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Abstract
The negatively charged nitrogen−vacancy (NV−) center ensembles in diamonds offer enormous potential for developing integrated sensors with an improved signal-to-noise ratio (SNR) and high sensitivity. However, the preparation and treatment of diamond samples with suitable NV− concentrations and dephasing time have remained challenging. This work provided insight into the NV− center formation mechanism and reconstruction via a comprehensive analysis of the concentration and dephasing time of a set of diamond samples treated by various parameters. By varying the electron irradiation dose and subsequent annealing duration, the conversion rate of nitrogen to NV− is up to 18.45%, and the corresponding maximum NV− concentration is 3.69 ppm. The dephasing time for all samples varies around 300 ns. The nitrogen-related NV− center ensemble dephasing rate per unit density is 146.4 (ppm·ms)−1, indicating that the treatment did not substantially alter the paramagnetic spin environment around the NV− center. This study not only offers support to exquisite sensitivities of NV-based sensors but also provides valuable experience for the preparation of unique properties of synthetic diamonds.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The negatively charged nitrogen−vacancy (NV−) centers in diamonds with extraordinary electronic and optical properties [1,2] offer enormous potential in quantum sensing (QS), such as magnetic fields, electric fields, and temperatures [3–6]. The NV− center ensemble can increase the number of NV− centers involved in sensing and substantially increase the signal-to-noise ratio (SNR) and sensitivity. The number of NV− centers and the dephasing time $T_2^*$ together determine the sensitivity of QS based on the NV ensemble in the form of a product [4], while the former is usually proportional to the concentration of the NV− centers ([NV−]). The longer the $T_2^*$, the higher the sensitivity [4], but this is not the case for the [NV−] [7]. The [NV−] and $T_2^*$ of the NV ensemble depend on nitrogen-containing diamond samples’ preparation and treatment parameters. A diamond sample with high nitrogen concentration ([N]) is the first condition for the preparation of high [NV−]. However, the remaining nitrogen (mainly substitutional nitrogen Ns, also known as the P1 center) not involved in NV formation will introduce a severe source of dephasing, which seriously affects the $T_2^*$ of the NV ensemble [7]. In addition, if the [NV−] is too high, the distance between adjacent NV− centers will be too short, and the interaction between the NV− centers will also reduce the $T_2^*$ [8]. Simulations show that the optimal [NV−] is several parts per million (ppm) [7]. In original diamond samples, most Ns are not converted to NV− centers due to insufficient grown vacancies [4]. Therefore, additional technical treatment is required to increase both the vacancy concentration ([V]) and the conversion rate of “Ns → NV−”. Two main methods to form vacancies are ion implantation and electron irradiation. The ion implantation method has a high NV generation rate while preventing the formation of competing and perturbing defects [9,10]. Electrons, with lower mass, transfer less kinetic energy to the carbon atoms and are better suited to creating isolated monovacancies [4]. Therefore, electron irradiation was selected in this paper [11]. Subsequent thermal annealing compensates for residual radiation damage and dramatically increases the [NV−] [12]. Luo et al. [13] irradiated diamond with 2 MeV energetic particles followed by annealing. Through optical characterization, the conversion of “Ns → NV−” was about 0.25%, and a sample with an [NV−] of 0.05 ppm was prepared. Farfurnik et al. [14] used 200 keV to irradiate Chemical-Vapor-Deposition (CVD) samples with an initial ([N]) of 113 ppb at a dose of 1020 e−·cm−2 and obtained the [NV−] of 5.68 ppb and the dephasing time of 180 µs. Balasubramanian et al. [15] used different concentrations of N2O as a gas phase dopant to grow diamond films and achieved [NV−] up to 800 ppb. These works promote the research on the preparation of NV− ensembles in a diamond. Although there is an advancement in the preparation of diamond samples with NV− ensembles, [NV−] still needs to be optimized via sample preparation for enhancing sensing performance based on the NV ensemble.
In this work, to improve the performance of advanced QS technologies based on NV− ensembles, a series of NV-diamond samples with different [NV−] and $T_2^*$ were obtained by subjecting a batch of CVD single-crystal diamond samples to high-energy electron irradiation and subsequent thermal annealing. The photoluminescence (PL) spectra were used to characterize the [NV−] and the conversion rate of “N → NV−”, and the optical detected magnetic resonance (ODMR) method was used to obtain the $T_2^*$. A systematic and comprehensive analysis of [NV−] and $T_2^*$ determined the optimal sample based on the production of [NV−] and $T_2^*$.
2. Experimental results and discussion
2.1 Sample preparation and treatment
This batch of single crystal diamond samples with a [N] = 20 ppm was prepared by the CVD method and were transparent and yellowish (see “Sample A” of Fig. 1). Almost all nitrogen atoms exist in the form of Ns (the P1 center). Because the initial [N] of 20 ppm was high enough, it was only necessary to introduce additional vacancies and combine them with nitrogen in the following experiments. The electron linear accelerator (ELA) was chosen to generate vacancies due to its advantages of environmental friendliness, high automation, uniform generation of vacancies, and reduction of lattice damage [16]. The irradiated electron energy is 10 MeV, and the dose is divided into three gradients: 1 × 1017 e−·cm−2, 5 × 1017 e−·cm−2, and 1 × 1018 e−·cm−2. After irradiation, the samples were annealed at a constant temperature of 800 °C [17] in a homemade tubular annealing system (see Fig. 1(a)). The samples were annealed under the protection of a high-purity nitrogen atmosphere (≥ 99.999%) to isolate external oxygen and ensure that the samples were not damaged by burning. The heating rate in the quartz tube is the same for each sample (Fig. 1 (a)): from room temperature (RT) to 800 °C in 30 minutes. After that, the temperature will be maintained at 800 °C for a certain period, which is one of the critical variables controlled by this work. After constant temperature annealing, the system was naturally cooled to RT. When the temperature dropped below 500 °C, oxygen was used to input the system to remove impurities on the diamond surface.
Fig. 1. (a) Annealing sequence in nitrogen (blue) and air (yellow) atmospheres. At the bottom of (a) is the annealing furnace (YHGS-1200). High-purity N2 enters from the left, passes through the pressure-reducing valve and flowmeter, and exits from the right. (b) Morphologies of samples under different treatment conditions. Sample A: the original sample; Sample B: irradiated with 1 × 1018 e−·cm−2 high-energy particles; Sample C: irradiated with 1 × 1018 e−·cm−2 followed by annealing at 800 °C for six hours.
Figure 1 (b) shows three samples (A, B, C) with different treatments, whose color difference can be explained by the principle of mixed color [18]. Sample A was the original sample; a specific concentration of P1 centers inside it caused its pale-yellow color. Sample B was only irradiated with electrons at a dose of 1 × 1018 e−·cm−2, slightly darker than Sample A due to the introduction of many vacancies and lattice damage. Sample C was prepared by annealing at 800 °C for six hours based on Sample B, which exhibits attractive pink color due to high [NV−] [18]. Furthermore, during any sample treatment, including irradiation and annealing, the sample’s surface will inevitably be contaminated with external impurities. Therefore, pretreatment with acid should be performed before each experimental treatment of the sample. In this work, the samples were first soaked in aqua regia for 12 hours, then slowly heated to 50 °C and held for two hours to allow the acid to react more fully with impurities on the samples’ surface, and finally sonicated with pure water. After treatment through the above steps, for the sake of presentation, the samples were numbered and shown in Table 1.
Table 1. Sample numbers of different irradiation doses and annealing times
2.2 NV− concentration analysis
The photoluminescence (PL) spectra with a wavelength range of 550 to 900 nm were obtained by the inVia confocal Raman microscope at RT, whose excitation wavelength is 532 nm. In this range, the zero-phonon lines (ZPL) and phonon sidebands (PSB) of both the neutral nitrogen-vacancy center (the NV0 center) and NV− center are almost entirely covered [19]. The PL spectrum intensity is positively correlated with the corresponding color center concentration. In the 560 to 700 nm range, the PL spectra measured by the spectrometer are only contributed by the ZPL and PSB of NV0 and NV− centers. Therefore, the PL spectra of the 560 to 700 nm range can be used to analyze the NV0 concentrations ([NV0 ]), [NV−], and conversion of NV0 to NV−. Alsid et al. [19] proposed a “Photoluminescence decomposition analysis” method for rapid and efficient quantitative characterization of the charge states using PL spectra at RT, which is more robust to noise than Debye-Waller decomposition. Following this method, all the PL spectra were decomposed into a linear combination of two reference spectra and satisfied the Eq. (1):
where c− and c0 represent the contribution of NV− and NV0 centers to the total PL spectra respectively, and c0 + c−= 1. M is the scale factor. For a rigorous comparison, all PL spectrum data used in this method are normalized. Figure 2(a) shows an example of the linear fitting spectral decomposition of the PL spectrum according to Eq. (1). Furthermore, the ratio η of [NV−] to [NV0] are corrected with the decay rates Γ− = 1/20 ns−1 and Γ0 = 1/12 ns−1 in the following relation [13]:Fig. 2. (a) Example decomposition of diamond PL spectra excited by 532 nm laser. The PL spectra can be decomposed as a linear combination of NV− (yellow) and NV0 (blue) PL spectra. (b) The η results under three different irradiation doses of 1 × 1017 e−·cm−2, 5 × 1017 e−·cm−2, and 1 × 1018 e−·cm−2.
We randomly selected five points for the PL spectrum test for each sample, and data of η results in Fig. 2(b) were obtained by processing each sample’s average value of five data sets. Results of S117 (all samples under electron irradiation dose of 1 × 1017 e−·cm−2, similarly from now on) have a higher ratio than S517 and S118, which indicates that there is sufficient nitrogen to donate free electrons to form NV− centers under S117 conditions. For S517 and S118, as the number of vacancies increases, the Ns used to form the NV− center (i.e., Ns that can donate electrons to NV0 to form NV−) become less and less. The nitrogen and vacancy binding rates approached saturation with the prolongation of the annealing duration, and the conversion between the NV center with different charge states also reached equilibrium. At last, the total NV concentration [NVT] can be expressed as:
However, the PL spectra obtained with the excitation of the 532 nm laser alone are not sufficient to get the absolute value of [NV−]. Hence, we tested the PL spectrum obtained by 632.8 nm laser excitation to shield the influence of the PL spectrum of the NV0 center and focus only on the PL spectrum of the NV− center. Figure 3 (a) shows an example of three samples: S1172 (see Table 1 for treatment parameters), S5172, and S1182. From Fig. 3 (a), there are ZPL peaks of other centers. To avoid the influence of these centers and other potential interfering factors, we took the ZPL peak at 637 nm instead of the integral of the full spectrum to represent the relative change in the absolute value of [NV−]. Figure 3(b) shows all the collected peak values and corresponding fitted curves, and each sample is also tested with five data sets. With the prolongation of annealing duration, the [NV−] of S117, S517, and S118 all reached equilibrium. The equilibrium value of S517 is about four times as large as S117, while the stable value of S118 is close to that of S517. From another point of view, Fig. 3(b) is the absolute value of [NV−] multiplied by a certain coefficient γ. Therefore, if one of the absolute concentrations of [NV−] represented by a point in Fig. 3(b) is confirmed, then the value of γ can be obtained, and [NV−] of all other samples can also be obtained.
Fig. 3. (a) Example of PL spectra of a set of samples under similar annealing duration (2 h) but different electron irradiation doses at RT. The wavelength of the exciting laser is 632.8 nm. (b) The extracted ZPL peaks for all samples. The error bar represents repeating the measurement many times. (c) The actual values of [NV−]. (d) The remaining vacancies are under three different irradiation doses.
Except for V0 , vacancies generated by electron irradiation may also exist as divacancy (ZPL: 733.1 nm [20]) and V− (ZPL: 393 nm [13]). In the tested PL spectra, there is no obvious peak at 733.1 nm and 393 nm, so these two kinds of vacancies are not considered in this work. Campbe et al. [21] provided a coefficient of 3.42 (vacancies/e−)·cm−1 for electrons when the electron's energy is 10 MeV using Monte Carlo simulations. In the sample of a volume of 3 × 3 × 0.5 mm3, the number of vacancies at different irradiation doses was calculated, and the results are shown in Table 2. The distance between the nearest vacancies was calculated as well. Similarly, the distance between the nearest nitrogen atoms in this set of samples is 6.6 nm.
Table 2. The concentration of vacancies generated for different irradiation doses
For samples of S117, the value of [V0 ] is 1.95 ppm and much smaller than [Ns]/2; then, it can be considered that the vacancies are completely consumed to generate NV centers [22]. Combined with the results in Fig. 2(b), The value of [NVT] in equilibrium (points in green dotted box) is 1.95 ppm and the corresponding value of [NV−] is 1.22 ppm. Then the value of γ is obtained as 6150 counts/ppm. Actual values of [NV−] in all other samples were obtained from the relative values of PL intensity in Fig. 3(b), and the results are shown in Fig. 3(c). Among them, sample-S1181 has the highest [NV−] at 3.69 ppm, corresponding to a maximum “N → NV−” conversion rate of 18.45%.
Based on the results in Fig. 2(b) and Fig. 3(c), the remaining [V0 ] have also been calculated, and the results are shown in Fig. 3(d). When a small number of vacancies migrate to a large number of nitrogen atoms, the number of vacancies N at time t will follow the formula of [23]:
2.3 Measurement of $T_2^*$
The inhomogeneous dephasing time $T_2^*$ is one of the main factors that dictate the sensitivity of the DC magnetic field based on the NV− ensemble [4], which depends on the spin environment around the NV center inner the sample. Characterizing dephasing effects in measured $T_2^*$ facilitates evaluating sample performance and sensitivity determination. For this batch of samples, due to the high nitrogen concentration with large ODMR linewidth Δv, it is difficult to test the $T_2^*$ employing free induction decay. Therefore, the $T_2^*$ was measured utilizing the Δv in the following form [4]:
Equation (5) is derived from the resonance spectral line of the Gaussian line shape because of the various noise source, mainly including single electron spins of the P1 center, nuclear spin of 13C isotope, stress field, and magnetic field fluctuation noise. From a technical perspective, the Δv is affected by both the optical and microwave (MW) power. This work uses pulsed ODMR measurement so that the optical power broadening can be ignored [4]. However, the MW power broadening still exists and can even overwhelm linewidths that correspond only to dephasing effects. Only when the MW power is low enough will the system not be affected by the MW power broadening [24], and only $T_2^*$ determines the Δv. The $T_2^*$ can be estimated from the ODMR at ultra-low MW power.
A homebuilt confocal optical path system (shown in Fig. 4) for measuring $T_2^*$ consists of three modules: the laser excitation module, the MW manipulation module, and the fluorescence-detecting module. An acousto−optic modulator (AOM) controls the 532 nm laser (Oxxius LMX-532-200) beam to generate optical pulses, and the laser power is controlled by a combination of a half-wave plate (λ/2) and a polarizing beam splitter (PBS). The focal lengths of the lenses on both sides of the AOM are different to reduce the diameter of the spot, and the subsequent diaphragm only allows diffracted first-order light to pass through. The dichroic mirror allows the 532 nm laser to be reflected and focused on the sample by the objective. The red fluorescence emitted by the diamond sample returns through the dichroic mirror and the long pass filter (cutoff wavelength: 650 nm) and finally reaches the detector of the Si-Avalanche-Photodetector (APD120A2/M). The MW source (SSG-4000 HP) outputs an MW field of a specific frequency and power. After the MW switch (ZASW-2-50DT+) and the MW amplifier (ZHL-16W-43-S+), the MW is emitted through a loop antenna close to the sample to manipulate the spin state of the NV ground states. The permanent magnets provide a stable magnetic field to induce Zeeman splitting of the |±1〉 of the ground triplet state.
Fig. 4. Diagram of the confocal optical path system for T* 2 measurements. The device mainly includes three parts: laser excitation light path (green), MW manipulation path (blue), and fluorescence receiving light path (red). The diamond sample is placed close to the loop antenna on the Printed Circuit Board (PCB).
The MW power broadening in pulsed ODMR linewidth was first investigated. First, the ODMR spectral lines under different MW source output powers were tested and analyzed. Figure 5(a) displays the selected ODMR spectral lines of several representative sets of MW source output power. With the decrease of the output power of the MW source, the contrast of the ODMR signal decreases, and the line width also becomes narrower until the hyperfine level splitting of 14N is clearly shown. Distinguishable hyperfine energy levels appear at the MW source output power of – 17 dBm. Figure 5(b) shows the variation of the linewidth of ODMR under different MW source output powers. As the MW power is reduced, the line width is also narrowed, and it does not change until the MW power is below – 30 dBm. Although ideally, the lower the output power of the MW source, the better. But if the output power is too low, the signal contrast will be extremely poor (see Fig. 5(a)). Therefore, the MW power of – 35 dBm is selected as the experimental parameter for measuring the $T_2^*$ in this work. The measurement results of $T_2^*$ of all samples are shown in Fig. 5(c), which all fluctuate around 300 ns (light yellow frame in Fig. 5(c)). The $T_2^*$ result indicates that elements affecting dephasing did not vary much across the samples for all treatment parameters. The remaining neutral substitutional nitrogen $\textrm{N}_{\textrm{r - s}}^0$ were calculated to be between 13-19 ppm. Considering that the samples used in this work were not purified by 12C isotope, hence, $\textrm{N}_{\textrm{r - s}}^0$ and 13C are both the dominant contributors to the dephasing and with a relationship of [25]:
Fig. 5. (a) Selected ODMR line shapes and contrasts at different MW source output powers. “−16” indicates that the output power of the MW source is −16 dBm, the same as below. (b) Variation of the linewidth of ODMR under different MW source output powers. (c) Measurement results of $T_2^*$. The light yellow shading indicates that the $T_2^*$ of all samples is around 300 ns. (d) Calculated results of AN. The light yellow shading indicates the mean and variance of AN.
2.4 Theoretical effect on sensitivity
The sensitivity of the magnetic field sensing based on the NV− ensemble scales as [4,25]:
where R is the ODMR signal contrast, C is the fluorescence collection efficiency, and τ is the measured time. N is the number of centers involved in sensing, generally considered proportional to the [NV−] in a sample with a uniform NV− center distribution. Equation (7) indicates that the sensitivity depends on the product of N and $T_2^*$, which is directly related to sample preparation and treatment. Combined with the measurement results of the [NV−] in Fig. 3(c) and the $T_2^*$ in Fig. 5 (a), the product was calculated, and the result is shown in Fig. 6. The sample with the largest product was considered to have the best sensing ability. From Fig. 6, the optimal treatment parameters of these samples are an electron irradiation dose of 1 × 1018 e−·cm−2 and an annealing time of 1 h (golden star in Fig. 6).3. Conclusions
In this work, the formation mechanism of NV− ensembles was deeply investigated via a comprehensive analysis of concentration and dephasing properties. To generate large-scale NV ensembles, 24 CVD-diamond samples with an initial nitrogen content of 20 ppm were treated by electron irradiation with three dose gradients and subsequent in situ thermal annealing at 800 °C with various durations. The [NV−] were obtained quantitatively via a combination of [V0] analysis and accurate extraction of PL spectral data. The [NV−]/[NV0] of S117 is slightly higher than S517 and S118, which indicates that more nitrogen atoms of S117 support the conversion of N to NV− than S517 and S118. The [NV−] of all samples reached equilibrium after annealing for more than 3 hours, and the highest value was 3.69 ppm. The results of $T_2^*$ proved that the dephasing characteristics are not sensitive to the two parameters of irradiation dose and annealing time, and experimental results of coefficient AN = 146.4 (ppm·ms)−1 were obtained. Finally, the optimal sample for sensing was S1181 with a conversion rate of 18.45%, [NV−] of 3.69 ppm, and $T_2^*$ of 300 ns. This work dwells on the physics behind electron irradiation and thermal annealing on diamond samples and facilitates NV-based quantum information processing applications.
Funding
National Natural Science Foundation of China (62173020, 62103381).
Acknowledgments
The authors thank Beijing Baoming Technology Co., Ltd. for providing diamond samples and valuable discussion with Lifu Hei.
Disclosures
The authors declare no conflict of interest.
Data availability
Data underlying the results presented in this paper are not available at this time but may be obtained from the authors upon reasonable request.
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