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 high-pressure/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 n-type 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 sp2 fraction in the deposited material.[5,18] Another less significant but non-negligible consequence of adding large amounts of N2 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 and CNH species. On the computational front, Larsson and co-workers[24,25] have explored how preadsorbed NH (x = 1, 2) species might affect gas–surface reactions involving CH 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 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 C2 radicals, and triplet N2 molecules) in MW-activated CH4/N2/H2 plasmas operating at pressures (≈150 Torr) and powers (≈1.5 kW) relevant to contemporary MWPACVD processes. The work builds on complementary diagnoses of N2/H2 and NH3/H2 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 N2 additions on the growth rates and morphologies of diamond films formed by CVD using MW-activated CH4/H2 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 lists the species and transitions probed in the present study.

Table 1

Probe Transitions Used for Monitoring H*, NH, CH, C2, CN, and N2* Species

species	CRDS	OES	[spectroscopic constants]; (A-coefficients)
H*	n = 3←n = 2	n = 3→n = 2	[[31]]; ([31])
NH	A3Π←X3Σ–	A→X	[[32]]; ([33, 34])
CH	A2Δ←X2Π	A→X	[[35]]; ([36])
	B2Σ–←X2Π		[[37]]; ([38])
C2	d3Πg←a3Πu	d→a	[[39]]; ([36])
CN	B2Σ+←X2Σ+	B→X	[[40]]; ([41])
N2*		C3Πu→B3Πg	[[42]]; ([43])

CRDS was used to determine column densities of electronically excited H(n = 2) atoms, NH(X), CH(X), and C2(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 B2Σ– ← X2Π transition rather than the more traditional A–X system. All of these species, plus electronically excited (triplet) N2 molecules, were also monitored by OES, using one of two similar optical set-ups.[29,45] H2, CH4, and N2 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(N2) = 3 standard cm3 per minute (sccm), F(CH4) = 20 sccm and F(H2) = 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 Tsub ≈ 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 N2. The experimentally established plasma chemistry informs simulations extended to lower N/C ratios later in the manuscript.

Experimental Results

Figure a shows a CRD spectrum measured over the wavenumber range 25732–25823 cm–1 at z = 8 mm for a CH4/N2/H2 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 b 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 CH4/O2/N2 and CH4/NO/O2/N2 flames that exploited this same spectral region.[48]Figure c 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 C2(d–a) spectra,[44] we regard as diagnostic of the gas temperature (Tgas ≈ 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 a and again on an expanded scale in Figure d.

Figure 1

Part of the CN(B–X) and CH(B–X) Δv = 0 systems (a) as measured by CRDS at z = 8 mm in a CH4/N2/H2 plasma operating under base conditions along with (b) a PGOPHER simulation that assumes Trot = 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 Trot and, by inference, Tgas, in the case of the CN(B–X) lines. The CH(B–X) features, in contrast, depend only weakly on temperature.

Absolute column densities {M(v = 0)} (where M = C2, CH, CN, or NH) can be derived from such spectra usingwhere L is the length of the cavity (here, 92 cm), gl and gu 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 (ν̅, in cm–1), and pline 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 ) if the radical is localized in a region of reasonably constant Tgas. Degeneracies, Einstein A-coefficients, and favorable lines for probing C2, CH (via the A–X transition), NH radicals, and H(n = 2) atoms by CRDS have been detailed in previous publications.[29,36,44] The corresponding quantities used for the CN(B–X) transition are gl = gu = 2 and A = 1.48 × 107 s–1 (ref (41)) and, for the CH(B–X) transition, gl = 4, gu = 2 and A = 2.80 × 106 s–1 (ref (38)). The present analyses assume pline = (6.27 ± 0.45) × 10–3 for the P1(18.5) line of the CN(B–X) (0,0) band at 25750.70 cm–1 and pline = (6.56 ± 0.16) × 10–3 for the R1(13.5) line of the CH(B–X) (0,0) band at 25736.53 cm–1, where the uncertainty in the effective Tgas along the column determines the quoted uncertainties in pline on the basis that Tgas = 2900 ± 300 K. 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 c,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 C2(a), 1.36 for CH, 1.58 for CN, and 1.28 for NH, all calculated assuming Tvib = Tgas = 2900 K.

The more obvious differences between optical emission spectra from MW-activated CH4/N2/H2 and CH4/H2 plasmas are in the near-UV region, where the former shows features attributable to some or all of CN*, N2*, or NH*, depending on the relative N and C fractions. The H*, C2*, and CH* emissions, in contrast, show no obvious changes upon addition of small F(N2) to a CH4/H2 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 a, which compares spectra of MW-activated gas mixtures comprising 3 sccm N2 and, respectively, 0, 3, and 10 sccm CH4 along with 500 sccm of H2, all operating at base input power and pressure. As Figure b shows, increasing F(CH4) leads to a strong initial increase in CN* emission and a progressive decrease in the NH* emission, while the N2* emission intensity is relatively insensitive to changing F(CH4).

Figure 2

(a) Optical emission spectra, measured at z = 7 mm, of MW activated gas mixtures comprising 3 sccm N2 and, respectively, (i) 0, (ii) 3, and (iii) 10 sccm CH4 along with 500 sccm of H2, operating at base input power and pressure. (b) Plot illustrating the variation in relative CN*, N2*, and NH* emission intensities with increasing F(CH4), with the maximum intensity of each emission normalized to unity.

Figure a shows z-profiles of the C2(d–a), H(n = 4 → n = 2), and CH(A–X) emission intensities from a CH4/N2/H2 plasma operating under base conditions measured using the earlier optical setup.[45]Figure b shows profiles for the N2(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 a match those reported previously for the same species in a MW-activated CH4/H2 gas mixture operating under very similar conditions in this same reactor.[45] As in the N2/H2 plasma,[29] the N2* 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 CH4/N2/H2 plasma than in a CH4-free N2/H2 plasma. The CN* emission profile maximizes at slightly larger z and is similar in shape to the CH* emission.

Figure 3

z-profiles of (a) the C2(d–a), H(n = 4 → n = 2) and CH(A–X) emission intensities and (b) the N2(C–B), NH(A–X), and CN(B–X) emissions from a CH4/N2/H2 plasma operating under base conditions measured using the two complementary optical set-ups summarized in the text.

From here on, we recognize that the C2*, 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 N2 and focus on the possible diagnostic value of the NH*, N2*, and CN* emissions and their variations with process conditions. Figure a, 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 N2* emission intensity (measured at z = 7 mm), similar to that observed in a pure N2/H2 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*/N2* and CN*/N2* intensity ratio plots shown in Figure b, wherein N2 (by virtue of its comparative unreactivity) is essentially acting as an actinometer. As discussed alongside the C/N/H plasma modeling (section , 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.

Figure 4

(a) NH*, N2*, and CN* emission intensities measured at z = 7 mm (CH4/N2/H2 20/3/500 sccm plasma) as a function of applied MW power under otherwise base conditions. The emission intensities of each species are normalized to the maximal value measured at any P. The P-dependence of the NH*/N2* and CN*/N2* intensity ratios are shown in panel b.

Absorption (CRDS) measurements return absolute column densities and thus provide a more direct measure of the effects of changes in process condition. Figure 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 c,d, and of {CH(v = 0)} measured using CH(A–X) lines, as previously,[44] with an assumption in all cases that Trot = 2900 ± 300 K. We recognize that this is likely to be an overestimate of Tgas at the lowest z value (2 mm) for which we report data, but using NH as an example, even if the effective Tgas is as low as 2200 K, the {NH(v″ = 0)} value plotted in Figure 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 CH4/N2/H2 flow rates, p = 150 Torr, and P = 1.5 kW. As Figure will show, {NH(v = 0)} declines greatly with increasing F(CH4); the z-profile for {NH(v = 0)} shown in Figure was thus measured with a CH4-lean, N2-rich, 2/15/500 sccm input mixture. As Figure also shows, the {CH(v = 0)} values obtained from analysis of the B–X lines shown in Figure d 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 same reactor under nominally identical process conditions in 2008.[44] Compared with {CN(v = 0)} and {CH(v = 0)}, {NH(v = 0)} peaks lower, at z ≈ 4–5 mm, and declines gently with increasing z. Relative to the CH4-free N2/H2 plasma,[29] the absolute magnitude of {NH(v = 0)} measured at z ≈ 4–5 mm is similar (although F(N2) is 2.5 times greater in the present experiments), and the decline to higher z is steeper, mimicking the spatial distribution of NH* emission shown in Figure b.

Figure 5

Profiles of {NH(v = 0)}, {CN(v = 0)}, and {CH(v = 0)} as a function of z, obtained by CRDS probing of CH4/N2/H2 plasmas operating with respective flow rates of 2/15/500 sccm (for NH) and 20/3/500 sccm (for CN and CH) and base values of total pressure and applied power. Note the good agreement in the {CH(v = 0)} values determined when monitoring via the two different electronic transitions. The solid curves through these data show the z-dependent column densities of these three species returned by the modeling described in section . Note that the calculated {CN(v = 0)} values have been increased by a factor of 3.5 prior to display.

Figure 6

Solid points show the measured variations in (a) {CH(v = 0)}, {CN(v = 0)}, and {NH(v = 0)} following addition of CH4 to pre-existing N2/H2 plasmas (3/500 sccm when probing CH and CN, 15/500 when monitoring NH) and (b){CH(v = 0)} and {CN(v = 0)} upon adding N2 to a pre-existing CH4/H2 (20/500 sccm) plasma. All measurements were made at z = 8 mm, and all plasmas were operating at base power and pressure. The corresponding quantities returned by the model calculations described in section are indicated by open symbols. As in Figure , the calculated {CN(v = 0)} values have been increased by a factor of 3.5 prior to display.

Figure a illustrates the contrasting dependencies of these three species (measured at z = 8 mm) upon introducing progressively greater F(CH4) to a pre-existing N2/H2 plasma operating at base power and pressure. Again, the {CH(v = 0)} and {CN(v = 0)} data were both recorded using F(N2) = 3 sccm, whereas to increase signal levels, the {NH(v = 0)} data were recorded at F(N2) = 15 sccm. {CH(v = 0)} is seen to exhibit the same X0(CH4)0.5 dependence as found previously in the case of (N2-free) CH4/H2 plasmas, where X0(CH4) is the CH4 input mole fraction.[44,49] {CN(v = 0)} shows a similar initial rise upon adding CH4, but plateaus at F(CH4) ≈ 2.5 sccm under the prevailing plasma conditions, while {NH(v = 0)} declines as X0(CH4)−0.5. The corresponding trends for {CH(v = 0)} and {CN(v = 0)} upon adding N2 to a pre-existing F(CH4)/F(H2) = 20/500 sccm plasma operating at base power and pressure are shown in Figure b. The former shows a modest (≈33%) increase as F(N2) is increased to ≈1.5 sccm, while {CN(v = 0)} scales almost proportionally with 0 ≤ F(N2) ≤ 7 sccm.

Figure shows the measured (at z = 8 mm) variations in {CH(v = 0)}, {NH(v = 0)}, and {CN(v = 0)} as a function of applied MW power. Again, practical considerations dictated that the {CH(v = 0)} and {CN(v = 0)} data were both recorded for base conditions with F(CH4)/F(N2)/F(H2) = 20/3/500 sccm while the {NH(v = 0)} data were obtained using modified flow rates of 2/15/500 sccm. {CH(v = 0)} is seen to increase near-linearly with P over the range 0.75–1.85 kW, as observed previously when using (nominally) N2-free C/H plasmas.[44] {NH(v = 0)} shows a similar P-dependence to {CH(v = 0)} in this CH4/N2/H2 plasma and to {NH(v = 0)} measured in the CH4-free N2/H2 plasma.[29] Comparing the absolute magnitudes of {NH(v = 0)} measured in the CH4/N2/H2 and N2/H2 plasmas at any given P, however, we again see that the {NH(v = 0)} values measured in the CH4/N2/H2 plasma at z = 8 mm (Figure ) are only ≈40% those measured in the N2/H2 plasma, even though F(N2) was 2.5 times higher and F(CH4) was only 2 sccm. {CN(v = 0)} shows the steepest P-dependence, increasing more than 10-fold over the measured range.

Figure 7

Solid points show measured variations in {CH(v = 0)}, {NH(v = 0)}, and {CN(v = 0)} with increasing MW power for plasmas formed using CH4/N2/H2 flow rates of 20/3/500 sccm (for CH and CN) and 2/15/500 sccm (for NH). All measurements were made at z = 8 mm. The corresponding quantities returned by the model calculations described in section are indicated by open symbols. As in Figure , the calculated {CN(v = 0)} values have been increased by a factor of 3.5 prior to display.

{CN(v = 0)} also shows greater sensitivity to total pressure than {CH(v = 0)}. Figure depicts data for two very different N/C input ratio ranges. As Figure a shows, {CN(v = 0)} and {CH(v = 0)} (monitored via the B–X transition and color coded accordingly), measured under base conditions at z = 8 mm, both scale with p across the range 75–200 Torr. {CN(v = 0)} is a tenth of {CH(v = 0)} at 75 Torr but has a steeper rate of increase with p and approaches one-fifth of {CH(v = 0)} at 200 Torr. Figure b 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 with F(CH4) = 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(N2), equivalent to 0.1 sccm or 200 ppm, introduced as 10 sccm of a 1% N2 in H2 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.

Figure 8

Measured variations in {CH(v = 0)} and {CN(v = 0)} as a function of total gas pressure measured (a) under base conditions, over the range 75–200 Torr, and (b) at P = 1.8 kW with F(CH4) = 20 sccm and an effective F(N2) = 0.1 sccm (in a total flow rate of 500 sccm) over the range 120 ≤ p ≤ 300 Torr. All measurements were made at z = 8 mm. The corresponding quantities returned by the model calculations described in section are shown by open symbols in panel a. As in Figure , the calculated {CN(v = 0)} values have been increased by a factor of 3.5 prior to display.

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, H2, CH (x = 0–4), C2H (y = 0–6), C3H (x = 0–2), C4H (x = 0–2), NH (x = 0–3), N2, and HCN (x = 0–2),[49−52] and kinetic data for C/N coupling, H-shifting, and thermal decomposition reactions involving the additional species H2CNH, H3CNH, and H3CNH2.[53] Also considered were the reaction kinetics of electrons in different C/N/H mixtures,[29,49,54,55] for electron–ion recombination reactions, and ion interconversion reactions involving H2+, H3+, C2H2+, C2H3+, N2H+, NH4+, and HCNH+.[56] The most important of the N2 dissociation reactions and C/N coupling reactions are listed in Table , 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, CH2CNH, and CH3CN) 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 Ftotal = 500 sccm, i.e., F(H2) = 477 sccm rather than the 500 sccm used in most of the experiments.

Table 2

Most Important N2 Dissociation and C/N Coupling Reactions Included in the Present Study with T-Dependent Rate Coefficients k (cm3 mol–1 s–1)a

	rate coefficient k = ATb exp(−E/RT)
reaction	A	b	E	ref
N2(A3) + H ⇌ NH + N	1.2 × 1012	0	3850	(29)
CH3 + N ⇌ H2CN + H	6.10 × 1014	–0.31	290	(50)
CH3 + N ⇌ HCN + H2	3.70 × 1012	0.15	–90	(50)
CH3 + NH ⇌ H2CNH + H	4.00 × 1013	0	0	(52)
CH + N2 ⇌ HCN + N	3.12 × 109	0.88	20130	(50)
C + N2 ⇌ CN + N	6.30 × 1013	0	46020	(50)
CN + H2 ⇌ HCN + H	2.95 × 105	2.45	2240	(50)
H + H2CN ⇌ HCN + H2	7.80 × 1013	0	0	(51)

Units: cal, cm, s, R = 1.9873 cal (mol K)−1. N2(A3) represents the metastable A3Σu+ state (the lowest-energy triplet state) of N2, and the gas temperature T is quoted in K.

Plasma-Chemical Conversions in C/N/H Plasmas. Modeling the Effects of Adding CH4 to a N/H Plasma

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 H2, (ii) there is rapid redistribution within the CH and C2H groups as a result of fast H-shifting reactions, and (iii) there exist three characteristic regions within the reactor volume, distinguished by the prevailing CH interconversion reactions.[44,49] A key result of our analyses of MW-activated N/H plasmas[29] was that the dominant N2 decomposition mechanism in an N2/H2 plasma involves formation of various N2* 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 A3Σ+u triplet state, henceforth abbreviated as N2(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 , 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 is only mildly endothermic (ΔrH < 0.2 eV), with a calculated maximal rate R4 ≈ 1.6 × 1014 cm–3 s–1 in the hot plasma center under the present base conditions. As such, it is of comparable importance to reaction 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 , rather than reaction , is calculated to make the greater contribution to N atom production for p ≥ 150 Torr and input methane fractions ≥4%. R4 drops sharply with decreasing p (e.g., maximal R4 ≈ 3 × 1013 cm–3 s–1 at p = 75 Torr) due to the fall of both [N2] and [CH], while the maximal rates of reaction 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 [N2(A3)] as a result of its reduced quenching by H and H2. Reaction ,is more strongly endothermic (ΔrH ≈ 2 eV) and its calculated rate is correspondingly lower than (namely, around a quarter) that of reaction under base conditions in the hot plasma region.

Reactions and 5 contribute also to HCN (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 HCNH (y = 0–2 for z = 0, and y = 2 for z = 1) group. The observed decrease in {NH(v = 0)} upon CH4 addition (recall Figure b) is one indicator of a family of reactions between NH and CH (x = 0–3) radicals that, taken together, are an important source of HCNH species. Of this set, reactions –8 involving CH3 radicals predominate under the present conditions:

Other members of the family, for example, CH2 + N ⇌ HCN + H and CH + NH3 ⇌ H2CNH + H, make lesser contributions. The NH and HCNH species are processed further, by thermal decomposition and through their participation in fast H-shifting reactions, in favor of NH3 and HCN (which is the most stable CN-containing species in the present environment). That said, N2 remains the dominant N-containing species, as in the MW-activated N2/H2 and NH3/H2 mixtures.[29] For the base C/N/H gas mixture, the present calculations suggest that N2 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 NH3 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 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 radicals in the hot plasma region, the above-mentioned 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 [C2] 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 Trot values returned by the corresponding CRDS measurements (Figure ) and the z-profiles shown in Figures and 5.

Figure 9

Two-dimensional (r, z) plots showing the predicted total number densities of CN and NH radicals in a 4%CH4/0.6%N2/H2 plasma, total flow rate F = 500 sccm, P = 1.5 kW, and p = 150 Torr. The model assumes cylindrical symmetry, a substrate diameter of 3 cm, and a reactor radius, r = 6 cm, and height, h = 6.2 cm.

The predicted (r, z) distributions of [N2], [N], and [NH3] are each similar to the corresponding distributions in an N2/H2 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 , for which the production and loss terms tend to be in local balance, the HCN distribution is determined by the balance between the production reactions outlined above and the outflow of HCN from the reactor.

We now consider the spatial distribution and the absolute values of the CN concentration in detail. The [CN] spatial distribution is determined by the product of [HCN] and the [H]/[H2] ratio as a result of the fast equilibration reaction

The forward reaction is exothermic (ΔrH ≈ −1.3 eV), and the excess energy is preferentially partitioned into HCN product vibration, particularly the C–H stretch mode (ν3).[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 × 1018 cm–3 s–1. These rates are higher than the vibrational–translational (V–T) relaxation rate of HCN(v > 0) molecules through collision with H2, C2H2 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 –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 Tvib(HCN, ν3) = Tgas. However, given the rapidity of reaction relative to likely relaxation processes, we cannot exclude the possibility that Tvib(HCN, v3) ≫ Tgas. 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(v3 > 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 –7 show, the experimental and model {CN(v = 0)} values are in excellent accord if we take b ≈ 3.5.

A square-root dependence, {CH(v = 0)} ∼ F(CH4)0.5, reminiscent of that shown in Figure a, was observed and explained previously for C/H plasmas.[49] {CN(v = 0)} in the present C/N/H plasmas shows a similar F(CH4)0.5 dependence for F(CH4) < 0.5 × F(N2) but saturates for F(CH4) ≈ F(N2), whereas {NH(v = 0)} varies as F(CH4)−0.5 while N2 is in excess. As Figure a shows, the present 2-D modeling reproduces all of these trends and dependences well. The saturation in {CN(v = 0)} with increasing F(CH4), and thus increasing [CH] (x = 0–3), reflects the concomitant reduction in [NH] (x = 0–2) due to reactions –8 and the saturation of HCNH sources.

The dominant ions in the plasma also change upon CH4 addition. The most abundant ions in the base N/H plasma considered in paper I are NH4+ and N2H+,[29] whereas the present calculations identify the most abundant ions in the base C/N/H plasma as C2H2+ and C2H3+, as in a C/H plasma, but supplemented by HCNH+ and NH4+. Other more complex HCN+ ions are not included in the reaction scheme as we assume them to be decomposed effectively in the hot plasma region.

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 (Vpl ∼ P, with Vpl ≈ 70 cm3 under base conditions, giving a spatially averaged power density, Q ≈ 21.5 W cm–3) while maintaining a broadly constant Te ≈ 1.25 eV at the plasma center. The 2-D modeling shows the maximum gas temperature, Tmax, increasing by ≈4% (from 2770 to 2890 K) as P is increased from 750 to 1500 W. As Figure 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, Vpl, while maintaining ne broadly constant and with a minor increase in the electron temperature: Te 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 a. As with the N/H plasma,[29] the z-dependent {NH(v = 0)} profile (shown in Figure 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 , 7, and 8). The p-dependence can be understood by recognizing that [CN] is determined by the equilibrium : [CN] = [H] × ([HCN]/[H2]) × k–9/k+9. [H2] and [HCN] are both stable species with concentrations that scale as [H2] ∼ p and [HCN] ∼ p1.5. The latter trend reflects the enhanced decomposition of N2 with increasing p via reactions –5, followed by reactions –9. [H] scales with [H2]2, given that the main H atom production route isThis simple analysis predicts that [CN] will show a p2.5 dependence, as should {CN(v = 0)} if we ignore the small p-dependence of the plasma radius, Rpl.

The equilibrium was also analyzed at different applied microwave powers P. At a constant pressure p = 150 Torr, modeling returns [HCN] ∼ P0.5 and [H] ∼ P. [H2] is essentially independent of P, and thus we predict the functional behavior [CN] ∼ P1.5. Recognizing the plasma expansion with increasing power (Rpl ∼ P0.5), we have {CN} ∼ P2, which is a little less steep than the experimentally observed dependence of {CN(v = 0)} ∼ P2.5 (Figure ).

Effects of Varying F(N2) and Implications for N-Doping of Diamond

The observed linear dependence of {CN(v = 0)} and {NH(v = 0)} on F(N2) (Figure ) is simply a consequence of their main sources, reactions –8. As discussed above in the context of adding CH4 to a N/H plasma, introducing N2 into a C/H plasma can both change the dominant ions and introduce additional subsidiary, but relatively complex and reactive, HCN+ ions. The observed jump in {CH(v = 0)} at low F(N2) (also seen in Figure ) provides indirect evidence for the appearance of such HCN+ species. Introducing X0(N2) < 0.1% to a 4% CH4/H2 mixture cannot have a significant effect on the neutral C/H chemistry or the CH species concentrations but, by replacing some of the dominant CH+ ions by more complex HCN+ 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 H3+ in a pure H2 plasma to a mixture of C2H2+ and C2H3+ ions upon introducing CH4.[44,49]

As noted in the Introduction, longstanding unresolved aspects of diamond CVD from C/N/H plasmas include the nature of the 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 N2 to the process gas.[5−7,9−15] The current study directly addresses the first of these questions. Table presents calculated species number densities just above the substrate center (r = 0, z = 0.5 mm) for four different N2 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 other value of p (75 Torr) with the base, 0.6% N2/4% CH4/H2 mixture. Two other C/N/H gas mixtures are also considered for which the input N mole fraction (0.6% and 3% N2, respectively) exceeds that of C (0.4% CH4), again with the balance being H2 and at base conditions of P and p. The values reported in Table are the raw model outputs, apart from the case of CN, where the values have been increased by the empirical factor b ≈ 3.5. Of the directly incorporable N-containing species included in the model, N, NH, NH2, and CN, atomic nitrogen is the most abundant close to the diamond surface under base P and p, and the near-surface N atom number densities, [N]ns, returned by the modeling are typically an order of magnitude higher than [CN]ns. However, [CN]ns increases more rapidly than [N]ns upon increasing P or p, so that the predicted [N]ns/[CN]ns ratio shows a ≈5-fold decrease upon doubling p from 75 to 150 Torr or P from 1.5 to 3 kW. This trend suggests that gas–surface reactions involving CN may become an increasingly important route to incorporating N within diamond grown at high P and p.

Table 3

Calculated Gas Temperatures, Tgas, [N]ns/([CN]ns × 3.5), and [N]ns/[CH3]ns Concentration Ratios, Rinc(N)/Rinc(CH3) and (Rinc(N)/Rinc(CH3))/(X0(N2)/X0(CH4)) 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

X0(N2) (%)	0.0001	0.002	0.01	0.6	0.6	0.6	0.6	0.6	3
X0(CH4) (%)	4	4	4	4	4	4	4	0.4	0.4
p (Torr)	150	150	150	150	150	150	75	150	150
P (kW)	1.5	1.5	1.5	1.5	0.75	3.0	1.5	1.5	1.5
Tgas (K)	1402	1403	1404	1399	1399	1453	1334	1376	1363
[N]ns/([CN]ns × 3.5)	8.16	8.30	8.05	6.75	11.9	1.23	32.0	14.8	9.57
[N]ns/[CH3]ns	4.28 × 10–8	8.78 × 10–7	4.42 × 10–6	2.32 × 10–4	1.54 × 10–4	1.08 × 10–3	3.94 × 10–4	1.34 × 10–3	4.58 × 10–3
([N]ns/[CH3]ns)/(X0(N2)/X0(CH4))	1.71 × 10–3	1.76 × 10–3	1.77 × 10–3	1.55 × 10–3	1.03 × 10–3	7.20 × 10–3	2.63 × 10–3	8.93 × 10–4	6.11 × 10–4
Rinc(N)/Rinc(CH3)	1.09 × 10–6	2.24 × 10–5	1.12 × 10–4	5.94 × 10–3	4.64 × 10–3	2.39 × 10–2	9.67 × 10–3	3.34 × 10–2	1.19 × 10–1
(Rinc(N)/Rinc(CH3))/(X0(N2)/X0(CH4))	4.37 × 10–2	4.47 × 10–2	4.48 × 10–2	3.96 × 10–2	3.10 × 10–2	1.59 × 10–1	6.44 × 10–2	2.23 × 10–2	1.59 × 10–2
H	7.49 × 1015	7.58 × 1015	7.60 × 1015	7.25 × 1015	4.19 × 1015	1.67 × 1016	2.35 × 1015	7.89 × 1015	6.62 × 1015
CH4	4.15 × 1014	4.10 × 1014	4.12 × 1014	4.45 × 1014	6.93 × 1014	1.55 × 1014	3.57 × 1014	1.54 × 1014	2.21 × 1014
CH3	5.25 × 1013	5.23 × 1013	5.29 × 1013	5.48 × 1013	5.36 × 1013	3.99 × 1013	3.19 × 1013	1.87 × 1013	2.33 × 1013
3CH2	2.67 × 1011	2.70 × 1011	2.74 × 1011	2.69 × 1011	1.57 × 1011	4.32 × 1011	9.50 × 1010	1.03 × 1011	1.05 × 1011
1CH2	7.35 × 109	7.45 × 109	7.58 × 109	7.36 × 109	4.18 × 109	1.50 × 1010	2.13 × 109	2.52 × 109	2.51 × 109
CH	8.96 × 109	9.16 × 109	9.31 × 109	8.73 × 109	2.96 × 109	3.21 × 1010	2.01 × 109	3.71 × 109	3.24 × 109
C	2.88 × 1010	2.97 × 1010	3.00 × 1010	2.65 × 1010	4.77 × 109	2.35 × 1011	3.65 × 109	2.92 × 1010	1.92 × 1010
C2(a)	4.93 × 108	5.00 × 108	5.04 × 108	4.45 × 108	5.00 × 108	1.16 × 109	8.22 × 108	5.78 × 108	4.06 × 108
C2(X)	1.50 × 107	1.55 × 107	1.61 × 107	1.45 × 107	5.67 × 106	1.38 × 108	5.27 × 106	3.47 × 106	2.77 × 106
C2H	4.49 × 1010	4.59 × 1010	4.76 × 1010	4.59 × 1010	2.68 × 1010	1.79 × 1011	9.98 × 109	5.73 × 109	6.33 × 109
C2H2	8.10 × 1015	8.11 × 1015	8.31 × 1015	8.73 × 1015	8.81 × 1015	9.60 × 1015	4.91 × 1015	1.22 × 1015	1.77 × 1015
C2H3	9.72 × 1012	9.74 × 1012	9.94 × 1012	1.04 × 1013	7.47 × 1012	1.25 × 1013	2.84 × 1012	1.68 × 1012	2.34 × 1012
C2H4	2.34 × 1014	2.32 × 1014	2.36 × 1014	2.58 × 1014	2.92 × 1014	1.33 × 1014	7.59 × 1013	4.05 × 1013	6.60 × 1013
C2H5	8.76 × 1010	8.64 × 1010	8.74 × 1010	9.70 × 1010	1.07 × 1011	4.15 × 1010	2.19 × 1010	1.66 × 1010	2.79 × 1010
C2H6	1.61 × 1011	1.58 × 1011	1.59 × 1011	1.84 × 1011	2.94 × 1011	3.57 × 1010	1.19 × 1011	2.72 × 1010	5.29 × 1010
C3	3.35 × 1012	3.44 × 1012	3.54 × 1012	3.44 × 1012	6.28 × 1011	2.50 × 1013	7.88 × 1011	4.39 × 1011	4.94 × 1011
C3H	6.12 × 1010	6.23 × 1010	6.42 × 1010	6.42 × 1010	1.92 × 1010	2.62 × 1011	1.53 × 1010	6.49 × 109	8.15 × 109
C3H2	7.07 × 1013	7.11 × 1013	7.29 × 1013	7.66 × 1013	3.97 × 1013	1.28 × 1014	2.99 × 1013	7.31 × 1012	1.09 × 1013
C4	1.69 × 105	1.75 × 105	1.85 × 105	1.75 × 105	6.47 × 104	2.00 × 106	6.68 × 104	1.02 × 104	1.02 × 104
C4H	7.35 × 107	7.52 × 107	7.92 × 107	7.86 × 107	5.28 × 107	3.38 × 108	5.17 × 107	4.37 × 106	5.21 × 106
C4H2	6.23 × 1012	6.26 × 1012	6.56 × 1012	7.19 × 1012	6.83 × 1012	9.94 × 1012	4.28 × 1012	1.73 × 1011	3.37 × 1011
H(n = 2)	2.49 × 106	2.55 × 106	2.56 × 106	2.18 × 106	1.56 × 106	7.58 × 106	1.64 × 106	3.58 × 106	2.17 × 106
H(n = 3)	1.37 × 105	1.40 × 105	1.41 × 105	1.19 × 105	8.61 × 104	4.22 × 105	1.16 × 105	2.13 × 105	1.25 × 105
H2	1.02 × 1018	1.02 × 1018	1.02 × 1018	1.02 × 1018	1.02 × 1018	9.67 × 1017	5.34 × 1017	1.04 × 1018	1.03 × 1018
N2	4.90 × 1011	9.82 × 1012	5.01 × 1013	3.18 × 1015	3.25 × 1015	3.38 × 1015	1.73 × 1015	2.94 × 1015	2.16 × 1016
N2(A3)	5.74 × 105	1.16 × 107	5.89 × 107	3.44 × 109	4.77 × 109	3.67 × 109	6.57 × 109	5.04 × 109	3.05 × 1010
NH3	7.21 × 107	1.44 × 109	7.25 × 109	4.37 × 1011	1.32 × 1012	1.40 × 1011	1.26 × 1012	6.53 × 1011	3.98 × 1012
NH2	8.73 × 105	1.76 × 107	8.94 × 107	5.13 × 109	9.38 × 109	3.78 × 109	8.70 × 109	7.68 × 109	3.97 × 1010
NH	4.95 × 105	1.00 × 107	5.11 × 107	2.86 × 109	3.44 × 109	3.96 × 109	3.92 × 109	4.61 × 109	2.20 × 1010
N	2.24 × 106	4.59 × 107	2.33 × 108	1.27 × 1010	8.26 × 109	4.30 × 1010	1.26 × 1010	2.51 × 1010	1.07 × 1011
CN(×3.5)	2.75 × 105	5.54 × 106	2.90 × 107	1.88 × 109	6.94 × 108	3.48 × 1010	3.93 × 108	1.70 × 109	1.12 × 1010
HCN	4.11 × 109	8.13 × 1010	4.21 × 1011	2.95 × 1013	1.83 × 1013	1.77 × 1014	1.16 × 1013	2.80 × 1013	2.36 × 1014
H2CN	9.58 × 104	1.90 × 106	9.80 × 106	6.76 × 108	3.10 × 108	4.65 × 109	1.93 × 108	7.38 × 108	5.92 × 109
H2CNH	1.86 × 105	3.71 × 106	1.89 × 107	1.18 × 109	2.28 × 109	6.31 × 108	3.24 × 109	7.13 × 108	5.43 × 109
H3CNH	1.33 × 102	2.65 × 103	1.35 × 104	8.26 × 105	1.29 × 106	3.60 × 105	1.08 × 106	5.18 × 105	3.59 × 106
H3CNH2	1.14 × 104	2.25 × 105	1.14 × 106	7.28 × 107	1.95 × 108	1.37 × 107	1.39 × 108	4.14 × 107	3.34 × 108
e	8.99 × 1010	9.07 × 1010	9.17 × 1010	8.75 × 1010	9.83 × 1010	1.21 × 1011	8.47 × 1010	6.34 × 1010	5.58 × 1010
C2H2+	6.51 × 1010	6.56 × 1010	6.68 × 1010	5.90 × 1010	6.62 × 1010	6.62 × 1010	5.56 × 1010	1.50 × 1010	8.39 × 109
C2H3+	2.48 × 1010	2.49 × 1010	2.44 × 1010	9.35 × 109	1.20 × 1010	2.72 × 109	1.62 × 1010	1.32 × 1010	5.84 × 108
H3+	1.82 × 107	1.84 × 107	1.77 × 107	7.90 × 106	9.96 × 106	5.93 × 106	1.57 × 107	9.71 × 107	1.34 × 107
H2+	2.52 × 104	2.56 × 104	2.55 × 104	2.20 × 104	2.85 × 104	3.42 × 104	7.60 × 104	4.20 × 104	2.68 × 104
N2H+	6.35 × 101	1.29 × 103	6.32 × 103	1.80 × 105	2.31 × 105	1.38 × 105	4.03 × 105	2.08 × 106	2.15 × 106
NH4+	6.90 × 105	1.38 × 107	6.97 × 107	3.58 × 109	9.11 × 109	1.95 × 109	6.02 × 109	5.41 × 109	1.81 × 1010
HCNH+	4.07 × 106	8.07 × 107	4.09 × 108	1.56 × 1010	1.10 × 1010	4.96 × 1010	6.89 × 109	2.97 × 1010	2.88 × 1010

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 = 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 CH3 radicals. The present modeling assumes a net sticking probability for CH3 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 (CH2, CH, C, NH2, 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 Cs*), and that the calculated steady-state fraction X(Cs*) of such sites at base growth conditions is X(Cs*) ∼ 0.1.[60] These sticking probabilities are thus ≈25 times greater than that derived for CH3 radicals under the present base conditions, but since [CH2]ns, [CH]ns and [C]ns are all much lower than [CH3]ns (Table ), even with their much higher assumed net incorporation probabilities ∼X(Cs*), 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 γCN. 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 γN, the ratios of the net incorporation rates (Rinc(N)/Rinc(CH3) ∼ (γinc(N) × [N]ns)/(γinc(CH3) × [CH3]ns)) reported in Table should definitely also be taken as upper limits.

The only difference in the input parameters for the data listed in the first four columns of Table is the value of X0(N2). The predicted value of [N]ns/[CH3]ns increases from ≈4 × 10–8 for X0(N2) = 0.0001% (1 ppm) to 9 × 10–7 for X0(N2) = 0.002%, 4.4 × 10–6 when X0(N2) = 0.01%, and 2.3 × 10–4 for X0(N2) = 0.6%. These are each much smaller than the respective X0(N2)/X0(CH4) ratios in the input source gas mixtures, but the ratio of these ratios, the “relative nitrogen activation fraction” ([N]ns/[CH3]ns)/(X0(N2)/X0(CH4)), is consistently (1.6 ± 0.1) × 10–3. The absolute value of the activation fraction will be process-dependent, but for small X0(N2) and an otherwise consistent set of process conditions, the [N]ns/[CH3]ns ratio varies essentially proportionally with input X0(N2). As Table 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 (Rinc(N)/Rinc(CH3))/(X0(N2)/X0(CH4)) (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 MW-activated C/N/H plasma operating at pressures and temperatures relevant to diamond CVD, by Yamada.[30] The earlier work treated the following conditions: F(CH4) = 25 sccm, F(N2) = 2.5 sccm, F(H2) = 500 sccm (i.e., X0(CH4) = 4.7% and X0(N2) = 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 Tmax ≈ 3000 K and the near-substrate gas temperature Tgas ≈ 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 are generally minor: [NH3]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 [NH3]ns can be traced to the role of reactions and 3 in providing a nonthermal route to activating and dissociating N2, which was not considered in the earlier modeling, while the lower [N]ns is likely due to our high assumed value of γN. 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, C2, CN, and NH), and triplet N2 molecule densities in MW-activated CH4/N2/H2 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 ≤ X0(N2)/X0(CH4) ≤ 7.5, than could be explored experimentally, as well as with a higher MW power of 3 kW.

Key findings include the following:

For base conditions of p = 150 Torr and P = 1.5 kW, strongly bound N2 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-containing species two or more orders of magnitude less abundant still.

Two reaction sequences enable N2 to participate in the plasma chemistry. Reaction , proposed as the dominant source of N atoms in the one previous modeling study of a MW-activated C/N/H plasma,[30] involves the reaction of N2 with CH radicals. Reactions and 3, identified in our recent studies of MW-activated N2/H2 plasmas,[29] involve electron impact excitation of N2 in the hot plasma region, energy pooling in the metastable N2(A3Σ+u) state, and subsequent reaction with H atoms. The former pathway is the more important route to forming N atoms at higher gas pressures, input powers, or CH4 input fractions.

Of the N-containing species that can be considered potentially reactive at the growing diamond surface, namely, N, NH, NH2, and CN, the near-surface gas-phase number density of atomic nitrogen under base conditions is higher than [NH]ns or [NH2]ns and typically an order of magnitude higher than [CN]ns.

Comparing the measured {CN(v = 0)} data with model predictions reveals an underestimation that hints at an unusual (for high pressures, p > 100 Torr) nonthermal vibrational population distribution in HCN molecules formed in the fast exothermic reaction and significantly enhanced rates for subsequent reactions involving these “hot” HCN molecules.

Changing the input N/C ratio in the process gas mixture under base conditions causes a proportional change in the [N]ns/[CH3]ns ratio but has little effect on the [N]ns/[NH]ns/[CN]ns ratios just above the growing surface. The [N]ns/[CH3]ns ratio is consistently much smaller than the X0(N2)/X0(CH4) ratio in the input gas mixture, reflecting the stability of N2 under these process conditions. Increasing p or P promotes N2 dissociation and so raises both the [N]ns/[CH3]ns and [CN]ns/[CH3]ns ratios for the same N input fraction.

Finally, we return briefly to consider the longstanding issue raised in the Introduction: how the presence of small amounts of nitrogen in the gas phase leads to an increase in diamond growth rate and influences the surface morphology. H atoms and CH3 radicals are generally accepted as the key species driving diamond CVD from MW-activated gas mixtures. As Table shows, increasing X0(N2) from 1 to 20 ppm has no perceptible effect on the [H]ns or [CH3]ns values. Even at X0(N2) = 100 ppm, [CH3]ns increases by little more than 1%. Clearly, the present analysis confirms that trace additions of N2 (a rather inert species) have very little impact on the C/H chemistry or on [H] or [CH3] close to the growing diamond surface. N atoms and NH and CN radicals will all be present in the near-surface volume, but for X0(N2) = 100 ppm, their number densities will be some 5–6 orders of magnitude smaller than [CH3]ns. Because of the small relative nitrogen activation fraction, this is some three orders less than the X0(N2)/X0(CH4) ratio, although this disparity in nitrogen activation versus methane may be partially compensated by the higher (assumed) incorporation efficiency of N atoms versus CH3 radicals at the growing diamond surface. Increasing p or P produces an obvious increase in [CN]ns relative to [NH]ns (x = 0–2), so we also recognize that different gas–surface chemistry could drive N incorporation under conditions of low and high gas activation. Energetically feasible reaction sequences providing for N, NH, or CN to be accommodated on a model diamond (100) surface have been identified, and are described in a companion paper,[61] but it is hard to imagine that such rare encounters could directly account for the observed rate enhancements or morphological changes. It is also widely accepted that these N-induced effects are just one factor in a multiparameter growth space, so that the result of adding N2 to the process mixture also depends on the substrate condition and its temperature during growth.[14] Hence, the present study tends to support prior suggestions that the key role of trace N incorporation is in locally chemically activating the diamond surface or otherwise enabling faster growth at high substrate temperature by somehow limiting strain[62] or nonepitaxial growth[14] in the resulting material that would typically result under such conditions. An additional effect of incorporated nitrogen could arise if the migration of an NH surface group along the diamond surface is significantly hindered relative to that of CH2. Such immobile NH groups could then serve as anchors for migrating CH2 groups (as does the step edge in regular step-flow growth), thus enhancing formation of difficult-to-etch chains of CH2 surface bridges. This decrease in the average migration length of CH2 groups before incorporation would reduce the rate at which they are etched and thus accelerate diamond growth.

All underlying experimental data is openly available under the DOI: .