We performed Borrmann effect x-ray topography (XRT) to observe dislocations and other structural defects in a thick β-Ga2O3 (001) substrate. The Borrmann effect was realized by working in a symmetrical Laue geometry (g = 020). Anomalous transmission occurred under the exact Bragg condition, producing a strong diffraction beam that allowed us to image defects across the entire thickness of the substrate. The analysis clearly revealed straight b-axis screw-type and curved dislocations and allowed assessing the corresponding behaviors. Other structural defects, including pipe-shaped voids and dislocation loops produced by mechanical damage, were also observed. Finally, we compared Borrmann effect transmission topography and conventional reflection topography and explained the appearance of some characteristic defects in the two modes. Our results show that Borrmann effect XRT is a powerful and effective technique to study the spatial distribution and structural properties of defects in highly absorbing β-Ga2O3.

Owing to its superior physical properties, β-Ga2O3 has attracted increasing attention as a promising wide-bandgap semiconductor for realizing high-voltage and large-current power devices able to operate at high temperatures.1 However, one of the factors limiting the performance and reliability of β-Ga2O3 devices is the occurrence of crystallographic defects, especially dislocations present at densities of 103–105 cm−2. Various techniques have been applied to obtain information on dislocation characteristics such as density, spatial distribution, and structural properties, including chemical etch pitting,2–8 transmission electron microscopy (TEM),6,8–10 and x-ray topography (XRT).11–18 Among these techniques, XRT is the only one that can image dislocations across a wide sample area in a non-contact and non-destructive manner, while simultaneously assessing the dislocation character in terms of the Burgers vectors.

However, XRT observations of β-Ga2O3 have been limited to reflection topography measurements based on the Berg–Barrett configuration (Bragg case).11–18 In this configuration, the penetration depth of the x rays is typically no greater than 20 μm;15 therefore, dislocations in the deeper regions of the crystals cannot be imaged. To the best of our knowledge, no successful transmission topography (Laue case) observations have been reported for this material. This is mainly due to the high x-ray absorption of β-Ga2O3 because of the presence of heavy Ga atoms. Obtaining transmission topography images of β-Ga2O3 based on extinction contrast would require a very thin crystal (<100 µm) to satisfy the μt ∼ 1 condition (where μ is the linear absorption coefficient and t is the sample thickness).19 It is extremely difficult to obtain such thin crystals because of the high cleavability and high brittleness of β-Ga2O3.20,21 Because transmission topographs are not available, the three-dimensional (3D) distribution of dislocations in the interior of β-Ga2O3 remains unknown; this precludes the analysis of the behavior of dislocations on a wafer scale, such as their generation, multiplication, and interaction during crystal growth.

To perform transmission topography measurements, one way to circumvent the thickness requirement is to take advantage of the anomalous transmission of x rays, a dynamical diffraction phenomenon also known as the Borrmann effect.22–24 For a highly perfect and thick (μt ∼ 10)24 crystal oriented for Laue geometry diffraction, the two plane waves, respectively, corresponding to the primary and diffracted x rays are coherently coupled in the crystal, and their interference produces a set of standing waves. When the zero-amplitude points (nodes) of the standing waves coincide with the atomic planes (i.e., the Bragg reflection planes), the intensity of photoelectric absorption is significantly reduced, with a corresponding marked increase in the intensity of the transmitted x rays, known as anomalous transmission.23 This phenomenon allows obtaining an XRT image based on the dynamical diffraction contrast, which would otherwise be impossible to achieve with the kinematical diffraction contrast, due to the strong x-ray absorption by the Ga atoms. This suggests that any crystallographic defect such as dislocations, inclusions, or voids will eliminate the local Borrmann effect because atoms would be displaced from the nodal planes, causing an increased photoelectric absorption. Contrasts corresponding to these defects will, thus, be observed in the XRT images. Although the Borrmann effect has been observed in many metal and semiconductor materials with high-symmetry structures, such as Cu,25–27 Al,28 Si,29–33 Ge,34,35 InSb,36 and GaN,37 it has never been experimentally confirmed for the low-symmetry and highly anisotropic monoclinic structure of β-Ga2O3.

In this paper, we demonstrate the application of Borrmann effect XRT for observing dislocations and other defects in a thick β-Ga2O3 single-crystal substrate using a synchrotron x-ray source. To the best of our knowledge, this is the first report of the 3D distribution and line direction of dislocations in the interior of this material, further revealing its characteristic dislocation propagation and interaction behaviors. In addition to grown-in dislocations, we also determined the image contrasts associated with surface polishing scratches, pipe-shaped voids, and mechanical damage-induced dislocation loops. Our results suggest that Borrmann effect XRT is a powerful technique to observe dislocations inside a thick and highly absorbing β-Ga2O3 crystal; this task cannot currently be performed with any other techniques. We also show that, for a low-symmetry crystal structure such as the monoclinic β-Ga2O3 studied here, it is necessary to use specific low-index planes [i.e., the (020) planes in this case] to allow the strongest Borrmann effect to occur.

The sample investigated in this study was a (001)-oriented β-Ga2O3 single-crystal substrate fabricated via edge-defined film-fed growth (EFG). The sample was doped with Sn at a donor concentration of 8.4 × 1018 cm−3. The substrate had a rectangular shape of 10 × 15 mm2 and a thickness of 680 µm. The 10-mm side was parallel to the [010] direction. Both surfaces of the substrate were polished to an epi-ready standard by chemical–mechanical polishing (CMP). The full-width at half maximum (FWHM) values of the (002) ω-rocking curves were ∼20 arcsec, as measured by x-ray diffraction (XRD).38 

Monochromatic beam XRT measurements were performed with a synchrotron radiation (SR) x-ray source at the beamlines BL-3C and BL-14B of the Photon Factory at the High-Energy Accelerator Research Organization (KEK), Japan. The optical system is shown schematically in Fig. 1. The sample was fixed to a supporting frame mounted on a five-axis goniometer with a minimum ω step of 0.0002°. The (020) planes were used as reflecting planes (i.e., g = 020) to achieve the Borrmann effect. As the entrance and exit surfaces of the crystal were perpendicular to the (020) planes, the above configuration corresponded to the symmetrical Laue case. The sample orientation was carefully adjusted so that it could exactly satisfy the Bragg condition for the g = 020 reflection at a certain ω position. Such an adjustment included two major steps: (1) positioning the incident x rays and the detectors onto the designated plane of incidence (the plane of the paper in Fig. 1) and (2) adjusting the ω angle to attain the maximum intensity of the forward and diffracted x rays.39 These intensities were monitored simultaneously using an image detector and a PiN x-ray photon counter, respectively. The g = 022 reflection was also used for comparison in order to assess whether the Borrmann effect could also be achieved for asymmetrical reflections, i.e., when the reflecting planes are not perpendicular to the entrance and exit surfaces.

FIG. 1.

Schematic illustration of the optical system.

FIG. 1.

Schematic illustration of the optical system.

Close modal

In the case of the transmission topography measurements using g = 020 and 022, the wavelength (λ) of the incident x rays was fixed at 1.25 Å so that the μt ∼ 10 condition was satisfied for the 680 μm-thick sample. For comparison, reflection topography measurements were also performed with g = 024 (a 0kl type g-vector) and g = 10̄05 (a h0l type g-vector) reflections with λ = 1.53 Å; in these cases, the penetration depth was estimated to be ∼6.9 μm.15 In all cases, the XRT images were recorded using the diffracted x rays (Fig. 1) on Agfa Structurix D2 x-ray films, or with a CMOS camera equipped with a scintillator and relay lenses.40 

The black symbols in Fig. 2(a) show the linear absorption coefficient μ as a function of the x-ray wavelength λ.41 The corresponding sample thickness required to satisfy the μt = 10 condition is shown by the red symbols. After crossing the K-edge of Ga at λ = 1.196 Å,42μ dramatically decreased on the longer wavelength side, enabling typical substrate thicknesses ranging from 500 to 800 μm to satisfy the μt ∼ 10 requirement for the Borrmann effect. Based on Fig. 2(a), λ was determined to be 1.25 Å for the 680 μm-thick sample. Figure 2(b) shows the intensity of the diffracted x rays as a function of ∆ω (representing the departure from the Bragg condition) for g = 020 and 022. A very intense diffraction was observed at the exact Bragg condition for g = 020, which was ∼80 times stronger than that observed for g = 022. The increase in intensity for g = 020 was too large to be solely attributed to the difference between the structure factors of the (020) and (022) planes, or between the entrance/exit angles for the two g-vectors. For comparison, we could not obtain an equally strong diffraction in transmission topographs, even with a thin AlN reference sample with μt < 1. The intensity of the forward x rays provided clear evidence that the strong 020 diffraction of β-Ga2O3 was due to the Borrmann effect: the forward diffracted x-ray intensity peaked at ∆ω = 0 for g = 020. This is consistent with the theoretical description of the Borrmann effect, according to which the x-ray energy flows along the reflecting planes and the standing waves decompose evenly into transmitted and diffracted beams upon leaving the Borrmann fan.43 The above results show that a strong Borrmann effect emerged under the exact Bragg condition for the symmetrical reflection g = 020,39 while the Borrmann effect was not so marked for the asymmetrical g = 022 reflection.

FIG. 2.

(a) Plot of linear absorption coefficient vs x-ray wavelength (black symbols) and corresponding sample thickness required to satisfy μt = 10 condition (red symbols). (b) Plot of intensity of diffracted x rays vs departure from the Bragg condition for g = 020 (black) and g = 022 (red). (c) Atomic arrangement along the projections of the (020) and (022) planes, visualized using the VESTA software.44 

FIG. 2.

(a) Plot of linear absorption coefficient vs x-ray wavelength (black symbols) and corresponding sample thickness required to satisfy μt = 10 condition (red symbols). (b) Plot of intensity of diffracted x rays vs departure from the Bragg condition for g = 020 (black) and g = 022 (red). (c) Atomic arrangement along the projections of the (020) and (022) planes, visualized using the VESTA software.44 

Close modal

Next, we explain why the anomalous transmission occurred readily with g = 020 but not with g = 022 and discuss which crystal planes can be used as reflecting planes to achieve the Borrmann effect. Figure 2(c) shows the atomic arrangement along the projections of the (020) and (022) planes, visualized using the VESTA software.44 β-Ga2O3 has a monoclinic structure belonging to the C2/m space group. The b-axis is perpendicular to the plane defined by the a- and c-axes, but the latter are not orthogonal to each other: they form an obtuse angle of 103.87°.45 As shown in Fig. 2(c), all the (020) planes are crystallographically equivalent and share the same interplanar spacing, equal to half of the lattice constant b; moreover, all the Ga atoms are contained in the (020) planes. In contrast, the structure presents two types of (022) planes [marked as (022)I and (022)II in Fig. 2(c)], whose spacing is not uniform. This is a direct result of the low symmetry of the C2/m space group. Consequently, the strongest Borrmann effect was realized with g = 020 in the monoclinic crystal but not with g = 022, because in the latter case, the nodal planes of the standing wave cannot simultaneously coincide with the two types of (022) planes. The same argument applies to other low-index planes, including (100), (001) (2̄01), and (102̄)16 (see supplementary material, Fig. S1). A similar phenomenon was reported for single-crystal Ge in which planes such as (220), (224̄), and (004) contain all the atoms, whereas the (111) plane does not.46 Based on these considerations, we anticipate that g-vectors that allow the strongest Borrmann effect to occur in β-Ga2O3 should have the form 0k0, i.e., without a- or c-axis components. Furthermore, taking into account the range of x-ray wavelengths available at our SR facility, g = 020 represents the most suitable option. The so-called super-Borrmann effect47,48 associated with n-beam diffraction appears extremely difficult to achieve for β-Ga2O3, in contrast with the highly symmetric Si, Ge, and diamond materials.

Figure 3 shows the Borrmann effect XRT images for g = 020, with dark contrast areas corresponding to a strong x-ray exposure (negative images). Figure 3(a) shows a region of 15 × 1.7 mm2, schematically illustrated as the red ribbon-shaped area in Fig. 3(b). The image was recorded on an x-ray film by single exposure for 10 s during which the ω angle was fixed. The image shows almost no contrast on the two sides of the 1.7 mm-wide area due to their extremely low x-ray exposure. The incident beam had a rectangular shape of ∼17 mm in the [100] vertical direction and 6 mm in the [010] horizontal direction. In the [100] direction, the full 15 mm-long sample could be imaged from edge to edge without notable contrast gradient, indicating that the crystal plane curvature in the [100] direction, if any, did not prevent the occurrence of the Borrmann effect; this is due to the fact that the [100] direction was orthogonal to the plane of incidence, making the Bragg condition insensitive to its curvature. This observation is in agreement with our previous study.49,50 In contrast, in the [010] direction, the Borrmann effect could only be realized within an ∼1.7 mm-wide ribbon-shaped area, despite the much greater beam width of 6 mm. This result clearly shows that the Borrmann effect in the present configuration is sensitive to the crystal plane curvature in the [010] direction, which is contained in the plane of incidence.49,50 Even a slight curvature in this direction results in a departure from the exact Bragg condition, leading to a reduced Borrmann effect. Assuming that the radius of curvature in the [010] direction was 100 m,50 the Bragg angle would change by ∼13 arcsec for every 1 mm variation in the sample position, which explains why the Borrmann effect was not achieved outside the 1.7 mm-wide area.26 An animation illustrating how the area where anomalous transmission can occur varies with the Bragg angle is shown in the supplementary material, Animation A1.

FIG. 3.

Borrmann effect XRT images for g = 020. (a) A 15 × 1.7 mm2 area recorded on an x-ray film by single exposure for 10 s, during which the ω angle was fixed. (b) Schematic model of the sample structure. (c)–(e) Dislocation images obtained from several representative areas.

FIG. 3.

Borrmann effect XRT images for g = 020. (a) A 15 × 1.7 mm2 area recorded on an x-ray film by single exposure for 10 s, during which the ω angle was fixed. (b) Schematic model of the sample structure. (c)–(e) Dislocation images obtained from several representative areas.

Close modal

The XRT image presented in Fig. 3(a) shows high-density straight lines parallel to the [010] direction, in addition to many curved lines running in random directions. The highly defective area near the bottom edge was a surface scratch, created as a position marker. Figures 3(c)3(e) shows the details of several typical areas. The dominant features of the XRT image were the [010] line contrasts, most of which were associated with b-axis screw-type dislocations having a Burgers vector (b) parallel to [010]. They can be considered as threading dislocations if viewed along the EFG pulling-up (i.e., ⟨010⟩) direction. Because the b-axis is the shortest among the three principal crystallographic axes of the monoclinic structure, the ⟨010⟩ Burgers vector corresponds to the smallest translation vector in this system. Consequently, b-axis screw-type dislocations have a high generation probability and are frequently observed by reflection topography11,13,15 and other techniques.3,9,10 The gb∥[010] relationship of the b-axis screw-type dislocations produces maximum contrast for these dislocations in the g = 020 topograph. In the transmission topograph, dislocations present along the entire sample thickness of 680 μm were observed as projected images; as a result, the b-axis screw-type dislocations significantly overlapped with each other. Individual dislocations of this type can only be resolved occasionally in areas with low dislocation density. Some examples are marked by yellow arrows in the enlarged image shown in Fig. 3(c). The dashed box in Fig. 3(d) (200 μm wide in the [100] direction) contains ∼10 lines, as counted from the contrast profile. This corresponds to a dislocation density of 7.4 × 103 cm−2 viewed from the (010) face, which is in good agreement with the reported value obtained from chemical etch pitting.3,51 The b-axis screw-type dislocations were typically long (>1 mm) and straight, presumably because this configuration was stable and represented the lowest dislocation energy during (010)-face EFG, but they could also deflect onto the (010) or pyramidal planes and then back to the [010] direction, leaving superjog-like features in the dislocation lines.52–54 Some examples are indicated by dotted circles in Fig. 3(d).

Curved line contrasts appeared at a much lower density than the [010] lines. Unlike reflection topography, transmission topography projects dislocations across the entire sample thickness; therefore, the length of the curved lines is not sufficient to conclude that they represent dislocations lying on the (001) plane parallel to the sample surface. However, in Borrmann effect topographs, dislocations close to the exit surface are known to exhibit sharper contrast32,55 than those located close to the entrance surface; therefore, the dislocation direction can be estimated from the line thickness. We found that a large proportion of the curved lines did correspond to (001) plane dislocations. Regarding the Burgers vectors, these curved dislocations had, or at least contained, the b-axis component, according to the gb invisibility criterion. It has been reported that ⟨010⟩(001) is one of the major slip systems in β-Ga2O3, which is active above ∼950 °C.15,16,56 During the cooling-down phase after crystallization from the melt (melting point >1700 °C21,51,57), dislocations with b = ⟨010⟩ can glide on the (001) plane.

We observed some characteristic dislocation propagation and interaction behaviors that have not been reported in previous reflection topography studies. One of these mechanisms resulted in the dislocation spiral marked by the yellow arrows in Fig. 3(d). The spiral consisted of five segments, labeled S1–S5 in the figure. Each segment had a different line thicknesses from its neighbors, indicating their different depths relative to the sample surface, i.e., they did not lie on the same (001) plane. The parts interconnecting two adjacent segments at the turnaround points likely represent edge-type superjogs nearly perpendicular to the (001) plane, which cannot glide in this system. Pinned by the jogs at two ends, each segment can glide on its own (001) plane. This configuration resembles the dislocation dipoles locked by an edge-type jog typically found in 4H–SiC grown by physical vapor transport,58,59 although the mechanism behind their formation might be different. The observation of the dislocation spiral confirms the conclusions that ⟨010⟩(001) is a major slip system. Other characteristic dislocation configurations included the w-shaped dislocations marked by the green arrows in Fig. 3(d). Based on their line thicknesses, these dislocations lay on the same (001) plane. Because their segments were typically straight, they might contain a Burgers vector component directed out of the (001) plane, which prevented them from gliding. The image in Fig. 3(e) displays an intriguing dislocation interaction. S1 and S2 originally lay on different (001) planes, as implied by their line thicknesses; then, they reacted by climbing and zipping a binary junction.60 Dislocation climbing between (001) planes has not been reported previously.

Because the Borrmann effect requires a high crystalline perfection, in theory any type of structural defect that destroys the lattice periodicity can be imaged. Figure 4 shows an area containing several polishing scratches on the exit surface. These scratches were made during mechanical polishing and were not completely removed by the subsequent CMP. The line thicknesses in the XRT image [Fig. 4(a)] are positively correlated with those in the optical image [Fig. 4(b), indicated by yellow arrows]. This is in agreement with our previous studies, which showed that, for a given material, the geometrical dimensions of the surface damage imprints are linearly proportional to the size of the dislocation loops generated beneath the imprints in both the lateral and vertical directions.61,62 Only the scratches on the exit surface were clearly observed, whereas those on the entrance surface generated diffuse contrasts that were barely discernible, consistent with previous studies.32,55 The dislocations in the interior of the crystal could be imaged without being affected by the presence of the scratches; as shown in Fig. 4(a), many dislocation line contrasts intersected the scratches without bending. It should be noted that carefully polishing both surfaces using CMP is a necessary requirement to obtain Borrmann effect x-ray topographs. Surface damage, especially that associated with large residual strain on the entrance surface, significantly affects the anomalous transmission.

FIG. 4.

(a) Borrmann effect XRT image of the area containing surface scratches (yellow arrows) and pipe-shaped voids (green arrows). (b) Optical image of the same area.

FIG. 4.

(a) Borrmann effect XRT image of the area containing surface scratches (yellow arrows) and pipe-shaped voids (green arrows). (b) Optical image of the same area.

Close modal

Another characteristic defect type consisted of pipe-shaped voids, with a length of several millimeters extending in the [010] direction. Some examples are indicated by green arrows in Fig. 4(b). When viewed from the (001) surface, these voids were located at different depths and could be observed with a normal optical microscope by adjusting the focus inside the crystal. They appeared in the XRT images [Fig. 4(a)] as thick bright lines in the [010] direction, which were difficult to distinguish from the lines corresponding to b-axis screw-type dislocations. It has been reported that Borrmann effect XRT is effective for imaging voids in nearly perfect crystals; this was explained by considering the dynamical diffraction caused from lattice distortion near the voids.35 The density of the pipe-shaped voids in the present sample was estimated to be 9 × 102 cm−2 when viewed from the (010) face. We could not estimate the [100] dimension of the voids from the Borrmann effect XRT images, because the lattice distortion extended far beyond the physically hollow region. Voids in the [010] direction were also reported by other groups. Using TEM, Nakai et al. observed nanopipe structures in β-Ga2O3 prepared by EFG.10 These structures had widths of ∼0.1 μm and were undetectable by XRT because they were not accompanied by strain. Similar voids were also found in separate studies of crystals grown by EFG9 and via the vertical Bridgman (VB) method.63 The origin of voids in EFG-grown β-Ga2O3 remains unclear. It was suggested that they might be associated with bubbles formed at the liquid–solid interface during crystal growth.2 It is reasonable to believe that the pipe-shaped voids can be detrimental to the performance of β-Ga2O3 electronic devices, based on results obtained for 4H–SiC64–67 and GaN68,69 devices.

Figure 5 shows the dislocation loops generated from mechanical damage, typically found near the sample edges. The position of the latter is indicated by red and blue lines. As shown in Fig. 5(a), many dislocation loops originated from the bottom edge parallel to the (100) face and glided on the (001) plane following the ⟨010⟩(001) slip system, presumably under shear stress during slicing. The sample edges appeared fairly sharp in the XRT image, indicating that the strained area was localized within no more than ∼20 μm from the edges. In contrast, at the edges of the (010) face indicated by blue lines, the strained area extended much deeper along the [01̄0] direction. As shown in Fig. 5(b), only diffuse contrast could be observed within ∼500 μm from the edges, and no individual dislocations were resolved. Dislocation loops forming ripple patterns were observed on the left side of the strained area and were also attributed to the ⟨010⟩(001) slip system. The dislocation loops deriving from surface scratches [Fig. 5(c)] resembled those observed near the edges of the (010) face. Two important conclusions can be drawn from these results. First, the (010) face is more vulnerable to mechanical damage than the (100) or (001) ones, which is consistent with the findings of Yamaguchi et al..70 This can be explained by the fact that the (010) face is perpendicular to both the (100) and (001) faces that are two major cleavage planes of β-Ga2O3. Second, mechanical damage can generate dislocation loops,71 and ⟨010⟩(001) appears to be a readily activated slip system.

FIG. 5.

Dislocation loops generated from mechanical damage (a) near the bottom edge parallel to the (100) face, (b) near the right edge parallel to the (010) face, and (c) near a surface scratch. The scale bar applies to all three images.

FIG. 5.

Dislocation loops generated from mechanical damage (a) near the bottom edge parallel to the (100) face, (b) near the right edge parallel to the (010) face, and (c) near a surface scratch. The scale bar applies to all three images.

Close modal

Figure 6 shows a comparison of Borrmann effect transmission and conventional reflection topography images taken from the entrance surface. The b-axis screw-type dislocations, indicated by red solid and hollow arrows, exhibited a much lower density in the reflection topograph, owing to the small x-ray penetration depth. When the g-vector was not orthogonal to [010], e.g., g = 024, the dislocations were displayed as thin lines; however, they exhibited no contrast at g = 10̄ 05, due to their pure screw character. Identifying the same dislocations in the transmission topograph is difficult, because of their high density. Several curved dislocations were marked by green solid and hollow arrows in Fig. 6. They exhibited contrast at g = 020 and g = 024, but not at g = 10̄05, indicating that their Burgers vector was parallel to the ⟨010⟩ direction. Their very weak contrast at g = 024 suggests they were located at some distance from the surface. The blue arrows indicate pipe-shaped voids. If close to the surface, these voids appeared in the reflection topograph regardless of what g-vectors were used,15 confirming that they were physical hollow regions rather than dislocations. Strained areas caused by mechanical damage near the sample edges appeared as diffuse bright areas in the transmission topograph [right side of Fig. 6(a)]; however, the reflection topograph was not affected by them.

FIG. 6.

Comparison of (a) Borrmann effect transmission topograph with g = 020 and reflection topographs with (b) g = 024 and (c) g = 10̄05.

FIG. 6.

Comparison of (a) Borrmann effect transmission topograph with g = 020 and reflection topographs with (b) g = 024 and (c) g = 10̄05.

Close modal

To examine dislocations and other structural defects in thick β-Ga2O3 substrates, we have performed x-ray topography measurements in the transmission mode, taking advantage of the Borrmann effect. It was found that the strongest Borrmann effect could be observed in symmetrical Laue geometry (g = 020 in this case), but the Borrmann effect was not as marked for asymmetrical g-vectors. This was explained by considering the atomic arrangement along the projections of the Bragg reflection planes, which showed that (020) planes had equal interplanar spacing and could, thus, contain all Ga atoms, whereas (022) planes did not. Anomalous transmission occurred at the exact Bragg condition g = 020, producing a strong diffraction beam that allowed imaging the dislocations and other defects across the entire sample thickness. Straight [010]-oriented lines were a dominant feature in the transmission topograph; most of them were attributed to b-axis screw-type dislocations, while the others were generated by pipe-shaped voids. Curved dislocations exhibited a lower density; the corresponding analysis revealed some characteristic propagation and interaction behaviors, including the formation of dislocation spirals and dislocation climbing. Dislocation loops originating from mechanical damage, either surface scratches or diced edges, were also observed and attributed to the ⟨010⟩(001) slip system under shear stress. Finally, we compared transmission and reflection topographs and discussed the appearance of the structural defects mentioned above in the corresponding images. The present results show that Borrmann effect XRT is a powerful and effective technique to study defects in highly absorbing β-Ga2O3.

See the supplementary material for the atomic arrangements along the projections of various crystal planes (Fig. S1). An animation illustrating how the area where anomalous transmission can occur varies with the Bragg angle is shown in Animation 1.

This study was supported by (1) the JSPS KAKENHI, Japan, under Grant No. 20K05355; (2) the Murata Science Foundation, Japan; (3) the Nippon Sheet Glass Foundation for Materials Science and Engineering, Japan; and (4) the Kazuchika Okura Memorial Foundation, Japan. K.S. and A.K. acknowledge support from the ATLA-S project. The synchrotron XRT observations were performed at KEK-PF under Proposal Grant Nos. 2018G501 and 2020G585. Y.Y. was deeply grateful to Professor Dr. Y. Tsusaka and Professor Dr. J. Matsui for helpful advice and discussions on dynamical XRD theory.

The authors have no conflicts of interest to disclose.

Y.Y. designed and performed the experiments, analyzed the data, and wrote the manuscript. K.H. built the optical system for XRT measurements. Y.S. helped with the XRT experiments. K.S. and A.K. grew the crystals. Y.I. supervised the work and helped revising the manuscript. All authors have reviewed and approved the manuscript.

Raw data were generated at the KEK-PF synchrotron facility. The data that support the findings of this study are available within the article and its supplementary material.

1.
S. J.
Pearton
,
F.
Ren
,
M.
Tadjer
, and
J.
Kim
, “
Perspective: Ga2O3 for ultra-high power rectifiers and MOSFETS
,”
J. Appl. Phys.
124
,
220901
(
2018
).
2.
K.
Hanada
,
T.
Moribayashi
,
K.
Koshi
,
K.
Sasaki
,
A.
Kuramata
,
O.
Ueda
, and
M.
Kasu
, “
Origins of etch pits in β-Ga2O3(010) single crystals
,”
Jpn. J. Appl. Phys.
55
,
1202BG
(
2016
).
3.
M.
Kasu
,
K.
Hanada
,
T.
Moribayashi
,
A.
Hashiguchi
,
T.
Oshima
,
T.
Oishi
,
K.
Koshi
,
K.
Sasaki
,
A.
Kuramata
, and
O.
Ueda
, “
Relationship between crystal defects and leakage current in β-Ga2O3 Schottky barrier diodes
,”
Jpn. J. Appl. Phys.
55
,
1202BB
(
2016
).
4.
M.
Kasu
,
T.
Oshima
,
K.
Hanada
,
T.
Moribayashi
,
A.
Hashiguchi
,
T.
Oishi
,
K.
Koshi
,
K.
Sasaki
,
A.
Kuramata
, and
O.
Ueda
, “
Crystal defects observed by the etch-pit method and their effects on Schottky-barrier-diode characteristics on (-201) β-Ga2O3
,”
Jpn. J. Appl. Phys.
56
,
091101
(
2017
).
5.
Y.
Yao
,
Y.
Ishikawa
, and
Y.
Sugawara
, “
Revelation of dislocations in β-Ga2O3 substrates grown by edge-defined film-fed growth
,”
Phys. Status Solidi A
217
,
1900630
(
2020
).
6.
Y.
Yao
,
Y.
Sugawara
, and
Y.
Ishikawa
, “
Observation of dislocations in β-Ga2O3 single-crystal substrates by synchrotron X-ray topography, chemical etching, and transmission electron microscopy
,”
Jpn. J. Appl. Phys.
59
,
045502
(
2020
).
7.
K.
Ogawa
,
N.
Ogawa
,
R.
Kosaka
,
T.
Isshiki
,
Y.
Yao
, and
Y.
Ishikawa
, “
Three-dimensional observation of internal defects in a β-Ga2O3 (001) wafer using the FIB–SEM serial sectioning method
,”
J. Electron. Mater.
49
,
5190
(
2020
).
8.
Y.
Yao
,
Y.
Sugawara
,
K.
Sato
,
D.
Yokoe
,
K.
Sasaki
,
A.
Kuramata
, and
Y.
Ishikawa
, “
Etch pit formation on β-Ga2O3 by molten KOH+NaOH and hot H3PO4 and their correlation with dislocations
,”
J. Alloys Compd.
910
,
164788
(
2022
).
9.
O.
Ueda
,
N.
Ikenaga
,
K.
Koshi
,
K.
Iizuka
,
A.
Kuramata
,
K.
Hanada
,
T.
Moribayashi
,
S.
Yamakoshi
, and
M.
Kasu
, “
Structural evaluation of defects in β-Ga2O3 single crystals grown by edge-defined film-fed growth process
,”
Jpn. J. Appl. Phys.
55
,
1202BD
(
2016
).
10.
K.
Nakai
,
T.
Nagai
,
K.
Noami
, and
T.
Futagi
, “
Characterization of defects in β-Ga2O3 single crystals
,”
Jpn. J. Appl. Phys.
54
,
051103
(
2015
).
11.
H.
Yamaguchi
,
A.
Kuramata
, and
T.
Masui
, “
Slip system analysis and X-ray topographic study on β-Ga2O3
,”
Superlattices Microstruct.
99
,
99
(
2016
).
12.
H.
Yamaguchi
and
A.
Kuramata
, “
Stacking faults in β-Ga2O3 crystals observed by X-ray topography
,”
J. Appl. Crystallogr.
51
,
1372
(
2018
).
13.
S.
Masuya
,
K.
Sasaki
,
A.
Kuramata
,
S.
Yamakoshi
,
O.
Ueda
, and
M.
Kasu
, “
Characterization of crystalline defects in β-Ga2O3 single crystals grown by edge-defined film-fed growth and halide vapor-phase epitaxy using synchrotron X-ray topography
,”
Jpn. J. Appl. Phys.
58
,
055501
(
2019
).
14.
N. A.
Mahadik
,
M. J.
Tadjer
,
P. L.
Bonanno
,
K. D.
Hobart
,
R. E.
Stahlbush
,
T. J.
Anderson
, and
A.
Kuramata
, “
High-resolution dislocation imaging and micro-structural analysis of HVPE-β-Ga2O3 films using monochromatic synchrotron topography
,”
APL Mater.
7
,
022513
(
2019
).
15.
Y.
Yao
,
Y.
Sugawara
, and
Y.
Ishikawa
, “
Identification of Burgers vectors of dislocations in monoclinic β-Ga2O3 via synchrotron x-ray topography
,”
J. Appl. Phys.
127
,
205110
(
2020
).
16.
Y.
Yao
,
Y.
Ishikawa
, and
Y.
Sugawara
, “
Slip planes in monoclinic β-Ga2O3 revealed from its {010} face via synchrotron X-ray diffraction and X-ray topography
,”
Jpn. J. Appl. Phys.
59
,
125501
(
2020
).
17.
Y.
Yao
,
Y.
Ishikawa
, and
Y.
Sugawara
, “
Dislocation classification of a large-area β-Ga2O3 single crystal via contrast analysis of affine-transformed X-ray topographs
,”
J. Cryst. Growth
548
,
125825
(
2020
).
18.
S.
Sdoeung
,
K.
Sasaki
,
K.
Kawasaki
,
J.
Hirabayashi
,
A.
Kuramata
, and
M.
Kasu
, “
Polycrystalline defects—origin of leakage current—in halide vapor phase epitaxial (001) β-Ga2O3 Schottky barrier diodes identified via ultrahigh sensitive emission microscopy and synchrotron X-ray topography
,”
Appl. Phys. Express
14
,
036502
(
2021
).
19.
Y.
Tsusaka
,
H.
Mizuochi
,
M.
Imanishi
,
M.
Imade
,
Y.
Mori
, and
J.
Matsui
, “
Identification of dislocation characteristics in Na-flux-grown GaN substrates using bright-field X-ray topography under multiple-diffraction conditions
,”
J. Appl. Phys.
125
,
125105
(
2019
).
20.
S. J.
Pearton
,
J.
Yang
,
P. H.
Cary
,
F.
Ren
,
J.
Kim
,
M. J.
Tadjer
, and
M. A.
Mastro
, “
A review of Ga2O3 materials, processing, and devices
,”
Appl. Phys. Rev.
5
,
011301
(
2018
).
21.
Z.
Galazka
, “
β-Ga2O3 for wide-bandgap electronics and optoelectronics
,”
Semicond. Sci. Technol.
33
,
113001
(
2018
).
22.
G.
Borrmann
, “
Die Absorption von Röntgenstrahlen im Fall der Interferenz
,”
Z. Phys.
127
,
297
(
1950
).
23.
B. W.
Batterman
and
H.
Cole
, “
Dynamical diffraction of x rays by perfect crystals
,”
Rev. Mod. Phys.
36
,
681
(
1964
).
24.
A.
Authier
,
Dynamical Theory of X-Ray Diffraction
, Revised ed. (
Oxford University Press Inc.
,
New York
,
2001
), pp.
139
147
.
25.
F. W.
Young
,
F. A.
Sherrill
, and
M. C.
Wittels
, “
Observations of dislocations in copper using Borrmann transmission topographs
,”
J. Appl. Phys.
36
,
2225
(
1965
).
26.
M. C.
Wittels
,
F. A.
Sherrill
, and
F. W.
Young
, “
Anomalous transmission of X rays in copper crystals
,”
Appl. Phys. Lett.
2
,
127
(
1963
).
27.
A.
Merlini
and
F. W.
Young
, “
Borrmann topographic investigation on dislocation configuration in well-annealed and lightly deformed copper crystals
,”
J. Phys., Colloq.
27
,
C3
-
219
(
1966
).
28.
K.
Nakajima
and
S.
Koda
, “
Borrmann effect observed in an aluminium single crystal
,”
Nature
187
,
53
(
1960
).
29.
J. R.
Patel
and
B. W.
Batterman
, “
Impurity clustering effects on the anomalous transmission of X rays in silicon
,”
J. Appl. Phys
34
,
2716
(
1963
).
30.
J. R.
Patel
, “
X-ray anomalous transmission and topography of impurity clustering in perfect crystals
,”
Bull. Soc. Fr. Mineral. Cristallogr.
95
,
700
(
1972
).
31.
A.
Hauer
and
S. J.
Burns
, “
Observation of an x-ray shuttering mechanism utilizing acoustic interruption of the Borrmann effect
,”
Appl. Phys. Lett.
27
,
524
(
1975
).
32.
E. D.
Jungbluth
, “
Dislocation contrast in anomalous transmission X-ray topographs of Si
,”
Appl. Phys. Lett.
7
,
302
(
1965
).
33.
I. A.
Smirnova
,
E. V.
Shulakov
, and
E. V.
Suvorov
, “
Forming an edge dislocation image at anomalous X-ray transmission
,”
Phys. Solid State
61
,
1444
(
2019
).
34.
D.
Ling
and
H.
Wagenfeld
, “
Anomalous transmission of X-rays in perfect single germanium crystals at liquid nitrogen temperature
,”
Phys. Lett.
15
,
8
(
1965
).
35.
K.-P.
Gradwohl
,
A. N.
Danilewsky
,
M.
Roder
,
M.
Schmidbauer
,
J.
Janicskó-Csáthy
,
A.
Gybin
,
N.
Abrosimov
, and
R. R.
Sumathi
, “
Dynamical X-ray diffraction imaging of voids in dislocation-free high-purity germanium single crystals
,”
J. Appl. Crystallogr.
53
,
880
(
2020
).
36.
L. T.
Kiss
,
D. C.
Miller
,
H. C.
Gatos
, and
A. F.
Witt
, “
Anomalous X-ray transmission studies in indium antimonide: Surface damage
,”
J. Appl. Phys.
42
,
5296
(
1971
).
37.
L.
Kirste
,
K.
Grabianska
,
R.
Kucharski
,
T.
Sochacki
,
B.
Lucznik
, and
M.
Bockowski
, “
Structural analysis of low defect ammonothermally grown GaN wafers by Borrmann effect X-ray topography
,”
Materials
14
,
5472
(
2021
).
38.
Y.
Yao
,
Y.
Ishikawa
, and
Y.
Sugawara
, “
X-ray diffraction and Raman characterization of β-Ga2O3 single crystal grown by edge-defined film-fed growth method
,”
J. Appl. Phys.
126
,
205106
(
2019
).
39.
T.
Fukamachi
,
R.
Negishi
,
S.
Zhou
,
M.
Yoshizawa
,
I.
Matsumoto
, and
T.
Kawamura
, “
Observation of X-ray topographs using Borrmann effect in the Bragg case
,”
Jpn. J. Appl. Phys.
43
,
5365
(
2004
).
40.
Y.
Yao
,
Y.
Sugawara
,
Y.
Ishikawa
, and
K.
Hirano
, “
X-ray topography of crystallographic defects in wide-bandgap semiconductors using a high-resolution digital camera
,”
Jpn. J. Appl. Phys.
60
,
010908
(
2021
).
41.
See https://x-server.gmca.aps.anl.gov/cgi/www_form.exe?template=x0h_form.htm for X-ray dynamical diffraction data on the web.
42.
B. D.
Cullity
and
S. R.
Stock
,
Elements of X-Ray Diffraction
, 3rd ed. (
Prentice-Hall Inc.
,
New Jersey
,
2001
), pp.
641
642
.
43.
G. H.
Schwuttke
, “
Direct observation of imperfections in semiconductor crystals by anomalous transmission of X rays
,”
J. Appl. Phys.
33
,
2760
(
1962
).
44.
K.
Momma
and
F.
Izumi
, “
VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data
,”
J. Appl. Crystallogr.
44
,
1272
(
2011
).
45.
International Centre for Diffraction Data, PDF 01-082-3844,
2014
.
46.
B.
Okkerse
and
P.
Penning
, “
Anomalous transmission of X-rays in highly perfect crystals
,”
Philips Tech. Rev.
29
,
114
(
1968
).
47.
A. R.
Lang
, “
From Borrmann to super-Borrmann effect: From 2-beam to n-beam diffraction
,”
Cryst. Res. Technol.
33
,
613
(
1998
).
48.
T. C.
Huang
,
M. H.
Tillinger
, and
B.
Post
, “
6-Beam Borrmann diffraction
,”
Z. Naturforsch. A
28
,
600
(
1973
).
49.
Y.
Yao
,
K.
Hirano
,
Y.
Takahashi
,
Y.
Sugawara
,
K.
Sasaki
,
A.
Kuramata
, and
Y.
Ishikawa
, “
Visualization of the curving of crystal planes in β-Ga2O3 by X-ray topography
,”
J. Cryst. Growth
576
,
126376
(
2021
).
50.
Y.
Yao
,
K.
Sato
,
Y.
Sugawara
,
N.
Okada
,
K.
Tadatomo
,
K.
Sasaki
,
A.
Kuramata
, and
Y.
Ishikawa
, “
Three-dimensional curving of crystal planes in wide bandgap semiconductor wafers visualized using a laboratory X-ray diffractometer
,”
J. Cryst. Growth
583
,
126558
(
2022
).
51.
A.
Kuramata
,
K.
Koshi
,
S.
Watanabe
,
Y.
Yamaoka
,
T.
Masui
, and
S.
Yamakoshi
, “
High-quality β-Ga2O3 single crystals grown by edge-defined film-fed growth
,”
Jpn. J. Appl. Phys.
55
,
1202A2
(
2016
).
52.
J. P.
Hirth
and
J.
Lothe
,
Theory of Dislocations
, 2nd ed. (
Krieger Publishing Co.
,
Florida
,
1992
), pp.
569
591
.
53.
M.
Dudley
,
H. H.
Wang
,
F. Z.
Wu
,
S. Y.
Byrapa
,
B.
Raghothamachar
,
G.
Choi
,
E. K.
Sanchez
,
D. M.
Hansen
,
R.
Drachev
,
S. G.
Mueller
, and
M. J.
Loboda
, “
Formation mechanism of stacking faults in PVT 4H-SiC created by deflection of threading dislocations with Burgers vector c+a
,”
Mater. Sci. Forum
679–680
,
269
(
2011
).
54.
F. Z.
Wu
,
M.
Dudley
,
H. H.
Wang
,
S. Y.
Byrapa
,
S.
Sun
,
B.
Raghothamachar
,
E. K.
Sanchez
,
G. Y.
Chung
,
D. M.
Hansen
,
S. G.
Mueller
, and
M. J.
Loboda
, “
The nucleation and propagation of threading dislocations with c-component of Burgers vector in PVT-grown 4H-SiC
,”
Mater. Sci. Forum
740-742
,
217
(
2013
).
55.
H.
Klapper
and
I. L.
Smolsky
, “
Borrmann-effect topography of thick potassium dihydrogen phosphate (KDP) crystals
,”
Cryst. Res. Technol.
33
,
605
(
1998
).
56.
H.
Yamaguchi
,
S.
Watanabe
,
Y.
Yamaoka
,
K.
Koshi
, and
A.
Kuramata
, “
Mechanical properties and dislocation dynamics in β-Ga2O3
,”
Jpn. J. Appl. Phys.
61
,
045506
(
2022
).
57.
K.
Hoshikawa
,
E.
Ohba
,
T.
Kobayashi
,
J.
Yanagisawa
,
C.
Miyagawa
, and
Y.
Nakamura
, “
Growth of β-Ga2O3 single crystals using vertical Bridgman method in ambient air
,”
J. Cryst. Growth
447
,
36
(
2016
).
58.
H.
Wang
,
F.
Wu
,
S.
Byrappa
,
S.
Sun
,
B.
Raghothamachar
,
M.
Dudley
,
E. K.
Sanchez
,
D.
Hansen
,
R.
Drachev
,
S. G.
Mueller
, and
M. J.
Loboda
, “
Basal plane dislocation multiplication via the hopping Frank-read source mechanism in 4H-SiC
,”
Appl. Phys. Lett.
100
,
172105
(
2012
).
59.
H. H.
Wang
,
S. Y.
Byrapa
,
F.
Wu
,
B.
Raghothamachar
,
M.
Dudley
,
E. K.
Sanchez
,
D. M.
Hansen
,
R.
Drachev
,
S. G.
Mueller
, and
M. J.
Loboda
, “
Basal plane dislocation multiplication via the hopping Frank-read source mechanism and observations of prismatic glide in 4H-SiC
,”
Mater. Sci. Forum
717–720
,
327
(
2012
).
60.
V. V.
Bulatov
,
L. L.
Hsiung
,
M.
Tang
,
A.
Arsenlis
,
M. C.
Bartelt
,
W.
Cai
,
J. N.
Florando
,
M.
Hiratani
,
M.
Rhee
,
G.
Hommes
,
T. G.
Pierce
, and
T. D.
de la Rubia
, “
Dislocation multi-junctions and strain hardening
,”
Nature
440
,
1174
(
2006
).
61.
Y.
Ishikawa
,
Y.
Sugawara
,
D.
Yokoe
, and
Y.
Yao
, “
Screw dislocations on {12--12} pyramidal planes induced by Vickers indentation in HVPE GaN
,”
Jpn. J. Appl. Phys.
59
,
091005
(
2020
).
62.
Y.
Ishikawa
,
Y.
Sugawara
,
Y.
Yao
,
H.
Takeda
,
H.
Aida
, and
K.
Tadatomo
, “
Dimensions of dislocations induced by Vickers indentation in hydride vapor-phase epitaxy GaN
,”
J. Appl. Phys.
(unpublished).
63.
E.
Ohba
,
T.
Kobayashi
,
M.
Kado
, and
K.
Hoshikawa
, “
Defect characterization of β-Ga2O3 single crystals grown by vertical Bridgman method
,”
Jpn. J. Appl. Phys.
55
,
1202BF
(
2016
).
64.
H.
Matsunami
, “
Technological breakthroughs in growth control of silicon carbide for high power electronic devices
,”
Jpn. J. Appl. Phys.
43
,
6835
(
2004
).
65.
T.
Kimoto
, “
Material science and device physics in SiC technology for high-voltage power devices
,”
Jpn. J. Appl. Phys.
54
,
040103
(
2015
).
66.
X. R.
Huang
,
M.
Dudley
,
W. M.
Vetter
,
W.
Huang
,
S.
Wang
, and
C. H.
Carter
, “
Direct evidence of micropipe-related pure superscrew dislocations in SiC
,”
Appl. Phys. Lett.
74
,
353
(
1999
).
67.
W. M.
Vetter
and
M.
Dudley
, “
Micropipes and the closure of axial screw dislocation cores in silicon carbide crystals
,”
J. Appl. Phys.
96
,
348
(
2004
).
68.
S.
Usami
,
A.
Tanaka
,
H.
Fukushima
,
Y.
Ando
,
M.
Deki
,
S.
Nitta
,
Y.
Honda
, and
H.
Amano
, “
Correlation between nanopipes formed from screw dislocations during homoepitaxial growth by metal-organic vapor-phase epitaxy and reverse leakage current in vertical p–n diodes on a free-standing GaN substrates
,”
Jpn. J. Appl. Phys.
58
,
SCCB24
(
2019
).
69.
S.
Usami
,
Y.
Ando
,
A.
Tanaka
,
K.
Nagamatsu
,
M.
Deki
,
M.
Kushimoto
,
S.
Nitta
,
Y.
Honda
,
H.
Amano
,
Y.
Sugawara
,
Y.-Z.
Yao
, and
Y.
Ishikawa
, “
Correlation between dislocations and leakage current of p-n diodes on a free-standing GaN substrate
,”
Appl. Phys. Lett.
112
,
182106
(
2018
).
70.
H.
Yamaguchi
,
S.
Watanabe
,
Y.
Yamaoka
,
K.
Koshi
, and
A.
Kuramata
, “
Subsurface-damaged layer in (010)-oriented β-Ga2O3 substrates
,”
Jpn. J. Appl. Phys.
59
,
125503
(
2020
).
71.
B. K.
Tanner
,
J.
Wittge
,
D.
Allen
,
M. C.
Fossati
,
A. N.
Danilwesky
,
P.
McNally
,
J.
Garagorri
,
M. R.
Elizalde
, and
D.
Jacques
, “
Thermal slip sources at the extremity and bevel edge of silicon wafers
,”
J. Appl. Crystallogr.
44
,
489
(
2011
).

Supplementary Material