Comparison of different methods of nitrogen-vacancy layer formation in diamond for widefield quantum microscopy
A. J. Healey, A. Stacey, B. C. Johnson, D. A. Broadway, T. Teraji, D. A. Simpson, J.-P. Tetienne, L. C. L. Hollenberg
CComparison of different methods of nitrogen-vacancy layer formation in diamond forwidefield quantum microscopy
A. J. Healey, A. Stacey,
2, 3
B. C. Johnson,
1, 2
D. A. Broadway,
1, 2
T.Teraji, D. A. Simpson, J.-P. Tetienne,
1, 2, ∗ and L. C. L. Hollenberg
1, 2, † School of Physics, University of Melbourne, Parkville, VIC 3010, Australia Centre for Quantum Computation and Communication Technology,School of Physics, University of Melbourne, Parkville, VIC 3010, Australia School of Science, RMIT University, Melbourne, VIC 3001, Australia National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan
Thin layers of near-surface nitrogen-vacancy (NV) defects in diamond substrates are the workhorseof NV-based widefield magnetic microscopy, which has applications in physics, geology and biology.Several methods exist to create such NV layers, which generally involve incorporating nitrogenatoms (N) and vacancies (V) into the diamond through growth and/or irradiation. While therehave been detailed studies of individual methods, a direct side-by-side experimental comparisonof the resulting magnetic sensitivities is still missing. Here we characterise, at room and cryogenictemperatures, ≈
100 nm thick NV layers fabricated via three different methods: 1) low-energy carbonirradiation of N-rich high-pressure high-temperature (HPHT) diamond, 2) carbon irradiation of δ -doped chemical vapour deposition (CVD) diamond, 3) low-energy N + or CN − implantation intoN-free CVD diamond. Despite significant variability within each method, we find that the bestHPHT samples yield similar magnetic sensitivities (within a factor 2 on average) to our δ -dopedsamples, of < µ T Hz − / for DC magnetic fields and <
100 nT Hz − / for AC fields (for a400 nm ×
400 nm pixel), while the N + and CN − implanted samples exhibit an inferior sensitivityby a factor 2-5, at both room and low temperature. We also examine the crystal lattice straincaused by the respective methods and discuss the implications this has for widefield NV imaging.The pros and cons of each method, and potential future improvements, are discussed. This studyhighlights that low-energy irradiation of HPHT diamond, despite its relative simplicity and low cost,is a competitive method to create thin NV layers for widefield magnetic imaging. I. INTRODUCTION
Widefield imaging based on ensembles of nitrogen-vacancy (NV) defects in diamond [1–7], also known asquantum diamond microscopy, is a promising tool withapplications in condensed matter physics [8–10], geol-ogy [11, 12] and biology [7, 13]. Common to all theseapplications is the need for a dense layer of NV defectsnear the surface of a single crystal diamond substrate.Depending on the exact application, the optimal thick-ness t of this layer can vary from t (cid:46)
10 nm to detectmesoscopic fluctuating signals e.g. from paramagneticions in solution [14–16], to several µ m for imaging of ge-ological samples over mm-scale fields of view [12].For applications related to magnetic imaging, it is de-sirable to achieve diffraction limited resolution (∆ x ≈
300 nm) and so the layer thickness should satisfy t < ∆ x .This regime is also convenient because it allows the NVlayer to be treated as a 2D layer when reconstructing thecurrent density or magnetisation of the sample [8, 17, 18],and it preserves the ability to image the sample via NVphotoluminescence (PL) quenching or laser interferenceeffects [19–21]. A thickness of order t ≈
100 nm isfound to be optimal as it allows one to maximise thenumber of NVs without impacting the spatial resolution, ∗ [email protected] † [email protected] while also permitting the addition of a spacing layer (e.g. t sp = 100 nm of Al O [17]) grown on the diamond sur-face, by satisfying t + t sp < ∆ x . The use of such a spacinglayer is required to mitigate proximity-induced artefactsarising from strongly magnetic samples [22].Several approaches exist to create such thin near-surface NV layers [23]. To localise NV centres near thesurface one must restrict the creation of vacancies orincorporation of nitrogen (but not necessarily both) tothe near-surface region. The N impurities can be intro-duced during the diamond synthesis, either via the high-pressure high-temperature (HPHT) method or via chemi-cal vapour deposition (CVD) [24], or via ion implantationof an N-containing species [25]. The vacancies are typi-cally introduced by irradiation with electrons, protons orions [26]. The diamond is then annealed at 800 − ◦ Cin a vacuum environment to allow the vacancies to diffuseand form NV centres [27]. The sensitivity of the resultingNV layer depends not only on the number of NVs but alsoon their “quality”, in particular their charge state (onlyNV − is useful for quantum sensing applications, whereasthe co-presence of NV produces background PL reduc-ing the sensitivity) and spin properties (coherence times T ∗ and T , optical contrast) [2, 28, 29]. These factors de-pend on the presence of other defects in the lattice (nonconverted N impurities or other growth- or irradiation-induced defects) and can vary significantly between dif-ferent NV creation methods, motivating a comparativestudy of the resulting magnetic sensitivities. a r X i v : . [ phy s i c s . a pp - ph ] J un Assuming shot noise limited measurements, the sensi-tivity to DC magnetic fields with the pulsed optically de-tected magnetic resonance (ODMR) protocol is approxi-mately given by [2, 29, 30] η dc ≡ γ e C T ∗ √ α R (1)where γ e ≈ . C (cid:28) T ∗ is the spin dephasingtime, R is the photon count rate under continuous wave(CW) excitation, and α = t R t R + t D + T ∗ is the readout dutycycle where t R and t D are the readout time and deadtime per cycle, respectively. As R will scale with theNV density, itself usually proportional to the density ofother unwanted paramagetic defects such as the substi-tutional nitrogen defect, it competes with the ensemble’s T ∗ and it is not a priori clear which attribute to pri-oritise. In addition, the sensitivity for given parametersdepends on the experimental conditions through t R and t D . For widefield imaging, the low laser intensities usedrequire a relatively long t R ( ≈ µ s), meaning α ≈ T ∗ dependence. Thiscontrasts with the confocal microscopy case, where of-ten α ≈ t R /T ∗ . The sensitivity to AC or fluctuatingmagnetic fields, η ac , has a similar expression where T ∗ isreplaced by T [2, 29, 31], which similarly scales inverselyto R .In this work, we focus on three commonly employedmethods to create thin NV layers: • Method 1: low-energy irradiation of N-rich HPHTdiamond; • Method 2: Irradiation of δ -doped CVD diamond; • Method 3: low-energy implantation of N-containing species into N-free CVD diamond.Method 1 aims to create vacancies confined to a distance ≈ t from the surface of an HPHT diamond that containsa high density of N throughout the bulk, typically of theorder of [N] ≈
100 ppm. This method has been previ-ously demonstrated using ∼
30 keV helium ions (He + ),producing NV layers with t ∼ −
200 nm [32–34]. Herewe employ C − ions, which is a readily available speciesin low energy negative ion sources. One advantage overHe + is the absence of He-related defects in the final NVlayer. Method 2 replaces the HPHT substrate with aCVD diamond in which nitrogen was selectively incorpo-rated during the growth so as to form a δ -doped layer ofdesired N density and thickness, on an otherwise N-freesubstrate [24, 35]. The vacancies can then be created bylow-energy ion implantation (here we also use C − ) [36–38], although higher energy particles could also be usedsince the vacancies do not have to be confined in depth,for instance NVs have been formed using 200 keV elec-trons from a transmission electron microscope [39, 40].Finally, Method 3 employs low-energy implantation ofan N-containing species (here we consider N + and CN − ) to simultaneously incorporate both N and V at the de-sired depth into an otherwise N-free diamond [41–43].Despite being a very popular method for producing NVsensing layers, this approach creates unnecessary dam-age to the diamond because of the large number of va-cancies created for each N [44, 45], which is especiallyproblematic for dense layers of near-surface NVs [28]. Incontrast, in Methods 1 and 2 the irradiation fluence canbe adjusted to reach a ratio of created vacancies to thenumber of N impurities present in the diamond optimalfor maximising NV yield, making them better candidatesto reach the regime in which T ∗ is limited only by theresidual N impurities [29, 46]. In practice, this conditionis likely to be given by a combination of the resultantFermi level position as well as the nitrogen and vacancyconcentrations, and thus optimising implant parametersis expected to require a level of fine tuning beyond thescope of this work. For simplicity, we focus on the regimewhere the number of vacancies created by the implanta-tion process is commensurate with the expected nitrogenconcentration.While these techniques have individually been the sub-ject of previous works [32–45], the large variability in theexperimental methods used to assess them make a reli-able comparison difficult. In particular, the quantities C , α and R in Eq. (1) all depend on the specifics of the opti-cal setup used to measure them, and can vary drasticallybetween confocal and widefield measurements. In wide-field magnetic imaging, the laser intensities are typicallymuch smaller than in confocal measurements, and so theper-NV sensitivity may appear smaller, which is a priceto pay to access a large field of view. Thus, the purposeof the present work is to provide a side-by-side compar-ison of the sensitivities ( η dc and η ac ) obtained with thethree NV creation methods outlined above, while keepingas many experimental parameters fixed as possible. Westress that, given the large number of experimental vari-ables for each method, we do not seek to optimise them.Instead, our aim is to generate a baseline of the perfor-mances that can be achieved with the different methodswithout advanced optimisation, so as to help users tobest choose the method that suits their capabilities andapplication, and to guide future efforts in optimising aparticular method.The paper is organised as follows. In Sec. II, we de-scribe the experimental procedures to form the NV layersstudied (II A) and to characterise them (II B). The resultsof these measurements are presented in Sec. III, followedby a discussion (IV) and conclusion (V). II. METHODSA. Samples
The sample creation methods used for this study aredetailed in Table I and depicted schematically in Fig-ure 1(a). Method 1 samples (referred to as HPHT
Vacancies (10 cm -3 )N Concentration (10 cm -3 ) D ep t h ( n m ) + Vacancies (10 cm -3 ) - D ep t h ( n m ) Method 2sample Method 3sampleMethod 1sampleNV - center[N] (ppm)0 ≈ ≈
100 100 keV C - irradiation(a)(b) (c)1100 º C ramped anneal, acid cleanCommercialHPHT susbtrate CN N Pure CVDsubstrate C Custom ẟ -dopedsample Various energy N + , CN - irradiation FIG. 1.
Overview of the NV layer formation methods investigated: a)
Schematic illustrating sample production.From left to right: Method 1, carbon irradiation of high-N, low-NV HPHT diamond to create a localised NV-rich layer; carbonirradiation of δ -doped CVD layer to improve NV conversion; implantation of a pure CVD substrate with a chosen nitrogen-containing species to incorporate nitrogen into the crystal at the cost of extra damage by vacancy over-creation. The colourscale used and relative NV densities are schematic only. b) and c) are SRIM simulations for the C − and N + implantationcases respectively, showing depth distributions of vacancies produced (both) and implanted ions (Method 3 only) produced byrepresentative implantation procedures. samples hereafter) are as-received commercially available(Delaware Diamond Knives) HPHT diamonds polishedto a surface roughness < <
200 ppm. Despite the high initial ni-trogen concentration, these samples showed limited NVfluorescence prior to implantation indicating poor N toNV conversion. C − irradiation with doses between 10 and 10 cm − , chosen to produce a number of vacanciescomparable to the expected nitrogen concentration, re-sulted in significant PL enhancement (by several ordersof magnitude). Samples were held on the implanter stageat a 7 ◦ tilt angle and 10 ◦ rotation to minimise ion chan-nelling, and the chamber pressure during implantationwas ≤ − mbar. The implant energy of 100 keV waschosen to confine vacancies produced to a ∼
100 nm layeras shown by Figure 1(b), which is a simulation producedusing the Stopping and Range of Ions in Matter (SRIM)software package.Samples fabricated by Method 2 (hereafter referred toas δ -doped samples) were created via CVD growth over acommercial type Ib HPHT substrate (Element Six). Anoxygen etch was performed to remove polishing damageand maximise subsequent overgrowth quality [47]. Anelectronic grade, N-free layer of a thickness order 10 µ mwas then grown to buffer the grown NVs from defectsin the substrate and to reduce the PL contribution fromthe substrate. The δ -doped layer was then grown on topduring a short growth designed to create a film between100 and 200 nm thick and with a level of nitrogen incor-porated set by the proportion of nitrogen present in theplasma during growth (varied between samples). The δ -doped layer was grown using a low microwave power of750 W and under a low pressure of 25 Torr to promoteslow, high quality crystal growth [35]. The proportion ofmethane (natural isotopic proportions) in the gas mix- ture was ≈ δ -doped diamonds. Prior to implantation the doped layerexhibited some fluorescence but it is expected that lessthan 0.5% of incorporated nitrogen forms NV centres inthe as-grown diamond [48]. This PL was increased byover an order of magnitude on average by 100 keV, 10 -10 cm − carbon irradiation, indicating an improved NVyield. The implant parameters were chosen to approxi-mately match the vacancy production to the expected Ndensity and depth profile of the doped layer.Method 3 samples were made from electronic-gradesingle-crystal CVD diamonds (purchased from DelawareDiamond Knives) and then overgrown with 2 µ m of C-enriched (99.95%) electronic-grade CVD diamond[49], although this step is not normally required for thismethod. The substrates were then implanted using N + (30-100 keV, 4 × -1 × cm − ) or C N − (54 keV,2 × cm − ) ions (hereafter referred to as N + and CN − implants), which were chosen as representative nitrogenimplant species as they are commonly available at mostlow energy ion implantation facilities. Figure 1(c) showsthis method produces an overlapping region of implantedions and vacancies but without the ability to tune den-sities (here the peak vacancy density is two orders ofmagnitude larger than the peak N density according toSRIM).Following implantation, all samples were annealed in avacuum of ∼ − Torr using a ramp sequence culminat-ing at 1100 ◦ C to form NV centres and repair part of theirradiation-induced damage [28]. The samples were thencleaned for 15 minutes in a boiling mixture of sulphuricand nitric acid prior to measurement. This is expectedto standardise the surface chemistry across all samples,avoiding the impact of the surface on our comparativemeasurements. Additional sample production details aregiven in Appendix C.
B. Measurements
The sensitivity measurements for all samples were car-ried out on a purpose-built widefield microscope de-scribed in detail elsewhere [10, 28]. Microwave delivery isfacilitated by a gold resonator deposited on a glass coverslip, onto which diamond chips are mounted NV face-down. A permanent magnet aligned with one family ofNV axes provides the bias field required to Zeeman splitthe NV resonances. NV centres are excited by a 532 nmlaser focussed to the back aperture of an oil-immersionmicroscope objective (Nikon 40x NA = 1.3), where thelaser power was measured to be 220 mW. The resultingNV fluorescence was filtered (660-735 nm) and imagedon a scientific complementary metal oxide semiconduc-tor (sCMOS) camera for processing. The measurementswere taken over a 50 µ m × µ m field of view as thiswas the region over which the laser intensity was roughlyuniform ( ≈ ). This region, typical for widefieldimaging experiments, contains 10 -10 NVs (dependingon the sample) which we average over in our spin mea-surements. A readout pulse time of t R = 5 µ s, chosen toreach a compromise between ensemble initialisation andreadout contrast, was held constant for all measurements.A dead time of t D = 1 . µ s was introduced following eachlaser pulse to allow relaxation from the metastable sin-glet state to the ground state. All room temperaturemeasurements, with the exception of T , were conductedunder a weak bias field of 60 G. T measurements wereundertaken at a higher field of 475 G to ensure that, forthe samples containing a natural abundance of C, theresulting revivals were closely spaced enough to allow ac-curate extraction of the decay envelope. The microwavepower was held to give a constant π time of 40 ns for allspin measurements. To remove common mode laser noise(where applicable), pulse sequences were normalised us-ing a reference measurement taken with respect to the |− (cid:105) basis rather than the usual | (cid:105) by using a π pulseprior to readout.To characterise the samples, we measure the quantitiespresent in Equation 1. The photon count rate R was av-eraged over the field of view under CW laser excitationover a consistent camera exposure time of 30 ms, andthen normalised in time and area. Estimated NV densi-ties listed in Table I were inferred from R using a scalingfactor obtained by comparing the fluorescence collectedon a confocal microscope for selected samples to thatfrom a reference single NV under identical conditions.The spin contrast is obtained by coherently driving theNV ensemble, with C taken as the peak-to-peak ampli- tude of the Rabi oscillations when fit to a damped sinu-soid. T ∗ is measured using the Ramsey pulse sequenceand the T is measured first with a Hahn echo sequenceand then with Carr-Purcell-Meiboom-Gill (CPMG) se-quences with variable numbers of π pulses. We also mea-sure the spin relaxation time T which represents an up-per limit to ensemble coherence times and, due to itssensitivity to resonant magnetic fluctuations, forms thebasis of many sensing experiments [6, 50]. It is measuredsimply as the decay of the | (cid:105) state under dark evolution.Further details on the measurements and data analysisare given in Appendix B and full results for each sampleare given in Table II (Appendix A).These measurements were repeated at lower tempera-tures (down to 4 K) for representative samples on a simi-lar widefield NV microscope within a close-cycle cryostat[51]. To minimise sample heating, a lower laser powerwas used for these measurements, which required a longerreadout time of t R = 10 µ s to be used to compensate forthe reduced rate of ensemble initialisation. III. RESULTSA. Basic spin properties
To benchmark sample quality we first consider the ba-sic NV spin properties at room temperature, summaris-ing the results in Figure 2. Focussing solely on PL fornow, we plot the photon count rate R against the im-plantation doses used for all the samples studied in Figure2(a), with the different methods separated by colour. TheHPHT samples are the brightest, which is to be expectedgiven their high initial N concentration ( ≈
100 ppm).Method 3 samples exhibit fluorescence within an order ofmagnitude of each other, mostly in line with the spreadin implantation doses as reflected by the fairly constantconversion ratios listed in Table I. These samples areless fluorescent than the HPHT samples and brightest δ -doped samples despite higher implant doses because theNV production is limited by the nitrogen incorporatedduring the implant process rather than the vacancy pro-duction. δ -doped samples feature the widest spread inbrightness due to nitrogen concentration in the CVD gasmixture being varied over several orders of magnitude,although we do not expect a direct conversion from ni-trogen concentration in the reactor gas mixture to thatincorporated into the crystal. Indeed, the similar PL ofthe three brightest δ -doped samples suggests we may beclose to saturating the nitrogen concentration under ourgrowth conditions.In Figure 2(b)-(e) the results of the spin measure-ments described above are plotted against the R as thisis the parameter from Equation 1 expected to vary moststraightforwardly between samples, being proportional toNV density. Figure 2(b) plots T against R and we seethat the T time varies significantly between the differentmethods and is inversely correlated to PL. T ranges from Sample Substrate type Surface Implanted Energy Dose Projected Estimated NV density Estimated NV yieldname finish species (keV) (ions/cm ) range (nm) (NV/ µ m ) (%)HPHT-1 HPHT Polished C −
100 5 ×
142 1.6 × C −
100 1 ×
142 1.5 × C −
100 1 ×
142 4.6 × C −
100 1 ×
142 1.3 × C −
100 1 ×
142 4.7 × C −
100 2 ×
142 4.5 × C −
100 1 ×
142 4.2 × δ -1 CVD ( δ -doped) As grown C −
100 1 ×
142 2.6 × δ -2 CVD ( δ -doped) As grown C −
100 1 ×
142 4.8 × δ -3 CVD ( δ -doped) As grown C −
100 1 ×
142 1.5 × δ -4 CVD ( δ -doped) As grown C −
100 1 ×
142 2.6 × δ -5 CVD ( δ -doped) As grown C −
100 1 ×
142 2.9 × N-1 CVD As grown N +
30 4 ×
42 1.7 × N +
30 4 ×
42 2.6 × N +
100 4 ×
122 2.6 × N +
100 5 ×
122 2.9 × N +
100 1 ×
122 2.0 × C N −
54 2 ×
42 9.1 × C N −
54 2 ×
42 7.7 × C N −
54 2 ×
42 7.2 × List of diamond samples used in this study.
Samples differ in (from left to right in the table) their diamondgrowth method, whether overgrowth took place after substrate polishing, and the implant species, energy, and dose chosen.NV density estimated by comparing fluorescence to that given by a single NV on a confocal microscope. Yields quoted arecalculated by comparing the inferred NV content with the known N fluence for the N implants and taking an estimated Nconcentration of 100 ppm for HPHT samples. No precise measure of doped nitrogen content is available for δ -doped layers. ∼ δ -doped samples, which weassume to be a nearly phonon-limited value, to (cid:46) µ sfor the highest PL HPHT samples. We attribute thisdramatic reduction in T proportional to the increasein nitrogen defects both to the general increase in mag-netic noise and to electron tunnelling to nearby defectsthat sees the NV − ionise to NV during dark evolu-tion [52, 53].Figure 2(c) shows that the Rabi contrast C also ap-pears to scale inversely with PL, although the variationis milder with most samples lying in the range of 2-4%.As in the T case, the availability of extra tunnellingsites in the higher density samples is likely responsiblefor the reduced measurement contrast. The lowest den-sity δ -doped sample is an exception to this trend, likelybecause this sample contains too low a nitrogen densityto sustain a high NV − yield in the presence of signifcantsurface-induced band bending [54].The inverse correlation between free induction decaytime T ∗ and R (Figure 2(d)) is expected as the increaseddefect density associated with brighter samples gives ahigher level of magnetic noise, which reduces T ∗ . Tosee how this impacts measurement sensitivity, we plotconstant sensitivity (calculated for a 400 nm ×
400 nm“pixel”, representing approximately diffraction-limitedspatial resolution) curves (red dashed lines) assuming 3% contrast in Equation 1. The data points roughly followthese curves, indicating that T ∗ and R offset one anotherto a large degree, consistent with previous studies [28].However, there is a large spread in this data and addi-tional trends within and between the methods are worthnoting. The largest variation in NV quality relative to PL(vertical spread in figures) is present in the HPHT sam-ples (with T ∗ ranging from 15 to 120 ns). This variationis due to this method’s reliance on a purchased substratenot produced to specification, as well as the variation indefect incorporation in different HPHT growth sectors.The best HPHT samples, however, appear to outperformthe nitrogen implanted samples, as do all of the δ -dopedsamples. This confirms that the additional damage as-sociated with nitrogen implantation produces a source ofdephasing that is significant alongside the contributionfrom the nitrogen spin bath. This is further evidenced bythe samples implanted with the larger CN − ion exhibit-ing comparable coherence times to the N + implants, butwith much lower PL. In other words, the extra damagecaused per ion (a 54 keV CN − implant produces 65%and 25% more vacancies than 30 keV and 100 keV N + implants respectively) amounts to a similar total param-agnetic defect density for a lower nitrogen concentration.Figure 2(e) plots Hahn echo T against R , again withconstant sensitivity curves to guide the eye. The trendsare similar to the T ∗ case, but with a reduction in spreaddue to the success of the Hahn echo sequence at removingquasi static magnetic noise contributions.To better analyse the trends in sensitivity versus fabri-cation method, we plot the calculated DC and AC sensi-tivities (using actual Rabi contrast values for each sam-ple) in Figure 3. We note that variance in NV layer thick-ness of up to a factor of 2 translates to a scaling in sensi-tivity of up to √
2. It is also worth noting that the laserpower used is far below optical saturation and so sensi-tivity could be improved by a further 10 times or morefor any given sample by focussing the laser and increas-ing the counts received per unit area by a factor of 100(at the cost of a decreased field of view). Nevertheless,the trends qualitatively noted earlier are confirmed: the δ -doped samples emerge as the highest quality, with themean magnetic sensitivity for this method being around afactor of 3 better than that of the others. The HPHT se-ries exhibits the largest amount of spread (almost 100 %of the mean), but the best HPHT samples provide com-parable sensitivity to the δ -doped samples. This spreadin sensitivity is accompanied by variability in the amountof fluorescence a given implantation dose promotes forHPHT samples, which is indicative of the variability innitrogen concentration in the purchased crystal. Thislack of foreknowledge can be compounded by a failureto correctly tune the vacancy production of the chosenimplantation procedure, and hence a failure to optimisethe process. Over-implanting will produce unnecessarydamage and under-implanting will result in a subopti-mal NV:N conversion ratio, and in both cases this willbe reflected by a decrease in sensitivity. This suggeststhat a way to improve the sensitivity of these samplescould be to determine the N density prior to implantationand adjust implant parameters accordingly. The HPHTsamples already achieving the best sensitivities are likelythose currently best optimised, and so it is reasonable toexpect refinement of the process to result in this level ofsensitivity being achieved (or improved upon) by a ma-jority of HPHT samples in future. There is also potentialto improve the δ -doped samples’ sensitivity in this wayas the N content is also initially unknown in this case,but this improvement does not exist for the implantationof an N-free substrate as there is no way to alter the ratioof vacancy production to N implanted at a given energy.These results indicate that the simple and relatively in-expensive Method 1 can offer competitive magnetic sen-sitivity in widefield NV imaging, with large potential forimprovement following further optimisation. B. Extended dynamical decoupling
In sensing AC fields, it is common to use more ad-vanced dynamical decoupling techniques than the Hahnecho pulse sequence to decouple from the spin environ-ment more efficiently, access higher frequencies, and im-prove spectral selectivity [55, 56]. To benchmark our T ( μ s ) PL, R (counts s -1 μ m -2 ) PL, R (counts s -1 μ m -2 ) T * ( μ s ) . HPHT(Method 1) ẟ -doped(Method 2)N implant(Method 3)CN implant(Method 3) (b) (a) (c)(d) (e) T ( m s ) R ab i c on t r a s t, C ( % ) P L , R ( c oun t ss - μ m - ) Implant dose (ions/cm ) FIG. 2.
Sample characterisation at room temperature:
Measured variation of a) R with implant dose; and b) T , c) Rabi contrast, d) free induction decay time T ∗ , and e) Hahn echo T with R . All measurements made at room tem-perature and at 60 G except for the Hahn echo, which wasconducted at 475 G to reduce the impact of C revivals onthe fits. Red lines in d) and e) denote lines of constant per400 nm ×
400 nm DC and AC sensitivity (in µ T Hz − / andnT Hz − / respectively) respectively at a constant Rabi con-trast of 3% to guide the eye. The error bars indicate onestandard deviation for R and the standard fitting errors forthe spin properties. Where not visible, error bars are smallerthan the marker size. η d c ( μ T / H z / ) η a c ( n T / H z / ) (b)(a) H P H T ẟ - d o p . N i m p . C N i m p . H P H T ẟ - d o p . N i m p . C N i m p . FIG. 3.
Sensitivity vs NV creation method:
Values of a) DC and b) AC magnetic sensitivities from Equation 1 (us-ing T ∗ and T respectively) for a 400 nm ×
400 nm pixel.Error bars obtained using standard propagation using mea-surement errors detailed in Figure 2. Sensitivities obtainedon a setup with t R = 5 µ s, t D = 1 . µ s, and a laser intensityof 3 kW/cm . samples for use in this regime, we test their performanceunder CPMG sequences of increasing length, charac-terised by the number of π pulses N .Figure 4(a) plots the CPMG T as a function of N for representative samples from each method. A clearextension of T is evident in all cases, with saturationabove N ≈ T extension to a powerlaw, T ( N ) = T (1) N s , gives values of s between 0.4 and0.8 across all samples, with the majority of samples ex-hibiting values below the theoretical s = 2 / T fell short of the T = T / ≤
20 nm) single NVs saw values of s < / T < T / T for allsamples in Figure 4(b). The enhancement varies between10 and 100 and is greatest for the CN − implants and someHPHT samples. The HPHT samples that see the leastextension could not be extended to N = 1024 due to thefinite pulse length (see below), while N implants saw less T extension than the other methods despite the major-ity supporting this number of pulses. The CN − implantsundergo greater T extension than the N + implants, in-dicating that the decoupling is successful in mitigatingthe effects of the extra vacancy production.Comparing CPMG-1024 T to R we see (Figure 4(c)),as before, that the data follows constant sensitivitycurves but in two apparently separate bands. The HPHTsamples that were successfully decoupled to N = 1024display comparable T to the N-implants, which are muchless fluorescent, and lie along a similar iso-sensitivity lineto the bright δ -doped samples. This is confirmed in Fig-ure 4(d), which shows the best magnetic sensitivities areobtained by δ -doped and HPHT samples.The lowest density δ -doped samples fall slightly behindin sensitivity compared to their DC or Hahn echo AC sen-sitivities despite achieving T values close to T . We canunderstand this by viewing Equation 1 in the long T limit ( T (cid:29) t R = 5 µ s), in which α tends towards t R /T rather than 1. This shows that as T is extended thedependence of the equation on R becomes stronger, andthis is part of the reason why the HPHT samples excelin this regime. The overall spread in sensitivity withinand between methods (ignoring samples that could notbe extended to N = 1024) is again reduced with addi-tional decoupling, with the Method 3 samples, althoughstill the least sensitive on average, only obtaining worsesensitivities by a factor ∼ π pulse). While H P H T ẟ - d o p . N i m p . C N i m p . T ( u s ) η C P M G ( n T / H z / ) C P M G - T ( μ s ) PL, R (counts s -1 µm -2 ) C P M G - T ( μ s ) Hahn echo T ( μ s) x x HPHT(Method 1) ẟ -doped(Method 2) N implant(Method 3) CN implant(Method 3) (a) (b)(c) (d) FIG. 4.
Extended decoupling characterisation: a) T scaling of selected representative samples of each sample typeas a function of the number of pulses N in the CPMG- N se-quence. Data displayed collected from samples δ -1 (green),CN-3 (yellow), N-3 (purple), and HPHT-6 (blue). b) Ex-tension of T from N =1 (Hahn echo) to N =1024, with greylines showing 10-fold and 100-fold improvement. c) Scal-ing of CPMG-1024 T with R , with iso-sensitivity curves innTHz − / . d) AC sensitivities calculated using Equation 1(using the CPMG-1024 T ), grouped by method. Data pointsmarked by squares in panels b)-d) belong to samples thatcould not be extended beyond N ≈
256 and see only modestimprovement over Hahn echo values. the idealised instantaneous pulse approximation is validwhen only a small number of pulses are applied, as N is increased the microwave duty cycle can become sig-nificant and the bulk of dephasing can occur during thisdriving, limiting the effectiveness of decoupling. This isespecially evident for the N-dense HPHT samples and isthe reason why the majority of samples reach limiting T values far shorter than T . In principle, faster pulsescould see additional coherence extension and the AC sen-sitivities of the worst-performing HPHT samples fall intoline with the others, further incentivising the creation ofhighly dense NV ensembles, but in practice this is a re-alistic experimental limitation.Overall, the conclusions in this sensing regime aremuch the same as in the previous section, apart fromthe most optimised HPHT samples becoming even morecompetitive and the impact of the disadvantages inherentto Method 3 appearing to be reduced. C. Crystal strain mapping
Separate from magnetic sensitivity, another importantquantity for widefield magnetic imaging is the crystalstrain homogeneity in the NV layer. In particular, straininhomogeneity can easily be conflated with the variationof a target field (in DC magnetometry), or constitutevariable detuning from resonant driving across the field ofview (AC measurements). Additional experiments can bemade to normalise out these effects, though this is oftenimpractical as it requires addressing multiple transitionfrequencies [60]. This could make an experiment less timeefficient or be technologically impossible for high fields,hence it is advantageous to have as little strain variationas possible.Our samples vary in their surface finish (polished vsovergrown) and their growth method (CVD vs HPHT),both factors which will contribute to near-surface strain.The samples also vary in their implant doses, which arein general high and therefore also expected to impactthe crystal quality. All samples began as purchased sub-strates polished by their manufacturer (details unknown)but while the HPHT samples were left as-received priorto implantation, Method 2 and 3 samples all underwentsome level of CVD overgrowth designed in part to mit-igate polishing-induced strain. CVD growth is knownto be susceptible to the incorporation of growth defectssuch as crystal lattice dislocations that may result in lo-calised strain [61], while the thermodynamically stableHPHT growth process can result in fewer strain-inducingextended growth defects.To assess the strain homogeneity within our samples,we mapped the strain over the full 50 µ m × µ m field ofview using ODMR spectroscopy. ODMR maps focussingon the aligned | (cid:105) → |± (cid:105) transitions under a bias fieldof 60 G were obtained for a variety of locations on arange of representative samples. From the two transitionfrequencies ( f and f ) the zero-field splitting constant D = f + f can be inferred as it is sensitive to strainbut not magnetic fields [60]. Assuming temperature andelectric fields are homogeneous across fields of view, D maps thus tell us about the strain variations (in unitsof frequency) within samples. A series of representativestrain maps for samples from each method is presented inFigure 5, where the colour scales denote the value of ∆ f ,which is defined as the deviation from D = 2870 MHz(though the absolute value is arbitrary due to the possibleco-presence of other fields which manifest as a constantshift across the field of view).In all four cases, strain variations over the scale ofa few microns are present over the whole field of view.The amplitude of these variations ranges from a few kHzfor the δ -doped sample (close to the noise floor of themeasurement) to 10-25 kHz in the others. In addition,stronger isolated features are sometimes visible, for ex-ample a 20 kHz spot in the δ -doped sample, and 1 MHzstreaks in the HPHT sample. We expect that the δ -dopedfeature is an example of a CVD growth dislocation, while the HPHT features are polishing marks which are espe-cially prevalent in the absence of any additional surfacetreatment.Background variation could originate in the crystalgrowth, polishing and implantation processes the samplesunderwent. The directionality of the pattern in Figure5(b) suggests the substrate’s polishing as the source, de-spite the subsequent 2 µ m CVD overgrowth this sampleunderwent. This highlights the necessity of performingan additional process such as reactive ion etching (RIE),with or without subsequent overgrowth, to completelyremove polishing damage [62–64]. Sample CN-1 under-went an RIE process prior to overgrowth and Figure 5(c)shows that this was successful in removing obvious pol-ishing features, although there is still a noticeable straingradient and variation of up to 25 kHz. This backgroundis unlikely to be due to the CN implantation alone as itis larger than samples subjected to higher doses and sois thought to be damage related to the RIE itself. Thisshows the importance of optimising the RIE process tobest prepare the surface, following an Ar/Cl etch like theone conducted here with an additional oxygen etch [64].The lowest level of background variation ( ∼ δ -doped sample (Figure 5(d)), whichbenefited from the lowest implantation dose as well asthe thickest CVD overgrowth ( > µ m) on a polished(HPHT) substrate. HPHT substrates were chosen forthese growths primarily to inherit their low dislocationdensities in the CVD overgrowth [65]. An oxygen etchprocess designed to remove polishing damage was con-ducted prior to the CVD overgrowth and appears to havebeen successful in preventing the appearance of polish-ing features in the final grown layer [47]. Large dislo-cation features are sparse and only of the same orderas background variation in the other samples, indicatingthat although the CVD process is susceptible to the in-corporation of crystal imperfections, this is a relativelysmall detraction compared to the polishing and implan-tation processes. This also shows that, with careful se-lection of growth conditions and underlying substrate,CVD growth is capable of producing mostly strain-freematerial.The large polishing marks observed in the HPHT sam-ples underline the importance of undertaking some formof post-polishing process. However they are in generalquite sparse, meaning that quick pre-screening of suchsamples should be adequate to ensure an uncompromisedimaging experiment. The background variation in thesesamples is of similar magnitude to that of Method 3 sam-ples despite the polished surface finish, which is likely anindication of the high strain uniformity of the originalcrystal.It is reasonable to expect some degree of variation inthe strain homogeneity between and even within sam-ples, however we can still draw informative conclusionsfrom these results. Even away from large features, typ-ical background variation of tens of kHz is significantfor high sensitivity magnetic imaging (corresponding to Δ f ( k H z ) Δ f ( k H z ) Δ f ( k H z ) (c) Δ f ( k H z ) Δ f ( k H z ) (b) Δ f ( k H z ) -60-70 Δ f ( k H z ) Δ f ( k H z ) (a) (d) Δ f ( k H z ) Δ f ( k H z )
10 μm
FIG. 5.
Representative strain maps from each methoda)
Sample HPHT-4: HPHT sample; b) Sample N-5: N + im-plant; c) Sample CN-1: CN − implant sample; d) Sample δ -2: δ -doped sample. The images show the variation ∆ f ofthe zero-field splitting constant D . The insets show linecutstaken along the red and blue solid lines. variations on the order of 1 µ T). This means that thespecifics of sample surface preparation, which the resultsof this section show is the single greatest contributor tostrain homogeneity even when viewed alongside high ionimplantation doses and variation in crystal growth, areespecially important for future applications of widefieldNV imaging. In contrast, the strain variations over afield of view are still sufficiently small in all cases to notlimit the measured T ∗ values presented in Section III A,hence T ∗ is likely limited by magnetic noise and the ef-fects of crystal strain will be less noticeable in measure-ments averaged over a field of view for this density of NVensemble. D. Temperature dependence
Some applications of widefield NV imaging require thesample of interest to be cooled to cryogenic temperatures.For example, superconducting phenomena (vortices andtransport currents) were recently imaged at 4 K [51].Thus, it is useful to investigate the temperature depen-dence of the magnetic sensitivity of the NV layers and sowe repeat the suite of measurements from Section III Aas a function of temperature from 4-300 K for a series ofrepresentative samples.We first plot T vs temperature in Figure 6(a). Atlow temperatures, we see significant extension of T forall samples. The largest extension (around two orders ofmagnitude) is seen for samples with long room tempera-ture T , consistent with them being governed by phononrelaxation. However, even the samples with short roomtemperature T show a significant extension (of aroundone order of magnitude for HPHT samples). This sug-gests that the dominant contribution to T in this case (a) (b)(c) (d)(e) (f) T ( μ s ) R ab i c on t r a s t ( % ) P L ( a . u . )
60 G Rabi1970 G PL60 G PL1970 G Rabi
HPHT(Method 1) ẟ -doped(Method 2) N implant(Method 3) CN implant(Method 3) -error bars-link points in b via lines-separate PL from C more inb? T ( m s ) η d c ( μ T / H z / ) Temperature (K) 1.51.00.50.0 3002001000 η a c ( μ T / H z / ) Temperature (K)0.20.10.0 T * ( μ s ) FIG. 6.
Spin property scaling with temperature: a) T ,plotted on a log scale. b): Rabi oscillations taken at 4 K afield of 60 G (blue) and 1970 G (red) in sample CN-1 show-ing increased measurement contrast at higher fields. Pointsmarked by triangles show PL measurements, showing reducedfluorescence at the higher field but not enough to explain thedifference in contrast. c) and d) show T ∗ and T variationwith temperature respectively. e) and f ) show the DC andAC magnetic sensitivity scaling respectively. Data presentedis for samples δ -2 (green), N-2 (purple), CN-1 (yellow), andHPHT-1 (blue) in all comparative plots, with the addition ofsample HPHT-3 as the bottom blue set in a) and d). depends on temperature as well, possibly through ther-mal activation of donor/acceptor defects, although fur-ther work is needed to fully understand this behaviour.In Figure 6(b) we plot Rabi contrast (Sample CN-1)against temperature and see a surprising reduction at60 G below 100 K. This trend is consistently observed butis most marked for N implants (a factor of 3), while δ -doped samples saw a lesser reduction (factor of 2), thoughit is unclear from the small sample size whether this dif-ference is significant. This reduction is largely recoveredat a higher field of 1970 G. This phenomenon has pre-viously been observed in single NV centres [66] and itsorigin is currently being investigated. The PL (also plot-ted in Figure 6(b)) does not vary significantly with tem-perature and although there is a minor reduction in PLat the higher field due to increased quenching of off-axisNVs [67], this is not enough to explain the differences inmeasured contrast. No other spin property was observedto change between the two fields apart from a slight ex-0tension of T at 1970 G.Figure 6(c) shows the T ∗ variation with tempera-ture, which is very small for all samples, indicating thattemperature-independent magnetic noise dominates thisquantity at all temperatures. Hahn echo T (Figure 6(d))is also broadly constant with temperature, with the ex-ception of a ≈
25% extension for the δ -doped samplewith long room temperature T . Decoupled, saturated T has previously been shown to have a phonon-coupledcomponent for dilute spin baths in bulk and near-surfaceregimes [58, 59]. Though we only consider Hahn echo ACsensing here for simplicity, the slight extension at lowtemperatures for the sample with the least dense spinbath suggests a similar phonon component to T whichwould be more obvious for higher order decoupling se-quences.In Figure 6(e) and (f), the measured quantities arepropagated to magnetic sensitivities to DC and AC fieldsrespectively at 60 G. There is little variation in sensitiv-ity with temperature except for the deterioration at lowtemperature due to reduction in spin contrast C . Theabsolute values are higher than in Section III A due tothe lower laser power and lower collection efficiency onthe cryostat system but the ordering between methodsremains unchanged, meaning the conclusions drawn inthe previous sections remain valid. This means that al-though this measurement regime does require additionalattention due to non trivial factors such as the contrastloss (resulting in reduced sensitivity below 100 K), thesuitability of samples themselves is similar to the roomtemperature case and so the findings of this study areequally applicable in the design of low temperature ex-periments. IV. DISCUSSION
We now discuss the pros and cons of each method androutes for improvement.Method 1 is by far the most cost effective and requiresonly a simple implantation procedure as the HPHT sub-strates used are commercially available at relatively lowcost. Carbon irradiation provides the required depth pro-file tunability and unnecessary damage to the crystal canbe avoided by tuning the process’s vacancy creation tothe existing N density. Relying on commercial substratesdoes mean, however, that this method lacks control overthe N density. In addition, the exact concentration isnot known ahead of time as it is only loosely specified bymanufacturers, and can even vary within individual dia-monds as they frequently contain different growth sectorsthat incorporate defects at different rates. This variabil-ity between (and within) samples is present in our resultsas a greater spread in sensitivity within this method thanthe others, though further optimisation of the procedureis expected to reduce this. The N density in these sam-ples is usually quite high ( ∼
100 ppm), resulting in shortercoherence times and this has typically been seen as a de- traction, resulting in HPHT diamonds seeing little usefor widefield NV imaging to date. However, our resultsshow that, following implantation, a bright ensemble pro-viding enough fluorescence to offset the short coherencetimes is produced. Our data shows that the best (mostoptimised) HPHT samples were among the highest sen-sitivity samples studied.No pre-measurement of nitrogen concentration was un-dertaken for this work and so there is obvious room forfurther optimisation in the future. Additional studiesinto the merit of implanting with lighter ions such ashelium could also improve the outlook, producing moreeven damage to the lattice at the cost of introducing de-fects related to the implant species.Like Method 1, in situ δ -doping (Method 2) has theadvantage of naturally incorporating nitrogen duringgrowth, allowing the creation of high-yield ensembles fol-lowing tuned vacancy production at a minimal damagecost. Being a custom process, δ -doping allows controlover N density and the depth profile of the doped layer.These benefits are, however, difficult to realise and re-produce due to the complexity of the process and it isin general the most cost intensive of the three methods.CVD growth also carries the detraction of possible in-corporation of unwanted point defects such as the NVHcomplex that limits the NV conversion ratio [68], as wellas crystal dislocation defects that may introduce addi-tional strain [61]. The results of Section III C, however,show that material with a high level of strain uniformitycan be produced using growth conditions designed to pro-mote slow growth and careful selection and preparationof the growth substrate. Additionally, it appears thatthe implant doses useful for creating the high density en-sembles that this study focusses on, and in particular thesurface preparation of the diamond, play more prominentroles in decreasing strain homogeneity than the methodof diamond growth.Samples grown in the slightly lower density regime(Samples δ -3 and δ -4, with an order of magnitude lowerNV density than other Method 2 samples) were ob-served to be susceptible to uneven nitrogen incorpora-tion. These low density samples exhibited fluorescencestriations expected to have arisen as a result of step-bunching growth patterns that see nitrogen defects pref-erentially incorporate at step-edges. This unevenness isundesirable for widefield imaging, especially in a modal-ity that may seek to image via fluorescence quenching,but would be less relevant in confocal microscopy. Thisindicates that while in principle δ -doping is highly tun-able, the complexity of the process requires careful re-finement to realise this. This behaviour appears to beoverridden at higher nitrogen densities as the other sam-ples exhibited highly even fluorescence, though the as-grown surface could still contain unwanted features suchas growth hillocks that are undesirable for imaging ex-periments.The complexity of the CVD growth process also meansthat there exists a lot of room for improvement within1this method, despite it already producing the highestmagnetic sensitivities. In addition to the improvementsidentified for Method 1, we note that further optimisationof (and finer control over) other key growth parameterssuch as gas composition and growth temperature couldsee higher quality crystals with fewer unwanted defects.Confining nitrogen to a well-defined layer during growthalso carries with it the advantage of being able to explorethe merits of introducing vacancies via electron irradia-tion [39, 40] rather than the implantation of more mas-sive particles. This possible improvement is incompatiblewith Method 1 as electrons cannot be confined in depthin the same way as carbon ions.Method 3 has the advantages of giving a predictableN density and depth profile that can be easily tuned.However, this comes at the considerable cost of excessvacancy creation (about two orders of magnitude at theenergies considered, as shown in Figure 1(c)) that can-not be tuned. This manifests itself in our results as re-duced coherence values relative to nitrogen concentrationcompared to samples that have N and V concentrationsroughly matched, ultimately resulting in inferior mag-netic sensitivity. This limitation will be inherent to anyprocedure that relies on incorporating nitrogen into thecrystal via implantation unless new techniques allow bet-ter vacancy removal during annealing (discussed below).This method also requires a high purity CVD substratewhich are generally more costly than HPHT substrates.Comparing the two species used to investigate thismethod, our results show that implanting with the largerCN − ion results in more damage to the crystal per ionimplanted, compromising both AC and DC sensitivity.Much of the AC sensitivity can be recovered, however,by using longer dynamical decoupling sequences, indicat-ing the effectiveness of this approach in protecting spincoherence against interactions with unwanted paramag-netic defects.Finally, method-agnostic improvements were beyondthe scope of this work but may include dynamic an-nealing during the implantation stage to better repaircrystal damage, and surface treatments to limit surfacenoise [64, 69]. Optimised RIE may be useful in miti-gating strain caused by polishing damage, resulting in amore homogeneous zero field splitting across a field ofview to be imaged and possibly improving NV coherenceby reducing surface magnetic noise [70]. Fermi level en-gineering via n-type doping (phosphorus, sulphur) hasbeen shown to promote the NV − charge state by charg-ing vacancies and other defects which then can be an-nealled out to improve the NV yield [71, 72]. It is un-clear whether this will have a significant effect in thehigher nitrogen concentration regime wherein the major-ity of samples measured in this study belong, so furtherwork is required in this area. V. CONCLUSION
Our results show that while δ -doping during CVDgrowth offers the best overall sensitivity across a range oftemperatures from cryogenic to room temperature, im-plantation of nitrogen-rich HPHT substrates is highlycompetitive, offering superior sensitivities to the muchmore expensive and currently ubiquitous approach of im-planting electronic-grade CVD substrates with nitrogen.Though the HPHT approach has a significant drawbackin its lack of reproducibility and precise control over NVdensity compared to current alternatives, its low cost anduntapped potential for further improvement by refine-ment of the implantation process leaves it as an appealingoption for future research.Even though the CVD growth for the δ -doped samplespresented here is not expected to be state-of-the-art, thebest sensitivities were achieved by these samples. Thisindicates that, if the cost requirements are not too stren-uous, δ -doping is an achievable method for the creationof high quality NV ensembles of varying density.The common method of nitrogen implantation resultedin the lowest magnetic sensitivity of the three methods.This is due to the large amounts of damage sustained bythe crystal during the high dose implantation proceduresrequired to incorporate the high levels of nitrogen desiredfor ensemble NV sensing. Unlike the other two methods,implanting nitrogen leaves no scope to tune vacancy pro-duction to nitrogen density and this looms as the mainlimitation of Method 3.It is clear from our results that the high nitrogen con-tent of the HPHT samples gives sufficiently high PL fol-lowing C − implantation to offset their short coherencetimes. Additionally, although it offers considerably lessflexibility than the other two methods, high PL HPHTsamples are particularly advantageous for measurementswith very low duty cycles (e.g. T measurements) or verylow laser power (e.g. to minimise sample heating [51]).Indeed, in these situations noise sources other than shotnoise, such as dark currents in an sCMOS camera, may bedominant if the PL level is too low, deteriorating the sen-sitivity. The flexibility of δ -doping makes it suitable forthe widest range of applications, with the lower densitysamples excelling in applications that allow long mea-surement times to reach the shot noise limit. Method3 is shown to be suboptimal in both absolute sensitivityterms and in practicality from a cost point of view in thiswork, however we note that further advances in anneal-ing procedures to repair crystal lattice damage sustainedduring implantation could entirely address the losses insensitivity. The NV layer formation methods themselvesappear to have relatively little impact on the strain ho-mogeneity of the final crystal compared to the diamondsurface preparation. The optimisation of these processesfor enhancing strain homogeneity and assessing the re-sulting improvement on NV ensemble quality for wide-field imaging is left for future work.2 ACKNOWLEDGEMENTS
We acknowledge support from the Australian Re-search Council (ARC) through grants DE170100129,DE190100336, LP160101515, CE170100012,LE180100037 and DP190101506. We also acknowl-edge the AFAiiR node of the NCRIS Heavy IonCapability for access to ion-implantation facilities. Thiswork was performed in part at the Melbourne Centrefor Nanofabrication (MCN) in the Victorian Node ofthe Australian National Fabrication Facility (ANFF).A.J.H. and D.A.B. are supported by an AustralianGovernment Research Training Program Scholarship.T.T. acknowledges the support of JSPS KAKENHI (No.20H02187 and 19H02617), JST CREST (JPMJCR1773)and MEXT Q-LEAP (JPMXS0118068379).
Appendix A: Full room temperature results
In Table II we list the full data plotted in Figures 2, 3,and 4 for comparison with the parameters in Table I.
Appendix B: Data collection
In this appendix we provide greater detail on the mea-surements undertaken as introduced in the main text. a. Photoluminescence (PL)
The PL rate, R , was measured by averaging over animage taken under constant laser illumination over a30 ms camera exposure and a 50 µ m × µ m area. Theper-pixel average obtained was converted into a per µ m per second value as a figure of merit. R was then con-verted into an approximate areal NV density by compar-ing the fluorescence of a representative set of samples ona confocal microscope (recorded by an avalanche photodiode) with that from a single NV (from a sample sep-arate to this study). Multiple samples were comparedto confirm an appropriate multiplicative factor to con-vert the widefield PL measurements to this density. Mi-nor background fluorescence from the HPHT substratepresent in the δ -doped samples was subtracted. b. Rabi contrast C was calculated by driving the NV ensemble at a highenough microwave power for the T ρ decay to be negligi-ble over the first Rabi oscillation and fitting, with C de-fined as the peak-to-peak amplitude. This is a measureof the maximum attainable contrast, an upper boundfor the actual contrast available for a measurement opti-mised at T or T ∗ . As with R , the impact of background fluorescence ar-tificially decreasing C was removed as a less fluorescentsubstrate could be used in future without affecting NVproperties.The lowest density CVD samples also exhibited PLstriations arising step bunching growth behaviour. Thismeant the PL was variable across the field of view usedand is also expected to reduce the contrast when averag-ing over the full region. This effect was not removed asit was observed to be a limitation inherent to growing atlow nitrogen concentrations under our growth conditions. c. Free induction decay time T ∗ was measured using the Ramsey pulse sequencewith a level of detuning of the microwave drive fromthe hyperfine resonances adjusted to each sample to en-sure an appropriate frequency of beating to allow accu-rate extraction from the resulting fit. The signal wasfit to a sum of cosines with frequencies given by the de-tuning from the respective hyperfine resonances modu-lated by an exponential envelope with decay constant T ∗ , e − ( τ/T ∗ ) (cid:80) Ni =1 cos ( ω i τ + φ i ), where the ω i are detuningsfrom the individual hyperfine resonances, φ i are phases,and N is the number of hyperfine resonances, equalling3 and 2 for N and N respectively. Care was taken toensure the measurement was not compromised by mag-netic field gradients across the field of view so that themeasured decay envelope could accurately be attributedto the free induction decay of the ensemble alone. d. Spin relaxation time T was measured by initialising the NV ensemble andreading out the state after set periods of dark evolution.The signal was normalised by subtracting the PL ob-tained by a sequence identical but for the application ofa π pulse prior to readout. This is a standard procedurein our measurements but is particularly important in themeasurement of T due to the wide range of wait timesinvolved that result in a variable laser duty cycle andthus changing charge state dynamics over the course of asingle sweep. The resulting decay was fit to a stretchedexponential e − ( τ/T ) k with k ranging between 0.5 and 1at room temperature. e. Spin coherence time The sensitivity of the samples to AC fields was mea-sured using a Hahn spin echo sequence at a field of 475 Gchosen to ensure that, for the samples containing a natu-ral abundance of C, the resulting revivals were closelyspaced enough to still allow us to accurately extract T from the decay curve. The envelope of the resulting3 Sample C (%) T ∗ ( µ s) T HE2 ( µ s) T CPMG2 ( µ s) T (ms) η dc η ac η CPMG name ( µ T Hz − / ) (nT Hz − / ) (nT Hz − / )HPHT-1 3.0 ± . ± .
020 1.04 ± .
03 60.2 ± . ± .
01 1.10 ± .
31 99.5 ± . ± . ± . ± .
080 0.94 ± .
01 63.5 ± . ± .
01 5.83 ± .
32 155.7 ± . ± . ± . ± .
008 0.67 ± .
02 4.5* ± .
01 0.02 ± .
01 4.42 ± .
43 174.0 ± . ± . ± . ± .
013 0.89 ± .
01 9.2* ± .
07 0.10 ± .
01 4.71 ± .
69 233.6 ± . ± . ± . ± .
010 0.49 ± .
05 3.5* ± .
01 0.11 ± .
01 3.77 ± .
46 234.7 ± . ± . ± . ± .
007 0.83 ± .
01 58.2 ± .
80 0.06 ± .
01 6.05 ± .
93 120.5 ± . ± . ± . ± .
009 1.17 ± .
05 50.9 ± .
00 0.14 ± .
01 0.49 ± .
08 54.2 ± . ± . δ -1 4.0 ± . ± .
058 8.19 ± .
16 285.3 ± .
17 1.88 ± .
10 0.52 ± .
10 32.1 ± . ± . δ -2 3.8 ± . ± .
098 7.49 ± .
12 301.8 ± .
00 1.54 ± .
07 0.64 ± .
30 27.1 ± . ± . δ -3 1.2 ± . ± .
173 152.53 ± .
78 1723.5 ± .
00 3.04 ± .
09 2.22 ± .
34 81.7 ± . ± . δ -4 3.1 ± . ± .
147 71.28 ± .
95 700.0 ± .
00 3.00 ± .
10 1.04 ± .
22 35.5 ± . ± . δ -5 4.0 ± . ± .
111 8.79 ± .
15 332.1 ± .
00 1.72 ± .
04 0.18 ± .
03 29.1 ± . ± . ± . ± .
009 2.46 ± .
12 51.6 ± .
60 0.50 ± .
02 5.23 ± .
08 176.2 ± . ± . ± . ± .
009 2.27 ± .
05 30.0* ± .
90 0.61 ± .
02 1.56 ± .
27 124.8 ± . ± . ± . ± .
011 4.20 ± .
01 64.9 ± .
00 1.05 ± .
05 2.78 ± .
49 92.9 ± . ± . ± . ± .
007 1.36 ± .
01 41.7 ± .
20 0.32 ± .
02 3.96 ± .
82 193.0 ± . ± . ± . ± .
012 2.67 ± .
09 61.0 ± .
70 0.54 ± .
03 2.05 ± .
34 117.9 ± . ± . ± . ± .
025 2.69 ± .
11 N-1.8 ± .
80 0.77 ± .
05 4.51 ± .
52 181.1 ± . ± . ± . ± .
033 2.26 ± .
06 112.1 ± .
50 0.66 ± .
04 5.03 ± .
52 204.1 ± . ± . ± . ± .
038 3.75 ± .
09 129.7 ± .
00 0.64 ± .
04 3.33 ± .
31 124.2 ± . ± . Full spin properties:
Summary of room temperature data presented in Section III. All measurements as definedearlier, with T CPMG2 being the CPMG-1024 T value (or highest N CPMG sequence for samples that could not be extendedthis far, marked with an asterisk). curves were fit to an exponential decay e − ( τ/T ) k and theHahn echo spin coherence time T extracted. k variedbetween 0.5 and 1.5. f. Extended dynamical decoupling The behaviour of the samples with respect to ex-tended decoupling was assessed using CPMG sequencesof increasing length until either T saturation or thetotal microwave duty cycle exceeded the sample’s T ρ (and hence no further meaningful extension could beachieved). These measurements were carried out at475 G so as to suppress the impact of any C revivals onour ability to fit the resulting curve and reliably extractthe decay constant. Fluorescence for all measurementsof a sample were normalised to the contrast obtained forthe shortest decoupling sequence ( ≈ C ) and fit to an ex-ponential decay of form e − ( τ/T ) k , modulated by C re-vival structure fit as Lorentzian dips where appropriate.No strong, consistent trend in the variation of k with N was observed across samples. g. Strain mapping To obtain maximum fidelity, the ODMR spectra usedto obtain crystal strain maps utilised low power mi- crowave driving to achieve T ∗ -limited linewidths. Theresulting data was fit to Lorentzian lineshapes (account-ing for hyperfine structure where appropriate) and eachresonant frequency extracted for each pixel. Pixel sizewas set to be comparable to the optical diffraction limit ≈
300 nm. Images were saved periodically until the levelof pixel-to-pixel noise reached a plateau, indicating thatphoton shot noise was no longer the dominant source ofnoise and any remaining variation could be attributed tostrain inhomogeneity. h. Low temperature measurements
The cryogenic widefield setup is functionally identicalto that used to take room temperature measurementsand so measurements taken on it proceeded as describedabove. The need to use a low laser power (to avoid sam-ple heating) and the lower collection efficiently as wellas the loss of measurement contrast at low temperaturesincreased the measurement uncertainty, particularly forfree induction decay measurements on less fluorescentsamples (ie CN − implants). Similarly, there is a largeuncertainty in the measurement of long ( (cid:29)
10 ms) T decays as the readout duty cycle becomes insignificantnext to the wait times and so camera dark currents (andtheir associated noise) begin to account for a large pro-portion of the total signal. Nevertheless, T extension4with decreasing temperature is clear, which is the mainobservation to make from this section.Although the base temperature of the cryostat is 4 K,the conditions used to access the full range of temper-atures without otherwise altering the experiment meantthat the cooling power was not always sufficient to main-tain this temperature under the influence of laser heat-ing. The temperature was measured after every sweep ofone camera exposure per data point and then averagedfor plotting. The temperature throughout an experimentwas usually mostly constant as the laser duty cycle doesnot change much from point to point. The laser heatingeffect was most significant for the Sample CN-1 T ∗ mea-surement as this was the closest to a CW laser duty cycleand undertaken under conditions of least cooling power.A minimal number of sweeps were used to maintain a lowtemperature for this measurement, which contributed toits high uncertainty.Temperatures above the base temperature were ac-cessed using a heater placed below the sample and fluctu-ations within these measurements were minimal. Roomtemperature measurements conducted on this system oc-casionally differed slightly from the original set due todifferences in ensemble initialisation and microwave driv-ing power and so data is directly comparable within thecontext of individual sections only. Appendix C: Further sample details
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