Lattice defects that form optical impurity centers are ubiquitous in many crystalline materials. Among these defects, color centers in diamond have emerged for a variety of applications in quantum communication1,2quantum photonics3,4, and biological sciences5,6. While diamond has been shown to host hundreds of impurity color centers7, very few such color centers have been well-characterized. The most studied color centers in diamond are nitrogen-vacancy (NV)8,9 and SiV10,11 defects which have drastically different optical properties. The NV color center has the quantum property of electron spin with long coherence time at room temperature. This electron spin can be prepared optically and then manipulated using optical, magnetic, and radiofrequency techniques12,13. Even so, using the NV center as a single photon source has two main drawbacks: (i) only about 4% emission light in the zero-phonon line (ZPL) and (ii) an electric dipole moment that generates strong inhomogeneous broadening of the spectral line14. By comparison, the SiV center consisting of one silicon atom located at halfway between two empty lattice sites has an inversion symmetry and no dipole moment. It shows great promise as a single-photon source, as it has a narrow ZPL (Debye-Waller factor) of 70%, a high photon emission rate (short excited-state lifetime at room temperature), and near-infrared emission (ZPL at 738nm)15. These optical properties of SiV center make them ideal for narrow-band photonic devices, including cavity and waveguides3, and for the application as a single photon emitter16.
Two approaches have been widely-employed for fabricating SiV centers in diamond, ion implantation15,17 and chemical vapor deposition (CVD) techniques10,18. Ion implantation using a focused ion beam is a widely available commercial approach. However, it induces extensive structural damage, and high-temperature annealing treatment in vacuum after ion implantation is required.
Furthermore, the conversion of the implanted silicon ions to SiV centers is far less efficient than that of the nitrogen ions to NV centers15,17 due to their structural difference. Compared with the structure of NV center, consisting of a substitutional nitrogen adjacent to a lattice vacancy, the size of silicon atom is too large (~ 1.5 times as large as nitrogen) to replace a carbon atom at a diamond lattice site. An understanding of how to best create and then stabilize the SiV color centers inside the diamond lattice could improve the brightness of these color centers. Towards this end, this work provides fundamental thermodynamic and kinetic insights into how Si ions and vacancies combine to form luminescent color centers.
The current solution for enhancing the conversion efficiency of the implanted silicon ions into SiV centers includes increasing the number of vacancies via additional electron irradiation. But this method concomitantly creates additional damage in the diamond lattice19. A sequence of high-temperature annealing treatment in vacuum is mandatory post ion implantation, but the conversion of implanted silicon ions to SiV centers is far less efficient than that of the nitrogen ions to NV centers15, 17. Alternatively, CVD technology can synthesize high-quality diamonds with the desired doping atom using an ionic plasma, but the ionic plasma makes it difficult to control the high-temperature growth environment. In addition, neither of the two methods allow us to fully understand the color center introduction and vacancy migration processes in situ. Here we present the first mechanistic study on the formation of SiV centers in diamond using temporally controlled annealing. We also develop a novel annealing scheme for improving the conversion efficiency that can be used to guide the synthesis of many other color centers of interest.
In this study, we performed a direct synthesis of SiV centers in diamond from a silicon-containing adamantane precursor (adamantylethyltrichlorosilane, AdaSi) using a high-pressure and high-temperature (HPHT) approach via a laser-heated diamond anvil cell (DAC)20–22. The laser-heated DAC described in this work offers several advantages over ion implantation and CVD including the ability to map out the temperature and pressure conditions necessary for SiV formation from AdaSi “diamondoids," and the ability to explore a variety of different growth and annealing conditions in the same diamond anvil cell. In addition, the transparency of the diamond window of the DAC allows penetration of both the continuous wave (CW) and pulsed laser for precise annealing control, and the in situ measurement of the sample temperature and pressure. The pressure was calibrated at room temperature by monitoring the spectral shift of the R-line fluorescence (694.25 nm) in ruby ball21 and Raman shift of the diamond peak at 1332 cm− 1 in DAC. While DAC was under applied stress, the first-order Raman peak of diamond resulted in the blue-shift of the diamond Raman peak 23.
Adamantane has been documented to be a superior precursor material for laser-induced HPHT diamond synthesis20. A nitrogen-functionalized adamantane has also been shown to convert to fluorescent diamonds at high pressure and moderate temperature24, validating the use of AdaSi for the synthesis of SiV emitting centers in diamond. In order to ensure homogeneous coupling between AdaSi and the laser absorber and reproduce a uniform laser power versus temperature profile across the entire sample chamber, all experiments were performed on a sandwiched sample stack where a 100-nm-thick tungsten layer as the laser absorber is deposited on top of a mica layer that is sandwiched between AdaSi. This sandwich geometry allows a 1064 nm Nd:YLF laser to uniformly heat AdaSi followed by annealing of the converted diamond, as illustrated in Fig. 1.
To elucidate the formation and migration dynamics of SiV centers in diamond, we developed a controlled laser heating apparatus in which high temperature is realized via the metal absorption of the Nd:YLF laser radiation. The temporal control of heating is accomplished by an acousto-optic modulator (AOM) to switch the CW laser into short pulses of light focused onto the tungsten film deposited on a mica substrate inside the DAC (Fig. 1 and Fig. S1). Temporal resolution of the laser heating is directly correlated to the rise/fall time of the AOM that is on the timescale of 150 ns (Fig. S2). Using our system, ultrafast heating at 0.1 GK/s and cooling at 0.1 MK/s can be achieved (Fig. S3).
We also implemented a simple and accurate thermometry system with 1\({\mu }\text{s}\) temporal resolution, which allows determination of the precise temperature when AdaSi is converted to SiV-containing diamond at varying pressures. Typically, temperature in the laser-heated DAC is determined by fitting the thermal radiation spectrum to the Planck radiation function. Instead of measuring the entire thermal radiation spectrum22, two different radiation windows of 900–1450 nm and 1550–2200 nm are selected. The intensity ratio of the two ranges are then converted to determine temperatures above 1000 K (Fig. 2a, and Fig. S1 & S4)25. Note that below 1000 K, the photodetector for 900–1450 nm is not sensitive enough to detect the radiation with negligible light being emitted. Filament lamps with a blackbody pyrometer were used to calibrate the optical intensities of the two photodetectors back to the experimental temperature. Temperature can be measured with a time resolution of better than 1 ms is limited by the bandwidth of the photodetectors (Fig. S5). The absolute accuracy of our ultrafast thermometer is estimated to be ± 50 K (Fig. 2a and Fig. S4).
An example of a detailed temperature response along heating and cooling is shown in Fig. 2b and Fig. S3, which width of laser pulse heating are 20 ms and 10 µs, respectively. Interestingly, we observe clear temperature oscillations with time in certain temperature curves, which might be due to melting/resolidification of the tungsten metal. The tungsten thin film was deposited via DC-magnetron sputtering. While this method produces a very dense film, the quality is far from being single-crystalline25. The melting temperature of a 100-nm-thick film containing tungsten atom-aggregation particles would be significantly lower than the reported value of a bulk sample26. We conjecture that the melted tungsten in this central region flows to the immediate surrounding region and resolidifies. The heat of fusion released plus the additional heat added by the laser pulse causes additional melting and cooling in this region. The temperature in these regions increases until additional melting occurs, which causes another around of cooling. During this time, additional heat continues to be deposited in the center of the focal spot so that multiple rounds of solidification and reheating occur. As a consequence, tungsten migrates away from the hottest, central area, as evidenced by clear thinning and eventual depletion of tungsten in the central region. This also explains why the temperature peaks at a pulse width of ~ 1 ms and is lower for pulses up to tens of microsecond (Fig. 2b).
We recorded the highest temperature for constructing the pressure-temperature synthesis diagram where AdaSi transforms to diamond with SiV centers (Fig. 2c). The diamond formed from AdaSi showed a clear photoluminescence signal of SiV’s ZPL. The photoluminescence of the SiV center due to 514 nm excitation light was measured using an optical spectrometer showed a linear blue shift upon compression (Fig. S6), consistent with the reported theoretical results27. Since the SiV-containing diamond was produced in a laser-heated DAC, the characterization of the diamond quality was performed ex situ. After fully releasing pressure, the retained diamond samples can be well characterized using scanning electron microscope and Raman spectroscopy at ambient conditions (Fig. S7 and S8).
By varying the pulse length of AOM-switched laser beam while recording the emission spectra of laser-heated spots, the laser energy required to form SiV was estimated to be above a threshold value of 0.18 kJ/cm2 (Fig. S9 − S11; Table S1) at 18–20 GPa. For example, at 18.4 GPa with the laser intensity of 33 MW/cm2 and a beam spot of 2.5 \({\mu }\text{m}\) full-width at half-maximum (FWHM), we observed a 5 \({\mu }\)s induction time (Fig. S9) for the formation of SiV centers (Fig. 2d) which equals an energy fluence of 0.165 kJ/cm2. Similarly, at 19.5 GPa with 0.5 MW/cm2 and a 21.5 \({\mu }\text{m}\) beam spot (FWHM), the delivery time was 200 \({\mu }\text{s}\) and the energy is equivalent to 0.100 kJ/cm2. For a nanosecond pulsed laser at 18.4 GPa, the energy delivered by a ~ 5 \({\mu }\)m beam at the peak energy of 25 \({\mu }\)J with a 5 ns pulse-width was 0.176 kJ/cm2 (Fig. S11).
After the conversion of AdaSi to diamond with SiV centers, the as-formed diamond crystals would present many disordered carbon phases and especially unpaired silicon and vacancy. An annealing process is needed to stabilize and further increase SiV concentrations while reducing unwanted defects in diamond. We thermally annealed the diamond crystals by irradiating a larger area of the tungsten film with a CW laser focused with an apochromatic objective lens (Fig. 1 and Fig. S1). An annealing laser beam of 21.5 \({\mu }\)m in diameter (FWHM) was used to surround the photoluminescent diamond particles which were synthesized via laser heating a 2.5 \({\mu }\)m sample spot in the DAC at 18 GPa. To avoid melting of the tungsten thin film, we lowered the intensity of the Nd:YLF laser to 260 kW/cm2. The ratio of SiV’s photoluminescent intensity after the CW laser annealing to the initial value decreased quickly as a function of annealing time and dropped to zero with a decay time of ~ 180 seconds at half maximum intensity (Fig. 3a), suggesting that the CW annealing treatment with a long annealing time is not suitable for stabilizing SiV centers in the diamond lattice.
A silicon atom with two vacancies would eventually anneal to the surface of the diamond crystal once the activation temperature that allows SiV mobility were achieved (e.g., at ~ 1000 K)28. Notably, the photoluminescent intensity showed an approximately 20% drop after the first 10-second annealing (Fig. 3a). This implies that a common thermal annealing technique29 with a time-scale of seconds may allow SiV centers to migrate to a surface or grain boundaries. We conjecture that very short annealing times may lower the probability of migration of SiV centers to the surface of the crystal while still allowing SiV centers to form.
For this reason, we investigated sub-\({\mu }\)s pulsed thermal annealing. The AOM-modulated laser was operated on different pulse repetition frequencies and pulse-widths. A set of pulse repetition frequencies at 10, 100, 1k, 10k, 50k Hz with the 1k, 100, 10, 1 \({\mu }\text{s}\), 200 ns pulse-widths, respectively was used to produce the same laser intensity of 260 kW/cm2 at 18 GPa. Figure 3 plots the ratio of the SiV’s photoluminescent intensity after the pulsed annealing treatment to the starting intensity (Ifinal/Iinitial) as a function of annealing time.
Pulsed annealing treatment with pulse-widths of 200 \(\text{n}\text{s}\) was found to enhance SiV’s photoluminescent intensities up to 250%. However, continued pulsed annealing treatment with a pulse-width of 100 and 10 \({\mu }\)s resulted in the decrease of photoluminescence to half of its intensity at 2 and 125 minutes, respectively. Interestingly, for the 100 \({\mu }\text{s}\) pulsed annealing, the photoluminescent intensity increases to 150% at the first 0.5 minute and then drops close to zero at 4 hours. For the 10 \({\mu }\text{s}\) pulse-width (Fig. S12), SiV’s photoluminescent intensity also increases to 150% after annealing 50 minutes and then decreases to 50% beyond which the intensity remains constant with increasing pulsed annealing time.
SiV photoluminescence keeps increasing to 200% under annealing with 1 \({\mu }\text{s}\) pulse-width. With a 200 ns pulse-width annealing treatment, SiV’s photoluminescence has the same rising trend as that with the 1 \({\mu }\text{s}\) pulse-width and SiV’s intensity increases to 250%. Significantly, the photoluminescent intensities with laser pulse widths of both 1 \({\mu }\text{s}\) and 200 ns do not show any visible decay after 10 hours of pulsed annealing. Simultaneously, the ZPL peak of SiV centers gradually becomes narrower as the diamond quality improves with pulsed annealing (Fig. S13).
To further understand the SiV and vacancy diffusion dynamics, we performed Nudged Elastic Band (NEB)30,31 calculation. In the NEB method, the minimum activation energy for chemical/physical processes can be obtained by constructing a series of fictitious intermediate transition states connecting the initial and final states, and searching for the energy saddle point and the corresponding three-dimensional structure for the minimum energy path. We prepared the initial and final states by enumerating all the “irreducible” diffusion pathways at the microscopic scale, and found the pathways for SiV and vacancies with lowest energy barriers, as shown in the schematic plots of Fig. 4a, 4b, and Fig. S14 & S15.
The initial and final state configurations of SiV and vacancies were optimized by relaxing all the internal atomic positions in the \(2\times 2\times 2\) supercell (64 carbon atoms without the SiV center) using density functional theory (DFT). NEB calculations, as implemented in Vienna Ab initio Simulation Package (VASP)32–35, were then performed for these pathways and the total energies of the initial, intermediate, and final states for a transition pathway would tell us the energy barrier for the microscopic diffusion process. As shown in Fig. 4a, 4b, and Fig. S16, the lowest diffusion energy barrier for the SiV center is 12.3 eV, while the lowest diffusion energy for vacancy is 2.7 eV, an order of magnitude lower.
We further applied the transition rate theory to calculate the corresponding diffusivity D for SiV and vacancy. The diffusivity can be calculated by \(D ={v}_{0}{d}^{2}\text{exp}(-\frac{\varDelta E}{{k}_{B}T})\), in which \({v}_{0}\) is the attempted diffusion frequency, \(d\) is the distance of each diffusion step, and \(\varDelta E\) is the diffusion energy barrier 36,37.
As shown in the Fig. 4c and 4d, theoretical calculations suggest that isolated vacancies have a diffusivity tens of orders of magnitude higher than SiV in crystal diamond within the temperature range of from 800 to 1600 K. This huge diffusivity difference mainly arises from the huge difference in the energy barriers to mobility of the two defects. This result indicates that these vacancies can diffuse much faster than a SiV center in diamond lattice under higher-temperature annealing. Under these conditions, vacancies uncoupled to Si impuities are much more likely to diffuse to the surface of crystal while the SiV remains stabilized in diamond. Although the NEB calculations and the theoretical diffusivity calculations were performed at ambient pressure, we expect that the relationship between SiV and vacancy diffusion would extend to high pressure since the lattice constant of diamond is rather robust up to tens of GPa.
In summary, we investigated the dynamics associated with the creation and stabilization of SiV centers in diamond via an AOM-modulated laser-heated DAC. We developed a \({\mu }\text{s}\) time-scale thermometer for precise temperature measurements in situ. At 20 GPa, the minimum temperature needed to form SiV centers in diamond from precursor AdaSi was 1200 K. Taking advantage of an AOM system that offers high temporal resolution up to tens of nanoseconds, we have elucidated the creation processes of SiV centers in diamond that include the formation energy (0.18 kJ/cm2).
Our combined theoretical and experimental results demonstrate that SiV centers can be stabilized while the crystalline quality improves during the creation of artificial SiV centers. The ultra-short pulse annealing strategy allowed the formation additional optically active SiV centers while limiting the diffusion of SiV defects. By means of a sequence of pulsed annealing treatment with a 200-ns pulse-width at 50k Hz, the concentration of SiV centers in diamond increased to 250% of its initial value and remained invariant after several hours of annealing. Our approach to annealing the diamond with SiV centers may be applicable to other impurity-vacancy structural defects in diamond of a group IV or V elements.
More generally, the repetitive, rapid pulsed-laser annealing and the optimization of time and temperature annealing conditions could be used to further improve the luminescent and electronic properties of condensed matter materials such perovskite solar cells38 and transition metal dichalcogenide-based transistors39.