To gain further insight into the trend of T2 with NV depth, we grew delta-doped
diamond films of different cap thicknesses (Fig. 3.9(b)) and compared the spin coherence times of a few NVs within each. Fig. 3.9(a) summarizes the results, where each color symbol refers to NVs in the corresponding film of Fig. 3.9(b). The ordering along the
NV axis is sorted by lowest to highest T2 times per sample. We emphasize two general
findings. First, the coherence times in each particular sample are quite consistent, with
none showing NVs with significantly shorter (e.g., few microsecond) T2’s. Second, the
samples with nominal depths of d = 21 nm (blue squares) and d = 5 nm (red circles)
show the largest variation in T2 times, and T2 tends to be shorter on average for the
shallower-NV samples. This observation suggests a strong dependence of coherence time on NV distance to the surface, particularly below 50 nm, and therefore hints at a source of surface-related noise. The surface-induced decoherence, at sufficiently short distances, may dominate over bulk sources of NV decoherence like nitrogen electronic spins.
3.4
Conclusions
We have demonstrated an in-situ N doping method to form NV centers via epitaxial diamond growth in combination with isotopically pure carbon-12 precursor gas to limit
decoherence from 13C spins. We showed, via electronic-nuclear spin coupling measure-
ments in a 13C/12C/13C structure, that the N delta-doped layer is localized to within a
dispersion of about ±4 nm. Delta-doped NV centers within 10s of nanometers of the
diamond surface, as estimated by growth rate, exhibited coherence times of T2 > 100
µs. These coherence times are consistent across several NVs in each sample that has a nominal depth of the delta-doping layer, and the shorter coherence times observed
rate. These initial results and the surface-related questions motivated the experiments in the remainder of this dissertation. In Chapters 4 and 5, we explore the depth de- pendence, frequency dependence, and origin of faster decoherence in near-surface NVs. Surface-proximate delta-doped or implanted NVs in these grown diamond films also en- able magnetic imaging of external spins, as we demonstrate in Chapter 6, and imaging of electromagnetic noise from metals, as in Chapter 7.
Both N implantation and N delta-doping are viable methods to form the spin sen- sors for magnetometry applications, and in fact the wide availability and long-studied tunability of N implantation has made it, as of 2016, remain the method most often used for nanoscale NMR demonstrations [155, 81, 195, 196]. Combined with vacuum and oxygen annealing techniques to mitigate implantation damage and surface effects [183, 88, 127, 196], implanted NVs can potentially have coherence times as long as those found in delta-doped films, though no systematic yield comparison has been done to date. NV-target distance is the most significant variable in magnetic sensitivity, in com- parison to coherence time, so research focus has been on ultra-shallow NVs first (depth 2-5 nanometers), and coherence second. In addition to depth-localization, delta-doped NVs have the advantage of NV-to-NV consistency in coherence times without special or extensive annealing techniques, as evidenced in this chapter and Chapter 4. The delta- doping technique of NV creation is a younger technology with much room for further research.
One of the important knobs on the delta-doping technique is the capability to sep- arate, in both process type and spatial position, the nitrogen incorporation and va- cancy creation. This degree of freedom allows optimization of the NV concentration and vacancy-related damage in the crystal. Thus, variation in the method of vacancy creation has constituted much of the ongoing delta-doping research. High-energy electron irradia- tion has been used in the above-described work, but these electrons penetrate the whole
diamond and thus do not localize vacancies well, for example producing some background
NVs in the non-film substrate [43]. 12C implantation has recently been used to tune the
NV density and to localize both vacancies and NVs when combined with carefully timed annealing steps [163]. Irradiation with a low-energy focused electron beam, such as in a transmission electron microscope, has also been used to localize NV creation in three dimensions while preserving millisecond-long coherence times of delta-doped NVs [164]. We have also found that nitrogen incorporation is not noticeably affected by nitrogen flow rates between 0.1-30 sccm in the CVD delta-doping process [164, 163], so 0.1 sccm is used for preserving the isotopic gas supply. Helium implantation [197] is another route for creating vacancies near or at the N delta-doped layer [198], and combination with low-damage etching processes can further tune the final NV depth and localization vol- ume [199, 200, 198, 91]. Shallow delta-doped NV centers may also be formed during the growth process itself, without separate crystal-damaging vacancy creation, by us- ing different gas ratios, temperatures, or post-growth surface treatments [201, 202, 203]. Low-energy (few keV) electron irradiation methods also suggest mechanisms of NV cre- ation that don’t necessarily rely on thermal annealing [204]. Altogether, the nitrogen incorporation modes provided by delta-doping CVD growth provide an important mate- rial framework for fundamental studies into how NV centers are formed, especially those close to the diamond surface.
Probing surface noise with
depth-calibrated nitrogen-vacancy
centers
Sensitive nanoscale magnetic resonance imaging (MRI) of target spins using nitrogen- vacancy (NV) centers in diamond will require a quantitative understanding of dominant noise at the surface. We probed this noise by applying dynamical decoupling to shallow NVs at calibrated depths. Results support a model of NV dephasing by a surface bath of electronic spins having a correlation rate of 200 kHz, much faster than that of the bulk N
spin bath.1 Our method of combining nitrogen delta-doping growth and nanoscale depth
imaging paves a way for studying spin noise present in diverse material surfaces.
0The contents of this chapter have substantially appeared in reference [87]: B. A. Myers, A. Das, M.
C. Dartiailh, K. Ohno, D. D. Awschalom, A. C. Bleszynski Jayich, Probing surface noise with depth- calibrated spins in diamond Phys. Rev. Lett. 113 027602 (2014) c 2014 American Physical Society.
1Although the depth dependence of the noise is consistent with a surface of fluctuating magnetic
dipoles, it can also be consistent with fluctuating electric dipoles. We observed this point later and it is discussed in Chapter 5, where we introduce a method to selectively probe electric fields.
4.1
Introduction
The negatively charged nitrogen-vacancy (NV) center in diamond is a robust quan- tum sensor of magnetic fields [25, 4, 26, 5]. Although an individual NV has the capability to detect small numbers of electronic [179, 39, 41] and nuclear spins external to diamond [205, 102, 206], its widespread application in spin imaging has been limited by the ability to form shallow NVs that retain spin coherence near the surface. Shallow spins with long
coherence time, T2, are important because quantum phase accumulation between two
electronic spin states of the NV provides signal transduction, and hence the minimum
detectable magnetic dipole moment scales as δµ ∝ r3/√T
2, with r the NV-target spin
distance [26, 5]. At odds with this figure of merit is strong evidence that the diamond
crystal surface adversely affects T2, reducing it from ∼ 2 ms for bulk NVs [132, 127] to less
than 10 µs for few-nm deep NVs [39, 183, 66, 40, 43], but the origin of this decoherence is an outstanding question. In this chapter, we consider a model of surface spin induced decoherence, a theory which has emerged from experiments on other systems [97, 207] where long coherence is a requirement, such as in superconducting circuits [208, 96] and spin qubits in silicon [209]. We show that an electronic surface spin model is quantita- tively supported for NVs in diamond. The key step we present is to link NV coherence with precise, independently measured NV depth data, as enabled by recent advancements in depth-controlled NV center creation and nanometer-scale magnetic imaging.
Recently, Ohno et al. demonstrated shallow, coherent NVs using delta-doping of nitrogen during chemical vapor deposition (CVD) of single-crystal diamond (SCD) [43], as described in Chapter 3. This crystal growth technique both permits nm-scale depth confinement and minimizes crystal damage incurred during nitrogen ion implantation
[183, 40, 182], the conventional method of generating shallow NVs. The long T2 of
external protons [206]. The consistent NV quality in delta-doped SCD makes depth measurements a suitable probe of surface physics, not masked by effects of other process- induced crystal variations. Therefore we used this promising material in the reported work: we exploit depth-calibrated NVs to understand how the surface contributes to decoherence and provide a way to mitigate surface noise for enhanced external spin sensing. Using dynamical decoupling (DD) with periodic spacing of π pulses for coherence analysis [100], we varied the number of pulses to deduce the noise spectral contributions from the surface and bulk environments as a function of depth. We show that using shorter inter-pulse spacing can progressively increase efficiency in decoupling from rapid magnetic fluctuations at the surface.