1. Introduction

The ensemble nitrogen-vacancy (NV) centers in bulk diamond exhibit high sensitivity, which has wide applications in quantum information and high precision sensing [1]. It can be utilized as a highly sensitive sensor for magnetic field [2,3], electric field [4,5], temperature [6–8], and biosensing [9–12]. The NV usually refers to negatively charged nitrogen-vacancy centers (NV^-), but in the formation of defects, NV⁰ can also be present [13–15]. The NV⁰ is the NV defect without charge and exists as electrically neutral. The existence of NV⁰ and NV^- defects is unstable. There is a transformation between the two types of defects. Prior studies have indicated that the intensity of laser beams can induce a photoelectron ionization process in NV, leading to the conversion of NV^- to NV⁰ [16]. Temperature changes can influence the interconversion between NV⁰ and NV^-, thereby impacting the excitation efficiency of NV^- fluorescence.

The study of the fluorescence behavior of diamonds with different NV^- concentrations is essential to improve the sensitivity of magnetic field and temperature measurements. Moreover, the sensitivity is also influenced by the temperature of the test environment [17,18]. Nevertheless, there has been a lack of research focusing on the examination of the photoluminescence (PL) characteristics of ensemble NV centers at varying temperatures following identical irradiation and annealing procedures. The zero-phonon line (ZPL) can reflect the concentrations of NV. At room temperature, the phonon sidebands of NV^- fluorescence spectra are broad, and the intensity of ZPL accounts for a relatively small proportion [19,20]. At cryogenic temperatures, the ZPL intensity is significantly enhanced, and the phonon sidebands are suppressed. Hence, a comprehensive investigation into the impact of ZPL attributes on NV center behavior across different temperature conditions is imperative.

This study aims to explore the influence of varying temperatures on the PL behavior of ensemble NV centers in various nitrogen (N) concentration samples. The PL temperature dependence of NV^- and NV⁰ in an ultra-low temperature to room temperature was measured using four diamonds with different N concentrations. The temperature-dependent of ZPL peaks, broadening of line widths, and reduction in intensities are studied. Additionally, to explore the impact of temperature on the transformation between the two different charge states of the NV center, the ratio of NV⁰ and NV^- in samples with different N concentrations was compared. These results build the foundation for conducting in-depth studies on the fluorescence characteristics of ensemble NV centers at various N concentrations.

2. Principles

Diamond crystals have a tetrahedral arrangement composed of carbon (C) atoms. The creation of NV involves the substitution of a carbon atom with a nitrogen atom within this structure, along with the replacement of an adjacent carbon atom with a vacancy [21]. This lattice defect structure demonstrates symmetry consistent with C_3V [22]. Based on the findings of Weber's initial computational analyses concerning NV centers, it has been established that the concentration of NV centers is correlated with the defect formation energy (${E^f}$) [23,24].

The Hamiltonian representing the electron spin ground state of the NV^- center can be formulated as follows [25]:

In the Eq. (3): ${\gamma _e}$ is the electron gyromagnetic ratio, $\boldsymbol{S} = ({{S_x},\; {S_y},\; {S_z}} )$ represents the quantum spin number S of the electron with spin operators, E refers to the transverse zero-field splitting (ZFS), which is mainly associated with stress in the diamond lattice and the presence of electric fields [26]. $\boldsymbol{B}$ is the external magnetic field, causing Zeeman splitting of the ${m_s} ={\pm} 1$ state of electron spin [27], and D is the ZFS energy, arising from the ZFS between the degenerate ${m_s} ={\pm} 1$ and ${m_s} = 0$. The source of instability arises from the spin interaction between the two unpaired electrons within the NV^- center, a phenomenon that is contingent upon their spatial separation and is further modulated by the thermal expansion characteristics of the diamond lattice. Consequently, this property can be harnessed for applications such as temperature sensing or thermal mapping. The fluctuation in D aligns with the pattern observed in ZPL [28]. The PL spectra are affected by temperature, specifically influencing the ZPL and its accompanying sidebands due to the temperature's impact on the energy gap [29].

3. Results and discussion

In the experiment, a 532 nm laser was used to emit the samples, and a 537 nm long-pass edge filter was employed to filter the emitted laser light. To avoid the influence of laser-induced NV⁰ and NV^- concentrations [16], we maintained a lower laser power for measurements (P = 140 mW). The samples consisted of four nitrogen-doped single-crystal diamonds synthesized via chemical vapor deposition (CVD). All samples underwent a 10 MeV electron irradiation for four hours, followed by a multi-stage annealing process. The annealing involved a cooling process at 600°C for five hours, followed by heating at 800°C for two hours, and finally, natural cooling to room temperature. Figures 1(a)-(d) show the PL spectra from 1.6 K to 300 K for different N concentrations. The sharp ZPL line of NV⁰ and the NV^- demonstrating the different changes can be observed. The concentrations of NV⁰ and NV^- can be approximately compared by the intensity of the ZPL [30]. At room temperature, the fluorescence intensity of the diamond with a nitrogen concentration of 0.01 ppm is very weak. Under the same conditions, the spectrometer's slit needs to be opened to the maximum position to detect the faint fluorescence. The fluorescence intensity of the other three samples is strong, indicating a high NV center concentration. At room temperature, the relationship between NV⁰ and NV^- in the four samples is not apparent.

 

Fig. 1. The PL spectra of NV centers in diamond with different N concentrations at the temperature range of 1.6 K-300 K. (a) 0.01 ppm. (b) 20 ppm. (c) 50 ppm. (d) 100 ppm.

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However, at cryogenic temperatures, the phonon sideband luminescence is suppressed, leading to enhanced emission of the ZPL. This enhancement facilitates a clear observation of the relative relationship between NV⁰ and NV^-. As depicted in Figs. 1(a) and (b), the ZPL of NV⁰ is higher than that of NV^- at concentrations of 0.01 ppm, 20 ppm, and 50 ppm, indicating that the majority of NV exist in the form of NV⁰ with low N concentrations. In Fig. 1(c) and (d), as the N concentration increases, the gap between the two defect concentrations gradually diminishes. In the 100 ppm N concentration sample, the number of NV^- is more than NV⁰, which indicates that with the increase of nitrogen concentration, the concentration of NV^- is gradually higher than the concentration of NV⁰. This is consistent with the concentration relationship described in Eq. (2). The total fluorescence intensity of the ZPL is lower than that of a N concentration of 50 ppm. The doping process affects the internal lattice structure of the diamond. Under the same conditions of irradiation and annealing, the diamond is more prone to graphitization, consequently affecting its fluorescence intensity.

Additionally, with an increase in N concentration, the fluorescence intensity generated by the phonon sidebands gradually rise, and multiple distinct sharp peaks of the phonon sidebands become evident at cryogenic temperatures [31,32]. This is due to the periodic phonon sideband structure of NV^- centers, arising from their respective quasilocalized vibrational resonance effects. From Figs. 1(c) and 1(d), it can be observed that these peaks also vary with changes in the ZPL. The fluorescence intensity is similar at room temperature, but the intensity with concentrations of NV⁰ and NV^- are significantly higher at cryogenic temperatures.

Figures 2(a) and (b) show the PL spectra intensity of NV⁰ and NV^- in the four CVD diamond samples at the temperature range of 1.6 K to 300 K. It can be observed that NV⁰ centers of different concentrations follow the fitting trend of the Boltzmann equation with changing temperatures, as indicated by the solid line. The fluorescence intensity of ZPL gradually decreased with the temperature increased. Both NV⁰ and NV^- centers exhibit a diminishing temperature dependence of the fluorescence intensity of the ZPL as the defect concentration increases. The NV⁰ centers show a stronger temperature dependence compared to NV^-. As shown in Figs. 2(c) and (d), the first derivative of the temperature dependence curve of the fluorescence intensity provides the rate of change in defect number as the temperature is increased. When the defect concentration is very low, the impact of temperature on NV⁰ centers is significantly greater than on NV^-. The highest temperature sensitivity of NV centers occurs in the range from 150 K to 170 K, and this behavior is attributed to the energy fluctuations within the system in this temperature range [33]. here is a phenomenon occurring within the temperature range of 10 K to 75 K, where the fluorescence of NV^- noticeably decreases, followed by a significant increase. This anomaly phenomenon in this range is also evident in the ZPL shift.

 

Fig. 2. (a) Fluorescence intensity variation of ZPL for different concentrations of NV⁰ centers. (b) Fluorescence intensity variation of ZPL for different concentrations of NV^- centers. (c) Relationship between the derivative of ZPL fluorescence intensity for NV⁰ and temperature. (d) Relationship between the derivative of ZPL fluorescence intensity for NV^- and temperature. The insert in (c) and (d) corresponds to the first derivative of the temperature dependence curve for the 0.01 ppm N concentration.

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As shown in Figs. 3(a) and (b), the curves depict the peak shift of ZPL for NV⁰ and NV^- with changing temperatures. From 1.6 K to 300 K, the ZPL peak of NV⁰ shifts from 574.4 nm to 575.2 nm, while the ZPL peak of NV^- shifts from 636.5 nm to 637.5 nm. Overall, the ZPL peak shift of NV^- is larger than that of NV⁰. The trends for both defects conform to the fitting curve [34]. As the concentration of NV⁰ increases, the ZPL peak shift gradually increases, and the temperature dependence becomes more significant. With the increase of the concentration of NV^-, the difference of the wavelength gradually decreases. The redshift of the ZPL peak position is attributed to the electron-phonon coupling effect. For high concentrations of NV^-, there is an anomalous temperature dependence in the wavelength shift within the 10 K-140 K range. As shown in Fig. 3(b), the ZPL peak position shown an abnormal blueshift at 10 K-75 K. This occurs because the emitted electrons are influenced by traps during the emission process, impeding their return to the ground state. Then, the curves increasing that show a redshift. It implies that some electrons are released from traps and contribute to the NV^- emission. This wavy variation in intensity has not changed the overall tendency of thermal quenching. It resembles some two-dimensional quantum slices [35] as a result of changes in electron-phonon scattering in NV, which lead to variations in the bandgap at different temperatures. This behavior can be described using the Fan-Shyun electron-phonon scattering model [36].

 

Fig. 3. The ZPL peak positions of the two types of ZPL lines vs. temperature: (a) NV⁰ and (b) NV^-. The ZPL linewidth of the two ZPL lines vs. temperature: (c) NV⁰ and (d) NV^-.

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In addition to the peak shift of the ZPL, the interaction between electrons and phonons also causes the ZPL line to broaden. The ZPL typically follows a Lorentzian shape, and its linewidth represents the decay rate of the radiative transition. In solid-state systems, as the defect is embedded within the lattice, its luminescence often involves coupling with the lattice vibrations of the host material, resulting in the emission of phonon bands. As temperature increases, optical phonons increasingly dominate. Simultaneously, the luminescence of various types of defects may become activated. On the other hand, as the temperature decreases, the excitation of optical phonons is gradually suppressed. The changes in linewidth with temperature rise are depicted in Figs. 3(c)-(d).The ZPL of NV⁰ is from 569.00 nm to 578.64 nm. The ZPL of NV^- is from 632.06 nm to 641.80 nm. The curves indicate that the thermal expansion rate of NV^- is higher than that of NV⁰. The linewidth of the ZPL of NV^- is affected by temperature. However, the negligible change in ZPL linewidth of NV⁰ indicates that the concentration of NV⁰ has a minor influence.

As illustrated in Fig. 4(a), the concentration of NV centers is notably greater at cryogenic temperatures compared to room temperature. With consistent processing parameters, the presence of NV rises in conjunction with an increase in nitrogen concentration, observed at both room temperature and cryogenic temperatures. In the temperature range of 1.6 K to 75 K, the concentration of NV exhibits a consistent level. Subsequently, with further temperature elevation, there is a notable decline in concentration, which gradually stabilizes beyond 225 K. The result presented in Fig. 4(b) illustrates that the proportion of NV^- to NV⁰ is dependent on the concentration of N, with this ratio progressively rising as temperature levels increase. In CVD diamonds, a higher N concentration does not result in a higher concentration of NV centers. Figures 4(c) and (d) illustrate that, when subjected to identical irradiation and annealing durations, the levels of NV⁰ and NV^- do not exhibit a substantial alteration in response to varying N concentrations at cryogenic temperatures. Conversely, at room temperature, the quantities of NV⁰ and NV^- initially rise rapidly before declining with escalating N concentrations. As illustrated in Fig. 4(d), it is observed that an increase in nitrogen concentration exceeding 50 ppm leads to a higher production of NV^- at room temperature. However, beyond a concentration of 100 ppm, the NV^- content decreases. This suggests the presence of an optimal concentration range between 50 ppm and 100 ppm for maximizing the quantity of NV^-.

 

Fig. 4. (a) The temperature dependence of the general intensity of NV⁰ and NV^- for four samples. (b) The temperature dependence of NV⁰ and NV^- intensity ratios for four samples. (c) The relationship between ZPL fluorescence intensity of NV⁰ and N concentration. (d) The relationship between ZPL fluorescence intensity of NV^- and N concentration.

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4. Conclusions

We studied the temperature-dependent of PL spectra in diamonds with different N concentrations. The results demonstrate that NV exhibits the different trend at different N concentrations. The temperature dependence of NV⁰ and NV^- can be explained through generalized quantum theory. As the concentration increases, both NV⁰ and NV^- centers concentrations increase, and the spectra properties conform to the Debye-Waller temperature model and the theory of temperature-induced band gap broadens. Different N concentrations show varying rates of PL intensity change, indicating that there is a best sensing temperature range. With the increase in temperature, the ZPL shows a peak redshift, decreased intensity, and increased linewidth. These phenomena can be attributed to the expansion of the diamond lattice and the synergistic effect of electron-phonon coupling. We also observed that in high-concentration NV^-, there is an anomalous temperature dependence in the peak of wavelength shift in the range of 10 K-140 K. The quantum anomalous variable-temperature bandgap renormalization phenomenon becomes more pronounced with the increase in NV concentration. The optimal N concentration for obtaining strong NV fluorescence is approximately 50 ppm to 100 ppm.

This study provides experimental evidence for obtaining more NV centers in CVD diamond, and offers detailed references for the study of the PL properties of NV centers. The temperature-dependent characteristics of the PL help improve the sensitivity and stability of temperature measurements. Additionally, they can extend the temperature measurement range of sensors, facilitating sensor design for different operating environments. On the other hand, the intensity and direction of magnetic fields may be influenced by temperature variations. Understanding the response of NV centers to magnetic fields at different temperatures can further optimize the sensitivity and stability of magnetic sensors.