The local structure around boron doped in 6H-type silicon carbide (SiC) was investigated using neutron holography. Three-dimensional atomic images reconstructed from multiple-wavelength holograms revealed the boron substitution for both silicon and carbon. To determine boron locations accurately, we calculated holograms with varying occupancies of six different sites and fit image intensities with those obtained from experimental holograms by the steepest descent method. As a result, it was found that boron atoms were selectively located at the Si–C-cubic site layer. Furthermore, boundaries right above the boron locations were suggested from the absence of atomic images in the upper region of reconstruction.

Silicon carbide (SiC) has attracted the great interest of researchers in the field of power devices because of its wide bandgap, low material cost, and high chemical and thermal stability. Since SiC devices enable the operation of semiconductors at high temperatures without extra cooling systems, their developments are important for energy saving and power electronics.1,2 Moreover, applications to white light-emitting diodes (LEDs) have been expected, because they do not require phosphors containing rare-earth elements, unlike GaN-based white LEDs.3 In addition, SiC has recently attracted much interest for its quantum computing applications.4,5 Therefore, it is becoming increasingly important in the semiconductor community.

Charge carriers in SiC have been controlled by the doping of B, N, and Al. However, a remaining issue of B-doped SiC is the two different levels of an acceptor dopant: ∼300 meV (shallow) and ∼650 meV (deep).6 It is believed that the shallow center originates from a boron atom on a silicon site.7 For the deep boron level, different defect models are suggested such as a B-containing complex8–10 or a B atom on the C site.11 Since the site-occupying behavior of B is still not understood well, researchers have desired a suitable method of revealing its local structures.

For local structure investigations with elemental selectivity, the extended x-ray absorption fine structure (EXAFS) is commonly used for various materials, solutions, and even clusters in gases. However, EXAFS is not applicable to B-doped SiC, because boron is a too light element for measurement. On the other hand, we have developed atomic-resolution holography (ARH) using x rays, electrons, and neutrons, which provides 3D atomic images around atoms emitting secondary radiation such as x-ray fluorescence.12–15 ARH provides detailed information on the local structures but is applicable only for single crystals or their dopants. Since the boron nucleus emits strong γ-rays after absorbing neutrons, neutron holography (NH) is suitable for the investigation of the local structure around B. To date, we have applied NH to the studies of Eu:CaF2,16 B:Mg2Si,17 and Sm:RB6 (R = Yb, La).18 In the present study, we measured neutron holograms of B-doped 6H–SiC by the time-of-flight (TOF) technique and estimated the occupancies of six different sites from the reconstructed atomic images.

A B-doped 6H–SiC boule was grown by the physical vapor transport method known as the seeded sublimation process. An on-axis-oriented (0001) 75 mm 6H–SiC prepared in own laboratory was applied. The Si face of the seed improves the 6H–SiC polytype stability vs unintentional 4H–SiC nucleation.1 As source materials, SiC powder was synthesized from elemental silicon and carbon with an addition of 0.065 at. % of B. The amount of doping was chosen so as to reach a chemical dopant incorporation of ca. 2 × 1019 cm−3.19 The growth temperature was 2150 °C, determined with an optical pyrometer on the top growth cell, and corresponds to ca. 2200 °C at the growth interface. The average growth rate was ca. 750 μm/h, which is a high value compared with the PVT growth rate of SiC boules with a diameter of 150 mm. The total crystal height (including the seed) in the center of the boule was 29 mm. From this single crystal, a measurement sample with a diameter of 20.1 mm and a height of 15.2–21.4 mm [see Fig. 1(b)] was prepared by wire-sawing and grinding.

FIG. 1.

Illustration of the setup and experimental hologram of B in SiC. (a) Schematic of the neutron holography setup for an inverse mode. (b) Picture of the B-doped 6H–SiC single crystal. (c) Experimental hologram at λ = 0.49 Å. The upper (0001) plane in (b) corresponds to the Si face.

FIG. 1.

Illustration of the setup and experimental hologram of B in SiC. (a) Schematic of the neutron holography setup for an inverse mode. (b) Picture of the B-doped 6H–SiC single crystal. (c) Experimental hologram at λ = 0.49 Å. The upper (0001) plane in (b) corresponds to the Si face.

Close modal

The NH experiment was performed at a beamline 10 (BL10) of the Materials and Life Science Experimental Facility (MLF) in Japan Proton Accelerator Research Complex (J-PARC) in Tokai, Japan. The measurement was carried out in the “inverse mode,”20 and the angular anisotropy of the sample orientation was measured from the intensity of prompt γ rays. Figure 1(a) shows the geometry of the setup for NH. A hologram is obtained by normalizing the angular anisotropy with respect to its background. In principle, the advantage of using the pulse neutron source is that a record of multiple-wavelength holograms in one scan can be obtained using the TOF technique, which greatly suppresses ghost images in the reconstruction.

The γ rays from the sample were detected using a Bi4Ge3O12 (BGO) detector with a diameter of 6 cm. The BGO detector was covered by Pb blocks to reduce the γ-ray background. The BGO measures γ-rays up to ∼500 keV. Therefore, we mostly measured prompt γ-rays at 477.6 keV from 10B, whose cross section is 3.85 × 103 barn.21 Since natural boron contains 20% 10B and 80% 11B, its cross section can be regarded as 7.67 × 102 barn. On the other hand, 28Si (92.2% in natural Si) emits prompt γ-rays at 477.1 keV, and its cross section is 3.4 × 10−4 barn, which is 2.4 × 10−6 that of natural B. This value is much smaller than the concentration of boron in the measured SiC crystal. For 12C (98.9% in natural C), there are almost no emissions up to 500 keV. Thus, the contributions of Si and C were negligible in the hologram measurement.

The sample was rotated by a dual-axis φω goniometer set on the experimental table of BL10. The ω axis is vertical, and the φ axis is horizontal. The angle ω is defined as the angle between the direct beam and the φ axis. The flight path from the neutron source to the sample position was 14.0 m long, and the typical distance between the sample and the detector was 170 mm. The crystallographic orientation was accurately determined using neutron Bragg reflections from the samples with an accuracy within 0.5°. The neutron beam size at the sample position was 30 × 30 mm2, meaning that the sample was completely within the beam spot. The wavelength range of the incident neutrons was at most λ = 0.38–5.2 Å, which were divided into 130 channels for recording multiple-wavelength holograms. The hologram data were scanned repeatedly four times within the single beamtime, and the four datasets were summed to increase the statistic level. The intensities at each φω angle and λ were normalized with respect to the intensities in the range of 7.06–11.3 Å. The neutron wavelength used for the reconstruction ranges from 0.50 to 0.92 Å. Figure 1(c) shows a hologram sliced at λ = 0.49 Å, which was sixfold symmetrized in accordance with symmetry of the local structure around all substitutional sites. Details of the experimental setup and data processing for obtaining the holograms are already reported elsewhere.16,22

Atomic images around B were reconstructed from the measured holograms using the Barton multiple-wavelength algorithm.23Figure 2 shows the atomic images of (0001) planes close to emitter B. Figure 2(a) shows the image of the basal (0001) plane, whose center is a B atom, and it exhibits distinct spots of the surrounding atoms. Here, the circles indicate ideal positions of C or Si obtained from the SiC crystal structure. The agreement between the spots and circles clearly shows that B atoms occupied the substitutional sites. Since we know the polarity of our sample, we can determine either C or Si sites by reconstructing the (0001) planes at z = −0.6 and −1.9 Å, as known from Fig. 3(a). Figures 2(b) and 2(c) show the reconstructions at z = −0.6 and −1.9 Å, respectively. However, atoms are seen in both images. Since circles in Figs. 2(b) and 2(c) indicate relative crystallographic positions of C and Si from Si and C, respectively, it is known that B atoms were substituted at both C and Si sites.

FIG. 2.

Images from experimental holograms. (0001) planes at z = (a) 0.0 Å, (b) −0.6 Å, and (c) −1.9 Å.

FIG. 2.

Images from experimental holograms. (0001) planes at z = (a) 0.0 Å, (b) −0.6 Å, and (c) −1.9 Å.

Close modal
FIG. 3.

Crystal structure of 6H–SiC. (a) View from the 112¯0 direction. The polar direction is the same as that of the crystal in Fig. 1(b). (b) Hexagonal arrangement of atoms. There are three types of layer indicated by A, B, and C, which have different arrangements of C or Si.

FIG. 3.

Crystal structure of 6H–SiC. (a) View from the 112¯0 direction. The polar direction is the same as that of the crystal in Fig. 1(b). (b) Hexagonal arrangement of atoms. There are three types of layer indicated by A, B, and C, which have different arrangements of C or Si.

Close modal

On the other hand, the atomic images in Fig. 2(b) are weaker than those in Fig. 2(c). This is mainly due to the reconstructions of two different environments even around one crystallographic site. Such an intensity reduction can be easily explained on the basis of Fig. 3(b), which shows the atomic arrangements in 6H–SiC along the c-axis. There are six different substitutional sites in 6H-SiC: C-h, Si-h, C-c1, Si-c1, C-c2, and Si-c2. h and c mean hexagonal and cubic cites, respectively, and “*” indicates equivalent sites. If the B atoms were substituted at the C-c1 site on layer A, the real-space image at z = −1.9 Å displays an atomic arrangement on the same layer B. This geometrical scheme is the same as that for C-c1′ site substitution. In contrast, if the B atoms are substituted for the Si-h or Si-h' site on layer A, the real-space image at z = −0.6 Å displays the atomic arrangement on layer B or layer C, respectively. Therefore, the number of possible atomic image positions increases twofold as shown in the dashed circles in Fig. 2(b), but their intensities decrease to half.

In addition to the images in Fig. 2, we reconstructed real-space images at other crystallographic planes and obtained atomic images. Figure 4(a) shows the real-space image of the 112¯1 plane. As seen in Fig. 4(a), no atoms are visualized in the region of z > 0.0 Å. Since such a peculiar image was observed, we initially suspected an extrinsic origin, perhaps from our holography setup. However, by changing the reconstruction condition, we confirmed no anomaly in the setup, which diminished the atomic images in the upper half region (see the supplementary material). Thus, we concluded that the diminishments originated from a specific feature in the atomistic structures.

FIG. 4.

Images of the 112¯1 plane from (a) experimental and (b)-(d) calculated holograms. Red circles indicate atomic positions for the element substituted by B atoms. Blue circles indicate the atomic positions for other elements. (If B atoms were substituted for C (Si) atoms, the red circles indicate the positions of C (Si) atoms.) (b) C-h and Si-h. (c) C-c1 and Si-c1. (d) C-c2 and Si-c2. Since all atomic images here have mirror symmetry with respect to the (1101) plane (the plane normal to the paper), for (b)–(d) only half of images are displayed to save space.

FIG. 4.

Images of the 112¯1 plane from (a) experimental and (b)-(d) calculated holograms. Red circles indicate atomic positions for the element substituted by B atoms. Blue circles indicate the atomic positions for other elements. (If B atoms were substituted for C (Si) atoms, the red circles indicate the positions of C (Si) atoms.) (b) C-h and Si-h. (c) C-c1 and Si-c1. (d) C-c2 and Si-c2. Since all atomic images here have mirror symmetry with respect to the (1101) plane (the plane normal to the paper), for (b)–(d) only half of images are displayed to save space.

Close modal

Such atomic images have been obtained for the local structures around surface adsorbates by photoelectron holography,24,25 because there are no atoms above the adsorbates. This is not the case in our present study, since the B atoms were doped into the SiC bulk. However, the present pattern can be explained by an assumption regarding the idea of surface adsorbates, namely, the B atoms would be located at some boundaries parallel to the (0001) plane such as dislocations or grain boundaries. Since the SiC single crystal was grown using the physical vapor deposition technique, atoms were stacked along the c-axis, that is, the growth direction was anisotropic. Suppose that a boundary occurred during the growth process and B atoms were deposited there. Then, if the structure below the boundary is coherent with the deposited B atoms and the upper structure is incoherent, the atomic images in Fig. 4(a) can be obtained. Similar atomic images could also be reproduced from the theoretical hologram calculated with such a structure model. To verify this structural specificity, we need further analysis combined with a theoretical approach such as the density function theory and molecular dynamics. Therefore, we refer to only atomic images in the region of z ≤ 0.0 Å for the following discussion.

As mentioned above, there are six crystallographic sites in 6H–SiC: C-h, Si-h, C-c1, Si-c1, C-c2, and Si-c2. To determine the occupancies of the B atoms for these sites, we calculated the corresponding holograms under the condition of the same wavelength ranges as the experimental ones. Here, two atomic images for equivalent sites, such as C-h and Si-h, were superimposed. Depending on the sites, overall patterns of the atomic images differ, as shown in information about the neutron absorption cross section.Figs. 4(b)–4(d). Moreover, even when atomic images appear at the same positions, their intensities differ owing to the difference in the scattering lengths of C and Si.

In principle, the experimental images can be regarded as the sum of reconstructions from holograms of different sites. Therefore, we can reproduce a theoretical image similarly to the experimental one by optimizing the occupancies of B for the six different sites. Here, the optimum parameters were obtained by the steepest descent method26 with iterative calculations. The following formula expresses the occupancies of the six sites, αn=(α1,α2,,α6), for the nth iteration:

αi(n+1)=αi(n)kfαnαi(n),
fαn=UexpriαinUir2dr.

Here, r is the coordinate of atomic images, k is the acceleration term, Uexp(r) is the experimental atomic images, and Ui(r)) is the theoretical atomic image for site i. fαnαn represents the gradient of the residual sum of squares (RSS) with respect to α(n). Since the gradient vector gradfαn must be directed with the steepest descent, the function yields the parameter of α for minimum fαn. This steepest descent method was implemented using Python.

Although our algorithm proceeded for 108 iterations, it was confirmed that the RSS settled down at around 107 iterations. From the finally obtained parameters, we converted into the fractions of site occupancies, as shown in Table I. This result revealed that B atoms do not have a strong preference between C and Si sites, but rather, they prefer the c2 sites, in other words, c2 layers. A distinct characteristic of the c2 layer is that it is located just between the hexagonal layers of C-h and Si-h, whereas c1 layers are adjacent to h layers. Another characteristic is that Si-c2 and C-c2 are next to each other. Consequently, it is suggested that the priority of B substitution for the cubic site is much higher than that for the hexagonal site. In the present analysis, we did not take into account the possibility of off-center displacements of B due to the adjacent vacancies, because we must deal with much complicated data treatment. In this case, the intensities of the theoretical atomic images would be modified, which causes a change in the occupancy rate. However, the fact remains that the substitution for c2-sites is dominant.

TABLE I.

Site occupancies of B doped in SiC.

SiteSi-hSi-c1Si-c2C-hC-c1C-c2
Occupancy (%) 0.0 ± 4.9 0 ± 2.2 37.5 ± 3.5 0 ± 3.0 1.1 ± 5.1 61.4 ± 2.4 
SiteSi-hSi-c1Si-c2C-hC-c1C-c2
Occupancy (%) 0.0 ± 4.9 0 ± 2.2 37.5 ± 3.5 0 ± 3.0 1.1 ± 5.1 61.4 ± 2.4 

Figure 5 shows a possible model of the local structure around B. We think that the B atoms substituting for c2-sites generated a boundary right above. Therefore, B atoms are likely concentrated at specific c2-site layers. A similar precipitation of impurities has been observed for an advanced Mg alloy with the “long-period stacking ordered” (LPSO) structure. The LPSO-structure Mg alloys are synthesized by doping a few heavier elements such as Zn and Y. Such elements precipitate at some specific layers, and they give rise to a stacking fault (SF) formation. In the layers of the stacking fault, the face-centered-cubic (fcc) structure forms.27,28 From this analogy, we can presume that the impurities in materials with a hexagonal crystal structure are likely to go to cubic sites.

FIG. 5.

A possible model of the environmental structure around B.

FIG. 5.

A possible model of the environmental structure around B.

Close modal

Among many studies on the SFs in SiC, some of them revealed a high proportion of SFs in heavily doped samples.29–31 However, there is no report that dopants are concentrated at the SFs, unlike the LPSO-structure Mg alloys, probably because of the difficulty in observing light-element dopants. Since the SFs could be induced by lattice strain caused by the substitution of dopants, whose atomic radii are different from that of Si or C, it is likely that boron atoms are concentrated in the SFs. For B-doped diamonds, it is considered that dislocations occur as a result of the proximity effect of the doped boron.32 Therefore, a similar phenomenon should be possible for SiC. On the other hand, by transmission electron microscopy, Yamashita et al. observed the insertion of partial dislocations near the SF and consequent disordering in the upper layer structure.33 If this phenomenon is applied to SiC, it is reasonable that the atomic image was not reconstructed at z > 0 in Fig. 4(a). The dashed lines in Fig. 5 show an interlayer shift. From our previous studies on x-ray fluorescence holography,34 if the displacement exceeds 0.4 Å, the images in the upper layer will be mostly vanished. However, to confirm this assumption, further theoretical approaches are necessary.35 

In conclusion, we applied NH to the determination of the site occupancy of boron in 6H–SiC. The atomic images were clearly visualized below the position of boron by reconstruction from the multiple-wavelength hologram. The intensities of the atomic images estimated by the steepest decent method proved that boron atoms were selectively located at the Si–C-cubic site layer. Moreover, the vertically asymmetric real-space image indicated the boron to be at SFs or boundaries. The results on boron doping in SiC are forming a basis for further studies on the impact of varying the growth conditions such as supersaturation at the growth interface and the study of boron incorporation in polytypes such as 4H–SiC and 3C–SiC. In a long-term, for optical applications in quantum computing, it is of great interest to intentionally tailor the local position of boron in a SiC lattice (and hence its electronic properties) by applying certain growth parameters.

See the supplementary material for atomic images obtained under different conditions from the main text. Crystal structure parameters of 6H–SiC are also listed.

This work was partially supported by JSPS Grants-in-Aid for Transformative Research Areas (A) “Hyper-Ordered Structures Sciences” via Grant Nos. 20H05878, 20H05881, and 21H05547, Innovative Areas “Hydrogenomics” via Grant Nos. 19H05045 and 21H00013, Scientific Research (A) through Grant Nos. 19H00655 and 20H00303, and Scientific Research (B) through Grant No. 21H01027. The neutron experiments were performed under the user program of the Materials and Life Science Experimental Facility of J-PARC (Proposal Nos. 2017B0166, 2018I0010, and 2018B0049). In addition, partial funding by the German Science Foundation in the framework of the international research training group IRTG-2495 between FAU and NITECH is greatly acknowledged. Technical assistance in the crystal growth lab at FAU by Philipp Schuh is greatly acknowledged. Y.Y. and K.H. gratefully acknowledge the support of JSPS Japanese-German Graduate Externship (Grant No. 2019/R1). Data processing was partially supported by Mr. Y. Fukui.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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