Dielectric properties of diamond using an X-band microwave split dielectric resonator

This work presents an easy-to-use microwave split dielectric resonator (MSDR) for X-band dielectric measurements of free-standing unpolished poly-crystalline diamond (PCD). PCD grown with varying CH 4 /H 2 and O 2 / CH 4 /H 2 in the gas phase show stark differences in dielectric loss. Low microwave dielectric loss PCD is found for CH 4 /H 2 concentrations of less than 5% while PCD grown with O 2 show very high loss tangents. Vacuum annealing introduces non-diamond carbon (NDC) impurities which increases the loss, however, even after significant discolouration the loss is still lower than the O 2 grown PCD. The loss mechanism of O 2 grown PCD is likely due to a high concentration of grain boundaries and grain boundary hopping conduction mechanisms as opposed to high concentrations of NDC impurities.

To circumvent lithography, non-contacting X-band waveguide and cavity resonator methods can be used.Large and specific sample areas are typically needed to perfectly occupy the cavity and avoid depolarisation fields; for example, a standard WR112 X-Band cross-sectional area is 28.5 × 12.6 mm.Geometrical constraints can be eased using perturbation methods such as the system presented by Molla et

Theoretical model
Microwave cavity perturbation (MCP) is a well-known method for permittivity measurements of carbonaceous materials, including diamond [20][21][22][23].The change in frequency ( ) and −3 dB quality factor () of a microwave resonator from the unperturbed state to the sample perturbed state can be used to extract the complex permittivity and permeability.For non-magnetic plate samples, permittivity measurements are typically extracted in minimal depolarisation field configurations for high sensitivity, shown in Fig. 1 for cylindrical transverse electric (TE) and magnetic (TM) resonators.In the minimal depolarisation configuration, complex permittivity can be extracted using the following MCP approximation [22,24]: where  is the resonant frequency of the cavity,  is the quality factor, '0' and '' denote the unperturbed and sample states,   =    is the mode volume,   is a linear calibration constant and   and  are the sample volume and thickness, respectively.For ease of construction, split cylindrical TE modes can be formed by stacking 2 resonators.The resonant frequency of the system can be designed and estimated to operate in the X-band using the theoretical solution for an ideal dielectric cylinder surrounded by perfect electrical conductors (PEC): where  is the speed of light in free space,  r,c and  r,c are the permittivity and permeability of the cavity, respectively and  ′  is the th root of the  ′  () Bessel function, as appropriate for the E field boundary conditions for TE modes,  and  are the cavity radius and height, respectively, ,  are integers and  is the longitudinal integer mode number.
Diamond samples are typically low loss and small in size (∼10 × 10 × 0.5 mm) and so placing a diamond inside of a larger cavity resonator will result in a small change in  and .To increase the sensitivity, either larger diamonds can be made (increase   ) or the cavity can be made smaller such that the E-field is focused into a smaller volume (decrease   or   ).For the latter, maintaining Xband operation whilst miniaturising can be achieved by increasing  r,c .This becomes a very useful alternative to waveguide methods which require large samples.With EM fields focused, the central regions of diamond plates can be probed with minimal sensitivity to the edges and reduce any depolarisation effects, making the measurement highly reproducible.The only sample requirement is a known thickness.Practically, stacked TE resonators are better suited over TM modes for plate samples as is shown in Fig. 1, where this work uses the circulating TE 011 and TE 013 modes.For 10 × 10 mm CVD diamond substrates, restrictions on the DR radius ( < 5 mm) and the aspect ratio ( < 2) are needed to fulfil non-depolarisation and reduce interference from unwanted higher TM modes.
Fig. 2a and b show the theoretical resonant frequency for the TE 011 mode as a function of  r,c and feasible resonator dimensions.As shown in Fig. 2a although shorter heights offer the least TM interference, a very high  r,c is needed for X-band operation.The proposed MSDR design (denoted 'DR' in Fig. 2b) uses a total height of 4 mm (or 2× stacked 2 mm resonators separated by a 0.5 mm gap) which can be easily achieved using commercial dielectrics; 2× stacked T-Ceram E-37 dielectrics,  = 3.5 mm and ∕2 = 2 mm.

Numerical model -Practical design
Modifications such as coupling antennas, sample slots and housing introduce discontinuities in the field distribution and alter the resonant frequency which cannot be estimated using Eq.(3).Their effects on the resonance can be investigated using finite element modelling (FEM), with discretisation of a 3D geometry into domains/nodes and solving for both eigenfrequency and frequency domain solutions of Maxwell's equations.FEM also ensures that modes can be identified through both their eigenvalues and simulated  parameters in the frequency domain to ensure the correct mode is identified in practice, as shown in later sections.
Fig. 3 shows the E-Field of the TE 011 mode (also known as the TE 01 mode for dielectric resonators, but henceforth referred to simply as the TE 011 mode) and the calculated eigenfrequency with incremental modifications.An ideal cylindrical dielectric resonator encased in PEC has a nominal frequency of 10.6 GHz (Fig. 3a).Introducing an airspaced gap allows the E-field to spill into sample measuring space which marginally increases the frequency to 11.7 GHz (Fig. 3b).Since  DR ceramics are fairly brittle, a malleable and low permittivity polytetrafluoroethylene (PTFE) support is used to maintain the gap height as opposed to a metal cavity (Fig. 3c).This modification results in a frequency reduction to 8.4 GHz and E-field spillage into the PTFE although remains circulating within the sample region.Finally, the coupling structures, housing and a recess to support 20 × 15 × 1 mm plates results in a small frequency reduction to 8.3 GHz (Fig. 3d).It is also important to note that the cross section in Fig. 3d shows that the active E-field region is contained to 9 × 9 mm area, with the highest sensitivity in the 7 mm diameter region in-between the dielectrics.

Microwave measurements
An exploded schematic of the MSDR is shown in Fig. 4. The housing is made of 2 pieces of aluminium which snap together using alignment posts and magnets.The pieces are made with point symmetry for ease of duplication during machining.A 15 × 20 × 0.5 mm recess is machined into each half for a total sample gap of ∼ 1 mm.PTFE inserts suspend 2× stacked T-Ceram E-37 dielectric resonators ( = 3.5 mm, total  height of 4 mm).Coaxial SMA antennas on the base of the structure provide E-field coupling to the TE modes for  21 measurements using a Keysight N5232A vector network analyser (VNA).
The calibration constant '  ' was obtained using a quartz sample of known permittivity and thickness (  = 3.8,  = 500 μm).A PTFE sheet was also measured to corroborate the calibration (  ≈ 2.05 to 2.1,  = 505 μm).Sample measurements were conducted  = 10 times, to average uncertainty in sample positioning and differences in the positioning of the two halves of the cavity.The cavity positioning error is the main source of random error, however is minimised using the magnets and alignment posts.The gap height error is therefore less important, and only the sample thickness is the critical parameter.Fig. 5 shows the S 21 spectra obtained by FEM and measurement.Owing to the tolerance in the positioning of the DR's in the PTFE, the simulated FEM results show a sample gap of 0.9 mm as opposed to 1 mm, thereby lining up with the experimental  21 data.The TE 011 mode has an unperturbed frequency of 8.3 GHz and an unloaded Q factor of 3445, with random measurement errors of 0.5% and 0.1%, respectively.TE 012 has a nominal frequency of 10.1 GHz and unloaded Q factor of 3768 with errors of 1.5% and 0.1%, respectively and TE 013 has an unperturbed resonance frequency of 16.1 GHz and unloaded Q-factor of 2719, respectively with random errors of 0.1% and 0.1%.Since the spectrum is fairly crowded, FEM is very important for identifying the practical high Q factor modes as labelled and highlighted  in blue, red and magenta.The interference from other modes seems problematic at first, however, the majority of these modes shift when the sample is introduced.The sensitivity is moderately high for quick and easy bench-top measurements (<30 s).Loss tangent measurements are limited by the finite loss of the dielectrics themselves, imposing a systematic measurement limit of tan min ∼ 1.4 × 10 −3 .

Diamond samples
Table 1 shows the various unpolished CVD diamond samples measured in the MSDR.Films were grown using MP-CVD with thicknesses of less than 0.2 mm and square areas larger than 10 × 10 mm 2 to fully cover the 7 mm diameter dielectrics.The films were grown on Si using a standard nanodiamond seeding process [25,26], followed by exposure to a microwave CH 4 /H 2 plasma at 5.5 kW at pressures > 140 mbar in gas flows > 300 sccm in a Carat Systems CTS6U using the small sample holder described in [27][28][29][30].The samples were then laser diced using an Oxford Lasers A-Series Laser Micromachining System equipped with a pulsed 1064 nm Neodymium-doped yttrium orthovanadate (Nd:YVO4) solid state laser, frequency doubled to 532 nm (Innolas NANIO 521-10-V).The nominal power output was 11.4 W at 40 kHz, with a pulse width of <30 ns and a pulse-to-pulse stability of < 1% focused to a spot size of ∼ 3 μm.The Si was then wet etched using a mixture of hydrofluoric acid, nitric acid and acetic acid [31] to produce free-standing unpolished diamond films.
In the first set, films were grown with a CH 4 /H 2 concentration of 3 and 5%.The deposition duration was adjusted to accommodate variations in growth rate (24 and 18 h for 3% and 5%, respectively).The increased CH 4 /H 2 concentration was used in an attempt to introduce more NDC impurities, and thus lower quality films [32][33][34].In the second set, 0.2% O 2 /H 2 was introduced to the gas phase for a fixed CH 4 /H 2 concentration of 4%.O 2 is known to reduce the formation of NDC impurities but also reduce the growth rate [33].To compensate for the increased etching, the growth was conservatively extended to 72 h.Finally for the third set, a film grown at 3% CH 4 /H 2 was vacuum annealed in a furnace at 800 • C at cumulative increments of 2, 7 and 15 h, to introduce very high concentrations of NDC impurities.With the exception of sample 3A, samples were successfully diced to areas greater than 10 × 10 mm.3A was damaged on silicon release and resulted in a smaller sample which still covers the 7 mm active DR diameter.
Qualitative measurements of non-diamond carbon (NDC) impurities were achieved with Raman spectroscopy using a Horiba LabRAM HR Evolution, equipped with 3 excitation lasers (  = 473, 532 and 660 nm) and a 50× objective.All spectra are obtained from the seeded side of the PCD film or the smaller grain side, as opposed to the growth or larger grain side in order to obtain sensitive characterisation of grain boundary impurities.Scanning electron microscopy (SEM) images were obtained using a Thermo Scientific Phenom at an acceleration voltage of 5 kV.

Diamond recipe variation
Fig. 6a and b shows magnified MSDR VNA traces of the TE 011 and TE 013 modes, respectively, for the diamond plates grown with different recipes.All samples shift the unperturbed response to lower frequencies and reduce the Q factor, the overall magnitude of which also varies depending upon the dielectric properties and volume of the sample.For both TE 011 and TE 013 , there are small differences in the complex frequency shift owing to the varying thicknesses.The calculated complex permittivity in Fig. 6c to f show small differences in dielectric constant and almost no measurable difference in loss between all of the samples grown at varying CH 4 concentrations with no O 2 in the gas phase.However, for samples grown with O 2 in the gas phase, a considerable damping of the Q factor is observed at both 8.3 GHz and 16.1 GHz.It is clearly shown that PCD grown using MP-CVD with O 2 in the gas phase significantly increases the microwave absorption.
Fig. 7a to c shows the Raman spectra of the diamond films grown with different CH 4 /H 2 concentrations in addition to the samples with O 2 in the gas phase.The results for all wavelengths show a sharp peak at ∼1332 cm −1 , associated with the first order sp 3 bonded carbon peak, a characteristic signature of diamond.Fig. 7d and e show the Lorentzian peak position and full-width at half maximum (FWHM), respectively, which in general show that the sp 3 carbon peak is shifted to towards higher wavenumbers, implying that the intrinsic film stress tends towards compression [35].This is better observed at   = 473 nm, however is less conclusive for   = 532 nm and   = 660 nm which show a randomly varying and overall lower peak position at ∼1332 cm −1 .This is likely due to the fact that higher wavelength lasers are far more sensitive to resonance and scattering caused by sp 2 carbon and NDC impurities owing to the greater cross-section compared to sp 3 carbon [36].Excitation wavelengths towards UV are therefore better suited for examining the diamond crystals themselves [37][38][39][40].Additionally, a significant feature in the   = 660 nm spectra is the broad band at 1580 to 1640 cm −1 .For carbonaceous samples, a band at 1580 cm −1 is typically designated as the bond stretching mode in sp 2 carbon or the 'G-band'.In this work, however, the band is closer towards 1620 cm −1 and is designated the D ′ -band which in the absence of a 1350 cm −1 disordered D-band typically refers to clusters of C=C bonded chains for sp 3 rich and diamond like carbon materials [41].This band is thus associated with significant concentrations of NDC impurities.
For the 3% sample, the NDC Band is much lower in intensity than the sp 3 peak, implying fairly low NDC impurities.As the CH 4 concentration is increased to 5%, a considerable increase in NDC is found such that the intensity is much higher than the sp 3 peak.Fig. 7f shows the peak intensity ratio of the NDC/sp 3 contributions, clearly demonstrating the significant increase in NDC in 5A compared to the others.This is fairly well-known for diamond recipes with increased CH 4 concentration [32][33][34].The recipe with O 2 in the gas phase ( ≈ 116 μm) appears to significantly reduce the NDC incorporation on the seeded side.The FWHM is generally a useful indicator of crystallite quality [42], which is much broader with the samples with O 2 at 2.2 to 2.6 cm −1 as opposed to ∼1.2 to 1.8 cm −1 without.This suggests that although there is a lower NDC incorporation at the growth side, the polycrystalline structure consists of more sporadic grain sizes and therefore a higher density of grain boundaries.
Fig. 8 shows the multi-wavelength PL spectra.At all wavelength excitations, a broad PL background is measured which is typically found in PCD.Minimal evidence is found for the neutral nitrogen vacancy complex NV 0 (∼575 cm −1 ) implying low nitrogen impurities [39].This background appears to increase with higher CH 4 concentration as is shown for sample 5A.Additionally, a prominent feature is the peak associated with SiV centres (∼738 nm) which becomes easier to identify with longer wavelengths.This is likely caused by plasma etching of the Si growth substrate and incorporation of these impurities into the diamond before the film coalesces.This is noticed for sample 3A and 5A, where in the case of the latter, this response dominates the spectra over the Raman line.For 4AO, the PL background is also similar to 3A, however, it is shown that the SiV peak is significantly reduced which suggests that O 2 in the gas phase suppresses the incorporation of Si.

Diamond annealing
Fig. 9a and b shows the traces for the 3A sample incrementally annealed at 800 • C. It is clear that vacuum annealing for durations less than 7 h does not result in a significant change in microwave absorption.This suggest only a small fraction of the diamond crystals are being converted to NDC.Fig. 9c and d shows the calculated dielectric constant only marginally changes at 8.3 GHz and 16.1 GHz as is shown by the small shifts in frequency.Fig. 9e and f shows that at 15 h, however, the Q factor is noticeably lower, translating to an increased dielectric loss tangent from 0.01 and immeasurable to 0.06 and 0.04, at 8.3 GHz and 16.1 GHz, respectively.Note that even for a diamond sample with a significantly darker colour, as shown in Table 1, the dielectric loss is still lower than the samples grown with O 2 .
Fig. 10a to c shows the Raman spectra of 3A after each increment of vacuum annealing.At a laser excitation of   = 473 and 532 nm, a similar spectra is obtained for all increments.Fig. 10d shows that for   = 473 nm, the sp 3 diamond peak clearly reduces from 1333.6 cm −1 to 1332 cm −1 .However for   = 532 and   = 660 nm, the position randomly shifts around 1332 cm −1 .While the former implies a relaxation of internal compressive stress in the film with annealing, higher wavelengths suggest random fluctuations in stress, again demonstrating the sensitivity of using UV lasers for stress measurements in the diamond crystals [38].Fig. 10e there is minimal difference in FWHM as the film is annealed, implying no significant change in the crystallinity of the film during the annealing process besides a reduction in stress.Fig. 10f shows that as with the previous diamond set, the   = 660 nm wavelength shows the NDC Band is clearly intensifying compared to the sp 3 peak when annealed, therefore implying that NDC impurities increase significantly at the seed side with incremental annealing time.Aside from this, the film at 15 h is also noticeably darker.
Fig. 11 shows the PL spectra of 3A at the start and end of cumulative vacuum annealing for 15 h.At all wavelength excitations, the same broad PL background is measured with the SiV band (∼738 nm).After annealing, this SiV band becomes far more significant, likely owing to the reduction in the Raman line due to conversion of sp 3 into NDC as opposed to an increase in SiV centres.Besides this feature, there is minimal difference between the before and after spectra.

SEM
Fig. 12 shows SEM images of the growth side of the PCD films used in this study.All images clearly show a coalesced film with large crystals and random grain morphologies.Samples 3B, 3A-15 and 5A both show similar grain structures, with sporadic surface impurities on both 3B and 5A.The grains in 5A are larger than 3B due to the increased film thickness.3A-15 shows patches of rougher regions which is likely NDC carbon that is formed during the annealing process.The contrast from the brighter spots is likely charging caused by diamond that is not converted to NDC (as shown in the inset).4AO shows the largest crystals owing to the thickness of the film, with some evidence of (111) triangular crystal growth.Interestingly, 4AO also shows the cleanest growth side of all of the films, despite being the most microwave lossy.

Discussion
This study suggests the controversial and less widely reported result that CVD diamond growth recipes with O 2 in the gas phase, while known for producing colourless and high 'quality' diamond, can also result in a significantly high microwave tan   .The cause of this loss is also less likely to be related to high concentrations of NDC impurities at the seed interface.The difference in the NDC band is significant between 3 and 5% CH 4 /H 2 , and yet there is little to no difference in the microwave complex permittivity.Only when large concentrations of NDC and sp 2 carbon are present in PCD films does the microwave tan   increase.Several studies on diamond particles corroborate this finding of increased absorption with increasing NDC and sp 2 carbon impurities [20,22,23,43].However, it is particularly well-known that O 2 suppresses the formation of large concentrations of NDC impurities in H 2 [33,44,45], making this less likely to be the culprit for a large microwave tan   .Thus, this discussion focuses on other ways O 2 grown samples could introduce a microwave absorbing effect.
Firstly, the dominant dielectric polarisation mechanisms in any material are those from electronic, ionic, dipole and interfacial polarisation.For diamond in the microwave frequency range, ionic and dipole polarisation can be discounted, leaving electronic polarisation (displacement of bound electrons around carbon atoms) and interfacial polarisation (free electrons which can migrate over percolating and short conduction pathways until they are met by a high energy barrier).Since electronic polarisation is very fast, this only contributes to  ′  and the relaxation loss mechanics do not contribute to  ′′  at gigahertz frequencies.In the case of PCD, the diamond grains act as the insulating barriers and grain boundaries or conducting impurities act as the transport pathways.Oxygen introduced during PCD growth must therefore introduce either conducting impurities or more grain boundaries in PCD.The incorporation of electrically conducting impurities, however, seems implausible.The reduction of the Si-V emission implies that it is not related to Si.Additionally, previous studies with O 2 in the gas phase also show reduced Si-V centres [46].N 2 is also not the likely reason owing to the low PL background in both Raman and PL data and the absence of a significant NV 0 peak.Although, there have been reports of high levels of O 2 in the gas phase, resulting in a higher N 2 impurity incorporation [42].Direct hydrogen incorporation into the bulk film at the grain boundaries is likely not the reason since previous studies using Ar/CH 4 gas mixtures have shown that hydrogen termination at the grain boundaries is useful for low dielectric loss micro-crystalline diamond [47].The surface conducting phenomenon of hydrogenated diamond is another potential reason [48], with surface conductivity being shown to be more stable with sub-surface incorporation from O 2 /H 2 plasma treatment [49].However, Tang et al. report that O 2 in the gas phase significantly reduces hydrogen incorporation, as identified by a reduction in the C-H stretching band in FTIR [50]; certainly a topic of controversy.Finally, the cause is not likely due to the direct oxygenation or incorporation of O 2 into the PCD during growth since several experimental studies demonstrate that increased surface oxygenation of diamond significantly increases the sheet resistance [51].DFT studies of oxygen-doped diamond also suggest it to be thermodynamically stable but with mid-gap impurity states that would not be measurable at room temperature [52].Based on this literature, the origin of this increased microwave loss in O 2 grown PCD films is likely not due to O 2 incorporation, nor is it related to large concentrations of NDC, N 2 , Si and H 2 .Hence an impurity based origin for the microwave loss remains nuanced.
The data presented here certainly points towards a grain boundary transport mechanism since the macroscopic crystalline quality is certainly worse, as inferred by the broad FWHM in the O 2 grown samples, despite the larger thickness.Previous work by Liu et al. show that films with a greater concentration of structural defects produced a larger Raman FWHM in addition to an increased microwave tan   [53].Additionally, this may not necessarily result in any measurable D or G Band and highlights the importance of Raman sensitivity.Thus the broadening of the FWHM implies a higher concentration of grain boundaries whereby surface states, dangling bonds and very localised sp 2 bonding that are not detectable by Raman pertains to a contributor to electrical transport on un-terminated surfaces of diamond [54,55].In PCD, Fiegl et al. have demonstrated that the frequency dependent electrical conductivity has been shown to be due to a single hopping transport mechanism due to the considerably high concentration of grain boundaries [56].Thus, this work therefore points towards a grain boundary hopping transport mechanism that is not related to H or O termination.
Assuming the thermal conductivity remains sufficiently high in these oxygen grown PCD samples, this potentially opens avenues to another route to high thermal conductivity microwave attenuator films.High loss tangent microwave absorbers can be achieved with boron doping (concentration of > 10 20 cm −3 ) [23,57,58] although, the caveat of using boron is that it severely contaminates the growth chamber.
Using oxygen based PCD recipes is a potentially more attractive solution to tuning the microwave properties of a diamond substrate.Additionally, in the utilisation of diamond substrates for increasing the quality factor of high kinetic inductance superconducting microwave diamond devices [59,60], this system is a valuable tool for screening diamond substrates before boron doped diamond is deposited.

Conclusion
This work presents an X-band microwave dielectric measurement system for PCD plates and demonstrates differences in diamonds grown with various recipes.Practically, the presented MSDR is an incredibly al. while Parshin et al. have shown a cylindrical cavity resonator system

Fig. 1 .
Fig. 1.Schematic of non-depolarisation field requirements for MSDR, with arrows showing E-field vectors for the cylindrical TE 011 and TM 010 configurations.

Fig. 2 .
Fig. 2. Theoretical frequency design requirements for the TE 011 mode where  and  denote the cylindrical radius and length, respectively and  r,c is the dielectric constant of the cylinder.The darker region denotes the X-band frequency range (8 to 12 GHz) and the point 'DR' denotes the chosen design.

Fig. 3 .
Fig. 3. FEM normalised E-field distributions of a cylindrical resonator ( = 3.5 mm and  = 4 mm).All outer extremities are modelled as PEC boundaries.Models show (a) air cavity  r,c = 1 and dielectric resonator  r,c = 37 at  0 = 64.3 and 10.6 GHz, respectively (b) a split dielectric with a 1 mm air gap at  0 ≈ 11.7 GHz (c) a split dielectric housed in a PTFE support at  0 ≈ 8.4 GHz and (d) a split dielectric in PTFE with hull housing including coupling antennas and sample slot  0 ≈ 8.3 GHz.

Fig. 5 .
Fig.5.Experimental and FEM wideband S 21 transmission spectra.Mode 0, 1 and 2 denote the TE 011 , TE 012 and TE 013 modes, respectively.FEM shows spectra for a sample gap of 0.9 mm.

Fig. 6 .
Fig. 6.MSDR measurements of diamond samples grown with different recipes.(a) and (b) show  21 traces of the TE 011 and TE 013 modes, respectively with FEM E-field shown in the inset.'E' denotes unperturbed, '3', '4' and '5' denote the CH 4 /H 2 percentage while 'O' denotes a 0.4% O 2 /H 2 ratio. scales are fixed to a 200 MHz span and  scales to 60 dB.(c) and (d) shows the dielectric constant and (e) and (f) loss tangent at 8.3 and 16.1 GHz, respectively, calibrated to a quartz standard denoted '*'.

Fig. 7 .
Fig. 7. Raman spectra (  = 473, 532 and 660 nm) of diamond plates.(a), (b) and (c) shows diamond plates grown with different recipes (CH 4 /H 2 at 3%, 5% and CH 4 /H 2 at 4% and O 2 /H 2 at 0.2%) at different wavelengths.All spectra are normalised to the maximum with a constant background removed and insets showing a magnified view of the diamond peak at ∼1332 cm −1 .(b) and (c) show the Lorentzian fitted sp 3 peak position and FWHM, respectively and (d) shows the peak intensity ratio of the NDC band to the sp 3 peak.

Fig. 9 .
Fig. 9. MSDR measurements of the vacuum annealed 3A diamond sample.(a) and (b) show  21 traces of the TE 011 and TE 013 modes, respectively with FEM E-field shown in the inset.'E' denotes the empty response, '0 Hr', '2 Hr','7 Hr' and '15 Hr' denote the annealing duration at 800 • C. All  scales are fixed at 200 MHz and  scales to a 60 dB range.(c) and (d) show the calculated dielectric constant and (e) and (f) loss tangent, respectively.

Fig. 10 .
Fig. 10.Raman spectra (  = 473, 532 and 660 nm) of the annealed diamond plate.(a), (b) and (c) show spectra of 3A grown at 3% CH 4 /H 2 that has been subsequently annealed at 800 • C for 2, 7 and 15 h at different wavelengths.All spectra are normalised to the maximum with a constant background removed and insets showing a magnified view of the diamond peak at ∼ 1332 cm −1 .(b) and (c) show the Lorentzian fitted sp 3 peak position and FWHM, respectively.
J.A.Cuenca et al.

Fig. 11 .
Fig. 11.PL spectra of vacuum annealed diamond plates: (bottom) initial film and (top) annealed film.All spectra are normalised to the Raman line 'R'.

Fig. 12 .
Fig. 12. SEM images of PCD diamond plates used in this study.Inset shows a magnified image of the annealed diamond plate, revealing clear contrasts in the smooth diamond region and rough NDC regions.

Table 1
Summary of unpolished PCD samples used in this study.3A-15 shows 3A after 15 h of vacuum annealing at 800 • C. 3A, 3B, 5A and 5B have been diced to 11 × 11 mm with some damage on 3A while 4AO and 4BO are diced to 10 × 10 mm.