Microwave Plasma-Activated Chemical Vapor Deposition of Nitrogen-Doped Diamond. II: CH4/N2/H2 Plasmas

We report a combined experimental and modeling study of microwave-activated dilute CH4/N2/H2 plasmas, as used for chemical vapor deposition (CVD) of diamond, under very similar conditions to previous studies of CH4/H2, CH4/H2/Ar, and N2/H2 gas mixtures. Using cavity ring-down spectroscopy, absolute column densities of CH(X, v = 0), CN(X, v = 0), and NH(X, v = 0) radicals in the hot plasma have been determined as functions of height, z, source gas mixing ratio, total gas pressure, p, and input power, P. Optical emission spectroscopy has been used to investigate, with respect to the same variables, the relative number densities of electronically excited species, namely, H atoms, CH, C2, CN, and NH radicals and triplet N2 molecules. The measurements have been reproduced and rationalized from first-principles by 2-D (r, z) coupled kinetic and transport modeling, and comparison between experiment and simulation has afforded a detailed understanding of C/N/H plasma-chemical reactivity and variations with process conditions and with location within the reactor. The experimentally validated simulations have been extended to much lower N2 input fractions and higher microwave powers than were probed experimentally, providing predictions for the gas-phase chemistry adjacent to the diamond surface and its variation across a wide range of conditions employed in practical diamond-growing CVD processes. The strongly bound N2 molecule is very resistant to dissociation at the input MW powers and pressures prevailing in typical diamond CVD reactors, but its chemical reactivity is boosted through energy pooling in its lowest-lying (metastable) triplet state and subsequent reactions with H atoms. For a CH4 input mole fraction of 4%, with N2 present at 1–6000 ppm, at pressure p = 150 Torr, and with applied microwave power P = 1.5 kW, the near-substrate gas-phase N atom concentration, [N]ns, scales linearly with the N2 input mole fraction and exceeds the concentrations [NH]ns, [NH2]ns, and [CN]ns of other reactive nitrogen-containing species by up to an order of magnitude. The ratio [N]ns/[CH3]ns scales proportionally with (but is 102–103 times smaller than) the ratio of the N2 to CH4 input mole fractions for the given values of p and P, but [N]ns/[CN]ns decreases (and thus the potential importance of CN in contributing to N-doped diamond growth increases) as p and P increase. Possible insights regarding the well-documented effects of trace N2 additions on the growth rates and morphologies of diamond films formed by CVD using MW-activated CH4/H2 gas mixtures are briefly considered.


INTRODUCTION
Nitrogen is a common impurity in both natural and highpressure/high-temperature (HPHT) synthetic diamond. In natural diamonds, nitrogen impurities are usually found aggregated in clusters (defined as type Ia diamond), whereas in synthetic HPHT diamonds, nitrogen is typically present at lower overall concentration and located in substitutional sites throughout the lattice (type Ib diamond). 1 Nitrogen is an ntype dopant in diamond, and thus nitrogen-doped diamond has attracted interest as a potential high-electron-mobility semiconductor. Nitrogen is a deep donor, 2 however, and the resulting material has not proved suitable for most electronic applications.
Given the abundance of nitrogen on Earth, it is very challenging to achieve nitrogen-free HPHT diamond growth. Producing such material by chemical vapor deposition (CVD) methods has long been seen as more practicable but still requires great care regarding source gas purity and the minimization of air leaks into the reactor. 3,4 Several previous studies have demonstrated that the presence of trace amounts of nitrogen significantly increases the rate of diamond growth in a microwave (MW) plasma-activated (PA) CVD process. 5−14 Small nitrogen additions have also been shown to affect the surface morphology, 5,6,14−16 and in particular to encourage the formation of {100}-rather than {111}-faceted surfaces: the former are typically less rough and hence attractive for mechanical applications. 17 Too much nitrogen in the source gas mixture, however, leads to smaller and less-well-oriented surface facets, and a higher sp 2 fraction in the deposited material. 5,18 Another less significant but non-negligible consequence of adding large amounts of N 2 is a reduction in the thermal conductivity of the process gas mixture, which can benefit power coupling efficiency by reducing diffusive transport of heat to the reactor walls. 19 How nitrogen reacts at the diamond surface and why its presence in the gas phase increases the growth rate and influences the surface morphology is still not fully understood. Various nitrogen-containing species have been proposed as participants in gas−surface reactions contributing to diamond growth. CN radicals have attracted attention based on observed correlations between CN(B → X) emission intensities from the hot plasma region and measured growth rates, 14,20−22 and CN adsorption on a diamond {111} surface has been suggested as a route to nucleating new layer growth. 23 Cao et al. 16 offered a more general view, recognizing possible contributions from a range of gas-phase NH x and CNH x species. On the computational front, Larsson and co-workers 24,25 have explored how preadsorbed NH x (x = 1, 2) species might affect gas−surface reactions involving CH x radicals (which are generally viewed as the dominant C precursor in diamond CVD 26 ), and ways in which previously incorporated near-surface substitutional N atoms can influence the energetics, and thus the rates, of the elementary reactions involved in CH x incorporation. 27,28 Here, we report spatially resolved absorption and emission measurements of several gas-phase species (H(n = 2, 3) atoms, NH, CH, CN and C 2 radicals, and triplet N 2 molecules) in MWactivated CH 4 /N 2 /H 2 plasmas operating at pressures (≈150 Torr) and powers (≈1.5 kW) relevant to contemporary MWPACVD processes. The work builds on complementary diagnoses of N 2 /H 2 and NH 3 /H 2 plasmas presented previously (henceforth paper I 29 ), and the experimental measurements are used to inform and tension companion 2-D modeling of the C/ N/H plasma chemistry. Similarities and differences between the present model outputs and those from the one previous 2-D simulation of MW activated C/N/H plasmas 30 are highlighted, and possible insights these data provide toward explaining documented effects of trace N 2 additions on the growth rates and morphologies of diamond films formed by CVD using MWactivated CH 4 /H 2 gas mixtures are briefly considered.

EXPERIMENTS
The MWPACVD reactor, the laser system, and the optical arrangements for the spatially resolved cavity ring down spectroscopy (CRDS) and optical emission spectroscopy (OES) measurements as a function of height (z) above the substrate surface are detailed in paper I 29 or in prior publications cited therein. Table 1 lists the species and transitions probed in the present study.
CRDS was used to determine column densities of electronically excited H(n = 2) atoms, NH(X), CH(X), and C 2 (a) radicals as functions of z, applied microwave power, P, total pressure, p, and gas mixing ratio, as described in previous publications. 29,36,44 The present work also relies on column density measurements of CN(X) radicals, as well as further measurements of CH(X) radicals using the B 2 Σ − ← X 2 Π transition rather than the more traditional A−X system. All of these species, plus electronically excited (triplet) N 2 molecules, were also monitored by OES, using one of two similar optical set-ups. 29,45 H 2 , CH 4 , and N 2 source gases were supplied via separate, calibrated mass flow controllers and mixed before entering through two diametrically opposed inlets located close below the top of the reactor, situated at an angle of ≈45°to the laser propagation axis. "Base" conditions for these experimental studies were defined as follows: p = 150 Torr, P = 1.5 kW, and input flow rates F(N 2 ) = 3 standard cm 3 per minute (sccm), F(CH 4 ) = 20 sccm and F(H 2 ) = 500 sccm, that is, an [N]/[C] ratio in the input gas mixture of 0.3. When varying one parameter, all others were maintained at their base values unless noted otherwise. The substrate temperature was monitored by two-color optical pyrometry, returning values T sub ≈ 1100 K. This source gas mixture represents a much higher N/C ratio than is used in the growth of high-quality CVD diamond but was chosen to allow more detailed study of the gas-phase chemistry of N 2 . The experimentally established plasma chemistry informs simulations extended to lower N/C ratios later in the manuscript. Figure 1a shows a CRD spectrum measured over the wavenumber range 25732−25823 cm −1 at z = 8 mm for a CH 4 /N 2 /H 2 plasma operating under base conditions. The spectrum is dominated by the P-branch band head of the CN(B− X) (0,0) transition, but as the accompanying PGOPHER 46 simulation in Figure 1b shows, also displays lines associated with the CH(B−X) (0,0) transition. For completeness, we note a previous CRDS study, in the context of diamond CVD, of CN radicals in an oxyacetylene flame with nitrogen addition, 47 and a study of CH 4 /O 2 /N 2 and CH 4 /NO/O 2 /N 2 flames that exploited this same spectral region. 48 Figure 1c shows an expanded view of a small region of the CRD spectrum centered around 25749 cm −1 . This is attractive from a diagnostic perspective because it is free from any contaminating CH(B−X) transitions and includes CN(B−X) (0,0) transitions originating from both high and low J″ levels. As such, it offers a convenient probe of the CN rotational temperature, which, given the operating pressure and prevailing collision frequency and as in our previous analyses of the C 2 (d−a) spectra, 44 we regard as diagnostic of the gas temperature (T gas ≈ 2900−3000 K) in the region containing the radicals of interest. The CH(B−X) features used for column density measurements are shown in Figure 1a and again on an expanded scale in Figure 1d.

EXPERIMENTAL RESULTS
Absolute column densities {M(v = 0)} (where M = C 2 , CH, CN, or NH) can be derived from such spectra using  [42]; (43) The Journal of Physical Chemistry A where L is the length of the cavity (here, 92 cm), g l and g u are the degeneracies of the lower and upper states involved in the respective transitions, A is the Einstein A-coefficient for the v′ = 0 to v″ = 0 transition, Δk is the measured change in ring-down rate (in s −1 ) at a given wavenumber (ν ̅ , in cm −1 ), and p line is the ratio of the integrated intensity of the spectral line under study to the total (0,0) band intensity, which can be calculated using PGOPHER and the relevant spectroscopic constants (Table 1) if the radical is localized in a region of reasonably constant T gas . Degeneracies, Einstein A-coefficients, and favorable lines for probing C 2 , CH (via the A−X transition), NH radicals, and H(n To reduce the influence of baseline variations and other interferences, the CRDS spectra were fitted with respect to the intensities of these lines within the groups of near-lying lines shown in Figure 1c,d, accounting for their known relative intensities and the temperature dependences thereof, rather than to the lines individually. To convert the experimental {M(v = 0)} values to total column densities (sums over all vibrational states) requires multiplication by the appropriate vibrational partition functions: namely, 1.83 for C 2 (a), 1.36 for CH, 1.58 for CN, and 1.28 for NH, all calculated assuming T vib = T gas = 2900 K. The more obvious differences between optical emission spectra from MW-activated CH 4 /N 2 /H 2 and CH 4 /H 2 plasmas are in the near-UV region, where the former shows features attributable to some or all of CN*, N 2 *, or NH*, depending on the relative N and C fractions. The H*, C 2 *, and CH* emissions, in contrast, show no obvious changes upon addition of small F(N 2 ) to a CH 4 /H 2 plasma. The dependence of the near-UV (324−360 nm) part of the optical emission spectrum on the C/N ratio is illustrated in Figure 2a, which compares spectra of MWactivated gas mixtures comprising 3 sccm N 2 and, respectively, 0, 3, and 10 sccm CH 4 along with 500 sccm of H 2 , all operating at base input power and pressure. As Figure 2b shows, increasing a PGOPHER simulation that assumes T rot = 3000 K and serves to illustrate lines associated with the different carriers. Expanded views of the spectral regions used for monitoring CN(X) and CH(X) column densities are shown in panels c and d, respectively, along with accompanying PGOPHER simulations that illustrate the spectral sensitivity to T rot and, by inference, T gas , in the case of the CN(B−X) lines. The CH(B−X) features, in contrast, depend only weakly on temperature. The Journal of Physical Chemistry A Article F(CH 4 ) leads to a strong initial increase in CN* emission and a progressive decrease in the NH* emission, while the N 2 * emission intensity is relatively insensitive to changing F(CH 4 ). Figure 3a shows z-profiles of the C 2 (d−a), H(n = 4 → n = 2), and CH(A−X) emission intensities from a CH 4 /N 2 /H 2 plasma operating under base conditions measured using the earlier optical setup. 45 Figure 3b shows profiles for the N 2 (C−B), NH(A−X), and CN(B−X) emissions, obtained using the more sensitive optical telescope arrangement described in paper I 29 because of the relatively weak near-UV emission. The spatial resolutions obtained with these two set-ups are estimated as ∼0.5 and ∼3 mm, respectively. Each profile is normalized such that the peak emission intensity is unity. The distributions shown in Figure 3a match those reported previously for the same species in a MW-activated CH 4 /H 2 gas mixture operating under very similar conditions in this same reactor. 45 As in the N 2 /H 2 plasma, 29 the N 2 * emission profile peaks at low z, lower than that of the H* emission. The NH* profile also peaks at low z, below the emission maxima of any of the C-containing species, and is less spatially extensive in the CH 4 /N 2 /H 2 plasma than in a CH 4 -free N 2 /H 2 plasma. The CN* emission profile maximizes at slightly larger z and is similar in shape to the CH* emission.
From here on, we recognize that the C 2 *, CH*, and H* emissions (and, as shown below, the absolute column densities and spatial profiles of these species as determined by CRDS) are changed little by small additions of N 2 and focus on the possible diagnostic value of the NH*, N 2 *, and CN* emissions and their variations with process conditions. Figure 4a, for example, shows the variation in the respective emission intensities with increasing MW power. Trebling P from 0.6 to 1.8 kW results in an approximately 2-fold increase in the N 2 * emission intensity (measured at z = 7 mm), similar to that observed in a pure N 2 /H 2 plasma operating in the same reactor and primarily attributable to an increase in plasma volume. 29 The NH* and CN* emission intensities show much steeper P-dependences, increasing by factors of ≈4 and ≈15, respectively. These differences are emphasized by the NH*/N 2 * and CN*/N 2 * intensity ratio plots shown in Figure 4b, wherein N 2 (by virtue of its comparative unreactivity) is essentially acting as an actinometer. As discussed alongside the C/N/H plasma modeling (section 4, below), the greater increases in the NH* and, particularly, CN* emission intensities can be understood in terms of the small P-induced increase in the maximal gas temperature, since a concomitant increase in the H atom density in the hot plasma region accelerates the chemistry responsible for forming these species.
Absorption (CRDS) measurements return absolute column densities and thus provide a more direct measure of the effects of changes in process condition. Figure 5 shows z-dependent profiles of {NH(v = 0)} measured using the NH(A−X) lines detailed in paper I, 29 of {CN(v = 0)} and {CH(v = 0)} measured using the CN(B−X) and CH(B−X) lines shown in Figure 1c,d, and of {CH(v = 0)} measured using CH(A−X) lines, as previously, 44 with an assumption in all cases that T rot = 2900 ± 300 K. We recognize that this is likely to be an overestimate of T gas at the lowest z value (2 mm) for which we report data, but using NH as an example, even if the effective T gas is as low as 2200 K, the {NH(v″ = 0)} value plotted in Figure 5 would only need to be increased by a factor of 1.1 (i.e., ∼10%). The {CN(v = 0)} and {CH(v = 0)} data were both determined under base conditions of 20/3/500 sccm CH 4 /N 2 /H 2 flow rates, p = 150 Torr, and P = 1.5 kW. As Figure 6 will show, {NH(v = 0)} declines greatly with increasing F(CH 4 ); the z-profile for {NH(v = 0)} shown in Figure 5 was thus measured with a CH 4 -lean, N 2 -rich, 2/15/500 sccm input mixture. As Figure 5 also shows, the {CH(v = 0)} values obtained from analysis of the B−X lines shown in Figure  1d agree well with those derived using the same CH(A−X) lines as in our previous studies of C/H plasmas, though we note that both are slightly (≈10%) lower than had been measured in this  , and the decline to higher z is steeper, mimicking the spatial distribution of NH* emission shown in Figure 3b. Figure 6a illustrates the contrasting dependencies of these three species (measured at z = 8 mm) upon introducing progressively greater F(CH 4 ) to a pre-existing N 2 /H 2 plasma operating at base power and pressure. Again, the {CH(v = 0)} and {CN(v = 0)} data were both recorded using F(N 2 ) = 3 sccm, whereas to increase signal levels, the {NH(v = 0)} data were recorded at F(N 2 ) = 15 sccm. {CH(v = 0)} is seen to exhibit the same X 0 (CH 4 ) 0.5 dependence as found previously in the case of (N 2 -free) CH 4 /H 2 plasmas, where X 0 (CH 4 ) is the CH 4 input mole fraction. 44 29 Comparing the absolute magnitudes of {NH(v = 0)} measured in the CH 4 /N 2 /H 2 and N 2 /H 2 plasmas at any given P, however, we again see that the {NH(v = 0)} values measured in the CH 4 /N 2 /H 2 plasma at z = 8 mm (Figure 7) are only ≈40% those measured in the N 2 /H 2 plasma, even though F(N 2 ) was 2.5 times higher and F(CH 4 ) was only 2 sccm. {CN(v = 0)} shows the steepest P-dependence, increasing more than 10-fold over the measured range.
{CN(v = 0)} also shows greater sensitivity to total pressure than {CH(v = 0)}.  Figure 8b shows data recorded under rather different conditions, closer to those used in practical CVD diamond growth, and over a wider range of p. Again, the measurements were made at z = 8 mm and  The Journal of Physical Chemistry A Article with F(CH 4 ) = 20 sccm (in a total flow rate of 500 sccm). The incident MW power was higher (P = 1.8 kW), but the most significant difference was a much lower F(N 2 ), equivalent to 0.1 sccm or 200 ppm, introduced as 10 sccm of a 1% N 2 in H 2 mixture. Again, {CN(v = 0)} is very much smaller than {CH(v = 0)} (here monitored via the A−X transition) at low p (120 Torr), but {CN(v = 0)} increases much more steeply, such that at p = 300 Torr, the measured {CN(v = 0)}/{CH(v = 0)} ratio has increased to ≈0.1.
As in paper I, 29 all of the measured trends are now discussed and interpreted in light of companion modeling studies of the prevailing plasma chemistry and composition.

C/N/H PLASMA MODELING
The 2-D (r, z) model used in the present C/N/H plasma modeling draws on previously reported plasma-chemical mechanisms for the two-component N/H and C/H gas mixtures. 29, 49 To these are added a C/N/H chemical mechanism for neutral species, H, 49 56 The most important of the N 2 dissociation reactions and C/N coupling reactions are listed in Table 2, but the full base reaction mechanism involved 45 species and ≈350 direct and reverse reactions. The effects of adding a few further species (e.g., HCCN, NCCN, CH 2 CNH, and CH 3 CN) were probed, but none were found to have any serious consequence and thus were ultimately omitted. All of the important plasma-chemical conversions identified in the C/H and N/H plasma modeling studies still play significant roles in the C/N/H plasma, but since these have been elaborated previously, 29,49 we henceforth concentrate particularly on C/N coupling effects. "Base" conditions for the calculations were the same as in the experiments except that the modeling assumes   Important findings from our previous investigations of C/H plasmas include that (i) the absorbed MW power is expended mainly on gas heating, via rotational and vibrational excitation of H 2 , (ii) there is rapid redistribution within the CH x and C 2 H y groups as a result of fast H-shifting reactions, and (iii) there exist three characteristic regions within the reactor volume, distinguished by the prevailing C x H y interconversion reactions. 44,49 A key result of our analyses of MW-activated N/H plasmas 29 was that the dominant N 2 decomposition mechanism in an N 2 /H 2 plasma involves formation of various N 2 * states by electron impact excitation, the radiative or collisional relaxation of which results in an overpopulation (relative to local thermodynamic equilibrium) of the lowest, metastable A 3 Σ + u triplet state, henceforth abbreviated as N 2 (A3). That is, which can be followed by reaction with H atoms: In the case of C/N/H plasmas, this source is complemented by reaction 4, which was assumed to be the dominant source of N atoms in the one previous modeling study of a MW-activated C/ N/H plasma: 30 Reaction 4 is only mildly endothermic (Δ r H < 0.2 eV), with a calculated maximal rate R 4 ≈ 1.6 × 10 14 cm −3 s −1 in the hot plasma center under the present base conditions. As such, it is of comparable importance to reaction 3 as a source of N and NH species in the plasma core, and its impact extends further into the cooler regions. Integrating over the whole reactor volume, reaction 4, rather than reaction 3, is calculated to make the greater contribution to N atom production for p ≥ 150 Torr and input methane fractions ≥4%. R 4 drops sharply with decreasing p (e.g., maximal R 4 ≈ 3 × 10 13 cm −3 s −1 at p = 75 Torr) due to the fall of both [N 2 ] and [CH], while the maximal rates of reaction 3 only vary by ≈30% upon decreasing p from 150 to 75 Torr. This latter result can be explained by recognizing that the ≈3-fold decrease in [H] upon decreasing p from 150 to 75 Torr is compensated by a corresponding increase in [N 2 (A3)] as a result of its reduced quenching by H and H 2 . Reaction 5, is more strongly endothermic (Δ r H ≈ 2 eV) and its calculated rate is correspondingly lower than (namely, around a quarter) that of reaction 4 under base conditions in the hot plasma region. Reactions 4 and 5 contribute also to H x CN (x = 0, 1) production, but as in our previous modeling of C/N/H gas mixtures in a hot filament CVD reactor, 51 the present analysis reveals other, more important, sources within the family of reactions involving the H y CNH z (y = 0−2 for z = 0, and y = 2 for z = 1) group. The observed decrease in {NH(v = 0)} upon CH 4 addition (recall Figure 6b) is one indicator of a family of reactions between NH x and CH x (x = 0−3) radicals that, taken together, are an important source of H y CNH z species. Of this set, reactions 6−8 involving CH 3 Other members of the family, for example, CH 2 + N ⇌ HCN + H and CH + NH 3 ⇌ H 2 CNH + H, make lesser contributions. The NH x and H y CNH z species are processed further, by thermal decomposition and through their participation in fast H-shifting reactions, in favor of NH 3 and HCN (which is the most stable CN-containing species in the present environment). That said, N 2 remains the dominant N-containing species, as in the MWactivated N 2 /H 2 and NH 3 /H 2 mixtures. 29 For the base C/N/H gas mixture, the present calculations suggest that N 2 constitutes >99.75% of the total nitrogen content within the reactor and ≈99.5% of the nitrogen content even in the hot plasma region. HCN accounts for ≲0.25% of the nitrogen content in the entire reactor; the total NH 3 content is roughly 2 orders of magnitude further less; and the fractions of all other N-containing species included in the model are orders of magnitude lower still. Figure 9 shows the spatial distributions of the CN and NH radical number densities, [CN] and [NH], returned by the 2-D model for base conditions. The observed localization is consistent with the combined effects of primary production of CN and NH x radicals in the hot plasma region, the abovementioned species interconversions, and diffusional and thermodiffusional transfer of both radical and stable species. The calculated [CH](r, z) distribution is very similar to that of [CN], and thus not shown; the calculated forms of the [CH] and [C 2 ] distributions are also very similar to those reported in our earlier modeling of MW-activated C/H plasmas. 49 The predicted localization of these radical species within the hot plasma region is fully consistent with the T rot values returned by the corresponding CRDS measurements (Figure 1) and the zprofiles shown in Figures 3 and 5.
The predicted (r, z) distributions of [N 2 ], [N], and [NH 3 ] are each similar to the corresponding distributions in an N 2 /H 2 plasma 29 and so are not repeated here. The present calculations show HCN distributed throughout the whole reactor volume, despite its production being concentrated in the hot plasma region, with a mole fraction distribution that maximizes in the cold (near-wall) regions as a result of thermodiffusional transfer. In contrast to the radical species featured in Figure 9, for which the production and loss terms tend to be in local balance, the HCN distribution is determined by the balance between the  The forward reaction is exothermic (Δ r H ≈ −1.3 eV), and the excess energy is preferentially partitioned into HCN product vibration, particularly the C−H stretch mode (ν 3 ). 57 The rates of the forward (R +9 ) and reverse (R −9 ) reactions in the hot plasma region under base conditions are both calculated to be ≈2.5 × 10 18 cm −3 s −1 . These rates are higher than the vibrational− translational (V−T) relaxation rate of HCN(v > 0) molecules through collision with H 2 , C 2 H 2 or HCN, 58 and could be comparable with the (unknown) rate of V−T relaxation through collision with H atoms. The measured CN column densities shown in Figures 5−7 are all ≈3.5 times those simulated on the basis of vibrational−translational equilibrium: this implies, in particular, the assumption that the vibrational temperature T vib (HCN, ν 3 ) = T gas . However, given the rapidity of reaction 9 relative to likely relaxation processes, we cannot exclude the possibility that T vib (HCN, v 3 ) ≫ T gas . Thus, while the 3.5-fold discrepancy could be due to imperfections in the assumed reaction mechanisms and/or temperature-dependent rate coefficients, given the quantitative accuracy with which the density distributions of the other species are reproduced, it could also be explained in a more restricted and physically motivated sense. Assigning an enhanced rate constant for HCN(v 3 > 0) molecules in the endothermic reaction (−9) would have the required effect of increasing the steady-state CN concentration by some factor b. As Figures 5−7  The dominant ions in the plasma also change upon CH 4 addition. The most abundant ions in the base N/H plasma considered in paper I are NH 4 + and N 2 H + , 29 whereas the present calculations identify the most abundant ions in the base C/N/H plasma as C 2 H 2 + and C 2 H 3 + , as in a C/H plasma, but supplemented by HCNH + and NH 4 + . Other more complex H x C y N z + ions are not included in the reaction scheme as we assume them to be decomposed effectively in the hot plasma region.
4.2. Effects of Varying the Applied Microwave Power and the Total Pressure. The consequences of varying power and pressure on N/H and C/N/H plasmas are deduced to be very similar. As for the N/H plasma, 29 the observed variations with increasing P can be explained in terms of a progressive increase in the plasma volume (V pl ∼ P, with V pl ≈ 70 cm 3 under base conditions, giving a spatially averaged power density, Q ≈ 21.5 W cm −3 ) while maintaining a broadly constant T e ≈ 1.25 eV at the plasma center. The 2-D modeling shows the maximum gas temperature, T max , increasing by ≈4% (from 2770 to 2890 K) as P is increased from 750 to 1500 W. As Figure 7 shows, the predicted variations in {CH(v = 0)}, {CN(v = 0)}, and {NH(v = 0)} match the measured trends well.
Modeling also shows that decreasing p at constant P is accommodated by a modest (less than proportional to the pressure drop) increase in the plasma volume, V pl , while maintaining n e broadly constant and with a minor increase in the electron temperature: T e increases ≈10% upon decreasing p from 150 to 75 Torr. The 2-D model succeeds in capturing all of the observed p-dependent trends in the species column densities, as shown in Figure 8a. As with the N/H plasma, 29 the zdependent {NH(v = 0)} profile (shown in Figure 5 for the case of p = 150 Torr only) is shown by both experiment and modeling to become flatter at lower pressure.
The measured {CN(v = 0)} column densities and CN* emission intensities both increase more steeply with increasing P or p than do the corresponding {CH(v = 0)} and CH* emissions (recall Figures 4, 7, and 8 This simple analysis predicts that [CN] will show a p 2.5 dependence, as should {CN(v = 0)} if we ignore the small pdependence of the plasma radius, R pl . The equilibrium 9 was also analyzed at different applied microwave powers P.  (Figure 6) is simply a consequence of their main sources, reactions 3−8. As discussed above in the context of adding CH 4 to a N/H plasma, introducing N 2 into a C/H plasma can both change the dominant ions and introduce additional subsidiary, but relatively complex and reactive, H x C y N z + ions. The observed jump in {CH(v = 0)} at low F(N 2 ) (also seen in Figure 6) provides indirect evidence for the appearance of such H x C y N z + species. Introducing X 0 (N 2 ) < 0.1% to a 4% CH 4 /H 2 mixture cannot have a significant effect on the neutral C/H chemistry or the C x H y species concentrations but, by replacing some of the dominant C x H y + ions by more complex H x C y N z + ions having higher electron−ion recombination rates, could change the plasma volume, power density, or maximal gas temperature sufficiently to induce the observed jump in {CH(v = 0)}. We have previously observed and explained a more dramatic jump in {H(n = 2)} induced by a change in dominant ion from H 3 + in a pure H 2 plasma to a mixture of C 2 H 2 + and C 2 H 3 + ions upon introducing CH 4 . 44,49 As noted in the Introduction, longstanding unresolved aspects of diamond CVD from C/N/H plasmas include the nature of the The Journal of Physical Chemistry A Article gas-phase precursor(s) responsible for N-doping and the cause of the growth rate enhancement upon small (even down to the level of a few ppm) additions of N 2 to the process gas. 5−7,9−15 The current study directly addresses the first of these questions. Table   3 presents calculated species number densities just above the substrate center (r = 0, z = 0.5 mm) for four different N 2 input mole fractions (1, 20, 100, and 6000 ppm) under otherwise base conditions and for two other values of P (0.75 and 3 kW) and one  (CH 3 ) and (R inc (N)/R inc (CH 3 ))/(X 0 (N 2 )/X 0 (CH 4 )) Incorporation Rate Ratios, and Selected Species Concentrations (in cm −3 ) above the Substrate Center (at r = 0, z = 0.5 mm) from Which These Ratios Are Derived for a Range of C/N/H Gas Mixtures and Process Conditions The near-surface species concentrations returned by the plasma modeling are necessary but not sufficient information for estimating the relative contributions different species make to diamond growth. This determination is also sensitive to the relative sticking coefficients, γ, of the various species at a growing diamond surface. These quantities, and their variation with process conditions, are still not well characterized however. Prior molecular dynamics simulations of CH x (x = 0−3) encounters with diamond (100) and (111) surfaces at temperatures relevant to diamond CVD found that sticking is more probable if the incident species has more free electrons and fewer H atoms: 59 for example, C atoms were predicted to have an order of magnitude higher sticking probability than CH 3 radicals. The present modeling assumes a net sticking probability for CH 3 radicals that has been derived by comparing near-surface gas-phase model outputs with experimentally measured growth rates, 60 while the sticking coefficients for other small, potentially reactive radical species (CH 2 , CH, C, NH 2 , NH, N, and CN) were all set at 0.1. This latter value is based on the assumptions that these species each have unit incorporation probability at a non-H-terminated surface radical site (henceforth C s *), and that the calculated steady-state fraction X(C s *) of such sites at base growth conditions is X(C s *) ∼ 0.1. 60 These sticking probabilities are thus ≈25 times greater than that derived for CH 3 (Table 3), even with their much higher assumed net incorporation probabilities ∼X(C s *), these species are still predicted to make little contribution to the overall growth rate. Furthermore, the rates R +9 and R −9 are so high that [CN] ns is rather insensitive to the choice of γ CN . However, the situation with the remaining species, and especially N atoms, is less clear. Given the choice of what is essentially an upper-limit value of γ N , the ratios of the net incorporation rates (R inc (N)/ R inc (CH 3 ) ∼ (γ inc (N) × [N] ns )/(γ inc (CH 3 ) × [CH 3 ] ns )) reported in Table 3 should definitely also be taken as upper limits.
The absolute value of the activation fraction will be processdependent, but for small X 0 (N 2 ) and an otherwise consistent set of process conditions, the [N] ns /[CH 3 ] ns ratio varies essentially proportionally with input X 0 (N 2 ). As Table 3 shows, doubling P from 1.5 to 3 kW is predicted to result in a ≈5-fold increase in relative nitrogen activation, which may have a yet larger impact on the relative N/C incorporation efficiency given the decrease in [N] ns /[CN] ns that also accompanies such an increase in P. However, that the activation fraction is always ≪1 and the ratio of ratios (R inc (N)/R inc (CH 3 ))/(X 0 (N 2 )/X 0 (CH 4 )) (i.e., the normalized incorporation rate) is fairly constant across a broad range of nitrogen input fractions and consistently <1, should offer a useful guide when it comes to predicting N concentrations and N incorporation efficiencies in CVD diamond.
Finally, it is instructive to compare the present findings with the predictions of the one previous modeling study of a MWactivated C/N/H plasma operating at pressures and temperatures relevant to diamond CVD, by Yamada. 30 The earlier work treated the following conditions: F(CH 4 ) = 25 sccm, F(N 2 ) = 2.5 sccm, F(H 2 ) = 500 sccm (i.e., X 0 (CH 4 ) = 4.7% and X 0 (N 2 ) = 0.47%), p = 120 Torr, and P = 3 kW into a plasma volume seemingly about twice that of the present work. The calculated maximum gas temperature in the hot plasma core was T max ≈ 3000 K and the near-substrate gas temperature T gas ≈ 1500 K. These temperatures are a little higher than found from the present modeling, while the pressure is a little lower. Differences between the earlier data and that shown in the fourth column of Table 3 are generally minor: [NH 3 ] ns is here about 1 order of magnitude larger than in the earlier work, even after correcting for the difference in pressure, but the [NH] ns and [N] ns values agree between the two studies to within a factor of 2. Our higher [NH 3 ] ns can be traced to the role of reactions 2 and 3 in providing a nonthermal route to activating and dissociating N 2 , which was not considered in the earlier modeling, while the lower [N] ns is likely due to our high assumed value of γ N . Importantly, the relative nitrogen activation fraction (≈6.7 × 10 −3 ) found by Yamada 30 is not very different from ours, highlighting the predominant roles of thermal chemistry and transport in determining the near-substrate species concentrations.

CONCLUSIONS
Spatially resolved optical emission and line-of-sight absorption spectroscopy methods have been used to probe selected atomic (H), radical (CH, C 2 , CN, and NH), and triplet N 2 molecule densities in MW-activated CH 4 /N 2 /H 2 gas mixtures such as are used in diamond CVD, as functions of the source gas mole fractions, total pressure, and applied MW power. These data have been rationalized using complementary 2-D (r, z) coupled kinetic and transport modeling, which succeeds, mostly quantitatively, in reproducing all of the measured trends in species column densities and OES intensities. After calibration against experiment, the model was run over a wider range of N/C input ratios, 2.5 × 10 −5 ≤ X 0 (N 2 )/X 0 (CH 4 ) ≤ 7.5, than could be explored experimentally, as well as with a higher MW power of 3 kW.
Key findings include the following: (i) For base conditions of p = 150 Torr and P = 1.5 kW, strongly bound N 2 molecules constitute >99.75% of the total nitrogen content in the reactor, falling only to ≈99.5% even in the hot plasma core. Less than 0.25% of the supplied nitrogen becomes HCN, with all other N- The Journal of Physical Chemistry A Article