Optical coherence of implanted silicon vacancy centers in thin diamond membranes

1. Introduction

Color centers in diamond have emerged as promising qubit systems for quantum information processing and especially for applications in optical quantum networks [1–4]. Negatively charged nitrogen vacancy (NV) centers in diamond have been used for the demonstration of spin-photon entanglement, two-photon quantum interference, and the creation of entanglement between distant NV centers [5–8]. There are, however, a number of technical hurdles for the development of optical quantum networks using NV centers. NV centers are highly sensitive to charge fluctuations in their surrounding environment [9]. The resulting excessive spectral diffusion of NV optical transitions can lead to severe degradation of optical coherence of NV centers in diamond nanostructures and in particular in diamond membranes with a thickness near or smaller than 1 µm [10]. The recent development of surface treatment techniques such as graded soft etching has reduced the NV optical linewidth to about 500 MHz in diamond membranes as thin as 700 nm [11]. Nevertheless, the NV optical linewidth still significantly exceeds 1 GHz for membranes with a thickness smaller than 500 nm [11]. In addition, a recent study reveals that NV centers formed from implanted nitrogen exhibit poor optical coherence, with optical linewidth exceeding 1 GHz [12]. These technical hurdles make it difficult to incorporate NV centers in nanophotonic structures, which are essential for the development of highly efficient spin-photon interfaces for optical quantum networks.

In comparison with NV centers, negatively charged silicon vacancy (SiV⁻) centers in diamond exhibit superior optical properties [13–15]. The zero-phonon line of SiV⁻ centers contains more than 70% of the total fluorescence. Because of their inversion symmetry, SiV⁻ centers are robust against charge fluctuations in their surrounding environment. Two-photon quantum interference from separated SiV⁻ centers has been demonstrated [15]. SiV⁻ centers created with ion implantation and annealing can exhibit nearly lifetime-limited optical linewidth [16]. SiV⁻ centers have been incorporated in diamond one-dimensional (1D) photonic crystal structures as well as whispering gallery mode (WGM) optical resonators for cavity QED studies [17–19]. Although the spin decoherence time of SiV⁻ centers is relatively short at elevated temperatures, spin decoherence time as long as 13 ms has been observed at temperatures near 100 mK [20]. In addition, recent development of neutral SiV centers indicates that the neutral SiV centers can exhibit robust spin coherence even at room temperature [21]. SiV-based systems can thus provide a highly promising platform for developing optical quantum networks.

An important issue that has not been adequately addressed is to what extent the optical coherence of SiV⁻ centers is degraded by the etching process, which is necessary for the fabrication of diamond nanophotonic structures. Optical linewidths near 300 MHz have been reported for SiV⁻ centers in 1D photonic crystal structures that feature a lattice constant of 260 nm and a triangular cross section with a side dimension of order 500 nm [17,18]. Similar linewidths have also been observed in diamond nanocrystals and nanopillars with a dimension of order 200 nm [22,23]. For the incorporation of SiV⁻ centers in diamond nanostructures including both photonic and phononic nanostructures, it is important to know whether excellent optical coherence can be maintained in nanostructures with even smaller feature sizes.

In this paper, we report studies of the optical coherence of implanted SiV⁻ centers in diamond membranes as thin as 100 nm. Variations in the thickness of the membranes fabricated from a 30 µm thick diamond film have enabled us to measure the optical linewidth of SiV⁻ centers as the membrane thickness is decreased from 1100 nm to 100 nm. We show that most of the SiV⁻ centers in these membranes feature optical linewidths ranging between 200 and 300 MHz. Remarkably, there is no discernable dependence of the optical linewidth on the membrane thickness. These results indicate the feasibility of incorporating SiV⁻ centers in a wide variety of diamond nanostructures and still maintaining the excellent optical coherence of the SiV⁻ centers.

2. Membrane fabrication

We have fabricated diamond membranes that were designed for use in our cavity QED systems. In these systems, color centers in a thin diamond membrane couple evanescently to optical WGMs of a silica resonator [24,25]. The fabrication started with electronic grade single-crystal diamond films, with the slicing and polishing of a chemical-vapor-deposition grown bulk diamond sample (Element Six, Inc.) into the thin films [with a dimension of (2, 4, 0.03) mm] carried out by Applied Diamond, Inc. Figure 1(a) shows schematically the steps of the membrane fabrication. The ion implantation and high temperature thermal annealing used in the fabrication follows essentially those developed in an earlier study [16].

 

Fig. 1. (a) A flowchart of the steps used for the fabrication of diamond membrane stripes. (b) An optical image of a diamond sample showing completely released membrane stripes. The color fringes reflect the thickness variation of the membranes.

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The first step is to remove mechanical-polishing induced surface damages and prepare the diamond film for ion implantation. For this step, we used Ar/Cl₂ plasma etching to remove about 2 to 3 µm diamond surface layers. The inductively-coupled-plasma (ICP) reactive ion etching (RIE) was carried out in a PlasmaPro NGP80 ICP65 etcher from Oxford Instrument, Inc., with an etching rate of 80 nm/minute. For the removal of the residual chlorine ions in the diamond film, the Ar/Cl₂ plasma etching was followed by a 5 minute O₂ plasma etching, with an etching rate of 100 nm/minute. The diamond film was then placed in a triacid solution with a 1:1:1 mixture of sulfuric, nitric, and perchloric acids at 380 °C for about two hours for the removal of surface contaminants.

For the second step, ²⁹Si⁺ ions with a kinetic energy of 150 keV and with a dosage of 1 × 10¹⁰/cm² were implanted near the surface of the diamond thin film. The implantation was carried out by Innovion, Inc. The kinetic energy used for the implantation leads to a mean silicon stopping depth of about 100 nm with a straggle about 20 nm [16].

The third step is high-temperature thermal annealing in high vacuum (< 10⁻⁶ Torr) [26]. The thermal annealing process consists of 2 hours at 400 °C, 8 hours at 800 °C, and 2 hours at 1200 °C. The temperature ramping rate is approximately 3 °C per minute. The fourth step is the wet chemical oxidation in the triacid solution discussed above for 3 hours. The thermal annealing assists the formation of SiV⁻ centers and repairs implantation-induced damages in the crystal lattice, as shown in the earlier study [16]. The wet chemical oxidation removes surface layers graphitized by the thermal annealing.

The fifth step patterned a Si₃N₄ mask on the front (i.e. the implanted) side of the diamond film. Though simple stripes of diamond membranes are used in our cavity QED systems, the same process can also be used for the fabrication of two dimensional (2D) photonic or phononic nanostructures. In this step, a 280 nm layer of Si₃N₄ was deposited on the front side of the diamond film with plasma-enhanced chemical vapor deposition (PECVD). This is followed by the deposition of a 10 nm layer of titanium to avoid charging during electron beam lithography (EBL). We then spun a 500 nm layer of Polymethyl methacrylate (PMMA) on the front side of the diamond film and carried out EBL and photoresist development to define a simple stripe pattern. This pattern was transferred from the PMMA layer to the Si₃N₄ layer with CHF₃ plasma etching.

The sixth step etched the stripe pattern onto the front side of the diamond film. O₂ plasma etching was used, with an estimated etching rate of 100 nm/minute and with the Si₃N₄ layer as a hard mask. The etching parameters include a RF power of 60 W, an ICP power of 420 W, a DC bias of 108 V, a chamber pressure of 10 mTorr, and an O₂ flow of 30 sccm. The etching depth is slightly over 1 µm.

The seventh step thinned the backside of the diamond film until the stripe pattern is completely released. For this step, we used an alternating process that consists of 30 minutes of Ar/Cl₂ plasma etching, with an etching rate about 80 nm/minute, and 2 minutes of O₂ plasma etching, with an etching rate about 100 nm/minute, followed by 10 minutes of soft O₂ plasma etching, for which the DC bias is set to zero and the RF power is turned off. The Ar/Cl₂ plasma etching used a RF power of 210 W, an ICP power of 280 W, a DC bias of 310 V, a chamber pressure of 5 mTorr, 16 sccm Cl₂, and 10 sccm Ar. The O₂ plasma etching used the same parameters as those for the front side etching. The soft O₂ plasma etching used an ICP power of 500 W, a chamber pressure of 10 mTorr, and an O₂ flow of 30 sccm, with an estimated etching rate of 6 nm/minute. A sapphire shadow mask was also used for the backside thinning such that only a small portion (< 10%) of the diamond film was etched. In this case, the membrane stripes are attached to and supported by the much thicker film. In addition, the remaining film can also be reused.

The eighth step in our fabrication process is the use of graded soft O₂ plasma etching to remove surface layers damaged by the harsh ICP-RIE process. For the graded soft etching process, the etching rate decreases gradually from 6 nm/minute to below 1 nm/minute, with the aim of removing the damaged surface layers without causing significant new damages [27]. The graded soft O₂ etching process consists of 1 hour with an ICP power of 500 W and an etching rate of 6 nm/minute, 2 hours with an ICP power of 200 W and an etching rate of 1 nm/minute, 10 minutes with an ICP power of 150 W, and 10 minutes with an ICP power of 100 W.

The patterning and etching of the membrane stripes, i.e. steps 5 to 8 discussed above, are essentially the same as those used for diamond nanostructures that are intended for studies of NV centers [11]. The main difference in the fabrication process is the surface treatment used after graded soft etching. While high temperature thermal annealing and wet chemical oxidation following the graded soft etching are used in both cases, oxygen annealing was not used as the surface termination step for SiV-based diamond membrane stripes.

Figure 1(b) shows an optical image of membrane stripes in a fabricated diamond sample. The membrane width is 20 µm and the length varies from 80 to over 100 µm. The variations in the thickness of the original diamond film lead to corresponding variations in the membrane thickness. The pronounced color fringes exhibited by the membrane stripes shown in Fig. 1(b) arise from optical interference. Each set of fringes corresponds to a thickness variation of approximately 110 nm [28]. The first fringe measured from the tip corresponds to a membrane thickness approximately 110 nm, as verified by additional measurements using an optical profilometer (Zygo NewView 7300). Note that the thickness variation of the 30 µm film, which originates from dicing and polishing, can be minimized via an additional carefully-designed polishing process, as shown in an earlier experimental study [28]. The variations in the membrane thickness, however, make it convenient to investigate the dependence of the optical coherence of SiV⁻ centers on the membrane thickness.

3. Optical coherence and discussions

SiV⁻ centers feature optical transitions with wavelengths near 737 nm. In the absence of an external magnetic field, both the ground and excited states are doublets due to spin-orbit interactions, as shown schematically in Fig. 2(a). The spin-orbit splittings for the ground and excited states are $\lambda _{so}^g$=47 GHz and $\lambda _{so}^u$=260 GHz, respectively. All transitions between the ground and excited states are dipole-allowed. The excited-state lifetime is 1.7 ns, corresponding to a lifetime limited optical linewidth of 94 MHz (full width at half maximum). An earlier experimental study on SiV⁻ centers implanted in bulk diamond samples has shown that most of the SiV⁻ centers feature an optical linewidth ranging from 200 MHz to 400 MHz [16]. A relatively small inhomogeneous linewidth (a few GHz) for SiV⁻ centers has also been observed [13,16].

 

Fig. 2. (a) Schematic of the optical transitions in a SiV⁻ center (with no strain). (b) A PLE spectrum obtained near the SiV⁻ optical transition wavelengths. (c) An extended scan of a PLE spectrum, combining together five individual scans. All data were obtained at a temperature of 12 K.

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To characterize the optical coherence of SiV⁻ centers in the diamond membranes, we have carried out photoluminescence excitation (PLE) measurements using membranes with a thickness ranging from 100 nm to over 1000 nm. The diamond sample was mounted on the cold finger of a close-cycled helium cryostat (CR-111 Cryostation from Montana Instruments). The PLE experiments were carried out with a home-built confocal optical microscope setup, which uses a 100x objective with a numerical aperture, NA = 0.9 outside the cryostat. For the PLE experiments, the SiV⁻ centers were resonantly excited with a tunable diode laser (New Focus Velocity TLB-6712). A relatively low laser power (< 1 µW) was used to avoid power broadening of the optical transitions. A dichroic beam splitter at 760 nm was used in the collection/excitation path of the fluorescence to reject the reflected and scattered laser light. A tunable long-pass optical filter with a cut-off near the laser wavelength was also used for additional rejection. The fluorescence from the SiV⁻ centers was detected with an avalanche single-photon counting module (Excelitas SPCM-AQRH-16-FC). PLE spectra shown in Fig. 2 are single scans with data averaging at each spectral position. A 532 nm laser irradiation was used at each data acquisition to initialize and stabilize the SiV⁻ centers in the negative charge state, with the detector gated off during the green laser pulse.

Figure 2(b) shows as an example a PLE spectrum obtained in the 30 µm thick film and at a temperature of 12 K. Multiple SiV⁻ centers are observed within the effective detection area of our confocal setup, indicating the relatively high density of SiV⁻ centers created in the sample. Figure 2(c) shows a PLE spectrum obtained in a bulk crystal with a spectral range about 175 GHz. For this spectrum, we stitched or combined together five PLE spectra of individual scans with a scan range of 40 GHz. From the extended PLE spectrum, we obtain a ground-state splitting of approximately 48 GHz, in agreement with the theoretical expectation. Note that the PLE resonances in Fig. 2(b) correspond to the D-transition in Fig. 2(a).

Figure 3(a) plots the optical linewidths obtained for SiV⁻ centers in membranes with a thickness ranging from 100 nm to 1100 nm. A total of 22 SiV⁻ centers were examined in this set of experiments. For these data, we measured the thinnest part of the sample with an optical profilometer and determined the membrane thickness through the number of fringes counted from the thinnest edge. The errors for the estimated thickness are less than 1/4 of the interference fringe. As shown in Fig. 3(a), 20 SiV⁻ centers exhibit optical linewidths between 200 to 400 MHz, while 17 SiV⁻ centers have linewidths between 200 and 300 MHz. Furthermore, there is no discernable dependence of the SiV⁻ optical linewidth on the membrane thickness. Figures 3(b) and 3(c) show, as an example, SiV⁻ optical resonances obtained in membranes with estimated thickness of 330 nm and 1100 nm, respectively. The solid lines in Figs. 3(b) and 3(c) are the least square fit to a Lorentzian. The numerical fit gives an optical linewidth of 226 MHz and 220 MHz for SiV⁻ centers in 330 and 1100 nm thick membranes, respectively.

 

Fig. 3. (a) A scatter plot of the optical linewidths for SiV⁻ centers in diamond membranes with varying thicknesses. PLE spectrum of a SiV⁻ center in a membrane with a thickness of 330 nm. (c) PLE spectrum of a SiV⁻ center in a membrane with a thickness of 1100 nm. Red lines in (b) and (c) are least square fits to a Lorentzian, showing a linewidth of 226 MHz for (b) and 220 MHz for (c), as also indicated by the arrows in (a). The error bars in (a) correspond to the uncertainties in the numerical fits to single Lorentzian. All data were obtained at 12 K.

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For the experimental data shown in Fig. 3, the optical resonances correspond to the transitions from the ground states to the lower-energy excited state, though we have not attempted to determine the specific transition. This is in part due to the relatively high density of SiV⁻ centers implanted in our sample. As discussed earlier, multiple SiV⁻ centers (typically >5) are observed within the effective detection area. This, along with the strain induced energy level shifts, makes it difficult to identify the specific transition. In addition, for the transitions to the lower-energy excited state, there has been no evidence that the optical linewidth depends on the specific transitions.

We note that while the average implantation depth used is 100 nm, the strangle is about 20 nm. For PLE measurements in the thinnest part of the sample, we have by default used relatively bright SiV⁻ centers, which are likely to be situated away from the surface. An average implantation depth of 100 nm was chosen because this was the depth used in our earlier work on NV centers and because we had expected SiV⁻ centers to retain good optical coherence in membranes as thin as 200 nm. It is remarkable that excellent optical coherence of SiV⁻ centers can still be seen in membranes as thin as 100 nm. For these thin membranes, an average implantation depth less than 100 nm should be a more optimal choice. It should also be noted that the implantation parameters we have used led to a relatively high density of SiV centers. It is relatively straight forward to reduce the SiV⁻ center density by adjusting the implantation parameters.

The experimental results shown in Fig. 3 are in sharp contrast to similar studies carried out for NV centers in diamond membranes [10,11]. The NV optical linewidth starts to broaden when the membrane thickness is decreased to a few µm. Without graded soft etching, the NV optical linewidth exceeds 1 GHz at a membrane thickness of 1 µm. With graded soft etching, the NV optical linewidth can remain close to 300 MHz at a thickness of 1 µm, but broadens to beyond 1 GHz when the membrane thickness is decreased to below 500 nm. NV centers are extremely sensitive to charge fluctuations and thus to etching-induced damages. In comparison, because of the inversion symmetry of SiV⁻ centers, the optical coherence of the SiV⁻ centers is robust against charge fluctuations, which is further confirmed by the independence of the SiV⁻ optical linewidth on the membrane thickness for membranes as thin as 100 nm. Based on these findings, we expect that optical coherence of SiV⁻ centers can be retained in diamond nanostructures with similar feature sizes.

Optical coherence of SiV⁻ centers can be affected by strong strain in the diamond sample. As shown in an earlier study [29], a relatively large strain can lead to a ground-state splitting far exceeding the intrinsic spin-orbit splitting, thereby strongly modifying the thermalization process. At a ground-state splitting of 400 GHz and at 4 K, the spin linewidth can be reduced from about 3.5 MHz to 1 MHz [29]. For the membranes studied in our work, the ground-state splitting was observed to range from 70 to 150 GHz near the clamping area, where the strain is the strongest. In comparison, the ground-state splitting observed near the tip, i.e. the thinnest part of the membrane, is close to that observed in bulk crystals. As such, we do not expect the strain in the thin membranes to appreciably change the optical linewidth of SiV⁻ centers.

Diamond membrane stripes as thin as 100 nm as shown in Fig. 1(b) can be incorporated into a cavity QED system that exploits the evanescent coupling between optical WGMs and color centers in the membrane [24,25], without spoiling the quality factor of the WMGs [30]. This type of cavity QED systems can reach the good cavity limit, in which the cavity linewidth is small compared with the linewidth of the SiV⁻ optical transitions as well as the relevant single-photon coupling rate, enabling a promising platform for optical quantum networks.

4. Summary

In summary, we have characterized the optical coherence of SiV⁻ centers implanted in diamond membranes. Using membranes with variable thicknesses, we show that excellent optical coherence of SiV⁻ centers can be maintained in membranes as thin as 100 nm. Diamond photonic nanostructures with SiV⁻ center can provide a promising and robust experimental platform for optical quantum networks. SiV⁻ center can also be used in the recently developed phononic networks of spins, which can potentially enable new experimental platforms for phonon-based quantum information processing [31,32].