b axis as the growth direction. The origin of the SFs is currently unclear. The SFs would be expected to elongate as the crystal grows along the b axis, which would increase their elastic energy. Eventually, the elastic energy would reach a critical value and the SF would then terminate to afford the rectangular shape observed in this study. The observed SF dimensions, 50-150 mm, may be typical values determined by the elastic energy. As no dislocations associated with the SFs were observed, SFs originating from dissociation of a dislocation are not considered here.
SFs were also observed in X-ray topographs of a (001)oriented wafer. Fig. 7 shows a comparison of images taken with 026 and 606 reflections. An SF was observed under the former but not the latter conditions, which is consistent with the contrast extinction rules for Shockley SFs as summarized in Table 1(b). The SF was as wide as 30 mm, which is less than the typical width observed in the ð201Þ wafers. Upon taking into account the crossing angle between the ð201Þ and ð001Þ planes, which is 50 toward the left-hand side in Fig. 7(a), the apparent width of the SF on the ð201Þ plane shrinks by a factor of cos 50 . Although the true width of the SF is unknown, the SF observed in the (001)-oriented wafer can be regarded as originating from a Shockley partial dislocation loop on the ð201Þ plane, which is identical to that observed in the ð201Þoriented wafers.
The SFs were found to be scattered in the wafers and possibly created by the crystal growth and/or subsequent cooling processes, although the underlying mechanism remains unclear at present. The observation of SFs in this study partially supports our hypothetical slip system, ð201Þh010i (Yamaguchi et al., 2016). This means that the SFs may be glissile, potentially leading to enlargement of the SFs by stress or other factors. As demonstrated for SiC diodes, glissile partial dislocations affect degradation in forward-bias operations owing to the recombination-enhanced dislocation glide effect (Maximenko et al., 2005). The SFs in -Ga 2 O 3 wafers, therefore, should be eliminated for electronic device applications.

Conclusion
X-ray topography analysis revealed the presence of SFs in -Ga 2 O 3 wafers grown by the EFG method. These SFs were found to be associated with a Shockley-type partial dislocation loop on the basis of the appearance rules determined by varying the value of g used during the X-ray topography. An SF model was proposed by considering the close-packed stacking structure of the GaO 6 octahedral units in the ð201Þ plane, on the assumption that the partial dislocation occurs at the gap in the Ga layer along the b axis. The occurrence of crystallographic defects such as dislocations and SFs is an important issue for the fabrication of electronic devices. Further studies of these SFs should be performed to elucidate their generation mechanism during the crystal growth process, their development during device processing and their effects on the electronic properties of the final devices, as well as the detailed characteristics and properties of SFs and other crystallographic defects.