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[T. Tsuji](https://orcid.org/0000-0002-7342-6198), [C. Shinei](https://orcid.org/0000-0003-4926-8641), T. Iwasaki, M. Hatano, [T. Teraji](https://orcid.org/0000-0002-7731-0547)

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[Evaluation of stress in (111) homoepitaxial CVD diamond films by Raman spectrum and nitrogen-vacancy centers](https://mdr.nims.go.jp/datasets/bd6db1cf-0250-4911-9376-2bbd89ecd19a)

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Applied PhysicsExpress      LETTER • OPEN ACCESSEvaluation of stress in (111) homoepitaxial CVDdiamond films by Raman spectrum and nitrogen-vacancy centersTo cite this article: T. Tsuji et al 2024 Appl. Phys. Express 17 115502 View the article online for updates and enhancements.You may also likeSurface and interface physics driven byquantum materialsShuji Hasegawa-Prospects for -Ga2O3: now and into thefutureKohei Sasaki-Single-qubit anisotropy induced bymicromagnet in Si-MOS quantum dotNing Chu, Xin Zhang, Rong-Long Ma et al.-This content was downloaded from IP address 144.213.253.16 on 09/07/2025 at 07:11Evaluation of stress in (111) homoepitaxial CVD diamond films by Ramanspectrum and nitrogen-vacancy centersT. Tsuji1 , C. Shinei2 , T. Iwasaki3, M. Hatano3, and T. Teraji2*1International Center for Young Scientists, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan2Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan3Department of Electrical and Electronic Engineering, School of Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8552,Japan*E-mail: TERAJI.Tokuyuki@nims.go.jpReceived September 6, 2024; revised September 28, 2024; accepted October 18, 2024; published online December 5, 2024The reduction of inhomogeneous stress in diamonds is crucially important for extracting excellent performance of semiconducting diamonds. Inthis study, to investigate elastic deformation in nitrogen doped (111) diamond films caused by stress, we evaluated the stress in these films usingconfocal Raman microscopy. The stress was detectable when the misorientation angle (qmis) was below 3.7° and it decreased as qmis increased.The Raman spectroscopic measurements, considered together with reported stress measurements by nitrogen-vacancy centers, suggest that thediamond film at low qmis was subjected to compressive stresses that were stronger in the [111] direction than [ ̅110] or [ ̅ ̅1 12] directions.© 2024 The Author(s). Published on behalf of The Japan Society of Applied Physics by IOP Publishing LtdSupplementary material for this article is available onlineNitrogen-vacancy (NV) centers in diamonds havefunctioned as quantum sensors that are sensitive tomagnetic1,2) and electric fields,3,4) temperature,5,6)and pressure,7,8) with spatial resolutions from nanoscale9,10)to millimeter scale.11–13) Specifically, magnetic sensors withlarge excitation volume, being larger than (0.1 mm)3, areexpected to achieve high sensitivity required for biomagneticmeasurements14–18) and battery current monitoring.19)The magnetic sensitivity of the NV center can be enhancedby increasing the spin dephasing time ( *T2 ) of the ensemble NVcenter.15) The *T2 is limited mainly by the electron spin bath,including factors such as substitutional nitrogen defects [Ns0](P1 centers) and the NV center,20) the nuclear spin bath of 13C,and the inhomogeneous stress applied to the NV center in thediamond.15) The stress applied to the NV center shifts theresonance frequency of a single NV center because of the spin–stress interaction with a shift magnitude proportional to themagnitude of the stress.21–23) The spatially inhomogeneousstress causes broadening of the electron spin resonance signal ofthe ensemble NV centers, leading to reduction of *T .215)We reported that *T2 increases concomitantly with theincreasing misorientation angle (qmis) of the High-PressureHigh-Temperature (HPHT) (111) diamond substrate used forCVD diamond film growth. In this previous study, the diamondsubstrate surface was tilted from its (111) orientation into the[ ̅ ̅ ]1 12 direction as presented in Fig. 1(a). Also, qmis is defined asthe angle between [111] and that is normal to the polisheddiamond surface. Then, we demonstrated that this *T2 improve-ment originated from reduction of the inhomogeneous stressapplied to the NV center in the CVD diamond film.24)In this study, to investigate the elastic deformation causedby stress in these nitrogen-doped CVD (111) diamond films,we used confocal Raman spectroscopy to evaluate the stressapplied to the diamond lattice. After a comprehensiveanalyses of the stress applied to both the diamond latticeand the NV centers in the CVD diamond films, we discussthe elastic deformation caused by stress in the CVD diamondfilm with low q .misHomoepitaxial CVD diamonds were grown on type-IbHPHT (111) diamond substrates with dimensions of1× 1× 0.3 mm3. The entire sample surface was thoroughlypolished for both the front and back sides of the (111)diamond substrate in the [ ]̅ ̅112 direction with qmis of 2.0, 3.7,5.0, and 10° as presented in Fig. 1(a). We created perfectlyaligned NV centers in the CVD diamond films by using thesubstrates with q ,mis which is effective in improving thesensitivity of the quantum sensors.24,25) The fluorescenceintensity of the NV center was measured using a confocalmicroscope. The CVD film thicknesses were estimated asapproximately 60–70 μm from the fluorescence depth profile.The details of the growth conditions are describedelsewhere.24)To analyze the stress applied to the diamond lattice in theCVD films, we used confocal Raman imaging (WITec alpha300 R; Oxford Instruments Plc.). The wavelength and theexcitation power of the laser being polarized into [ ̅ ̅ ]1 12direction were, respectively, 532 nm and 25 mW. The mag-nification and the numerical aperture of the objective lenswere, respectively, 50 and 0.75. Figure 1(b) portrays anillustration of the diamond sample and the definitions of thex, y, and z axes. The Raman spectra were measured at80× 80 positions within the film plane (x–y plane) of40× 40 μm2 at a given z, as presented in Fig. 1(c). (In thesupplementary material, we show the area where the Ramanmeasurements were performed with birefringence images ofeach CVD diamond films.) Fig. 1(d) shows the Ramanspectra in the CVD films with qmis of 2.0 and 10°. Thefirst-order Raman line of the diamond (≈1332.5 cm−1) andthe fluorescence from the NV0 center (≈1400–1420 cm−1)were observed. The first-order Raman line of the diamondwas fitted with a Lorentzian function. The respective fittingerrors of the peak position (Ppeak) of the Lorentzian functionfor qmis of 2.0, 3.7, 5.0, and 10° were approximately 0.020,0.020, 0.020, and 0.025 cm−1. The differences of these fittingerrors were due to the difference of the fluorescence intensityof the NV0 center depending on q .mis The values of [Ns0]Content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of thiswork must maintain attribution to the author(s) and the title of the work, journal citation and DOI.115502-1© 2024 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdApplied Physics Express 17, 115502 (2024) LETTERhttps://doi.org/10.35848/1882-0786/ad88d4estimated from the spin coherence time T2 for qmis of 2.0, 3.7,5.0, and 10° were, respectively, 31.6 ± 0.2, 22.4 ± 0.1,22.9 ± 0.1, and 25.1 ± 0.2 ppm.24)Figures 2(a)–2(d), respectively, show the shift of thediamond Raman peak (Pshift) with respect to the interfacebetween the substrate and the CVD diamond film (z= 0) as afunction of the depth direction (z) for the CVD diamond withqmis of 2.0, 3.7, 5.0, and 10°. Here, the plots and error bars,respectively, represent the average value and the standarddeviation of the diamond Raman peak positions for the80× 80 points at a given z. As presented in Fig. 2(a), Pshiftwas decreased by approximately −0.056 cm−1 from thesubstrate to the CVD film surface at qmis of 2.0°. By contrast,the change of the Pshift was as small as within approximately±0.020 cm−1 at qmis of 3.7°, 5.0, and 10°, as shown inFigs. 2(b)–2(d). These results indicate that the stress appliedto diamond lattice for qmis of 2.0° was higher than that forhigher q .mis Considering the fitting error of Ppeak(0.020–0.025 cm−1) as described above, the stresses appliedto the diamond lattice in CVD films at qmis of 3.7, 5.0, and10° were smaller than the detection limit of these measure-ments.Next, we discuss the elastic deformation of the CVDdiamond film with a qmis of 2.0° based on the measurement(a) (b)(c) (d)Fig. 1. (a) Schematic image of the CVD diamond film and (111) diamond substrate. (b) Illustration of the diamond sample and definition of the x–y–z axis.(c) Schematic image of the x–y plane where the Raman spectra were measured at 80 × 80 points for a 40 × 40 μm2 at a given z. The open circle represents themeasurements position. Instead of drawing 80 white circles, many measurement positions were represented by black circles. (d) Typical Raman spectrum in theCVD films with qmis of 2.0 and 10°.(b)(a) (c) (d)Fig. 2. The shift of diamond Raman peak (Pshift) with respect to the interface between the substrate and CVD diamond film (z = 0) as a function of the depthdirection (z) for the CVD diamond with qmis of 2.0, 3.7, 5.0, and 10°, respectively. The plots and error bars, respectively, present the average value and thestandard deviation of the diamond Raman peak positions for the 80 × 80 points at a given z.115502-2© 2024 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 17, 115502 (2024) T. Tsuji et al.results of the stress applied to the diamond lattice and the NVcenters. The stress applied to the diamond lattice wasestimated from the Pshift of the Raman measurements per-formed for this study, whereas the stress applied to the NVcenters was evaluated from the shift of the spin–stressinteraction Mz reported from our earlier work.24) As mightbe apparent from Eq. (3) shown below, the value ofMz varieswith the amount of stress applied to the NV centers. Aspresented in Fig. 2(a), the distribution of averaged values ofthe Pshift in the depth direction (z) was larger than the standarddeviation of Pshift at a given z (in the x–y plane). This resultindicates that the stress was more distributed in the directionof the CVD film growth, i.e., the [111] direction than in the[ ̅110] or [ ̅ ̅1 12] direction. Therefore, we evaluate themagnitude of the stress in the CVD film surface (z= 70)with respect to the interface between the substrate and theCVD film (z= 0) as the reference point. Figures 3(a) and 3(b)respectively show the shift of the diamond Raman peak (Pshift) in the x and y directions at the CVD diamond surface(z= 70) of the sample with qmis of 2.0°. Here, the plots anderror bars, respectively, represent the average value and thestandard deviation of the diamond Raman peak positions forthe 80 points at a given x or y. The change of the averagevalue of Pshift were as small as within the standard deviationof Pshift depending on the x and y direction. This resultsuggests that the magnitudes of the stress in the [ ̅110] and[ ̅ ̅1 12] directions were almost equal. Therefore, we assumethat the stress was applied parallel (the [ ̅110] and [ ̅ ̅1 12]direction) and perpendicular ([111] direction) to the (111)CVD surface at z= 70, represented respectively as ( s ) and(ŝ ), as depicted in Fig. 3(c). In this case, a stress tensor at theCVD surface (T) can be expressed in the following form.( )⎛⎝⎜⎜⎞⎠⎟⎟sss=^T0 00 00 01It is given with respect to the diamond unit cell coordinatesystem (X= [ ̅110], Y= [ ̅ ̅1 12], Z= [111]) and such that thecompressive stress is positive. The shift of the first-orderRaman line Pshift is expressed by the following equation usings and ŝwhere p, q, and r are the deformation potential constants( /w =p o2 −2.80, /w =q o2 −1.770 and /w =r o2 −1.900), =s11(b)(a)(c)Fig. 3. (a) and (b) The shift of the diamond Raman peak (Pshift) as a function of the x and y direction, respectively, at the CVD diamond surface (z = 70) ofthe sample with a qmis of 2.0°. The plots and error bars, respectively, represent the average value and the standard deviation of the diamond Raman peakpositions.Raman measurements were performed with 80 points along both the x and y direction. However, for clarity in the figure, only data for 21 points alongeach of the x and y direction was shown.. (c) Assumption of the stress in the CVD diamond film in this study. We assume that the stress was applied parallel s(the [ ̅110] and [ ̅ ̅1 12] direction) and perpendicular ŝ ([111] direction) to the (111) CVD surface at z = 70.[ ( )( ) ] [( )( ) ]( )s sw+ + + + + + -=^p q r p q rP2 2 s 2s 2 s 2 s 2s 2 s6211 12 44 11 12 440shift115502-3© 2024 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 17, 115502 (2024) T. Tsuji et al.−0.952, =s12 0.099, =s44 −1.737 are compliance constants(10−3 GPa−1), and w0 = 1332.5 is the frequency of the triplydegenerated phonon (cm−1).26) The supplementary materialprovides details of the derivation of this formula. It is knownthat when these two stresses ( s and ŝ ) are applied to thediamond lattice, the Raman peak of the diamond, i.e., thefrequency of the triply degenerated phonon, is generally splitinto two peaks by the change of the TO and LO phononmodes.27) For this experiment, the laser polarized in the[ ̅ ̅ ]1 12 direction was used for Raman measurements. In thisconfiguration, the TO phonon mode produced four timeshigher fluorescence intensity than the LO phonon modebased on the Raman’s selection rule. Therefore, we consid-ered that the diamond Raman peak detected in this study wasmainly attributable to the TO phonon mode (the supplemen-tary material provides additional details.). As presented inFig. 2(a), the diamond Raman peak of the samples with qmisof 2.0° decreased from the substrate to the CVD film surfaceby Pshift of −0.056 ± 0.02 (cm−1).The shift of the spin–stress interaction Mzshift is expressedas following equation using s and ŝ( ) ( ) ( )s s- + + =^ Ma a a a2 3z1 2 1 2 shiftwhere a1 = 4.86 and a2 =−3.70 are the stress susceptibilityparameters (MHz/GPa).21,22) The supplementary material pre-sents details of the derivation of this formula. Figures 4(a)–4(d),respectively, present variations of the spin–stress interaction Mzin the z-direction for the CVD diamond with qmis of 2.0, 3.7,5.0, and 10°. The average value Mz was distributed fromapproximately −0.6 to +1.1MHz in a sample with qmis of 2.0°.The distribution of Mz became narrower as qmis increased. Thisresult indicates that, as in the case of the stress investigationusing the Raman spectroscopy presented in Fig. 2, the stressapplied to the NV centers decreased as qmis increased. The Mzof the CVD diamond film with qmis of 2.0° was increased fromthe substrate to the CVD film surface by Mzshift of 1.7 ± 0.7(MHz). By substituting the values of Pshift and Mzshift intoEqs. (2) and (3), s and ŝ were estimated, respectively, as0.064 ± 0.03 and 0.71 ± 0.4 GPa. The positive values of s andŝ indicated that the CVD diamond film at low qmis wassubjected to compressive stress, which was higher in the [111]direction than in either the [ ̅110] or [ ̅ ̅1 12] direction at the CVDdiamond film surface. In addition, the fact that the diamondwas subjected to the compressive stress indicated that thelattice constant of the CVD diamond surface was smallerthan that of the HPHT substrate. This finding is consistentwith a report describing the lattice constant of nitrogen-doped CVD diamond films as smaller than that of Ib HPHT(111) diamond substrates.28)In conclusion, we evaluated the stress applied to a diamondlattice in the nitrogen-doped CVD film grown on an Ib HPHT(111) substrate using confocal Raman microscopy. The diamondRaman peak was shifted by approximately −0.053 cm−1 fromthe substrate to the CVD film surface when qmis was 2.0°.However, the shift was within approximately ±0.020 cm−1 at qmisof 3.7°, 5.0, and 10°. Therefore, the stress applied to the diamondlattice was reduced at q ³mis 3.7°. For the diamond CVD film atqmis of 2.0°, the Pshift shifted by −0.053 cm−1; also, the spin–stress interaction Mz shifted by 1.7MHz in the diamond growthdirection of [111]. From these values, we estimated the stressparallel ([ ̅110] and [ ̅ ̅1 12] direction) and the perpendicular ([111]direction) to the (111) CVD surface as 0.064 ± 0.03 and0.71 ± 0.4GPa, respectively. We believe that such compressivestress at low qmis was reduced by increasing q .misAcknowledgments We gratefully acknowledge the constructive discus-sions and insightful comments provided by Dr Junichi Inoue, Dr KimiyoshiIchikawa and Dr Takeharu Sekiguchi. This work was partially supported byMEXT Q-LEAP (Grant Nos. JPMXS0118068379, JPMXS0118067395), JSTMoonshot R&D (Grant No. JPMJMS2062), MIC R&D for construction of aglobal quantum cryptography network (Grant No. JPMI00316), CSTI SIP“Promoting the application of advanced quantum technology platforms to socialissues,” JSPS KAKENHI (Grant Nos. 20H05661, 24H00406).ORCID iDs T. Tsuji https://orcid.org/0000-0002-7342-6198 T. Terajihttps://orcid.org/0000-0002-7731-05471) F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup,“Observation of coherent oscillation of a single nuclear spin and realization of atwo-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).2) D. Budker and M. 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