RU2798040C1 - Method for determining local deformation in diamond crystal using optically detected magnetic resonance nv-defects - Google Patents

Abstract

FIELD: nanotechnology.

SUBSTANCE: used in the manufacture of materials for magnetometry, quantum optics, biomedicine, as well as in information technology based on the quantum properties of spins and single photons. A method for determining local deformation in a diamond crystal using optically detectable magnetic resonance (ODMR) of NV-defects includes exposing the diamond crystal to focused laser radiation, which excites photoluminescence (PL) of the NV-defect in the working volume of the diamond sample, by which the ODMR signal of NV-defects is recorded in the form of a change in the intensity of photoluminescence from frequency. First, the ODMR spectra of NV-defects are recorded as a change in the intensity of photoluminescence from frequency in control diamond samples with different voltages. In each control sample, the splitting caused by local stress near the NV-defect and caused by the deviation of the crystal field from the axial field is determinedΔ, MHz of the ODMR signal of NV-defects between the levels degenerate in the axial crystal field with spin projections +1 and -1, while the zero reference point is the frequency of 2870 MHz for an ideal structure in which there are no internal stresses. Next, determine the local stressσ from the relationσ=28.5*Δ , where 28.5 is a constant, MPa/MHz,Δ is a level splitting with spin projections +1 and -1, MHz. After that, a calibration curve of the dependence of the local stress is builtσ from the valueΔ in control samples. From the ODMR spectra of NV-defects of the crystal under study, the valueΔ is determined in the test sample. Using the previously constructed calibration curve, by valueΔ in the test sample determine the local stressσ of the studied sample, and then - local deformation in the studied diamond crystal from the following ratio:ε =σ /E_diam, whereε is the local deformation, dimensionless quantity,σ is the local stress, MPa, E_diam. is the Young's modulus in diamond, equal to 1.2⋅ 10⁶ MPa. To excite photoluminescence in the working volume of a diamond crystal sample by focused laser radiation, confocal optics are used. An array of diamond nanocrystals can be used as a sample of a diamond crystal and a single NV-defect can be chosen. A sample of a diamond crystal is placed in water or in a liquid transparent in the visible optical range with a refractive index in the visible range lower than in diamond.

EFFECT: simplification of the process for determining local deformation in a diamond crystal.

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Description

The invention relates to nanotechnology and can be used in the development of diamond-based materials for magnetometry, quantum optics, biomedicine, as well as in information technology based on the quantum properties of spins and single photons.

After the discovery of the unique radiating properties of NV defects in diamond, which made it possible to optically detect magnetic resonance in the ground state of NV centers at room temperature, up to the registration of magnetic resonance on single defects of atomic sizes (see A. Gruber, A. Drabenstedt, C. Tietz, L Fleury, J. Wrachtrup, C. Von Borczyskowski - Scanning Confocal Optical Microscopy and Magnetic Resonance on Single Defect Centers - Science, v. 276, pp.-2012-2014, 1997, J. Wrachtrup, F. Jelezko, Processing quantum information in diamond - J. Phys.: Condens Matter, v. 18, S807, 2006), it became possible to widely use NV defects in diamond in sensors and to create an element base for quantum computing. The NV defect, which is a carbon vacancy (V), in the nearest coordination sphere of which one of the four carbon atoms is replaced by a nitrogen atom (N), has the ground triplet spin state S = 1, denoted as ³ A ₂ , the populations of the spin levels of which are selectively populated under by the action of optical radiation. Optically induced spin polarization in the ground state occurs due to a combination of optical excitation and spin-selective nonradiative intersystem transitions, which predominantly empty the sublevels M _S = ±1 and populate the sublevel M _S = 0 and, as a result, lead to spin-dependent optical photoluminescence ( FL), which makes it possible to read the spin of the ground state by the method of optical magnetic resonance detection (ODMR). Thus, the spin of the ground state of an NV defect can be coherently manipulated by microwave fields, as well as initialized and detected using PL, since the sublevels M _S =±1 are dark states emitting reduced fluorescence.

To use NV defects in quantum operations and sensors, it is necessary to control the stresses in diamond or nanodiamond near the NV defect. Stresses can also occur in different areas of the diamond structure used, both on the surface and inside. Thus, it becomes necessary to construct a map of local stresses with a submicron spatial resolution.

Stress, σ, Pa, is related to relative strain, ε, dimensionless quantity, through Young's modulus, E, Pa, according to the formula in accordance with Hooke's law

stress expression

expression for determining relative strain

where Young's modulus for diamond E _diam =1200 GPa.

The use of native NV defects as nanoscale sensors makes it possible to measure local stresses and strains and create corresponding maps of local stresses and strains in diamond crystals and nanocrystals with submicron spatial resolution. A non-destructive control method is used by the form of the ODMR spectrum at room temperature in a zero magnetic field and with a spatial resolution limited by diffraction.

The ODMR signal of the NV center in the ³ А ₂ ground state in zero magnetic field is described by the simplified spin Hamiltonian (without taking into account the hyperfine and quadrupole interactions in the NV defect):

where spin S=1, dimensionless quantity, S _Z , S _X and S _Y - projections of spin S onto coordinate axes Z, X and Y, respectively; the coordinate axis Z coincides with the trigonal symmetry axis NV of the center. Under ideal conditions of the absence of stresses/strains in diamond, the parameter D in zero magnetic field and the spin quantization axis are determined by the molecular structure of the NV center in the form of a trigonal distribution of the spin density of unpaired electrons in the ground state, D=2870, MHz, at room temperature; parameter E=0. The presence of stresses in a diamond crystal or diamond structure leads to a change in the values of the parameters D and E, while the stresses introduce an insignificant relative variation in the parameter D, while the changes in E are absolute, since they are counted from the zero value of E. When the crystal is deformed, violating the trigonal symmetry center, the degeneracy of the sublevels M _S =±1 is removed with further splitting, depending on the stress (strain), designated Δ=2E, MHz. Thus, the value of the parameter E carries unambiguous information about the presence of stresses at the location of the NV center. Given the atomic dimensions of the NV center, local stresses and strains can be measured with submicron spatial resolution.

A method is known for measuring stresses in semiconductors using Raman spectroscopy (see application WO 2015109144A1, IPC G01L 1/241 published 2015-07-23), in which local residual stresses are determined in a non-destructive manner in a semiconductor that is active in Raman scattering, where known peak positions of a transverse optical (TO) phonon and a longitudinal optical (LO) phonon without load, and one or more Raman spectra of the material, presumably under load, are obtained. The displacement observed for the position of the phonon of the stressed material from the position of the phonon for the unstressed material is calculated from which the magnitude of the stress can be determined from the linear relationship between the phonon shift and stress. A Raman spectrometer can use a laser excitation source with a submicron cross section to selectively excite areas on a material to create a stress field map for the material.

The disadvantage of this method is the lack of connection between the Raman measurements and the properties of defects that can potentially be introduced into the semiconductor structure under study.

A known method of measuring the distribution of local stresses of dislocations in homoepitaxial chemical vapor deposition of single-crystal diamond using Raman (Raman) scattering [see. Y. Kato, et al., Local stress distribution of dislocations in homoepitaxial chemical vapor deposite single-crystal diamond, Diamond & Related Materials 23 (2012) 109-111]. It is noted that for high and stable operation of diamond-based power devices, high-quality crystals with a flat surface and a low defect density are required. A method for measuring the two-dimensional distribution of local stresses of dislocations in a homoepitaxial diamond single crystal using a confocal Raman microscope is presented. It was possible to quantify the local stresses, since the image of the shift of the optical phonon peak at the center of the zone is shifted in the stressed regions by 3 cm-1/GPa. It has been shown that local stresses around a dislocation range from -93 to +40 MPa.

The disadvantage of this method is the lack of connection between the Raman measurements and the properties of NV defects, which can potentially be embedded in the investigated diamond structure.

A known method of measuring stresses by ODMR NV-defects under conditions of hydrostatic pressure up to 60 GPa [see. M. W. Doherty et al. Electronic Properties and Metrology Applications of the Diamond NV-Center under Pressure, PRL 112, 047601 (2014)]. The experiments were carried out using single-crystal CVD type Pa diamond samples with a low nitrogen content of <1 ppm (1 ppm - 1 impurity atom per million atoms of a diamond crystal). Under the action of hydrostatic pressure, an increase in the parameter D was observed, which linearly depended on the value of the applied pressure up to a pressure of 60 GPa and had a gradient dD(P)/dP=14.58, MHz/GPa. Theoretical estimates made in the work based on the calculation of shifts of atomic orbitals as a result of lattice deformation under pressure gave a gradient of ≈6.2 MHz/GPa, i.e., a discrepancy of more than two times.

The disadvantage of the method for determining stress/strain is the lack of results for determining stress/strain in the perpendicular direction, that is, the gradient of the parameter E (dE(P)/dP). At the same time, broadening and splitting of the ODMR line was observed at a pressure of >4.5 GPa, since at a pressure above 4.5 GPa, the medium used for pressure transfer (in the form of Ne) freezes at room temperature and becomes quasi-hydrostatic. As a consequence, the stress applied to the crystal is slightly anisotropic (<0.4 GPa at 50 GPa) and the crystal is deformed. However, no quantitative data are given for the E parameter gradient.

A known method for determining the deformation coupling of the spin of an NV defect with a diamond mechanical oscillator [see. J. Teissier, et al., Strain Coupling of a Nitrogen-Vacancy Center Spin to a Diamond Mechanical Oscillator, PRL 113, 020503 (2014)]. It is shown that NV defects embedded in single-crystal diamond nanomechanical resonators are considered as a valuable resource for future experiments with hybrid systems in the quantum regime. The method is implemented in the form of a device that consists of single-crystal diamond cantilevers with built-in NV defects, while applying various degrees of deformation to the NV defect near the cantilever clamping point by controlled bending of the cantilever. Using ODMR, the parameters of the relationship between strain and the spin properties of an NV defect considered as a stress/strain sensor were determined: the ODMR line splits when the cantilever is displaced as a result of transverse deformation, and longitudinal deformation causes a slight shift in the center of mass of the two resulting ODMR lines. As a result, the coupling constants of longitudinal and transverse strains with parameters D and Δ=2Е were obtained: dD(P)/dP=4.55 MHz/GPa and dE(P)/dP=16.358 MHz/GPa.

The disadvantage of the method for determining the gradients of parameters D and E is the discrepancy with the data of other studies, as well as the use of an additional magnetic field in ODMR measurements. In this case, all parameters were obtained under external pressure and do not reflect the intrinsic stresses/strains that occur in the environment of the NV defect.

There is a method of demonstrating the relationship between the deformation caused by the mechanical movement of a diamond cantilever and the spin properties of the built-in NV defect, which makes it possible to quantitatively characterize the axial and transverse sensitivity to deformation in the region of the NV defect [see. P. Ovartchaiyapong, et al., Dynamic strain-mediated coupling of a single diamond spin to a mechanical resonator, NATURE COMMUNICATIONS | 5:4429 | DOI: 10.1038/ncomms5429lwww.nature.com/naturecommunications]. Here, the NV defect is an atomic scale sensor, and spin-based strain imaging with high strain sensitivity is demonstrated. In the proposed method, NV interacts with the main mechanical mode of the cantilever through deformation. At small displacements of the cantilever, the deformation felt by the NV center is linear in the position of the cantilever. As a result, the coupling constants of longitudinal and transverse strains with parameters D and Δ=2Е were obtained: dD(P)/dP=11.08 MHz/GPa and dE(P)/dP=17.928 MHz/GPa.

The disadvantage of the method for determining the gradients of parameters D and E is the discrepancy with the data of other studies, as well as the use of an additional magnetic field in ODMR measurements. In this case, all parameters were obtained under external pressure and do not reflect the intrinsic stresses/strains that occur in the environment of the NV defect.

A known method of visualization of deformations with predominantly aligned NV centers in polycrystalline diamond [see. Wide-field strain imaging with preferentially aligned nitrogen vacancy centers in polycrystalline diamond ME Trusheim, D. Englund New J. Phys. 18 123023 (2016)] using optically detected magnetic resonance imaging of nitrogen vacancy centers in polycrystalline diamond of the Pa type. In a heterogeneous crystalline medium, a different density of NV centers is created. Intrinsic NV defects are used as nanoscale sensors for 3D visualization of local deformation with a spatial resolution limited by diffraction. We used ODMR spectroscopy to characterize the properties of hundreds of NV defects with a resolution of about 300 µm ² . The authors of the work used the average values of the gradients dD(P)/dP and dE(P)/dP according to the results of [J. Teissier, et al.] and [P. Ovartchaiyapong, et al.], which we took as analogues: dD(P)/dP=7.82 MHz/GPa and dE(P)/dP=17.17 MHz/GPa. An important feature of polycrystalline diamond is the ability to grow it on the scale of a wafer of considerable size, but the main problem is the diversity of the crystal structure, including grain boundaries and different growth regimes, which worsens the coherent properties of NV defects and limits their use. Stresses along the z direction, determined by the axis of the NV defect, correspond to shifts in the lattice that preserve the trigonal symmetry of the NV defect and equally affect both spin levels M _S =±1, while the levels split in the presence of off-axis deformations that violate this symmetry. The possible presence of several orientations of NV can lead to an underestimation of the deformation both in terms of axial and non-axial parameters by about a factor of two. The measurements were carried out in a weak magnetic field mode to compensate for external magnetic fields.

Flaws. It is argued that the voltage can be very large; the observed strain shifts in the area of the NV defect are more than 8 MHz in the axial direction, that is, higher than those reported in cantilever-based experiments [analogues], and to create them from the outside would require a pressure of tens of GPa. In the work-analogue [M.W. Doherty et al.] showed that 8 MHz corresponds to fractions of a GPa, i.e. the above statement does not correspond to the available data. The deformation maps obtained, taking into account the above statement, raise doubts, especially since the ODMR spectra are recorded with high noise.

A known method for measuring the stress of diamond based on the color center NV (see application CN114858314 A, IPC G01L-001/12, published 2022-08-05), characterized in that a laser beam with a wavelength of 532 nm passes through a half-wave plate, a polarizing beam splitter a prism, an acousto-optic modulator that creates a controlled pulse of a laser beam, a dichroic mirror, a set of lenses, focuses on a sample with NV centers for collecting fluorescence, while the sequence and duration of high-power laser pulses and the duration and frequency of microwave pulses, mutual synchronization of pulses are created by the control unit, also the analysis of data and obtaining information from the spectra of pulsed ODMR NV defects about the emerging stresses is carried out.

The disadvantage of this method is the use of a complex ODMR pulse circuit, which requires additional devices for pulse modulation of the laser beam, pulse modulation of radio frequency power, pre-registration of Rabi oscillations to determine the duration of microwave pulses, complex hardware and software for data collection, expensive equipment and highly qualified service personnel in connection with with the complexity of setting up equipment. The method requires additional equipment in the form of components for light polarization. There is no analysis of the available experimental data on the values of local stresses and strains near NV centers, fixing the limiting values of stresses and strains.

A known method of measuring the deformation directly at the place of manufacture of diamond photonic structures, using their own color centers in the diamond [see. S. Knauer, J.P. Hadden and J.G. Rarity, In-situ measurements of fabrication induced strain in diamond photonic-structures using intrinsic color centres, npj Quantum Information (2020) 6:50; https://doi.org/10.1038/s41534-020-0277-1], coinciding with the claimed solution for the largest number of essential features and taken as a prototype. The method is a prototype for determining local deformation in a diamond crystal using pulsed optically detected magnetic resonance of NV defects, which includes exposing the diamond crystal to a focused initial polarizing laser pulse of 532 nm, followed by a single microwave pulse of duration n, the duration of which is estimated by recording Rabi oscillations, where the amplitude of the luminescent signal is measured as a function of the length of the microwave pulse, and the final laser pulse reads the luminescence. ODMR measurements were carried out using a homemade scanning confocal setup equipped with Helmholtz coils for magnetic field control and a frequency-tunable RF field generator, the power of which was pulse modulated.

Fabrication of nanoscale devices in combination with high quality NV defects is challenging due to their sensitivity to magnetic, electric and strain fields in their local environment. In this paper, we show how the spin of an electron in the ground state of an NV center can be used as an atomic-scale built-in probe of local deformation caused by focused ion beam grinding of nanoscale devices.

Since the parameter D practically did not change (that is, the splitting between the levels M _S =0 and M _S =±1 did not change), it was concluded that the main recorded deformation field is perpendicular to the axes of the NV centers, so the authors are focused on detecting perpendicular deformation fields.

The possibility of using NV defects as sensors of the deformation field caused by the process of manufacturing solid immersion lenses, which leads to damage to the diamond lattice resulting from the refinement of the photonic structure, as well as a decrease in deformation fields as a result of annealing, is demonstrated. The external magnetic field was aligned perpendicular to the axes of the NV centers by minimizing the observed Zeeman splitting using ODMR spectra. The residual magnetic field was estimated at ~0.3 μT in the direction of the NV quantization axes. The strain fields were measured from the additional splitting in the ODMR spectrum. The field of equivalent strains is given in dimensionless quantities.

A splitting of 0.15±0.07, MHz was observed, after a single impact on the sample, it was concluded that the calculated strain field was 3.7±2.0×10 ^-6 , a dimensionless value, while for the case of a double impact on the sample, where we see a splitting of 720± 4 kHz, we can infer a strain field of 17±1×10 ^-6 . Thus, the resulting stress in diamond after a single impact on the sample corresponds to a stress of 4 MPa, after a double impact on the sample it corresponds to a stress of 20 MPa. Young's modulus for 1200 GPa diamond was used.

The disadvantage is the use of a complex ODMR pulse circuit, which requires additional devices for pulse modulation of the laser beam, pulse modulation of radio frequency power, pre-registration of Rabi oscillations to determine the duration of microwave pulses, complex data acquisition hardware and software, expensive equipment and highly qualified service personnel due to Difficulties in setting up equipment. There is also a contradiction with the analogue [M. E. Trusheim, et al.] according to the change in the value of the parameter D due to mechanical stresses. In the presented work, it was concluded that the parameter D practically did not change in the studied diamond structure, while in the analog, a significant change in this parameter was observed under the action of deformations, which makes these estimates ambiguous. The uncertainty in these estimates is due to the uncertainty in the used literature values of the strain field susceptibility. There is no analysis of the available experimental data on the values of local stresses and strains near NV centers, fixing the limiting values of stresses and strains.

The objective of the present invention is to develop a method for determining local deformation in a diamond crystal using optically detected magnetic resonance NV of defects, operating in a continuous mode, which would be simple in execution and did not require the use of a complicated device for its implementation, could be used for measurements under ambient conditions in the absence of an external magnetic field and without the use of a pulse circuit that requires the use of a pulsed laser radiation modulator, a pulsed RF power modulator, pulse switches, complex hardware and software.

For the limiting values of internal local stresses in a diamond crystal, it is proposed to take as a zero reference point an ideal structure in which there are no stresses, that is, the parameter of the spin Hamiltonian (4) E=0. For the limiting reference point, it is proposed to take the splitting between the levels M _S =-1 and M _S =+1, equal to Δ=2E=46 MHz in a detonation nanodiamond with a diameter of ~5 nm and which is the maximum splitting observed for internal local stresses/strains in diamond in the location of the NV center, measured in [C. Bradac et al. Nature Nanotechnology, vol. 5, 345 (2010)]. In this case, naturally, the stresses will change the parameter D, which is due to the trigonal symmetry of the NV defect; however, due to the lack of an exact value of this parameter in an unstressed structure, conventionally accepted in a number of works as D = 2.870 GHz, these changes do not give an accurate picture of the stresses. However, since the stresses can have different signs (compression or tension of the lattice at the location of the NV center), an increase or decrease in the parameter D with respect to this (zero) stress value can provide information about the nature of the stresses. In this case, the sign of the parameter E cannot be determined from traditional ODMR measurements.

In the article [S. Bradac et al. Nature Nanotechnology, vol. 5, 345 (2010)] parameter D=2880 MHz, that is, the shift with respect to the NV defect in unstressed diamond is +10 MHz. In accordance with the calibration dependence D(P) given in the analogue [M.W. Doherty et al.] there is local compression with a stress of 0.685 GPa. We rule out a possible temperature shift due to laser excitation, since an increase in temperature leads to a negative shift in the parameter D. An important result is the positive stress sign (compression), which we can also transfer to the stress sign in the plane perpendicular to the trigonal axis NV of the defect, that is, the sign of Е will also be considered positive (local compression at the location of the NV defect). Splitting of levels M _S =-1 and Ms=+1 Δ=2E=46 MHz, such splitting corresponds to stress σ=1310, MPa; relative strain ε=1.09×10 ^-3 .

The problem is solved by the fact that the method for determining local deformation in a diamond crystal using optically detected magnetic resonance of NV defects includes exposure of the diamond crystal to focused laser radiation, which excites photoluminescence (PL) of the NV defect in the working volume of the diamond sample, by which the NV ODMR signal is recorded. -defects in the form of a change in the intensity of photoluminescence from frequency. New in the claimed method is the fact that, first, in the control samples of diamond with different voltages, the ODMR spectra of NV defects are recorded in the form of a change in the intensity of photoluminescence from frequency, in each control sample, it is determined caused by local stress near the NV defect and due to the deviation of the crystal field from the axial field splitting Δ, MHz of the ODMR signal of NV defects between the levels degenerate in the axial crystal field with spin projections +1 and -1, while the zero reference point is the frequency of 2870 MHz for an ideal structure in which there are no internal stresses, then the local stress σ from the relation

where 28.5 is a constant, MPa/MHz,

Δ - level splitting with spin projections +1 and -1, MHz,

a calibration curve is constructed for the dependence of the local stress σ on the magnitude of the mentioned splitting Δ of the ODMR signal of the NV defects of the crystal in the control samples, the value of Δ in the test sample is determined from the spectra of the ODMR of the NV defects of the crystal under study, using the previously constructed calibration curve, the local stress a is determined from the value of Δ of the test sample, after which the local deformation in the test diamond crystal is determined from the following ratio:

where s - local deformation, dimensionless quantity,

σ - local stress, MPa,

E _diam. - Young's modulus in diamond, equal to 1.2⋅10 ⁶ MPa.

Excitation of photoluminescence in the working volume of a diamond crystal sample by focused laser radiation can be carried out using confocal optics.

An array of diamond nanocrystals can be used as a diamond crystal sample.

A single NV defect can be selected.

A sample of a diamond crystal can be placed in water or in a liquid transparent in the visible optical range with a refractive index in the visible range lower than that of diamond, which results in an increase in the luminescence signal. The claimed technical solution is illustrated by drawings, where in Fig. Figure 1 shows the structure of an NV defect consisting of a carbon vacancy in the nearest environment of which one of the four carbon atoms is replaced by a nitrogen atom. The trigonal orientations of the NV defect coincide with one of the four <111> directions of the crystal. The NV defect is in the negatively charged state NV" and is characterized by the electron spin S=1;

in FIG. Figure 2 shows the ODMR signals of NV defects in diamond recorded at room temperature in a zero magnetic field in a series of control samples of diamonds and nanodiamonds with different nitrogen concentrations of N and NV defects, into which NV defects were introduced by various methods (curves 1–12);

в нулевом магнитном поле с расщеплением D=2870 МГц в отсутствие напряжений/деформаций; и в присутствии нетригональной деформации с расщеплением между уровнями M_S=+1 и М_S=-1, зависящим от напряжения/деформации, обозначенным Δ=2Е;in FIG. Figure 3 shows the fine structure of the spin levels of the NV center in the ground state.

in zero magnetic field with splitting D=2870 MHz in the absence of stresses/strains; and in the presence of non-trigonal strain with splitting between levels M _S =+1 and M _S =-1, depending on stress/strain, denoted by Δ=2E;

in FIG. 4 shows a calibration curve 13 of the dependence of stress/strain, σ/ε, on the amount of splitting between the levels M _S =+1 and M _S =-1 Δ=2E: σ(MPa)=28.5*Δ (MHz), which makes it possible to determine stresses in location area of the NV center;

in FIG. Figure 5 shows the ODMR signals in two regions of the crystal (region 1 - curve 14) and (region 2 - curve 15) emitted by focused laser radiation in an artificial single crystal grown at high pressure and high temperature, with a varying nitrogen concentration of ~10 - 100 ppm along a diamond wafer irradiated with ~2 MeV electrons followed by annealing at 850°C. The nitrogen concentration of N and NV defects is conventionally shown in gray, the density of which reflects this concentration; the gain used to normalize the ODMR signal in region (2) is indicated. For comparison, curve 16 shows the ODMR signal in a natural diamond crystal (curve 4 in Fig. 2), where the hyperfine structure (HFS) for ^14N nitrogen, which is part of the NV defect, appears in the form of three lines with a splitting of ~2 MHz;

in FIG. 6 (curve 17) shows small values of local stresses/strains observed at the location of the NV defect in polycrystalline diamond (taken from an analogue [J. Teissier, et al.]), plotted on the calibration curve 13 of Fig. 4. It can be seen that there is a huge difference in local stresses/strains in the polycrystal and detonation nanodiamond, while local stresses/strains in various samples presented in this figure and in Figs. 2 are strictly within the calibration curve 13 of FIG. 4.

The inventive method for determining local deformation in a diamond crystal using optically detected magnetic resonance NV defects is carried out as follows. A diamond sample is placed in a frequency-tunable radio-frequency field, the sample is exposed to focused laser radiation, which excites photoluminescence in the working volume of the sample, by which the ODMR signal NV of defects is recorded using a standard modulation technique, at different frequencies of the mentioned radio-frequency field; frequencies are determined by the formulas

where f - radio frequency, MHz; D=2870 - splitting of triplet energy levels in an axial (trigonal) crystal field in the absence of stress/strain for electron spin projections M _S =0 and degenerate levels in the axial crystal field M _S =±1, MHz; the splitting of levels M _S =-1 and M _S =+1 is determined, dimensionless values, equal to Δ, caused by local stress/strain near the NV defect, due to the deviation of the crystal field from the axial (trigonal) field, MHz, which is shown in Fig. 3.

ODMR spectra are measured in a series of control samples of diamonds and nanodiamonds (Fig. 2) with different concentrations of nitrogen N and NV defects, in which NV defects were introduced by various methods, differing in different stresses/strains at the location of the NV defect. The series of control samples includes: (curve 1) an artificial single crystal diamond plate grown by CVD with a minimum nitrogen concentration of less than 1 ppm (parts per million), NV defects are created in the near-surface layer of ~500 nm by nitrogen implantation and subsequent annealing at a temperature of 850 °С, Е~0 MHz; (curve 2) an artificial single crystal grown at high pressure and high temperature (HPHT), with a varying nitrogen concentration of ~10 - 100 ppm along a diamond plate, irradiated with electrons with an energy of ~2 MeV, followed by annealing at 850°C; the ODMR signal was registered in the region of the crystal with the minimum nitrogen concentration, E=1.5 MHz; (curve 3) natural diamond type Pa with a minimum nitrogen concentration (less than 1 ppm), irradiated with neutrons at a dose of ~1018 cm ^-2 followed by annealing at 850°C for 2 hours, E=2.4 MHz; (curve 4) natural diamond without irradiation, E=2.9 MHz; (curve 5) polycrystalline nanodiamond, not irradiated and not annealed, NV defects formed during sample preparation, E=4.5 MHz; (curve 6) an artificial single crystal grown by the HPHT method, substituting nitrogen concentration ~200 ppm, NV defects created in the near-surface layer ~500 nm by nitrogen implantation and subsequent annealing at a temperature of 850°C, Е=5.5 MHz; (curve 7) an artificial single crystal grown by the HPNT method, with a nitrogen concentration of ~100 ppm, irradiated with neutrons with a flux of ~1018 cm ^-2 followed by annealing at 850°C for 2 hours, E=5.5 MHz; (curve 8) polycrystalline nanodiamond, not irradiated and not annealed, NV-defects were formed during sample preparation, Е=6.0 MHz; (curve 9) artificial Element-b, grown by the HPHT method, nitrogen concentration ~100 ppm, irradiated with protons with a flux density of 1017 cm ^-2 , followed by annealing at 850°C for 5 hours, E=6.5 MHz; (curve 10) Commercial sample NDJJSA, Adamas, "40nm-Hi", concentration of NV-defects 3 ppm, concentration of substituting nitrogen 100-120 ppm, E=7.0 MHz; (curve 11) nanodiamonds sintered under HPHT conditions were not irradiated; a high concentration of NV defects (~50 ppm) and a substituting nitrogen concentration N (according to EPR data) up to 500 ppm, Е=7.0 MHz were registered in the sample; (curve 12) single NV defects in detonation nanodiamond (DND), 5 nm, according to [Bradac et al. Nature Nanotechnology (2010)], _DND E=23 MHz.

Two limiting values of internal local stresses/strains in a diamond crystal are introduced: (i) an ideal structure in which there are no stresses, that is, the parameter of the spin Hamiltonian (1) E=0, is taken as the zero reference point; (ii) splitting between levels M _S =-1 and M _S =+1, equal to Δ=46 MHz, in a detonation nanodiamond with a diameter of ~5 nm and being the maximum splitting observed for internal local stresses/strains in diamond at the location of the NV center measured in [C. Bradac et al. Nature Nanotechnology, vol. 5, 345 (2010)], is taken as the ultimate maximum point. A wide series of diamond samples was studied, which we will consider as a control series of samples, and as a result it was shown that all splitting values Δ = 2E are within the two limiting values proposed by us, 0 and 46 MHz. According to the values of Δ in each control sample, the stresses σ, MPa, and the stress-proportional relative strain ε, a dimensionless value, are determined with a linear dependence coefficient in accordance with Hooke's law in the form of Young's modulus E _diam equal to 1200 in diamond, GPa, in the form

build a calibration curve 13 of the dependence of the voltage a on the splitting between the levels M _S =+1 and M _S =-1 Δ: σ(MPa)=28.5* Δ(MHz), using the available averaged experimental data from analogues in which the voltage gradient /strain was determined by applying an external pressure, allowing you to determine the stress/strain in the region of the NV center (Fig. 4).

On FIG. Figure 5 shows the ODMR signals in two regions of the crystal (region 1 - curve 14) and (region 2 - curve 15) emitted by focused laser radiation in an artificial single crystal grown at high pressure and high temperature, with a varying nitrogen concentration of ~10 - 100 ppm along a diamond plate irradiated with electrons followed by annealing. The nitrogen concentration of N and NV defects is conventionally shown in gray, the density of which reflects this concentration, the gain used to normalize the ODMR signal in region 2 is indicated. For comparison, curve 16 shows the ODMR signal in a natural diamond crystal (curve 4 in Fig. 2), where the hyperfine structure (HFS) for 14N nitrogen, which is part of the NV defect, manifests itself in the form of three lines with a splitting of ~2 MHz;

STS with the same splitting ~2 MHz, which does not depend on the splitting Δ=2E, is also visible in the ODMR spectrum of NV defects localized at the point of the lowest nitrogen concentration (curve 1 of Fig. 2). In this case, the minimum splitting A is recorded, which corresponds to the minimum stress/strain in the sample. The photoluminescence intensity and, accordingly, the ODMR signal are about 500 times lower than the signal intensity in the darkest part of the sample (point (2)) with the maximum nitrogen concentration.

For a more accurate determination of E, it is necessary to decompose the ODMR spectrum into two lines with splitting Δ. The dashed lines show the results of such a decomposition; we obtain 5.4 MHz for the distance between the maxima in the experimental spectrum and 6.3 MHz as the result of the decomposition. Thus, the error in determining the splitting without decomposing the spectrum into two component lines can be about 15%, that is, on average, the splitting is Δ=5.85±0.45 MHz.

The terrestrial magnetic field on the order of 0.5 G leads to a broadening of the ODMR line within 1 MHz, which does not greatly affect the measurement results, since the hyperfine splitting due to interaction with nitrogen ¹⁴ N inside the NV center is ~2 MHz, which also leads to line broadening ODMR. However, in precision measurements of small values of splitting A (less than 1 MHz), the external magnetic field should be compensated using Helmholtz coils, then the ODMR lines can be narrowed and as a result the hyperfine structure from nitrogen will be resolved and a more accurate splitting Δ can be established, as shown in Fig. . 5. In this case, the CGS splitting serves as the absolute scale of the change in the radio frequency in the region of the ODMR signal. Note that when measuring the ODMR spectra shown in FIG. 2 and FIG. 5, external magnetic field compensation was not applied.

Example 1. In the analogue [M. W. Doherty et al.] presents the results of determining the effect of hydrostatic pressure on the parameter D and obtained a calibration dependence of the value of D on the external pressure. However, data on the effect of external stresses/strains on parameter E, i.e., stresses/strains in the direction perpendicular to the trigonal axis NV of the defect, are not given, which severely limits the results obtained. This drawback was also noted in the analogue [P. Ovartchaiyapong, et al.]. However, in [M. W. Doherty et al.] along with a calibration curve for the parameter D, the ODMR spectra at different hydrostatic pressures are shown and it is noted that due to the freezing of the pressure-transmitting substance (Ne), there is an anisotropy in pressure and an uncontrolled perpendicular stress component appeared, which led to to the splitting of the ODMR line. The most pronounced splitting between the spin levels M _S =-1 and M _S =+1 Δ=2E=26 MHz was observed at a hydrostatic pressure of 60.4 GPa. In accordance with our calibration curve, this splitting corresponds to stress σ=740 MPa, relative strain ε=6.17×10 ^-4 .

Example 2 In [C. Bradac et al. Nature Nanotechnology, vol. 5, 345 (2010)] parameter D=2880 MHz, that is, the shift with respect to the NV defect in unstressed diamond is +10 MHz. In accordance with the calibration dependence D(P) given in analogue [M. W. Doherty et al.] there is local compression with a stress of 685 MPa. We rule out a possible temperature shift due to laser excitation, since an increase in temperature leads to a negative shift in the parameter D. An important result is the positive stress sign (compression), which we can also transfer to the stress sign in the plane perpendicular to the trigonal axis NV of the defect, that is, the sign of Е will also be considered positive (local compression at the location of the NV defect). Splitting levels M _S =-1 and M _S =+1 Δ=2E=46 MHz, such splitting corresponds to stress σ=1310 MPa, relative compression strain ε=1.09×10 ^-3 .

Claims (9)

1. A method for determining local deformation in a diamond crystal using optically detected magnetic resonance (ODMR) of NV defects, including exposure of the diamond crystal to focused laser radiation, which excites photoluminescence (PL) of the NV defect in the working volume of the diamond sample, by which the ODMR signal is recorded NV defects in the form of a change in the intensity of photoluminescence from frequency, characterized in that first, in control samples of diamond with different voltages, the ODMR spectra of NV defects are recorded in the form of a change in the intensity of photoluminescence from frequency, in each control sample, the effect caused by local stress near the NV defect is determined and due to the deviation of the crystal field from the axial field, splitting Δ, MHz of the ODMR signal of NV defects between the levels degenerate in the axial crystal field with spin projections +1 and internal stresses, then local stress σ is determined from the ratio σ=28.5*Δ, where 28.5 is a constant, MPa/MHz, Δ is the splitting of levels with spin projections of +1 and -1, MHz, a calibration curve of the dependence of local stress is built σ from the value of the mentioned splitting Δ of the ODMR signal of the NV defects of the crystal in the control samples, from the ODMR spectra of the NV defects of the crystal under study, the value of Δ is determined in the test sample, using the previously constructed calibration curve, the local stress σ of the test sample is determined from the value of Δ, after which the local deformation in the studied diamond crystal from the following relation: ε=σ/ _Ediam , where ε - local deformation, dimensionless quantity, σ - local stress, MPa, E _diam. - Young's modulus in diamond, equal to 1.2⋅10 ⁶ MPa. 2. The method according to claim 1, characterized in that the excitation of photoluminescence in the working volume of a diamond crystal sample by focused laser radiation is carried out using confocal optics. 3. The method according to claim 1, characterized in that an array of diamond nanocrystals is used as a diamond crystal sample. 4. The method according to p. 2, characterized in that a single NV defect is selected. 5. The method according to claim 1, characterized in that a sample of a diamond crystal is placed in water or in a liquid transparent in the visible optical range with a refractive index in the visible range lower than in diamond.

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