Tunable and Transferable Diamond Membranes for Integrated Quantum Technologies

Color centers in diamond are widely explored as qubits in quantum technologies. However, challenges remain in the effective and efficient integration of these diamond-hosted qubits in device heterostructures. Here, nanoscale-thick uniform diamond membranes are synthesized via “smart-cut” and isotopically (12C) purified overgrowth. These membranes have tunable thicknesses (demonstrated 50 to 250 nm), are deterministically transferable, have bilaterally atomically flat surfaces (Rq ≤ 0.3 nm), and bulk-diamond-like crystallinity. Color centers are synthesized via both implantation and in situ overgrowth incorporation. Within 110-nm-thick membranes, individual germanium-vacancy (GeV–) centers exhibit stable photoluminescence at 5.4 K and average optical transition line widths as low as 125 MHz. The room temperature spin coherence of individual nitrogen-vacancy (NV–) centers shows Ramsey spin dephasing times (T2*) and Hahn echo times (T2) as long as 150 and 400 μs, respectively. This platform enables the straightforward integration of diamond membranes that host coherent color centers into quantum technologies.

Standard 3 mm by 3 mm by 0.25 mm single crystal, optical grade diamond substrates (Element Six, ≤1 ppm [N]) are used for the membrane synthesis. These are initially fine-polished to a surface Rq of ≤0.3 nm (Syntek LLC.) as to minimize morphological inconsistencies (see Figure S1 (a)). Next, the samples are implanted with 4 He + ions (CuttingEdge Ions LLC.) at 150 keV to create a graphitized layer at ≈410 nm depth. This is done at an incidence angle of 7°to avoid ion channeling. The dose is set to 5 × 10 16 cm −2 , which is closely above the graphitization threshold as to minimize crystal damage (see section 1.5). In this work, a threestep annealing process was employed after the implantation: a 400°C soak for 8 h, followed by a 800°C soak for 8 h, completed with a 1200°C anneal for 2 h. 1 This was done in a forming gas environment (Ar:H 2 of 96 : 4). The implantation and annealing had no negative impact on the surface roughness (see Figure S1 (b)). The phase transition of the carbon bonds during membrane formation is studied via room temperature Raman spectroscopy (see section 2.2).

PE-CVD diamond overgrowth and δ-doping of 15 N
Homoepitaxial PE-CVD of diamond is performed in a custom configured SEKI DIAMOND SDS6350 system. Before loading into the growth chamber, the diamond substrates are chemically tri-acid cleaned (see section 1.7). The diamond sample is placed on a grooved molybde-num substrate to keep it flat with the rest of the plasma exposed surface, allowing for a uniform growth rate across the sample, while minimizing edge effects. The chamber is pumped down to a 2 × 10 −8 Torr to 5 × 10 −8 Torr base pressure in order to reduce background contamination. Thereafter, high purity H 2 (99.999 999 % chemical purity) is introduced into the chamber, with the gas flow ratios constant and pumping rate monitored as to maintain a constant process pressure of 25 Torr. Throughout the process the microwave power is maintained at 900 W (11.5 W mm −2 ). Before introducing the carbon precursor, the substrate is heated to a 500°C or 700°C setpoint which translates to a pyrometer assessed plasma temperature of 540(10)°C or 740(10)°C, respectively. The H 2 -only plasma conditions are maintained for 20 min (500°C) and 1 h (700°C) as to etch away any residual surface carbonaceous contaminants -the approximated sp 3 etch depth is ≤1 nm. 2 Thereafter, 12 CH 4 (99.999 99 % chemical purity, 99.99 at.% isotopic purity) is introduced as the carbon precursor, this injection is substantiated in-situ via increase of the pyrometer detected substrate surface temperature to 765(10)°C (580(10)°C for the 500°C set-point grown substrate). The methane-to-hydrogen ratio is maintained constant at 0.05 % (H 2 : 12 CH 4 = 400 sccm : 0.2 sccm) as to ensure step-flow growth. 3,4 Growth rates for the 700°C and 500°C membranes were determined to be 6.2(4) nm h −1 and 9.3(8) nm h −1 , respectively (see section 2.3). The reduction in growth rate is explained by an increased surface mobility and desorption of precursor adatoms 5 and likely due to a non-linear reduction of nucleation sites.
In-situ nitrogen doping is accomplished by introducing 0.06 sccm of 15 N 2 gas (99.99 % chemical purity, 99.9 at.% isotopic purity) for 2 min during the growth phase. This creates a 36 nm depth localized layer with a SIMS quantified [ 15 NV -] density of 30.8(57) ppb (see section 4.5). Thereafter, a cap layer is overgrown to encapsulate the δ-doped layer as deep in the membrane as desired. Subsequent irradiation and annealing allows the conversion of this layer into ≈0.9 ppb of [ 15 NV -], resulting in an average color center creation efficiency of ≤2.5 %, in agreement with previous studies (see section 4.5). 3

Membrane patterning and EC etching
Atomic layer deposition (ALD) is used to deposit 25 nm of Al 2 O 3 on the overgrown membrane samples. This oxide layer serves as selective hard mask for subsequent ICP etching. Thereafter, a photoresist layer (AZ MiR 703) is applied to the sample, followed by a lithography exposure (Heidelberg MLA150, 375 nm laser, with a 150 mJ cm −2 dose). A total of 56 square-shaped membranes are patterned on a single substrate. Next, the sample is developed (AZ 300 MIF) and two-step etched in a chlorine-based ICP chamber (Plasma -Therm, Al 2 O 3 etched with BCl 3 chemistry first, with diamond subsequently etched in O 2 chemistry, see Table S2). This step exposes the underlying graphitic layer. After etching, the sample is ultrasonicated in 80°C N-Methyl-2-pyrrolidone (NMP) solution and placed in a buffered oxide etch (BOE) solution to remove excess resist and oxide layers.
For the EC etching step, the sample is held by double side tapes at the bottom of a DI waterfilled petri dish which is mounted on a probe station (Signatone S1160). Unlike previous studies which required customized platinum tips, 6 we use commercially available tungsten tips (Signatone SE-T) as the cathode and palladium tips (Signetone SE-P) as the anode (see Figure S3 (b)). These tips are mounted to 3-axis micropositioners (Signatone S926), which are connected to a DC power supply (B&K Precision 1787B). Typically, a voltage between 15 V and 36 V is applied to undercut the membranes, with larger undercut areas requiring larger potentials and longer time. The EC etch is visually tracked, with the voltage cut at the moment that the desired undercut tether has been achieved. This process, while relatively simple, requires constant supervision as the final tether feature size is typically less than 50 µm in any direction. Practically speaking, at the typical voltages quoted above, this translates to an etching time of ≈30 min per membrane (see Figure S3 (c)). This processing step is a great candidate for future automation.

Membrane transfer and post-processing
Prior to the membrane dry transfer, the intended carrier wafers or devices are prepared with pre-defined structures and features (see section 1.8). In this work, we use 7 mm by 7 mm fused silica (SiO 2 , JGS2 grade) and thermal oxide (280 nm SiO 2 Si) wafers. Alignment markers and 5 µm deep trenches are patterned and etched into substrates to suspend part of the transferred membrane (see Figure S5 (a)). In this way, both surfaces of the membranes are exposed, enabling double-sided surface termination via wet-chemical or dry processes with acid cleaning and oxygen annealing used in this work. As for the dry-transfer itself, we start by mounting the diamond substrate on a transfer station rotational chuck (Signatone S1160). Parallel to this, we prepare a PDMS/PC stamp on a glass slide and mount it into a computer-aided micropositioner (Signatone CAP -946). Next, we slowly bring the stamp down and allow it to fully adhere to the target membrane. With a quick movement of the now-adhered stamp, we break the membrane from the tether. Then, we replace the substrate on the chuck with a second PDMS stamp on a glass slide. The detached membrane can be transferred to this second stamp by slowly bringing the PDMS/PC stamp into contact with the "stickier" PDMS-only stamp and lifting the PDMS/PC stamp afterwards. Finally, with the membrane fully adhered to the PDMS-only stamp, we use the micropositioner to mount the membrane to an HSQ-covered carrier wafer on the chuck. After careful alignment, we gradually bring the stamp down until the membrane is fully attached to a freshly spin-coated HSQ layer (14 % HSQ in methyl isobutyl ketone (MIBK) solution, DisChem Inc.), and then slowly release the stamp. The membrane is left on the carrier wafer due to stronger adhesion from the HSQ polymer and the residual MIBK solvents (see Figure S4).
After membrane transfer, the carrying wafer is annealed at 600°C for 8 h in Ar environment. The HSQ adhesion layer fully collapses during the annealing and forms a nearly strain-free ≈250 nm thick layer. This thickness can be tuned by using different concentration of HSQ solvents or by varying the spinning parameters. In the case of partially suspended membranes, we applied a vapor HF treatment (Memsstar ORBIS ALPHA) to fully remove the HSQ in the trench (see section 2.4). Additionally, in order to etch the original damaged underlayer (the etched side of the membrane), improve surface morphology, and tune the final thickness, we submit the mounted membrane to a three-step ICP process (see Table S2). 1 We start with the "Ar/Cl 2 " recipe (2 min to 5 min, depending on the target thickness) to polish the surface, then we use the "O 2 /Cl 2 " recipe (30 s to 90 s) to remove most of the chlorine-based compounds on the diamond surface. Finally, we apply a 30 s "O 2 " etch to remove the residual chlorine compounds and correctly terminate the surface. In order to avoid chemical contamination, etching steps are separated by multiple pump-purge cycles. AFM characterizations are added post-etching to ensure no micromasking occured during ICP processes. 7 The membrane thickness is monitored via either a profilometer (Bruker DektakXT) or an ellipsometer (Horiba UVISEL2) (see section 2.3).

Additional information on ion implantation
Two distinct ion implantation runs were performed in this work: 4 He + ion implantation for the creation of the graphitized underlayer and 14 N + , 28 Si + , 74 Ge + , and 120 Sn + ion implantation for the creation of color centers. Both implantation processes were performed at CuttingEdge Ions, LLC.
To achieve the formation of the graphitized underlayer, a low energy 4 He + -ion implantation into the diamond substrates was done as depicted in Figure 1 (a). This step forms a depthlocalized graphitized underlayer ≈410 nm deep via a damage-induced phase transition from sp 3 to sp 2 . The implantation energy was kept at 150 keV to minimize crystal damage along the 4 He + trajectory. The dose was set to 5 × 10 16 cm −2 , which is above the graphitization threshold, but minimized to avoid unnecessary crystal damage. Separate implantation tests showed that lower doses of ≤2 × 10 16 cm −2 were insufficient to generate a reliable graphitized layer, with the diamond substrate remaining transparent. Therefore, the desired damage threshold was established to be between 2 × 10 16 cm −2 to 5 × 10 16 cm −2 .
We use the Stopping and Range of Ions in Matter software (SRIM) 8 to estimate the ion implantation depth and straggle. For the simulations, the density of carbon is set to 3.51 g cm −3 , and the incidence angle is 7°to avoid ion channeling. For color center incorporation, we simultaneously implanted 14 N + , 28 Si + , 74 Ge + and 120 Sn + at a dose of 2 × 10 8 cm −2 in order to achieve an individual-level color center density. Details about the implantation parameters and simulated depths and straggles are shown in Table S1.
All of the implantation steps were followed with the three-step 1200°C anneal 1 (see section 1.1) to form the graphitized layer and color centers, in the case of the He + and color center implantation, respectively.

Electron irradiation
For the synthesis of delta-doped color centers, an electron radiation of 10 × 10 18 cm −2 at 2 MeV at the low energy accelerator facility (LEAF) at Argonne National Laboratory was performed to form vacancies throughout the diamond crystal. This was followed by a 6 h vacancy mobilization anneal at 850°C in forming gas (96 : 4 of Ar:H 2 ).

Surface cleaning and termination
In order to remove contamination and passivate the surface, acid-related surface cleanings and terminations are applied multiple times during membrane synthesis. Firstly, diamond substrates receive a tri-acid cleaning (1 : 1 : 1 nitric, sulfuric, and perchloric acid) at 200°C for 2 h right before the overgrowth to eliminate surface contamination 9 . Secondly, the diamond membrane template receives a di-acid cleaning (1 : 1 nitric and sulfuric acid) at 225°C for 2 h after every transfer step to prevent accumulated contamination induced by EC etching or PDMS/PC stamping. Finally, before optical measurements, membrane samples receive another di-acid cleaning and an optional oxygen termination, depending on the type of color centers being characterized. For group IV centers, we only apply the di-acid clean procedure. For NVcenter measurements, an additional oxygen termination is applied following di-acid cleaning, which includes a 4 h annealing at 400°C in O 2 atmosphere, with 5 min rinse in freshly prepared Piranha solution (3 : 1 sulfuric acid and hydrogen peroxide) before and after the annealing. The oxygen termination is intended for optimizing the NV 0 to NVconversion and stability 10 . The incorporation of higher temperature oxygen annealing while avoiding surface etching is an ongoing study and beyond the scope of this work.

Carrier wafer preparation
In this work, we dice thermal oxide and fused silica wafers to 7 mm by 7 mm squares (Disco DAD3240) as carrier wafers. Some wafers receive ≈5 µm trench fabrication on the surface to allow membranes to receive double-side surface treatment and obtain low background fluorescence during optical measurements.
In order to etch the trenches, we deposit a ≈6 µm photoresist layer (AZ 4620) as the etching mask. The spinning speed is set to 500 rpm for 10 s and then 4000 rpm for 50 s, with a ramping rate of 100 rpm s −1 and 2000 rpm s −1 , respectively. After resist spinning and pre-baking, the sample is lithographically exposed (Heidelberg MLA150, 405 nm laser with 320 mJ cm −2 dosage), followed by development in AZ 400K 1:4 solution. We use fluorine-based ICP (Plasma -Therm) for SiO 2 and Si etching. After etching, samples are ultrasonicated in 80°C N-Methyl-2-pyrrolidone (NMP) solution to remove the resist.

Additional discussions on diamond membrane fabrication
The membrane creation process highlighted herein advances scalable diamond quantum research in several important ways. While the process requires initial diamond substrates with sufficient crystallinity and smoothness, it is agnostic to moderate impurity and defect concentrations within the substrate. This eliminates the need for highly purified bulk diamond substrates, which are costly and scarce. Additionally, while bulk diamond crystals are commercially grown and available for purchase in a limited range of dimensions, the size and the shape of the membranes are fully defined and can be tailored to specific applications, with the maximum size only limited by the substrate dimensions. While our choice of membrane size (200 µm × 200 µm) is well motivated by scientific applications, such delaminations over millimeter size have been achieved 11 , and there are no technical barriers to realizing larger dimensions with our technique.

Material characterization 2.1 AFM characterization
We extensively apply AFM measurements (Bruker Dimension Icon) to monitor the surface morphology throughout the synthesis steps. The scanning ranges and resolutions in both directions are set to 10 µm and 512 lines (except for Figure S1 (f), 5 µm with 256 lines) to observe the surface morphology and growth-or etching-related features.
The surface maps of overgrown and back-etched diamond membranes are shown in Figure 2 (a-c) of the main text, with maps of other key steps shown in Figure S1. Since the as-purchased diamond substrates are only roughly polished (Ra ≤ 30 nm), we applied another fine-polish (Syntek LLC.) step to reduce the roughness to Rq = 0.30 nm (Ra = 0.20 nm), as shown in Figure S1 (a). The final surface miscut, relative to the crystallographic (001) axis, is specified to ≤3°. Unfortunately, while this value is relatively consistent within a single substrate batch, it can vary between substrate lots, affecting the effective implantation angle and overgrowth characteristics 4 .
The He + -graphitized and subsequently annealed substrate is shown in Figure S1 (b), with the same level of surface morphology (Rq = 0.27 nm). Figure S1 (c) exhibits the 40 h overgrown diamond surface with a pre-growth 60 min hydrogen plasma etch. The inconsistency of surface roughness under the same duration of hydrogen plasma etch (see Figure 2 (b)) may come from the residual surface strain from fine polishing. A surface strain release step 1 after the fine-polish should improve this in future iterations of the fabrication process. Another 40 h growth without proper surface preparation is shown in Figure S1 (d). Residual contamination on the diamond surface generates growth defects (such as pits or pyramids) along the process. Figure S1 (e) shows the etched side of the diamond membrane after the dry transfer. The excess roughness (Rq = 1.17 nm) comes from the straggle of the He + implantation and can be reduced by subsequent "Ar/Cl 2 " etching. It is crucial to apply "Ar/Cl 2 " to prevent roughness deterioration. Figure S1 (f) shows the etched side of the membrane if the O 2 etching is applied directly, where the surface deteriorates noticeably due to the preferential etching nature of an O 2 -based plasma on crystallographic defects and polish-induced damage.

Raman characterization
Throughout the process, we applied Raman spectroscopy (Horiba Scientific LabRAM HR Evolution) to investigate both the phase of the carbon during membrane formation and the diamond crystal quality. A 633 nm excitation laser is used instead of the more popular 532 nm to avoid broad fluorescence from NVcenters in the substrates. We use the finest grating (1800 gr mm −1 ) for data collection, with a quoted resolution of ≈0.3 cm −1 . The resulting peak position uncertainty is caused by this instrument resolution, while the linewidth uncertainty comes from the fittings. The pinhole of the Raman confocal microscope is set to either 30 % or 50 % to reduce artificial broadening.
To effectively evaluate the crystal quality of our overgrown membranes, we used a reference diamond for the Raman measurements. In order to achieve the cleanest Raman signature, we chose an electronic grade single crystal diamond from Element Six. Furthermore, we ICPetched the top ≈5 µm of the reference sample, and subsequently annealed the substrate in order to remove the residual strain induced by surface polish. The etching procedure is described in 12 , with our exact process flow detailed in Table S2. Figure S2 (a) shows the comparison of implanted diamond substrates pre-and post-annealing. Prior to annealing, only a weak diamond peak from the back substrate and low sp 3 amorphous carbon features are observed at ≈1500 cm −1 13 . Post annealing, three peaks are observed. The ≈1595 cm −1 and ≈2268 cm −1 peaks are strongly correlated with high sp 3 amorphous carbon composite 13 , while the ≈1325 cm −1 peak represents the partially recovered top membrane layer 14 . Figure S2 (b) shows the Raman peak of a 110 nm thick, ≈250 nm overgrowth diamond membrane grown in high temperature condition for 40 h. The sample is named as "N doped membrane" because of the in-situ doping of 15 N during overgrowth. The Raman linewidth of this membrane (1.486(14) cm −1 ) is slightly broader than the low temperature one. It is likely that this slight broadening of 0.11 cm −1 originates from the higher heterogeneity of the crystal quality due to slight change in growth conditions from the delta doping and higher synthesis temperatures.

Membrane thickness and growth rate characterization
In this work, we applied two different approaches to ascertain the thicknesses of the membranes. For the growth rate analysis and thickness-insensitive applications, we used a profilometer (Bruker DektakXT) to measure the height difference between the diamond membranes and the carrier wafers supporting them. For thickness-sensitive applications, we use an ellipsometer (Horiba UVISEL2) to optically monitor the thickness during etching processes.
For the profilometry characterizations the height limit is set to 6.5 µm and the typical scanning length is set to 500 µm with scanning time ≈200 s. The scanning trajectory covers the full length of the membrane for a more accurate value. This measurement is launched after the HSQ annealing and before the "Ar/Cl 2 " etching. According to the characterization results, transferred membranes without overgrowth are 340(5) nm thick. The thicknesses of the 40 h overgrown membranes are 680 nm to 740 nm (low growth temperature of 500°C) and 570 nm to 600 nm (700°C growth temperature), resulting in growth rates of 9.3(8) nm h −1 and 6.2(4) nm h −1 , respectively (growth rate uncertainty from multiple membranes measured). For thickness-insensitive applications, the ICP etching recipe for each membrane is calculated from measured initial thickness, the target thickness, and the ICP etching rates (Table S2).
We also used profilometry characterization to ascertain the overall membrane height and flatness. A scan across a 15 N-doped diamond membrane after the transfer is shown in Figure S5 (e). The result indicates an average membrane thickness of 603(10) nm before the back etching. This value shouldn't be affected by the back etching process as the ICP etching rate is uniform within the area of the membrane. Due to the angle between the membrane edge and the scanning direction, the length of the membrane in this figure seems to be longer than 200 µm. Since the scanning result includes some local height variation on the membrane, the real flatness should be less than 10 nm, which indicates a very uniform thickness across the whole membrane area. This excellent uniformity is crucial for future device fabrication and potential applications.
For thickness-sensitive applications, we used the ellipsometry scanning to the diamond membranes. This technique was firstly applied in nanophotonic integration studies 15 . The scanning area is set to 85 µm × 35 µm and is carefully aligned to the membrane surface. The scanning step is set to ≈0.05 eV with long probing time at each step (≈1 s) to reduce the fitting error. To fit the diamond layer, we use Cauchy's equation for transparent material where A = 2.378, B = 1.300 and C = 0.000, extracted from 16 . By using this model, we are able to get a ≤4 nm height uncertainty for ≤50 nm membranes.

HSQ fluorescence analysis and vapor HF treatment
As the adhesion layer between diamond membranes and carrying wafers, the HSQ introduces extra fluorescence under laser excitation. These additional counts mostly span from 560 nm to 850 nm and can affect the PL measurements to some extent, depending on the types of color centers being measured. The resonant PLE measurements are not affected due to their narrow optical linewidths, which allows for the use of exceptionally low excitation power (≤100 nW) and realize a large contrast of ≈30 against the background and APD dark counts. Therefore, for experiments and technologies that rely on resonant interactions, such as those proposed for quantum networking, the HSQ background will have minimal impact on device performance. The off-resonant photoluminescence measurements on group IV color centers (such as GeV -) are mainly used for identifying the center locations, and are not critical for their performance in quantum networking. Due to the high Debye-Waller factors, group IV centers are typically measured with a narrow bandpass filter, which filters out most of the fluorescence from HSQ. With 10 mW excitation (532 nm) and appropriate filter sets, the HSQ fluorescence is ≈10 kHz to 20 kHz, which is less than the ZPL counts from individual centers (≈20 kHz to 40 kHz, shown in Figure 3(b) of the main text). Therefore, the presence of HSQ does not fundamentally hinder the optical characterization of GeVcenters or preclude the usage of GeVin quantum networking applications, the primary technology driver for group IV color centers. Despite its limited impact, the HSQ background can be further reduced as wish via membrane suspension (≈2 kHz to 5 kHz) or vapor HF undercut (≈0.5 kHz to 1.5 kHz).
For NVcenters, the usage of a single longpass filter (561 nm) leads to a relatively high HSQ counts (300 kHz to 500 kHz under 10 mW green laser excitation), which hinders the PL and ODMR measurements. Therefore, NVmeasurements benefit from reducing the HSQ background counts. In this work, we combined the suspended membrane fabrication (discussed in section 1.8) and the vapor HF treatment (discussed below) to reduce the total background to 15 kHz to 30 kHz, which is comparable to the bulk diamond background. Other potential methods to reduce the HSQ background, such as HSQ patterning before transfer, usage of tri-acid clean to oxidize the HSQ layer, or material substitution with less optical fluorescence, will be explored in future studies.
The vapor HF treatment was used optionally to further minimize the background fluorescence from the HSQ underneath the suspended membrane region. During the vapor HF treatment, the chamber pressure is set to 24.5 Torr, with H 2 O flow at 18.9 mL min −1 and HF flow at 40 sccm. Figure S5 (a) shows a bare carrier wafer after trench fabrication, and Figure S5 (b) shows one of the trenches after the HSQ deposition, annealing, and vapor HF. The image of the wafer prior to vapor HF can be seen in Figure S4 (d), where a colorful interference gradient can be observed. By carefully tuning the process duration (2 s), we are able to remove most of the HSQ on the sample, while leaving the thermal oxide layer almost untouched. Thus the HSQ has a negligible contribution to the background fluorescence under laser excitation. The sample shown in Figure 3 (a) of the main text received an excess HF treatment (10 s). The zoomed in image is shown in Figure S5 (c), where an undercut region (rainbow color) with ≈18 µm width can be seen, as well as some undesired surface patterns on the SiO 2 -Si carrier wafer (dark dots). Those unwanted effects are largely suppressed by shortening the process duration to 2 s, as seen in Figure S5 (d). The undercut width is ≈5 µm with no visible damage on the carrier wafer.

Dopant and isotope characterization via SIMS
The quality of the isotopic enrichment (replacement of naturally abundant 13 C with 12 C) is characterized via SIMS (EAG labs) and a typical carbon isotope scan is shown in Figure S9 (a). We reproducibly achieve 99.99 at.% 12 C diamond during overgrowth, a two orders of magnitude reduction compared to natural abundance as shown in Figure S9 (a). This is currently limited only by the isotopic enrichment of the precursor CH 4 gas.
Nitrogen doping effectiveness as a function of nitrogen precursor gas flow rate was also characterized via SIMS (EAG labs). Characterization of this was done via multiple scans on multiple delta doped samples with specific nitrogen doped layers (multiplicity for statistics). Fitting of the Gaussians (given the delta-doping layer thickness, a Gaussian serves as a valid approximation for the nitrogen distribution) was used to quantify the nitrogen density, which was only restricted by the depth distribution of these delta-doped layers. The FWHM is then used as an approximation of the delta-doping layer thickness, whereas the amplitude is used as an approximation of the atomic density (cm −3 ) within that layer. A typical characterization run for a 15 N triple delta-doped diamond is presented in Figure S9 (b). It remains to be noted that we also regularly characterize the presence of 14 N to look for contamination, however, this value is regularly below the SIMS detection limit of about 2 × 10 −15 cm −3 .

Experimental setup for group IV center measurements
The membrane samples are mounted in a closed-loop cryostation (Montana S200) for low temperature measurements. The sample temperature during the measurements is 5.38 K as ascertained by a sensor (Lakeshore Cryotronics) installed directly on the sample mount. The position of the membrane is controlled by three closed-loop piezo positioners (Attocube ANC 350). The incident light beams are navigated by a fast steering mirror (Newport FSM-300) controlled by an analog output device (National Instruments, PCIe-6738). For the PL measurements, we use a 532 nm continuous wave (CW) laser (Lighthouse Photonics Sprout-G) as the excitation source. For photoluminescence excitation (PLE) measurements of GeV -, the excitation laser is generated by a wave mixing module (AdvR Inc.) combining a tunable CW Ti:Sapphire laser (M Squared Solstis) and a monochromatic CW laser in telecommunication band (Thorlabs, SFL 1550P). We use this laser to scan across the GeV -ZPL wavelength (C line) and collect phonon sideband counts. At the collection ports, we use a 50 : 50 cube beam splitter (Thorlabs Inc. BS013) to divide signals to two branches for counts collection and spectroscopy measurements. A single photon counting module (SPCM) (Excelitas Technologies) is mounted to the counting beam, while a 1200 gr mm −1 spectrometer (Princeton Instruments, SpectraPro HRS) is fiber coupled to the spectra beam. The camera of the spectrometer (Princeton Instruments, PIXIS) is maintained at ≤ − 70°C to minimize background counts. The spectrometer branch can also be connected to another SPCM to perform autocorrelation measurements. We use a combination of bandpass filters (Semrock FF01-615/24-25, Semrock FF01-600/14-25) for GeV -PL measurements. When performing PLE measurements, we collected the phonon sidebands via double filters (2× Semrock FF01-647/57-25). All lenses in the confocal setup are achromatic doublets with AB coatings (Thorlabs Inc.) to reach maximum transmission efficiency over broadbands. The PL map obtains a very low background fluorescence (≈1500 Hz) even under 10 mW excitation, as shown in Figure 3 (b) of the main text. The optical setups for SiVand SnVcharacterizations are almost identical, except for the bandpass filter (Semrock FF01-740/13-25 for SiVand a Semrock FF01-615/24-25 for SnV -). Since GeVcenters are also present in the PL map of SnVcenters, we use the spectrometer to identify the center type before proceeding with further characterizations.

GeVcreation efficiency
We estimate the creation yield of GeVby counting the number of fluorescent centers in a certain area. Given the good signal-to-background ratio of ≈30, any resolvable centers when counting each 20 µm by 20 µm PL map were included in our counting. The average number of centers per areal spot is 53(3) (≈0.13 µm −2 ), yielding a creation yield of 6.6(4) % from the implantation dose (2 × 10 8 cm −2 ≈2 µm −2 ). This yield is higher than the previous reported value 17 . We note the high signal-to-background ratio can improve the visibility of darker GeVcenters, which potentially increase the estimated yield.

Spectra of Group IV centers and GeV auto-correlation measurements
The GeVmembrane sample were co-doped with Si + and Sn + with the same density and target depth. Figure S6 (a-c) shows the representative spectra of GeV -, SiVand SnVcenters under 5.4 K. Like GeVcenters, the ZPL peaks of SiVand SnVare comparable with the bulk diamond values 18,19 . The A and B peaks of SnVare not resolvable due to large spin-orbit coupling and limited phonon population under such a low temperature. More in-depth studies of SiVand SnVcenters are left for subsequent work to explore.
Off-and on-resonance measurements are performed on GeVcenters, as shown in Figure  S6 (d). Both curves exhibit anti-bunching features with g (2) (0) well below 0.5, originated from their single center nature. During PL auto-correlation measurements, the off-resonance laser (532 nm) is operated at a slightly lower power (3 mW) to avoid bunching effects. The PLE autocorrelation measurement indicates a clear Rabi oscillation pattern induced by an on-resonance excitation.
The reasons for the non-zero g (2) (0) values (0.17 (2) for PL and 0.19 (5) for PLE) depend on the specific type of measurements. For PL autorrelation measurements, we observed a slowly decreasing ZPL signal with respect to the measurement time. This can be explained by a gradually changing surface termination with the presence of the excitation laser, which affects the preferred electronic configuration of GeVcenters. As a result, the color centers may experience more times in their optically dark state, slowly quenching the overall signal. In the future, a more rigorous surface termination scheme, such as a tri-acid clean or oxygen termination can be applied to improve the GeVstability. For the PLE autocorrelation measurements, the average ZPL linewidth is ≈2.4 times wider than the single scan values. With the frequency of the excitation source fixed, the spectral diffusion causes considerable fluctuations of phonon sideband counts, raising the PLE g (2) (0) value. Future optimizations on the linewidth of the GeVemissions can effectively enhance the average signal and suppress the g (2) (0).

GeVemission linewidth and spectral jump analysis
The optical linewidth of GeVcenters approaches the lifetime limit by a factor of 3 (6) during single (average) scans. While the synthesis of optimized narrow linewidth color centers is beyond the scope of this work, multiple strategies can be introduced to overcome the extrinsic broadening factors. To begin with, the optical coherence is impacted by thermal effects via electron-phonon interactions, as modeled and characterized in 20 . Therefore, narrower linewidths may be achievable at lower characterization temperatures. Additionally, some inhomogeneous broadening is attributed to the implantation-induced damage 21 . In theory, this can be minimized by doping Ge in-situ during the overgrowth process 22 , which is left for subsequent studies to explore. Furthermore, optimized surface terminations should contribute to reducing surface charge related noise. We excluded the optical power broadening in this work by characterizing the saturation power and tuning the excitation to be slightly lower than this saturation point before every linewidth measurement.
We also observed the switching phenomena for GeVin most membrane samples during PLE measurements. A long term scan (25 min) of a single GeVis shown in Figure S6 (e). This center is located in a 20 h membrane sample with only Si + and Ge + implantation. The origin of the switching is currently under investigation.

GeVzero phonon lines distribution
To evaluate the inhomogeneous broadening of the implanted GeVcenters, we included an electronic grade diamond as a reference sample during the Ge + implantation and subsequent annealing. Therefore, the reference diamond received identical ion implantation and annealing steps. Under the same cryostation temperature (5.4 K), we measured a total of 75 GeVcenters in diamond membranes and 30 centers in the reference sample, shown in Figure S6 (f) left and right. If all centers are included in deriving the inhomogeneous broadening, we find a standard deviation of σ =1.16 nm for the membrane and σ =1.52 nm for the reference sample. However, these numbers are mostly influenced by ≈10 % of the centers with large wavelength shifts (such as 607 nm). These shifts are possibly induced by local strain distortion from the implantation process, and can be found in both membrane and bulk cases. Moreover,these σ values are expected to have a large uncertainty due to limited sampling. Following a similar analysis 23 , confining the ZPL wavelengths of GeVcenters to within a range between 601.5 nm and 603.2 nm (which includes ≈90 % of the centers) may give a better value for comparison. Compared to the inhomogeneous broadening in the reference (σ = 0.18 nm), the values we obtained are σ = 0.18 nm for the reference diamond and σ = 0.19 nm for the diamond membranes. These similar inhomogeneous broadening values indicate comparable crystal environments between the diamond membrane and bulk diamond.

NVcharacterization 4.1 Experimental setup for NVcharacterization
The room temperature NVcoherence measurements were performed in a custom-built confocal microscope with a 532 nm, free-space laser (Oxxius 532S-150-COL-PP) and a 100X, 0.9NA air objective (Olympus MPLFLN100X). The laser spot position is controlled with a fast steering mirror (Newport FSM-300) and a 4f lens pair. The laser is gated with an acousto-optic modulator (AOM) (Gooch & Housego) and PL is measured with a PDM photon counter (MPD PD-050-CTD-FC). Microwave pulses are generated by a SRS SG-396, amplified by a Mini-Circuits ZHL-15W-422-S+, and gated by both a Mini-Circuits ZASWA-2-50DR+ RF switch and external amplitude modulation of the signal generator. Pulses are applied to the NVcenters via a 25 µm Al wire draped over the sample. The experiment timing is handled by a Swabian Pulse Streamer.
A static magnetic field of 15 gauss is applied at approximately 35 • to the [100] sample surface. Given the orientation of the sample, the field is at a 10 • angle to the [111] crystal axis.

NVcoherence measurements and T 2 comparison with delta-doped results from previous studies
We use standard free induction decay (FID) and spin echo (SE) sequences to measure T * 2 and T 2 , respectively. Each sequence, shown in Figure S8, is composed of two branches, which measure both the |0 and |−1 projections. After applying a π/2-pulse on the NV -, we allow the spin to evolve for a time τ (and apply a π y pulse at τ /2 for the SE) before applying either another +π/2-pulse or a −π/2-pulse to project into the readout basis. The readout windows at the beginning of each laser pulse are binned as the readout signals, S 0,−1 , and the readout window at the end is binned as a reference, R, which allows us to correct for slow drift over each measurement cycle 24 . All measurements are processed as where the second term accounts for absolute count discrepancies between readout at the beginning and end of the laser pulse that arise from the finite rise time of the AOM. Each pulse sequence is a different length due to sweeping τ , but run for the same amount of time overall, necessitating normalization by the reference to cancel this variation. Ultimately this means that shorter-τ data are average over more instances than longer-τ data. We fit T * 2 measurements to the following 25 Where B is a background offset, a i , f i , and φ i are the amplitude, frequency, and phase of each sinusoid corresponding to each hyperfine peak, and I is the nitrogen nuclear spin (1/2 for 15 N, 1 for 14 N) . T 2 measurements are fit to Where B is an offset, A is the amplitude, and n is either a free parameter or fixed at 3 25 , when the former does not fit.
Previous delta-doping work demonstrated T 2 times for deep NVcenters (≥52 nm) on the order of ≈700 µs 3 , with measured values dropping drastically (≤100 µs) as the delta-doped layer was brought close to the diamond surface (≤35 nm). Indeed, it is expected that surfacerelated decoherence is a main limitation for the T 2 times presented in this work 12 . The impact of surfaces is further amplified in membranes, as the color centers are in close proximity to two surfaces rather than one.

NVstrain measurements
The NVcenter is sensitive to both strain and electric field (Π) through spin state coupling, as shown in the Hamiltonian Parallel strain/electric field (Π z ) shifts the effective zero-field splitting, while the perpendicular components (Π x,y ) split the upper and lower spin transitions 26 . However, there is a discrepancy in the strength of the couplings for each physical origin. The electric field susceptibilities d : ,⊥ =0.35 Hz cm V −1 and 17 Hz cm V −1 27 , while the strain susceptibilities d σ: ,⊥ =13.3 GHz and 21.5 GHz 28 . We thus expect that if local electric fields dominate, the splitting between the upper and lower transitions should be much larger than the shifts in zero-field splitting, whereas if strain dominates these effects should be of similar magnitudes.
Through zero-field ODMR measurements, we found in all but one case that the splitting was greater than or the same magnitude as the shifts. In Figure S7 (a) we present the shifts in zero-field splitting versus the NV orientation, as determined at non-zero field, to extract an upper bound on the strain in the membrane. If we assume the larger shifts of ≈1 MHz arise entirely from strain -an over-estimate, given the above discussion -we arrive at a strain of < 10 −4 .
Multiple factors can contribute to the built-in strain. For instance, the dry transfer step might introduce in-plane strain due to approach angle and speed. This can be reduced by reducing the approaching speed of the PDMS stamp with a smaller angle. Additionally, although the HSQ layer collapses above 465°C and potentially releases the strain during the annealing, some residual strain might still remain. Furthermore, due to different thermal expansion ratios between the diamond membrane and carrier wafers, a thermal-induced strain appears when the sample is cooled down to room temperature or at 5.4 K of PL characterizations. The direction and the magnitude of the strain depend on the material of the carrier wafers. Finally, some on-chip structures (such as trenches) can alter the strain distribution across the membrane.

NV -T 1 comparison
We compare T 1 population decay times for two NVcenters with an order of magnitude separation in coherence times to confirm that a reduction in T 1 is not responsible for the reduction in T 2 . Figure S7 (b) shows the differential T 1 measurement for NVX (T 2 = 13(1) µs) and NVY (T 2 = 146(53) µs). Over 5 ms there is no observable increased decay for NVX, indicating T 1 plays no role in limiting coherence. The nitrogen implanted membrane sample was subjected to a 48 keV, 2 × 10 8 cm −2 [N] dose. At this energy, the straggle (standard deviation of implantation as approximated with SRIM) is 14 nm. Assuming the bulk of the nitrogen resides in a ≤30 nm thick region, the expected [N] from the implantation to be 6.7 × 10 13 cm −3 (≈0.4 ppb) within the implanted region. Comparing this to the observed [ 14 NV -] of 1.8 × 10 12 cm −3 (0.01 ppb) obtained from a typical count of a 10 µm by 10 µm region of the 120 nm thick membrane. This suggests an upper bound on the N-to-NV conversion efficiency at ≤2.5 %. Realistically, in-grown background [N] are also being converted to [NV -], causing an overestimation of this conversion efficiency. The ambiguity of the [N] origin can be avoided by implanting 15 N in future iterations of experiments.

[N] and [NV -] estimation
Isotopic tagging of dopant species in the 15 N δ-doped membrane was used to provide further insight into this. From a PL survey of a 12 µm by 12 µm area of the 110 nm thick delta-doped membrane (post-irradiation and annealing), we noted a relative ratio of 7 : 11 for [ 15 Fig. 4 (a), showing electron spin echo envelope modulation, which is aliased in the main text data. Figure S8: Coherence measurement sequences. Both the spin echo (a) and free induction decay (b) sequences have readout, initialization, state preparation, and state projection pulses. The spin echo sequence has a central π-pulse to refocus the spin.  14 N not shown but done parallel to this) for a triple delta-doped overgrowth sample. Fitting of the Gaussians was used to quantify the nitrogen density. The FWHM is used as an approximation of the delta-doping layer thickness, whereas the amplitude is used as an approximation of the atomic density (cm −3 ) within that layer. The detection limit is shown in graph. We also note a significant amount of nitrogen at the substrate/overgrowth and surface interfaces with ratios consistent of natural abundance of 15 N in atmospheric nitrogen (measured via peak area ratio).