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[Takeyuki Tsuji](https://orcid.org/0000-0002-7342-6198), Shunta Harada, [Tokuyuki Teraji](https://orcid.org/0000-0002-7731-0547)

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[Evaluation of stress tensor around a threading defect in diamond: Application of NV center-based measurement and comparative multi-modal analysis](https://mdr.nims.go.jp/datasets/f19f41e2-ad11-4a00-aae8-12a382a08573)

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Evaluation of stress tensor around a threading defect in diamond: Application of NV center-based measurement and comparative multi-modal analysisViewOnlineExportCitationRESEARCH ARTICLE |  NOVEMBER 06 2025Evaluation of stress tensor around a threading defect indiamond: Application of NV center-based measurement andcomparative multi-modal analysis Takeyuki Tsuji  ; Shunta Harada  ; Tokuyuki Teraji  J. Appl. Phys. 138, 174401 (2025)https://doi.org/10.1063/5.0292833Articles You May Be Interested InNondestructive analysis of threading mixed dislocations in SiC using x-ray topography and birefringenceAIP Advances (February 2025)Focused light birefringence for three-dimensional observation of dislocations in silicon carbide wafersRev. Sci. Instrum. (August 2025) 27 November 2025 07:04:33https://pubs.aip.org/aip/jap/article/138/17/174401/3371180/Evaluation-of-stress-tensor-around-a-threadinghttps://pubs.aip.org/aip/jap/article/138/17/174401/3371180/Evaluation-of-stress-tensor-around-a-threading?pdfCoverIconEvent=citejavascript:;https://orcid.org/0000-0002-7342-6198javascript:;https://orcid.org/0000-0002-3076-6678javascript:;https://orcid.org/0000-0002-7731-0547https://crossmark.crossref.org/dialog/?doi=10.1063/5.0292833&domain=pdf&date_stamp=2025-11-06https://doi.org/10.1063/5.0292833https://pubs.aip.org/aip/adv/article/15/2/025208/3333893/Nondestructive-analysis-of-threading-mixedhttps://pubs.aip.org/aip/rsi/article/96/8/083901/3358212/Focused-light-birefringence-for-three-dimensionalhttps://servedbyadbutler.com/redirect.spark?MID=188841&plid=3318698&setID=1044475&channelID=0&CID=1578996&banID=524060199&PID=0&textadID=0&tc=1&rnd=4456399295&scheduleID=3474758&adSize=1640x440&data_keys=%7B%22%22%3A%22%22%7D&metadata=%5B%5D&mt=1764227073417232&spr=1&referrer=http%3A%2F%2Fpubs.aip.org%2Faip%2Fjap%2Farticle-pdf%2Fdoi%2F10.1063%2F5.0292833%2F20790198%2F174401_1_5.0292833.pdf&request_uuid=c5f2ee03-12b9-4697-ba9c-b8d345235878&hc=fea703a30bd25e4f78f75f57c0e72e0bd02b072b&location=Evaluation of stress tensor around a threadingdefect in diamond: Application of NV center-basedmeasurement and comparative multi-modalanalysisCite as: J. Appl. Phys. 138, 174401 (2025); doi: 10.1063/5.0292833View Online Export Citation CrossMarkSubmitted: 24 July 2025 · Accepted: 15 October 2025 ·Published Online: 6 November 2025Takeyuki Tsuji,1 Shunta Harada,2,3 and Tokuyuki Teraji4,a)AFFILIATIONS1International Center for Young Researchers, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan2Center for Integrated Research of Future Electronics (CIRFE), Institute of Materials and Systems for Sustainability (IMaSS),Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan3Department of Materials Process Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan4Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba,Ibaraki 305-0044, Japana)Author to whom correspondence should be addressed: TERAJI.Tokuyuki@nims.go.jpABSTRACTThreading defects in diamond degrade the performance of diamond-based quantum and electronic devices. Although the disorder of theatomic arrangement induced by the threading defects is considered to be the cause of the performance degradation, yet quantitative andspatially resolved evaluation of the stress tensor that characterizes the magnitude of the disorder has remained challenging. In this study, weapplied the evaluation technique of the stress tensor based on nitrogen-vacancy (NV) centers to the mapping of the stress field around athreading defect in a chemical vapor deposition diamond film. Furthermore, we compared the stress tensor measured using NV centerswith that obtained by conventional methods such as Raman spectroscopy and x-ray topography. Around the threading defect, the compo-nents of the stress tensor σxy, σyz, σzx, and σxx + σyy + σzz varied by approximately 0.2, 0.2, 0.3, and 1.2 GPa, respectively, and each compo-nent exhibited a rotationally symmetric distribution extending over a diameter of approximately 10–20 μm. We calculated the Raman shiftmapping from the stress tensor obtained using NV centers, and the Raman peak was estimated to decrease by approximately 0.9 cm−1 dueto the stress tensor at the center of the threading defect. This value was comparable to the experimental result of Raman shift mapping.These results indicate that the components of the stress tensor measured by NV centers accurately reflect the stress induced by the threadingdefects. The stress tensor and x-ray topography images suggest that the threading defect measured in this study was a bundle dislocation.© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0292833INTRODUCTIONDiamonds are known as one of the promising materials forelectronic1,2 applications because diamond has excellent electronicproperties with wide bandgap, high carrier mobility, and highthermal conductivity.3 Nitrogen-vacancy (NV) centers in diamondsare color centers with unique quantum properties4–6 and expectedto be applied to quantum sensors,7,8 networks,9–11 and comput-ers.6,12 Regarding quantum sensor applications, NV centers aresensitive to several external fields, such as magnetic fields,13,14 elec-tric fields,15,16 and temperature.17,18Homoepitaxial chemical vapor deposition (CVD) diamondfilms typically contain threading defects propagated from the sub-strate such as dislocations in the range of 102–106 /cm2, while het-eroepitaxial diamond films contain those of over 106 /cm2.19–21Threading defects such as dislocations degrade the performance ofelectronic and quantum applications. In electronic applications, itJournal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 174401 (2025); doi: 10.1063/5.0292833 138, 174401-1© Author(s) 2025 27 November 2025 07:04:33https://doi.org/10.1063/5.0292833https://doi.org/10.1063/5.0292833https://pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0292833http://crossmark.crossref.org/dialog/?doi=10.1063/5.0292833&domain=pdf&date_stamp=2025-11-06https://orcid.org/0000-0002-7342-6198https://orcid.org/0000-0002-3076-6678https://orcid.org/0000-0002-7731-0547mailto:TERAJI.Tokuyuki@nims.go.jphttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1063/5.0292833https://pubs.aip.org/aip/japis well known that local disruptions in the atomic structure at thecore of these defects induce midgap states within the bandgap,causing leakage currents.19,22–24 In addition to the deterioration ofcrystal quality in the threading defects themselves, we consider thatthe stress fields around these threading defects can alter the semicon-ductor properties of diamond and even promote the formation ofadditional threading defects. Through evaluating the stress fieldaround threading defects, we expect to clarify the influence of thestress field on semiconductor properties and the formation of thread-ing defects. In the case of quantum application, the stress alters theenergy levels of the NV centers,25,26 which deteriorates the propertiesof the quantum network27 and computers.28 In addition, inhomoge-neous energy levels of NV centers lead to a decrease in the spindephasing time T2* of the NV centers,29 which deteriorates the sensi-tivity of quantum sensors.4 Therefore, it is technologically essential toreduce threading defects in the CVD diamonds. For this purpose, theevaluation of the stress caused by the threading defect is important.Stress in a crystal is applied along the x axis, y axis, and z axis,corresponding to the x-plane, y-plane, and z-plane, respectively, inthe three-dimensional space as shown in Fig. 1(a). Thus, the stressin a crystal is primally presented as the following matrix, known asthe stress tensor:σxx σxy σxzσxy σyy σyzσxz σyz σzz2435: (1)This tensor contains six independent components including axialstress (σxx, σyy, σzz) and shear stress (σxy, σyz, σzx) [Figs. 1(b) and 1(c)].Thus, measuring the stress tensor is important to evaluate the stressfield in the diamond. Despite its importance, measuring the compo-nents of the stress tensor has been a challenging task for conventionalmethods including Raman spectroscopy,30 birefringence microscopy,31and x-ray diffraction.32 In each of these techniques, the measurementoutput data related to stress are only one—such as the peak shift ofRaman emission, phase difference, or change in the diffraction angle—making it difficult to uniquely determine the components of the stresstensor. Thus, in the case of Raman spectroscopy, stress in the crystalhas been evaluated assuming a hydrostatic pressure (σxx ¼ σyy ¼ σzz ,σxy ¼ σyz ¼ σzx ¼ 0).In contrast, in this study, the components of the stress tensorwere directly extracted by employing NV centers in diamond. Thismethod has already been demonstrated in previous studies.33–35 NVcenters are a color center with a spin-1 electronic ground state, con-sisting of one nitrogen and one vacancy in diamond. The two reso-nance frequencies of a single NV center, i.e., differences in the energylevels between ms = 0 and ms = +1 and between ms = 0 and ms = 1,can be read out by microwave irradiation and detecting the fluores-cence intensity. This scheme is called optically detected magnetic res-onance (ODMR).36 These two resonance frequencies are varieddepending on the stress tensor applied to the NV center. As shownin Fig. 1(d), the NV center arranges in four directions (i = 1, 2, 3, 4)depending on the positional relationship between the nitrogen andthe vacancy. Thus, we can reconstruct the components(σxy, σyz, σzx, σxx þ σyy þ σzz) of the stress tensor by reading out atotal of 2 × 4 (directions) = 8 resonance frequencies varied by thestress tensor. In a previous study, components of the stress tensorFIG. 1. (a) Schematic of the unit cell of the crystal and stress. (b) Schematic ofthe unit cell of the crystal under axial stress components (σxx, σyy, σzz): A crystalsubjected to axial stress, transitioning from a black to a red cell. (c) Schematic ofthe unit cell of the crystal under shear stress components (σxy, σyz, σzx): A crystalsubjected to shear stress undergoes, transitioning from a black to a green cell.(d) NV centers in the diamond arranged in the four different axes.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 174401 (2025); doi: 10.1063/5.0292833 138, 174401-2© Author(s) 2025 27 November 2025 07:04:33https://pubs.aip.org/aip/japinduced by scratches, implantation damage, nanoindents, and devicesfabricated on diamond were measured using this technique.34,35In this study, we applied the stress tensor measurement tech-nique based on NV centers to measure the stress tensor around athreading defect in the CVD diamond film. The stress tensorobtained using NV centers was compared with that obtained by aconventional method, Raman spectroscopy, to verify the validity ofthe NV-center-based measurements. Finally, the stress tensorobtained in this study, together with x-ray topography images, wasused to clarify the structure of the threading defect.METHODSWe characterized the threading defect in the nitrogen-dopedhomoepitaxial CVD diamond film with a thickness of 20 μm. Ahigh-pressure and high-temperature (HPHT) type-Ib (001) singlecrystal with a thickness of 500 μm was used as a substrate. The topsurface of the substrate was mechanically polished along the [110]direction under a fine polishing condition. The CVD growth condi-tion was as follows: 110 Torr reaction pressure, 1.4 kW microwavepower, 10% 12C purified methane concentration ratio (flow rateratio of CH4 to the total gas flow), 0.2% nitrogen concentrationratio (flow rate ratio of N2 to the total gas flow), 2% oxygen con-centration (flow rate ratio of O2 to the total gas flow), and 1020–1090 °C substrate temperature. The oxygen adding growth condi-tion was applied because oxygen adding has a role in decreasingthe number of newly generated dislocations in the CVD diamondfilms.37–39 Figure 2(a) shows the optical microscope image of theCVD diamond film. The step-bunching feature was observed alongthe [110] direction, indicating that nitrogen was doped in the CVDdiamond film.40 Figures 2(b) and 2(c) show the birefringenceimages taken at the same position before (HPHT substrate) andafter CVD growth, respectively. In Figs. 2(b) and 2(c), petal-shapedbirefringence patterns were observed at the same position, confirm-ing the presence of a threading defect that propagated from theHPHT substrate into the CVD diamond film.The fluorescence from NV centers around the threadingdefect was detected using a confocal microscope as shown inFig. 2(d). We used a 514 nm laser with polarization aligned in the[010] direction. Figure 2(e) shows the fluorescence image in thecross section (XZ plane) of the CVD film using the confocal micro-scope. The high intensity region in Fig. 2(e) indicated the CVDdiamond film with NV centers. Figure 2(f ) shows the fluorescenceimages in the XY plane of the CVD diamond film at a depth ofapproximately 10 μm from the surface of the CVD diamond film.The threading defect observed by the birefringence image waslocated near the center of this image. The continuous-wave ODMRmeasurements were performed at the laser power of approximately4 mW. The copper wire with a diameter of 20 μm was used formicrowave irradiation. The wire was placed so as to be parallel tothe [010] direction, and all ODMR measurements were performedat approximately 30 dBm. Figure 2(g) shows the ODMR spectrameasured at positions P and Q in Fig. 2(f ). Position P indicates themeasurement location close to the threading defect, while point Qrepresents the location farther from the defect. The resonance fre-quencies were varied by approximately 1–3MHz between locationsP and Q. This change in frequencies was due to the change thestress tensor between the positions P and Q. The eight resonancefrequencies ( f+i) (i ¼ 1, 2, 3, 4) were determined by fitting theODMR spectrum with eight Lorentzian functions. Here, i denotesthe number corresponding to the direction of the NV center, asshown in Fig. 1(d). We defined Si asSi ¼ fþi þ f�i2: (2)We determined the three shear stress components (σxy, σyz,σzx) and trace of the stress tensor (σxx + σyy + σzz) using the follow-ing equations:34σxy ¼ S1 � S2 � S3 þ S48a2, (3)σyz ¼ S1 þ S2 � S3 � S48a2, (4)σzx ¼ S1 � S2 þ S3 � S48a2, (5)σxx þ σyy þ σzz ¼S1 þ S2 þ S3 þ S44� Da1, (6)where the stress susceptibility parameters are a1 = 4.86,a2 =−3.7 (MHz/GPa). (The derivation of these equations wasdescribed in the supplementary material). The measurement errorof the components of the stress tensor was calculated using theequation shown below:Sierror(i ¼ 1, 2, 3, 4) ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi( fþierr )2 þ ( f�ierr )2q/2, (7)σxy error ¼ σyz error ¼ σzx error ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX4i¼0(Sierror)2vuut /8a2, (8)σxx þ σyy þ σzz error ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP4i¼0 (Sierror)24s/a1, (9)where fþierr and f�ierr were the fitting error of the resonance frequen-cies ( f+)i. Here, compressive stress and tensile stress were definedas positive and negative, respectively. Finally, by scanning thesample stage with respect to the laser irradiation position and mea-suring the resonance frequency at each sample position accordingto the procedure described above, the mapping of the stress tensorcomponents around the threading defect was obtained. The acqui-sition time per pixel, as well as the pixel dwell time, was 3 min. Wemeasured the stress tensor at 40 × 40 points over a region of 30 μmalong the X = [100] axis and 25 μm along the Y = [010] axis aroundthe threading defect. Thus, the total acquisition time was approxi-mately 80 h.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 174401 (2025); doi: 10.1063/5.0292833 138, 174401-3© Author(s) 2025 27 November 2025 07:04:33https://doi.org/10.60893/figshare.jap.c.8091550https://pubs.aip.org/aip/japRESULTS AND DISCUSSIONMapping of stress tensorFigures 3(a-1)–3(a-4) show the spatial map of components ofthe stress tensor, σxy, σyz, σzx and σxx þ σyy þ σzz , around thethreading defect, respectively. The variation in the magnitude ofthe stress of the components, σxy, σyz, σzx and σxx þ σyy þ σzz ,was approximately 0.2, 0.2, 0.3, and 1.2 GPa, respectively. Thus, wefound that the trace of the stress tensor (σxx + σyy + σzz) was thedominant stress induced by the threading defect. The distributionof the components of shear stress, σxy, σyz, σzx, exhibited apoint-symmetric stress distribution with respect to the center of thethreading defect. As described in the supplementary material, thestress tensor of a single dislocation has a petal-like symmetrical dis-tribution. In addition, the variation in signal contrast in the bire-fringence image is sensitive to the distribution of the in-plane shearstress component of σxy.41 The spatial variation in signal contrastobserved in the birefringence image of the diamond CVD filmshown in Fig. 2(c) was comparable to the distribution of σxymeasured using NV centers, as shown in Figs. 3(a-1). Thus, it isreasonable that such a symmetrical stress distribution was observedaround the threading defect in this study. It should be noted thatthe birefringence image reflected the stress integrated from the sub-strate up to the surface of the CVD film, whereas the stress tensorshown in Figs. 3(a-1)–3(a-4) presented the in-plane stress at adepth of approximately 10 μm from the surface of the CVDdiamond film.Regarding the components of the trace of the stress tensor,σxx + σyy + σzz, shown in Fig. 3(a-4), we found that the tensile stressof approximately 1.2 GPa was applied at the center of the threadingdefect comparing the maximum and minimum value of the stress.The volumetric change rate of the CVD diamond ( ΔV/V) causedby the stress tensor can be delivered from the sum of the traceof the stress tensor (σxx + σyy + σzz), as shown in the followingequation:ΔVV¼ V� V0V¼ �(σxx þ σyy þ σzz) (s11 þ 2s12) , (10)FIG. 2. (a) Optical microscope imageof the CVD diamond film. (b) and (c)Birefringence images measured at thesurface of the HPHT diamond sub-strate and CVD diamond film, respec-tively. (d) Schematic of a confocalmicroscope for measuring the stresstensor field around the threadingdefect. By moving the sample stagewith the diamond, the fluorescencedetection point was moved around thethreading defect. (e) The fluorescenceimage in the cross section (XZ plane)of the CVD film using the confocalmicroscope. (f ) The fluorescenceimage of the XY plane within the CVDdiamond film (z = 25 μm). (g) ODMRspectra at measured at positions P andQ in (f ).Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 174401 (2025); doi: 10.1063/5.0292833 138, 174401-4© Author(s) 2025 27 November 2025 07:04:33https://doi.org/10.60893/figshare.jap.c.8091550https://pubs.aip.org/aip/japwhere V is the initial volume and V0 is the final volume throughdeformation due to stress applied, and s11 ¼ 0:952� 10�3 ands12 ¼ 0:099� 10�3 GPa�1 are compliance constants42 (the deriva-tion of this equation is described in the supplementary material).The tensile stress of σxx + σyy + σzz =−1.2 GPa was applied near thecenter of the threading defect. This means that the volume of thediamond crystal was increased approximately 6 × 10−2% near thecenter of the threading defect.Figures 3(b-1)–3(b-4) show the spatial map of the measure-ment error of the stress tensor, σxy, σyz, σzx and σxx þ σyy þ σzz ,around the threading defect, respectively. The measurement errorof σxy, σyz, σzx and σxx + σyy + σzz was approximately under 0.025,0.025, 0.025, and 0.05 GPa, respectively, in most areas, althoughregions with measurement error exceeding 0.1 GPa were observed,as shown in Figs. 3(b-1)–3(b-4). The areas with high measurementerrors of approximately 0.1 GPa correspond to regions wherestep bunching occurs on the CVD diamond film, as indicatedby the optical microscope (OM) image and PL image shown inFigs. 2(a) and 2(f ). Figures 3(c-1)–3(c-4) show the ODMR spectraat positions A, B, C, and D, as indicated in Fig. 3(b-4). Comparedto position A, which had low measurement error, the baseline indi-cated by the red line in Fig. 3(c-1) was curved on the ODMRFIG. 3. (a-1)–(a-4) Spatial map of the stress tensor components (σxy, σyz, σzx, σxx + σyy + σzz) of stress tensor components around the threading defect, respectively.(b-1)–(b-4) Spatial map of measurement error of stress tensor components (σxy_error, σyz_error, σzx_error, σxx + σyy + σzz_error) around the threading defect, respectively.(c-1)–(c-4) ODMR spectra measured at the positions of A, B, C, and D shown in (b-4), respectively. (d) Experiment result of the diamond Raman peak shift around thethreading defect. (e) Calculation result of the diamond Raman peak shift caused by the stress tensor around the threading defect.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 174401 (2025); doi: 10.1063/5.0292833 138, 174401-5© Author(s) 2025 27 November 2025 07:04:33https://doi.org/10.60893/figshare.jap.c.8091550https://pubs.aip.org/aip/japspectra at points B, C, and D, leading to high fitting errors andhigh measurement error of stress. Decreasing the measurementerror is essential for evaluating smaller stress variations below0.1 GPa, such as the stress tensor of a single dislocation. Althoughwe have not clarified the reason why the baseline of ODMR wascurved induced by step bunching, we considered that the introduc-tion of the Ramsey sequence43 is effective for reducing measure-ment errors. In the Ramsey sequence, the difference (or ratio)between the off resonance and on-resonance intensities of theODMR signal can be determined, leading to improved baselineaccuracy (the measurement error of the stress tensor in this studywas discussed in detail from the viewpoints of the stability of theconversion matrix from NV frequencies to the stress tensor and oferror propagation in the supplementary material).Next, to verify the reliability of the stress tensor obtained inthis study, we compared the stress tensor measured by NV centerswith stress measured by a conventional method, Raman spectro-scopy. (The experimental method was described in detail in ourprevious study.25) The change in the wavenumber of the diamondRaman peak indicated that stress was caused near the center of thethreading defect. Figure 3(d-1) shows the Raman peak shift imagenear the threading defect. Subsequently, we calculated the Ramanshift mapping from the stress tensor obtained using the NVcenters. Typically, a given stress tensor modifies the phonon modesof diamond, changing the two transverse optical (TO) phononmodes and one longitudinal optical (LO) phonon mode to shift. Asa result, the Raman peak of diamond—the frequency of the triplydegenerate phonon—splits into three peaks. Please note that, in ourexperimental setup, only the LO phonon mode was detected basedon the Raman selection rule (details are provided in thesupplementary material). Assuming hydrostatic pressure(σxx = σyy = σzz = (σxx + σyy + σzz)/3) and using the component ofshear stress (σxy, σyz, σzx) measured by the NV centers, we calcu-lated the Raman shift of the LO phonon mode, and the result isshown Fig. 3(e) (the detailed calculation procedure is provided inthe supplementary material). Near the step-bunching region, wherethe measurement error of the stress tensor exceeded 0.1 GPa, a dif-ference of approximately 0.4 cm−1 was observed between the exper-imental and calculated Raman shifts. In contrast, around thethreading defect, the area in which the Raman shift was calculatedto change was comparable to the measurement results shown inFig. 3(d-1). Furthermore, comparing the maximum and minimumRaman shift values, the Raman shift was calculated to be decreasedabout 0.9 cm−1 at the center of the threading dislocation, whichwas comparable to the experimental results. Therefore, we consid-ered that the components of the stress tensor measured by NVcenters accurately reflect the stress induced by the threadingdefects. In other words, in this study, we were able to extract com-ponents of the stress tensor that could not be distinguished by con-ventional measurement techniques.Structure analysisThis threading defect was analyzed in detail by combining thestress tensor obtained in this study with data obtained from x-raytopography, in order to clarify its structure. Figures 4(a)–4(c) showthe x-ray topography images near the threading defect. The diffrac-tion vector g of x-ray topography images in Figs. 4(a)–4(c) wasg ¼ [�2�24], [044], and [404], respectively. When the Burgers vectorof a dislocation is denoted as b, the dislocation image disappearswhen b⋅g = 0, whereas it becomes visible when b⋅g≠ 0. The blacklines in Figs. 4(b) and 4(c) disappeared when g was [�2�24]. Thisresult confirmed that these lines were dislocations with Burgersvector of b ¼ [�110], as shown in Fig. 4(d). Kato et al. have alsoreported that edge dislocations with b ¼ [�110] dominantly exist in(001) CVD diamond films,19 making this result consistent with ourresult. On the other hand, the diameter of the darker area of thethreading defect measured in this study, indicated by the red circle,was larger than that of dislocation with a single Burgers vector. Inaddition, the image of the threading defect does not disappearunder any g vectors. These results means that this threading defectwas not a single dislocation. We compared the stress field of thisthreading defect to that of single edge dislocation. In elasticitytheory,44 the trace of the stress tensor (σxx + σyy + σzz) generated bysingle edge dislocations is applied in the range diameter of approxi-mately 4 μm from the center of the dislocation in diamonds (theimage of the stress tensor around single edge dislocation estimatedby elastic theory is shown in the supplementary material). Asshown in Fig. 3(a), the area affected by the trace of the stress tensor(σxx + σyy + σzz) was approximately 10–15 μm diameter from theFIG. 4. (a)–(c) X-ray topography images near the threading defect. The diffraction vector g of each image was g ¼ [�2�24], [044], and [404], respectively. (d) The schematicof the positions of threading defects and dislocations.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 174401 (2025); doi: 10.1063/5.0292833 138, 174401-6© Author(s) 2025 27 November 2025 07:04:33https://doi.org/10.60893/figshare.jap.c.8091550https://doi.org/10.60893/figshare.jap.c.8091550https://doi.org/10.60893/figshare.jap.c.8091550https://doi.org/10.60893/figshare.jap.c.8091550https://pubs.aip.org/aip/japcenter of the threading defect. Thus, the area affected by the stressof the threading defects was approximately three to four timeslarger than that by single dislocation. Furthermore, Ichikawa et al.have reported that the Raman peak position shifted by approxi-mately 0.1 cm−1 near the center of a single dislocation.45 As pre-sented in Fig. 3(d), comparing the maximum and minimumRaman shift values, the Raman peak position near the center of thethreading defect decreased by approximately −0.9 cm−1. Theseresults mean that the threading defect measured in this study hadgreater stress than a single dislocation. These results suggest thatthis threading defect was bundle dislocation.CONCLUSIONWe demonstrated the spatial imaging of the stress tensoraround the threading defect propagated from the HPHT substratein the nitrogen-doped CVD diamond film. We found that the dis-tribution of the shear stress components, σxy, σyz, σzx, exhibited apoint-symmetric stress distribution with respect to the center of thethreading defect. In addition, the dominant component of thestress tensor induced by the threading defect was tensile stress witha magnitude of approximately 1.2 GPa. This tensile stress increasedthe volume of the diamond crystal near the center of the threadingdefect by approximately 6 × 10−2%. The magnitude and the spatialdistribution of stress tensor components measured by the NVcenter were consistent with the Raman peak shift image. The stresstensor obtained in this study and x-ray topography images suggestthat this threading defect was a bundle dislocation.SUPPLEMENTARY MATERIALSee the supplementary material for the details of the experi-ment method, measurement errors, calculation method of Ramanpeak shift caused by stress tensor, stress tensor of a single edge andscrew dislocation, and benchmark of experiment specification inthis study comparing that in the previous studies.ACKNOWLEDGMENTSThis work was partially supported by MEXT Q-LEAP (No.JPMXS0118068379), JST Moonshot R&D (No. JPMJMS2062),CSTI SIP “Promoting the application of advanced quantum tech-nology platforms to social issues,” JST ASPIRE (No. JPMJAP24C1),and JSPS KAKENHI (Nos. 24H00406 and 24K22963). 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