Microwave Plasma-Activated Chemical Vapor Deposition of Nitrogen-Doped Diamond. I. N2/H2 and NH3/H2 Plasmas.

: We report a combined experimental/modeling study of microwave activated dilute N 2 /H 2 and NH 3 /H 2 plasmas as a precursor to diagnosis of the CH 4 /N 2 /H 2 plasmas used for the chemical vapor deposition (CVD) of N-doped diamond. Absolute column densities of H( n = 2) atoms and NH(X 3 Σ − , v = 0) radicals have been determined by cavity ring down spectroscopy, as a function of height ( z ) above a molybdenum substrate and of the plasma process conditions, i.e., total gas pressure p , input power P , and the nitrogen/hydrogen atom ratio in the source gas. Optical emission spectroscopy has been used to investigate variations in the relative number densities of H( n = 3) atoms, NH(A 3 Π ) radicals, and N 2 (C 3 Π u ) molecules as functions of the same process conditions. These experimental data are comple-mented by 2-D ( r , z ) coupled kinetic and transport modeling for the same process conditions, which consider variations in both the overall chemistry and plasma parameters, including the electron ( T e ) and gas ( T ) temperatures, the electron density ( n e ), and the plasma power density ( Q ). Comparisons between experiment and theory allow re ﬁ nement of prior understanding of N/H plasma-chemical reactivity, and its variation with process conditions and with location within the CVD reactor, and serve to highlight the essential role of metastable N 2 (A 3 Σ +u ) molecules (formed by electron impact excitation) and their hitherto underappreciated reactivity with H atoms, in converting N 2 process gas into reactive NH x ( x = 0 − 3) radical species.


INTRODUCTION
One of the key classifiers of natural diamonds is their nitrogen impurity content. 1 Nitrogen is the dominant impurity in type I diamonds, where it is typically present at the ∼0.1 atom % level. These constitute ≈98% of all natural diamonds and are traditionally further subdivided according to the way in which the nitrogen impurities are distributed within the carbon lattice (e.g., as isolated atoms, or aggregated as larger clusters), but all exhibit characteristic absorption features in the infrared (IR) and ultraviolet (UV), and visible fluorescence under UV illumination. Type II diamonds contain much lower N impurity levels (too low to be revealed by IR absorption spectroscopy) and are much rarer in nature. Natural type IIa diamonds are both very scarce and particularly prized, as they are almost entirely devoid of impurities and, as a result, are essentially colorless and display the highest thermal conductivity.
In contrast, given minimal air leakage into the reaction chamber and sufficiently pure process gases, diamonds grown by chemical vapor deposition (CVD) can be produced with very low nitrogen content, and are thus normally type IIa material. For example, Tallaire et al. 2 reported single-crystal homoepitaxial growth of diamond with total defect concentrations <200 ppb using high-purity CH 4 /H 2 gas mixtures and a high-power-density microwave (MW) plasma process. These workers also showed that even trace (2−10 ppm) additions of N 2 to the CH 4 /H 2 process gas mixture caused a substantial (up to 2.5-fold) increase in growth rate, 2 reinforcing and extending earlier 3 and subsequent 4,5 studies that demonstrate growth rate enhancements at higher nitrogen atom input mole fraction, X 0 (N). Careful studies of CVD growth on synthetic (100) highpressure, high-temperature (HPHT) single-crystal diamond substrates by Achard et al. 6 served to illustrate not just the evolution in growth mechanism, from a unidimensional (step flow) to a bidimensional nucleation mode, upon increasing X 0 (N), but also the interdependence of diamond deposition rate, growth mechanism (hence morphology), and substrate temperature.
Here we report the first in a sequence of studies designed to provide an in-depth analysis and understanding of the roles of nitrogen in diamond CVD. The presence of nitrogen in MWactivated CH 4 /H 2 plasmas can be traced by optical emission spectroscopy (OES). Several previous studies have reported the variation in CN(B−X) emission intensity upon varying X 0 (N) in CH 4 /H 2 plasmas, 3,7,8 but quantifying the CN number density is much harder, and it remains to be established what measurements of relative CN emission intensities (normally from the plasma core) tell one about the densities of the various different N-containing species near the growing diamond surface.
This question will be addressed in a future publication (paper II), via spatially resolved absolute and relative density measurements of H(n = 2, 3) atoms, CH, NH, C 2 , and CN radicals, and metastable triplet N 2 molecules in MW-activated CH 4 /N 2 /H 2 gas mixtures, using a combination of absorption (cavity ring down) spectroscopy (CRDS) and OES. 9 These data will be discussed and interpreted in light of complementary two-dimensional (2-D (r, z), where r and z are, respectively, the radial distance and the vertical height from the center of the substrate surface) modeling 10 of the C/N/H plasma chemistry and composition as a function of process conditions, i.e., CH 4 and N 2 fractions, total pressure p, and applied MW power P. Such analysis returns absolute number density estimates for the more abundant N-containing radical species, such as NH x (x = 0−2) and CN radicals, in the immediate vicinity of a growing diamond surface. The results can then be used to inform models of elementary reaction sequences, whereby such species can add to, and migrate on, a diamond (100) surface, as modeled using a mixture of quantum and molecular mechanical (QM and QM/MM) methods. This gas−surface chemistry modeling work will form the basis of a future third paper in this series (paper III). 11 The present paper (paper I) reports spatially resolved absorption and/or emission measurements of H(n = 2, 3) atoms, NH radicals, and triplet N 2 molecules in MW-activated N 2 /H 2 and NH 3 /H 2 plasmas operating at pressures (∼150 Torr) and powers (∼1.5 kW) relevant to commercial MW plasma-activated (PA) CVD reactors. These results inform and tension companion 2-D modeling of the N/H plasma chemistry, and represent an essential precursor to the detailed analysis of MW-activated C/N/H plasmas reported in paper II. N 2 /H 2 plasmas have been studied previously, in low-pressure direct current (dc) 12 and MW 13 discharges, and at higher pressures in an expanding arc reactor, 14,15 but we are not aware of any quantitative investigations at the conditions of pressure, temperature, and electron density normally prevailing in MWPACVD reactors used for diamond growth.

EXPERIMENTAL METHODS
The MWPACVD reactor, the laser system, and the optical arrangements for the spatially resolved CRDS measurements as a function of height (z) above the substrate surface have been described elsewhere. 16 CRDS was used to determine absolute column densities of electronically excited H(n = 2) atoms (monitoring the n = 3 ← n = 2 Balmer-α transition) 17 and ground state NH(X 3 Σ − , v = 0) radicals (using selected lines within the A 3 Π−X 3 Σ − system, as in our previous study of hot filament-activated NH 3 -containing C/N/H gas mixtures). 18 The previously described optical setup for OES measurements 19 was revised for the present work, with a simple Keplerian telescope arrangement providing greatly enhanced light-gathering ability relative to the prior approach. With the trade-off of spatial resolution (now ≈3 mm) for improved spectral resolution (now 0.15 nm fwhm) and signal-to-noise ratio, partially rotationally resolved UV emission spectra were obtained that show detailed (but strongly overlapped) rovibronic structure due to N 2 and NH (and, in the case of C/N/H plasmas, also CN and CH) radicals, as described below. The N 2 and NH OES data reported here and in paper II were all taken with the spectrometer transmission centered at ≈336 nm. Though not important for N/H plasmas, this choice is crucial in the case of C/N/H plasmas since it avoids the much stronger CN, CH, and C 2 emissions lying further to the red, which would otherwise limit the maximum possible integration time before detector saturation and thus render our measurements insufficiently sensitive toward N 2 and NH. An important difference with respect to the previous configuration 19 is that the present OES measurements are sampled from a volume nominally at the radial center of the plasma, rather than attempting to emulate the line-integrated sampling mode of CRDS.
The H 2 , N 2 , and NH 3 source gases were introduced through separate, calibrated mass flow controllers (MFCs), and mixed prior to entering the reactor through two diametrically opposed inlets located close below the fused silica window (which constitutes the top of the reactor), at an angle of ≈45°to the probe axis. "Base" conditions for the experimental studies were defined as follows: total pressure p = 150 Torr, input power P = 1.5 kW, and input flow rates F(N 2 ) = 3 standard cm 3 per minute (sccm) for OES measurements or 6 sccm for CRDS, F(NH 3 ) = 6 sccm, and F(H 2 ) = 500 sccm. When one parameter was varied, all others were maintained at their base values, except where noted. The substrate temperature T sub was monitored using a two-color optical pyrometer operating in the wavelength range 700−1000 nm, which indicated a higher value (≈1100 K) under base conditions than the ≈973 K estimated by one-color pyrometry as used in our previous work. 10 We consider the new value more reliable due to its independence of an (usually problematic) estimate of substrate emissivity, which is itself a function of temperature as well as sensitively dependent on surface condition. Figure 1a shows a CRDS measurement of a small part of the NH(A 3 Π−X 3 Σ − ) Δv = 0 band system obtained at z = 8 mm from a N 2 /H 2 plasma operating under base conditions. Given literature values for the relevant spectroscopic constants 20 and Franck−Condon factors, 21,22 a simulation (as shown in the figure) can be constructed using PGOPHER 23 that provides assignments for rotational lines originating from the v″ = 0 and v″ = 1 vibrational levels, and which may be fitted to the experimental spectrum to recover absolute column densities. Both the fitted simulation and that of the complete NH(A−X) Δv = 0 progression, shown in Figure 1b, assume rotational and vibrational temperatures (T rot and T vib ) of 2900 K.

EXPERIMENTAL RESULTS
The optical emission spectrum displayed in Figure 2a spans a much wider (≈50 nm) wavelength range, and reveals not just the NH(A−X) Δv = 0 band system at ≈336 nm, but also progressions of vibronic bands associated with the second positive (C 3 Π u −B 3 Π g ) system of N 2 . 24, 25 Figure 2b,c shows expanded views of parts of this system. The former shows the N 2 (C−B) Δv = −1 and Δv = −2 progressions along with a PGOPHER simulation using the appropriate spectroscopic constants, 24 while the latter illustrates the separation of the The Journal of Physical Chemistry A Article overlapping N 2 (C−B) (0,0) band and NH(A−X) Δv = 0 progression, which must be accomplished with high fidelity 26 in order to track the variation in emission intensity for each species with z and/or process conditions. For brevity, the N 2 (C−B) (0,0) and NH(A−X) (0,0) band emissions, the intensities of which we consider representative and report exclusively in the remainder of this work, will henceforth be referred to simply as N 2 * and NH*. Spectra recorded at longer wavelengths showed the usual intense H Balmer series emission 19 (henceforth H*), but no detectable emissions from atomic nitrogen, even when X 0 (N) was raised to 30%.
The various multiplets associated with the 2p 2 3p 1 → 2p 2 3s 1 transition of N lying near 744, 820, and 865 nm all possess large A-coefficients (≈10 7 s −1 ) 27−29 and occur in a wavelength range for which our detection is relatively more sensitive than in the UV. Thus, they should be readily observable if the N(2p 2 3p 1 ) densities were comparable to those of the other species, but this is far from the case. 30 OES is a valuable technique for determining variations in relative species concentration with changes in process parameters, providing that the latter changes have minimal confounding influence on that part of the electron energy distribution responsible for exciting the optical emission. CRDS, in contrast, provides absolute column densities. The procedure for obtaining H(n = 2) column densities from CRDS measurements on the n = 3 ← n = 2 Balmer-α transition is unchanged from that used in our previous studies, 16 and so is not repeated here. The experimental measurable is the change in ring down rate (Δk, s −1 ) versus wavenumber (ν ̅ , cm −1 ). For a radical species such as NH, eq 1 provides the link from CRDS measurements of an individual spectral line to the absolute column density, which we notate as, e.g., {NH(v = 0)}: Here, L is the length of the cavity (92 cm), g l and g u are the degeneracies of the X 3 Σ − and A 3 Π states (3 and 6, respectively), and A is the Einstein A-coefficient for the (0,0) band of the A−X transition. In the present work, A has been taken as ≈2.44 × 10 6 s −1 per ref 21, although it should be noted that other similar values have been given in the more recent ref 22 and references therein. p line is the ratio of the integrated intensity of the spectral line under study to the total band intensity, which is calculated assuming that the NH radicals are localized in a volume of reasonably constant gas temperature, T. Given the collision frequency at the pressures of interest, and informed by rotational temperatures obtained by fitting to the observed band contour of the NH* optical emission spectrum, we assume T gas = T rot = T = 2900 ± 300 K, and hence calculate p line using PGOPHER and the relevant spectroscopic constants, 20,21 with the total band intensity obtained as the integrated intensity over all rotational lines within the (0,0) band. The calculated p line values for the lines contributing to the simulation shown in Figure 1 are 5.44(12) × 10 −3 , 4.81(11) × 10 −3 , and 1.07(7) × 10 −3 for the (0,0) p P 1 (10) (29 466.02 cm −1 ), (0,0) q P 32 (9) (29 471.65 cm −1 ), and (1,1) p P 1 (7) (29 471.80 cm −1 ) lines, respectively, where the quoted uncertainties are due to the range of T considered. Given the experimental resolution (≈0.3 cm −1 fwhm), the latter two lines are unresolved, and line-integrated Δk values were obtained by simultaneously fitting one (assumed Gaussian) profile to the p P 1 (10) line, and another of equal width to the sum of the other two lines, with the relative area of the latter fixed to its temperature-determined value of 0.925(15). From these three lines we hence recovered " p P 1 (10)-equivalent" values of Δk, from which column densities were calculated using the corresponding p line . The choice of lines was guided partly by the uncertainty in temperature, and thus minimal variation of the relative intensities was sought: the values of p line and the intensity ratio, even including implausibly high (3600 K) and low (2200 K) average temperatures, span the fairly narrow ranges 5.02 × 10 −3 −5.74 × 10 −3 and 0.884−0.980, respectively, for the lines used in the present analysis.  The Journal of Physical Chemistry A Article Figure 3a,b shows z-dependent profiles for {H(n = 2)} and {NH(v = 0)} as measured by CRDS in N 2 /H 2 and NH 3 /H 2 plasmas, respectively, operating under base conditions. The {H(n = 2)} profiles in these dilute N/H plasmas appear insensitive to the choice of nitrogen precursor, and are reminiscent of those reported previously when using dilute C/H/(Ar) 16 and C/H/O 17 gas mixtures in this same reactor, peaking at z ≈ 6 mm and decreasing both toward the substrate and (less steeply) at larger z. The {NH(v = 0)} distribution is clearly more extensive in both cases, and the measured {NH(v = 0)} values in the two plasmas are very similar despite the approximately 2-fold difference in X 0 (N) between the two precursor gases for any given flow rate. Figure 4 shows measured variations in {H(n = 2)} and {NH(v = 0)} at z = 8 mm with changing X 0 (N) for (a) N 2 /H 2 and (b) NH 3 /H 2 plasmas. The results are presented with respect to N/H atom ratio, defined in terms of the flow rates as F(N 2 )/F(H 2 ) and F(NH 3 )/[3F(NH 3 ) + 2F(H 2 )], respectively, depending on the N precursor. We further note that X 0 (N) and the N/H atom ratio are almost equal for small nitrogen additions. {H(n = 2)} appears insensitive to small additions of N 2 or NH 3 , while {NH(v = 0)}, unsurprisingly, increases with X 0 (N). The rate of increase is less than directly proportional in both cases, with the rate of rise diminishing as X 0 (N) further increases. A sharp rise of {NH(v = 0)} for F(NH 3 ) < 1 sccm can be inferred from the zero-offset observed in Figure 4b, which contrasts with the roughly linear trend seen for small F(N 2 ). The continuous curves drawn through the data points are power laws of the form const × X 0 (N) a , with best-fitting exponents (a) a = 0.70 and (b) a = 0.36. We discuss the interpretation of these values in the following section.
Column density variations with power and pressure, again measured at z = 8 mm, with all other parameters maintained at their base values, are shown in Figure 5. The {NH(v = 0)} versus P plot, Figure 5a, clearly demonstrates sensitivity to the choice of nitrogen precursor. In the case of the N 2 /H 2 plasma, {NH(v = 0)} increases approximately 4-fold as P is raised from 0.8 to 1.8 kW, whereas the same increase in P in the case of NH 3 /H 2 leads to a modest reduction in {NH(v = 0)}. The value of {NH(v = 0)} is, however, consistently greater in the NH 3 /H 2 plasma for all powers, even though X 0 (N) is only onequarter of that for the corresponding N 2 /H 2 plasma. Changes in pressure have an effect roughly analogous to those of power: as seen in Figure 5b, {NH(v = 0)} largely follows {H(n = 2)} in the N 2 /H 2 mixture, but shows only weak dependency on either variable when using NH 3 as the N source gas. We emphasize, however, that the trends shown in Figure 5 reflect the changing size and power density of the plasmas as well as their local compositions and parameters, so that physical interpretation must necessarily rely in large part on the complementary modeling studies.
OES measurements show many of the same trends. Spatial profiles of the H* emission from the N 2 /H 2 and NH 3 /H 2 plasmas (Figures 6a,b), respectively) are very similar to each other and, peaking at z ≈ 6 mm, have overall envelopes comparable to those given in Figure 3 for {H(n = 2)} as measured by CRDS. The N 2 * emission spatial profile closely resembles that of H*. It should be noted that the relative emission intensities given for z = 0 mm are consistently and necessarily underestimates relative to the other spatial locations, since the substrate (rather than the plasma) then fills the lower  The Journal of Physical Chemistry A Article half of the imaged region; CRDS measurements, in contrast, are impossible with the substrate partially occluding the beam path. The shapes of the NH* emission profiles are insensitive to the choice of nitrogen source, but peak at larger z than the H* profiles, which is again consistent with the CRDS measurements of {NH(v = 0)}. In both plasmas, the NH*/N 2 * emission ratio increases approximately 2-fold across the range z = 0 to 18 mm, reflecting this more extensive NH distribution.
The measured NH* emission from the NH 3 /H 2 plasma is more intense than that from the equivalent N 2 /H 2 plasma. So, too, is the N 2 * emission. The former observation may be explained, at least partially, by the finding from CRDS that the (ground state) NH density is greater for NH 3 additions than with the same X 0 (N) from N 2 , but the latter also implies some contribution from increased electron density n e and/or temperature T e in the NH 3 /H 2 case. This finding is illustrated more clearly in Figure 7, which shows the scaling of the emission intensities with N/H atom ratio for both plasmas. The H* emission shows a small, but sharp, increase upon small additions of NH 3 , and a similar but more gradual increase when using N 2 , while no comparable effect was seen for {H(n = 2)} in Figure 4a; any differences in the N 2 * emission intensities are hard to discern. The small increases in H* and the linear increase in N 2 * emission intensity imply that increasing X 0 (N) in the source gas mixture causes only minor variations in the plasma parameters. Such variations as are observed could reflect changes in the dominant ion(s) and in electron−ion recombination rates and/or minor changes of the maximum gas temperature T max and T e . We return to this issue in section 4, but the similar N 2 * emission intensities, and the fact that this quantity scales essentially directly proportionally to the input N/H atom ratio, both suggest that the strongly bound N 2   The Journal of Physical Chemistry A Article molecule is the predominant reservoir for nitrogen in both plasmas. Similarly to {NH(v = 0)}, the NH* emission intensity exhibits an approximate power-law relationship to X 0 (N), again with a smaller exponent (a = 0.47) for the NH 3 /H 2 mixture than for N 2 /H 2 (a = 0.81).
The N 2 * and NH* emissions from N 2 /H 2 and NH 3 /H 2 plasmas respond similarly to changes in applied microwave power as do {H(n = 2)} and {NH(v = 0)}, as may be seen by comparing the relevant data in Figures 8a and 5a. One notable observation is that the N 2 * emission intensity increases less steeply with P than does {H(n = 2)}, despite the H(n = 2) energy (with respect to ground state H) being a little below that of N 2 (C 3 Π u ) with respect to its ground state, i.e., 10.2 and 11.0 eV, respectively. Further discussion and interpretation of these various observations draws on companion modeling studies of the plasma chemistry and composition which are described below.

N/H PLASMA MODELING
Our description of the N/H plasma modeling starts by highlighting similarities (with regard to both processes and effects) associated with adding small amounts of N 2 or NH 3 (up to a few percent) to a H 2 plasma. For both N source gases, the 2-D model (elaborated below) shows N 2 molecules to be the dominant N-containing species, representing ≈99.99% (N 2 /H 2 ) and ≈92% (NH 3 /H 2 ) of the total nitrogen content in the reactor under "base" conditions of power P = 1.5 kW, pressure p = 150 Torr, and input mole fraction X 0 (N 2 or NH 3 ) = 1.2%. The N/H plasma-chemical kinetics and species concentrations in the hot plasma region thus share many common features. However, it is important to recognize a significant difference in the case of the NH 3 /H 2 gas mixture: the additional source of NH x (x = 0−2) species resulting from NH 3 diffusion from the peripheral, cold regions of the reactor (primarily near the gas inlets) into the central hot plasma region.
Addition of either N-containing gas leads to a similar change in the dominant ions, from H 3 + in the case of the pure H 2 plasma, to a mix of NH 4 + and N 2 H + ions in a N/H plasma operating at base conditions. With 1.2% addition of either N 2 or NH 3 precursor, [H 3 + ] is reduced to less than 0.3% of ([NH 4 + ] + [N 2 H + ]). We note, however, that the "pure" H 2 plasmas used in the present experiments for measurements with no deliberately added N-containing gas will still contain trace amounts of air (i.e., N 2 and O 2 ). Assuming, as in our previous studies of MW-activated B/H plasmas, 31 a worst-case scenario of 50 ppm air impurity (containing 40 ppm of N 2 and 10 ppm of O 2 ), H 3 + would already have been supplanted as the dominant ion by a mixture of H 3 O + , N 2 H + , and NH 4 + ions with total concentration ≈10 11 cm −3 and associated ion−electron recombination coefficients β ≈ (0.5−2) × 10 −8 cm 3 s −1 . In practice, therefore, the ionization−recombination balance associated with the charged particles and the resulting plasma parameters (electron temperature T e and density n e ) will be perturbed little by small additions of N 2 or NH 3 . This expectation is consistent with the small increase in H α emission ( Figure 7) and the lack of any discernible jump in the H α absorption measurements (Figure 4), and stands in marked contrast to the previously reported >100% increase in H α emission and {H(n = 2)} when adding C x H y to a H 2 plasma. 10,16,19 In the case of an N 2 /H 2 plasma, N 2 H + is progressively supplanted as a major ion by NH 4 + upon increasing F(N 2 ) as a result of the reaction N 2 H + + NH 3 → NH 4 + + N 2 . The N/H thermochemistry and plasma-chemical mechanism used in the present study were developed on the basis of GRI-Mech 3.0 for H, H 2 , N 2 , and NH x (x = 0−3), 32 expanded to involve (i) N 2 H x (x = 1−4) species 33,34 and (ii) plasma chemistry for charged species and excited states involved in various ion conversion and electron−ion recombination reactions. 35,36 Also considered were species ionization, excitation of rovibrational states H 2 (v, J), and electron impact (EI) excitations forming H(n = 2, 3), an "effective" excited state of molecular hydrogen with E i > 11 eV (H 2 *), and N 2 *. As before, 10 rate coefficients for processes within block (ii) and their dependence on the local electron energy distribution function (EEDF) and reduced electric field (E/N, where N is the total number density) were estimated using a 0-D framework, wherein the kinetic equations for the EEDF and the local balance equations describing the plasma-chemical kinetics for the charged and neutral species were solved consistently for the range of E/N and T values of interest. Extensive chemical database analysis and test 2-D model calculations assuming various chemical schemes for the additional blocks (i) and (ii) result in the core N/H reaction mechanism presented in Table 1 (where some reactions found  ] ratio, but also to transport processes (diffusion, thermodiffusion, and flow transfer) and gas−surface reactions at the substrate, the substrate holder, the quartz window, and the reactor walls. The less stable N 2 H x (x = 1−4) species survive only in the cold, near-wall regions. The most problematic parts of the mechanism are the less-wellestablished exchange processes between the N 1 H x and N 2 H x families, which could involve contributions from both heterogeneous reactions and reactions involving excited species (e.g., N 2 *), as discussed below. 4.1. N 2 /H 2 and NH 3 /H 2 Plasma Activation and Dependences on X 0 (N). 4.1.1. N 2 /H 2 Mixtures. The present analysis of the N/H chemistry in MWCVD reactors starts with the simpler N 2 /H 2 gas mixtures, wherein nitrogen species conversion begins with dissociation of N 2 . The ground state N 2 (X 1 Σ + g ) molecule, henceforth identified as simply N 2 , has a high bond strength: D 0 (N≡N) = 9.78 eV. Thus, the first issue to address is the dominant N 2 dissociation mechanism under typical plasma conditions of T e ≈ 1.1−1.3 eV and (r, z) distributions of gas temperature T and electron density n e as in Figure 9. The obvious inhomogeneity of these distributions serves to illustrate some of the challenges to reproducing and interpreting experimental CRDS and OES data. Two-dimensional model runs with the available N/H chemistry rule out a purely thermal mechanism given prevailing gas temperatures T < 3000 K: reactions involving ground state neutral species (e.g., N 2 + H → NH + N) simply do not provide sufficient activation, and calculations on this basis return NH column densities that are orders of magnitude lower than the measured {NH(v = 0)} as given in Figures 3 and 4.
We note that previously proposed wall reactions 14,15 are also unable to provide NH densities comparable to those observed. Given the calculated EEDF, we estimate a rate coefficient, k 1,diss < 5 × 10 −13 cm 3 s −1 , for N 2 dissociation by EI: Reaction 1 is thus a relatively more important N 2 dissociation route, but still fails (by an order of magnitude) to support the measured NH column densities. Other suggested dissociation mechanisms in N 2 plasmas, involving electronically excited N 2 * and vibrationally excited N 2 (v ≥ 14) molecules, 37 are also unimportant in the present case. Seeking other possible N 2 dissociation mechanisms, we considered excited states of N 2 , and particularly its lowest, metastable A 3 Σ + u state, henceforth denoted as N 2 (A3). This has an excitation threshold ε = 6.2 eV, and higher triplet states, including the C and B states involved in the N 2 * OES a N 2 (A3) represents the metastable A 3 Σ u + state (the lowest energy triplet state) of N 2 . The last two columns show the forward and reverse reaction rates calculated in the core (i.e., r = 0, z = 10.5 mm) of a 1.2% N 2 /H 2 plasma with T = 2882 K and T e = 1.21 eV (14 042 K), for P = 1.5 kW and p = 150 Torr. Units: cal, cm, s, K, R = 1.987 262 cal (mol K) −1 , M is a third body, and the gas temperature T and electron temperature T e are quoted in K. Figure 9. Two-dimensional (r, z) distributions of gas temperature T and electron concentration n e for base conditions and 1.2% N 2 /H 2 mixture. The model assumes cylindrical symmetry, a substrate diameter of 3 cm, and a reactor radius, R r = 6 cm, and height, h = 6.2 cm.
The Journal of Physical Chemistry A Article spectrum, can also decay (radiatively and/or collisionally) to N 2 (A3). Thus, N 2 (A3) has been included in the kinetic scheme (Table 1) and an excitation rate coefficient k 2 for the process (2) calculated from the EEDF, with additional contributions to account for cascades from higher triplet states of N 2 . Typical values of k 2 for the present MW plasma conditions are k 2 [cm 3 s −1 ] = 1.8 × 10 −8 × exp(−6.2/T e [eV]). From the perspective of dissociating N 2 , the most effective way to use this electronic excitation appears to be through the spin-allowed reaction 3 with H atoms, which is the most populous radical in the present study, with typical mole fractions X(H) ≈ 5−10% in the plasma core. That is with rate coefficient k 3 yet to be determined. One fast discharge flow study 38 concluded that reaction 3 is improbable, but careful inspection of that data allows an alternative interpretation that is compatible with the kinetics proposed here. The prior conclusion was based on an observation that H atom addition to a N 2 (A3)/H 2 mixture caused no discernible increase in measured NH. Our simulations of the earlier experimental conditions suggest that the NH concentration would actually increase at early reaction times by reaction 3, but then decline (due to the reaction NH + H → N + H 2 ) in contrast to the steady growth in [NH] observed in experiments with no added H atoms. Assuming k 3 < 2.8 × 10 −15 cm 3 s −1 at T = 295 K (the temperature of the fast discharge flow experiment), the predicted NH concentration at the time of measurement, t = 14 ms, is indeed lower than with no added H atoms, which is consistent with the prior observation. More detailed discussion and reinterpretation of the earlier experimental results is reserved for the Appendix. The proposed source of NH x through reaction 3 will, however, be reduced by competition with the fast deactivation of N 2 (A3) through collision with H and H 2 : The evaluation by Herron 39 recommends rate coefficients k 4 = 2.1 × 10 −10 cm 3 s −1 and k 5 (298 K) ≈ (4 ± 2) × 10 −15 cm 3 s −1 , while Slanger et al. 40 have k 5 (T) = 2.2 × 10 −10 exp(−3500/ T) over the limited temperature range 240 < T < 370 K. The present MWCVD model requires k 5 (T), as well as k 3 (T), over the much wider temperature range 300 < T < 3000 K. Given typical values of X H ≈ 5−10% in the plasma region, reaction 4 will be the dominant quenching reaction provided that k 5 shows only a limited increase with T, i.e., if k 5 < 5 × 10 −12 cm 3 s −1 at T = 3000 K. For determinacy, we have assumed this condition and hence set k 5 (T) = 8.3 × 10 −12 exp(−2239/T), which reproduces both the Slanger et al. measurements 40 at T = 370 K and Herron's recommended value 39 of k 5 (298 K). A consequence of this assumption, however, is that the k 3 (T) values that we now deduce for the plasma core region (at T ≈ 2500−3000 K) should be regarded as lower bounds. Proceeding as such, we note that the rate coefficient for NH + N → N 2 + H is temperature-independent (k = 5 × 10 −11 cm 3 s −1 , cf., Table 1), and have taken k −3 to be similarly independent of temperature. Combining an assumed value of k −3 = 7.5 × 10 −14 cm 3 s −1 with known thermochemical data gives the rate coefficient k 3 (T) [cm 3 s −1 ] ≈ 2 × 10 −12 exp(−1937/T), which is able both to reproduce the {NH(v = 0)} values measured in the present N 2 /H 2 MW plasma and to reinterpret the fast discharge flow data 38 with k 3 (295 K) = 2.8 × 10 −15 cm 3 s −1 .
Having resolved the issue of the primary sources of N and NH species, we are now able to describe further interconversions between the N-containing species. N and NH formed in the plasma region, mainly via reaction 3, participate in fast Hshifting reactions resulting in populations of NH 2 and NH 3 . The family of reactions 6, with rates that depend on the local [H], [H 2 ] and gas temperature T(r, z), along with NH x transport mainly by diffusional and thermodiffusional transfer between hot and cold regions, determine the complex equilibrium between the various NH x species throughout the entire reactor.
In addition, the global balance of N-containing species is determined by the input flow F(N 2 ) and outflow from the reactor (wherein [N 2 ] is still very much greater than the sum of the concentrations of all other N-containing species, including NH 3 ), and the slow interconversion between NH x and N 2 H x species. As discussed above, N 2 H x → 2NH y conversion is mainly via reaction 3 and, to a lesser extent, reaction 1. The reverse conversion is determined by the reaction with additional contributions from many (generally poorly determined) two-body recombination reactions where w = (x + y) − z, as well as the analogous three-body recombinations Among these, the reactions N + NH 2 ↔ N 2 + 2H and 2NH ↔ N 2 + 2H are the most important under the conditions of the present study. Heterogeneous recombination reactions of NH x species at the metal reactor walls and/or the hot quartz window are also possible, but seemingly unimportant for N 2 /H 2 mixtures. This is, however, in marked contrast to the case with NH 3 /H 2 mixtures, as discussed below.
The above-mentioned processes have obvious parallels with those reported previously 10,16 for carbonaceous species in MWactivated C/H plasmas, wherein C 2 H 2 is the dominant Ccontaining species in the hot plasma region irrespective of the choice of carbon source gas, and {CH} was shown both experimentally and theoretically to scale as X 0 (C) 0.5 , where X 0 (C) is the input carbon atom mole fraction. Here, N 2 is the dominant N-containing species, and we can undertake a similar analysis of the production and loss rates for the NH x species in the hot plasma region per reactions 1, 3, and 7−9. The resulting overall balance of N 1 species can be written as  ) where [N 1 ] = ∑[NH x ] (x = 0−3), and the proportionality coefficients b are independent of X 0 (N) in the process gas. The terms on the left-hand side represent N 1 loss processes, namely, The Journal of Physical Chemistry A Article through diffusion out of the hot region of the plasma (with relative rate b diff,plasma ) and reaction (b reac ) according to any of reactions 7−9, while the terms on the right represent sources, i.e., the dissociation reactions 1 and 3, respectively. This illustrative balance can be used to obtain the functional dependence of {NH x } on X 0 (N), and for the NH radical, which is concentrated in the hot plasma core, eq 10 predicts {NH} ∼ X 0 (N) a . The exponent a may lie between 0.5, in the case that reactions 7−9 are the dominant NH loss processes, and 1.0, if NH x loss is instead dominated by axial diffusion from the hot plasma core to colder regions near the quartz window and the reactor base plate. The 2-D model predicts a near-linear relationship between {NH} and X 0 (N), implying that diffusion should dominate, whereas the CRDS and OES measurements are best described by intermediate exponents, as shown in Figure 4a, where a = 0.70, and Figure 7, which has a = 0.81. The foregoing analysis identifies the hot plasma as the main source of NH x (x = 0−3) species in a MWCVD process employing a N 2 /H 2 gas mixture, and the spatial distributions of the N 2 , NH 3 , N, and NH mole fractions returned by the 2-D model, shown in the form of (r, z) maps in Figure 10, are all consistent with production of N 1 species in the plasma core and their subsequent diffusion out to the cooler regions. (The spatial distribution of the NH 2 mole fraction closely resembles that for NH, and is therefore not shown.) N 2 molecules, in contrast, diffuse into the plasma region, where they decompose via reactions 1 and 3. Figure 11 shows net production rates for selected species, including NH x (x = 0−3), calculated at r = 0 as a function of z (i.e., vertical distance above the center of the substrate). The local maxima and minima at z ≈ 19 mm are due to a boundary volume characterized by extensive recombination of ions and electrons diffusing away from the plasma, but without any compensating ionization because of the declining electric field in this region. The N data illustrates much of the complex reactivity: the calculations reveal net production of N atoms in the hot plasma region (z ≈ 12 mm) through reactions 1 and 3, net loss at smaller z due to re-equilibration into the various N 1 species, and net production again as z → 0, reflecting the temperature dependence of both the equilibrium constants for the various H-shifting reactions 6 and the local [H]/[H 2 ] ratio. Numerical experiments confirm that the conversion and transport of N-containing species described in this section will be (at most) only weakly perturbed by surfacemediated heterogeneous reactions of NH x species, in marked contrast to the case of MW activated NH 3 /H 2 mixtures, which we now consider.
4.1.2. NH 3 /H 2 Mixtures. Two-dimensional modeling of the MW-activated NH 3 /H 2 plasma following the same N/H gasphase chemistry described above (Table 1) yields more extended NH x spatial distributions ( Figure 12), with the positions of maximal mole fraction for each species lying further from the plasma core and more toward the source gas inlets than in the N 2 /H 2 case ( Figure 10). Furthermore, the predicted directions of diffusional flux are here species-specific due to the presence of an alternative, and dominant, NH x source term: axial and radial diffusion of NH 3 from the near-inlet region to all other parts of the reactor volume. Two terms dominate the N 1 species balance within the measurement region (0 < z < 20 mm), namely, NH 3 diffusion from the gas inlet region and reactive loss: Equation 11 implies a square-root dependence, i.e., {NH} ∼ X 0 (N) 0.5 , which is reproduced in both the 2-D model results and the OES measurements, with the latter being welldescribed by an exponent a = 0.47. Analysis of the CRDS measurements, however, returns a = 0.36. Such a (close to) cube-root dependence on X 0 (N) could be realized if NH x loss was dominated by one or more three-body reactions, such as but the present calculations suggest that any such reaction would need to have an improbably large rate coefficient (k > 10 −28 cm 6 s −1 ) to be practically important. The global N 1 balance for NH 3 /H 2 plasmas constitutes another, and more serious, discrepancy between the calculated and measured {NH(v = 0)} z-profiles. The predicted {NH} Figure 10. Two-dimensional (r, z) plots showing the mole fractions of N 2 , NH 3 , N, and NH in a 1.2% N 2 /H 2 gas mixture with P = 1.5 kW, p = 150 Torr, and reactor dimensions as defined in the caption to Figure  9. Figure 11. Net production (i.e., production−loss) rates of selected species plotted as a function of z in a 1.2% N 2 /H 2 gas mixture, for r = 0, P = 1.5 kW, and p = 150 Torr.

The Journal of Physical Chemistry A
Article values exceed the measured column densities by factors of 2−3 at z < 15 mm, peaking at z ≈ 35 mm, far from the hot plasma core; however, the measured {NH(v = 0)} has maximized by z ≈ 15 mm. Various processes could lead to a reduction in the calculated [N 1 ] at large z: (i) Conversion of N 1 species to N 2 , by adsorption of NH x (x = 0, 1) at the reactor walls and on the hot quartz window, with subsequent gas−surface reactions with NH 3 producing gas-phase N 2 H 4−x , finally becoming N 2 through a sequence of H-abstractions. Calculations show that such conversions will indeed reduce [N 1 ], but not sufficiently to match the experimental observations given that [NH 3 ] > 10 16 cm −3 near the gas inlet far exceeds [N] and [NH]. Consequently, an adequate reduction of [N 1 ] would require NH 3 loss at the surface with probability γ > 2 × 10 −4 , independent of the local N and NH fluxes. Such a large value of γ appears unphysical, however, on the basis of the critical sensitivity of the model results to the properties of the nearinlet region. (ii) Contributions from three-body reactions stabilized by collisions with H 2 , e.g. Such reactions cannot be important in practice, however, as they only give a useful reduction of [N 1 ] if we assume unrealistically large rate coefficients, k > 10 −29 cm 6 s −1 .
The most likely cause of this discrepancy, therefore, is the use of a cylindrically symmetric model geometry to describe the gas inlet scheme of the experimental PACVD reactor. Indeed, a similar situation arose in our previous study of MW-activated CH 4 /CO 2 /H 2 plasmas. 17 The process gas enters the reactor through two diametrically opposed ports positioned at φ ≈ 45°t o the probe axis, whereas the 2-D (r, z) model assumes gas entry at r = 60 mm. As Figure 12 shows, the calculated NH 3 mole fraction in a 1.2% NH 3 /H 2 plasma falls rapidly with increasing distance from the inlet, which suggests that, in the experiment, there are two sharply localized near-inlet regions where [NH 3 ] > 10 16 cm −3 and which extend <10 mm from the respective inlets. The combined volume of these two regions is far smaller than the cylindrically symmetric approximation of a cloud extending from an inlet ring 2πr ≈ 38 cm in circumference. Acknowledging the sensitivity of the NH x radical densities to the NH 3 spatial distribution, we anticipate this difference between the experimental and modeled reactor geometries to be primarily responsible for the observed discrepancies. In contrast, in the N 2 /H 2 mixtures, N 2 molecules are so stable and so dominant relative to all other N-containing species that they inevitably adopt a near cylindrically symmetric concentration distribution throughout the reactor volume, so that the calculated N 2 distribution ( Figure 10) deviates little from that of the experiment, regardless of inlet geometry.
A comparison of calculated (r, z) maps of the N 2 , NH 3 , N, and NH mole fractions for an NH 3 /H 2 plasma ( Figure 12) and the corresponding z-dependent net production rates at r = 0 ( Figure 13) with the corresponding plots for the N 2 /H 2 case ( Figures 10 and 11) highlights major differences, both in the regions in which the NH x radicals are initially activated, and in the directions of their respective diffusional fluxes. The relatively weak bonding in NH 3 , in contrast to that of N 2 , is illustrated by the net loss of NH 3 and production of N seen in Figure 13 at z ≈ 50 mm. In the region 45 > z > 35 mm, T increases, and the equilibria associated with the H-shifting reactions 6 shift in favor of NH x (x > 0). Further increasing T at 35 > z > 25 mm leads again to NH 3 loss, the net rate of which reaches a local maximum, with corresponding N 2 and N formation, in the warm recombinative region at z ≈ 19 mm. Below this lies the plasma proper, where the rising electron density and significant power absorption contribute to a maximum of T, and therefore of [H]. At still smaller z, T falls and n e further increases, leading to the loss of N and N 2 and production of both NH 3 and the major ions, N 2 H + and NH 4 + . Very close to the substrate, z < 3 mm, NH x (x > 0) is consumed and N atoms are generated, with the latter constituting the dominant N-containing species in this region.  Overall, the present calculations succeed in rationalizing the basic conversions and balance within the N/H plasma-chemical kinetic scheme, and are able to account qualitatively (and, in many cases, quantitatively) for the experimental observations. Table 2 summarizes the calculated concentrations of selected species at the approximate center of the plasma, (r, z) = (0 mm, 8.0 mm), and immediately above the substrate, at (0 mm, 0.5 mm), for both N 2 /H 2 and NH 3 /H 2 mixtures under base conditions. The calculated concentrations of the various NH x (0 ≤ x ≤ 2) species are similar in the hot plasma core, but among this family, N is predicted to be dominant close to the substrate. The calculations also predict only modest (less than a factor of 2) differences in these species concentrations in the N 2 /H 2 and NH 3 /H 2 plasmas. We note, however, that X 0 (N) in the modeled NH 3 /H 2 plasma is only half that used in the N 2 / H 2 plasma modeling.
4.2. Variations with Applied MW Power and Total Gas Pressure. The calculated EEDF is primarily determined by the reduced electric field (E/N), and does not vary with pressure p at constant E/N. 10 Here, we use the previously derived functional form of the absorbed power density, eq 12, to understand the possible changes in plasma parameters and the plasma volume V pl , with changes in p. 10,36 That is (12) where the input power P = ∫ Q·dV pl . Here, the power density Q has units of W cm −3 , E/N is in Townsend units (1 Td = 10 −17 V cm 2 ), p is in Torr, and n e is in cm −3 . The coefficient C ≈ 0.25 is essentially constant for the present H 2 -rich plasmas. 4.2.1. Power Dependences. Two-dimensional model calculations for the 1.2% N 2 /H 2 mixture under base conditions and P = 0.8 kW suggest that the measured changes upon increasing P from 0.8 to 1.5 kW are largely explicable by taking V pl ∼ P, per eq 12, while n e ≈ 2.2 × 10 11 cm −3 and T e ≈ 1.24 eV at the plasma center both remain essentially constant. The calculated maximum gas temperature, T max , increases by ≈4%, from 2770 to 2890 K, as a result of this increase in P. These increases in T max and V pl are predicted to cause a 3-fold increase in total [H] within the entire reactor volume and a more than 2-fold increase in maximal [H], in good accord with the observed increases in {H(n = 2)} when using both dilute N 2 / H 2 and NH 3 /H 2 source gas mixtures (as shown in Figure 5a). This increase in [H] elicits a more than 4-fold increase in the calculated {NH(v = 0)}, consistent with the measured increases in both {NH(v = 0)} and the NH* emission intensities from the N 2 /H 2 plasma, as shown in Figures 5a and 8a. The N 2 concentration is barely affected by these changes in [H]; the 2-D modeling predicts a modest increase in N 2 * emission intensity over the range 0.8 ≤ P ≤ 1.5 kW, in accord with experimental observation (see Figure 8a), as a result of the increasing N 2 (C ← X) EI excitation rate.
In the case of the NH 3 /H 2 plasma, however, this same increase in P causes a modest decrease in {NH(v = 0)}, a smooth increase in the N 2 * emission intensity, and no clear change in NH* emission. As noted earlier, the predicted {NH(v = 0)} values with the NH 3 /H 2 plasma far exceed those observed experimentally, but the present modeling succeeds (qualitatively at least) in reproducing the observed decrease in {NH(v = 0)}. This is attributable to the order of magnitude decrease in [NH 3 ], particularly in the hot plasma region, as a result of a 3-fold (over the entire reactor volume) increase in [H], which promotes the conversion of NH x to N 2 .
4.2.2. Pressure Dependences. As eq 12 shows, decreasing p at constant P could be accommodated by (i) a compensating change in V pl (i.e., V pl ∼ 1/p), with no effect on E/N, T, or n e ; (ii) V pl remaining constant with increasing E/N and n e ; or (iii) a combination of both effects. Inspecting the model outputs for the 1.2% N 2 /H 2 mixture under base conditions and at p = 80 Torr suggests that scenario (iii) is most applicable. Reducing p from 150 to 80 Torr is predicted to result in a ≈35% increase in V pl (from ≈74 to ≈100 cm 3 ), with corresponding increases of ≈30% in the maximal n e (from 2.2 × 10 11 to 2.8 × 10 11 cm −3 ) and ≈10% in T e (from 1.24 to 1.36 eV) at the plasma center. The maximal value of X(H) is reduced by ≈45%, from 7.3% to 4.0%, reflecting the ∼[H 2 ] 2 dependence of the thermal dissociation source term.
The present modeling of the N 2 /H 2 plasma captures the observed increases in {H(n = 2)} and {NH(v = 0)} upon increasing p, as depicted in Figure 5b. The calculated zdependent {NH(v = 0)} profile at lower p is also flatter, in accord with the CRDS measurements (not shown). The model also provides a rationale for the very different p dependences of the N 2 * and NH* emission intensities displayed in Figure 8b. These intensities are sensitive to the N 2 (C ← X) and NH(A ← X) EI excitation rates. The former, for example, is given by the product k e (N 2 (C−X)) × n e × [N 2 (X)], where the EI rate coefficient for N 2 (C ← X) excitation is derived from the calculated EEDF, k e = 2.1 × 10 −8 × exp(−11/T e [eV]) ≈ 3 × 10 −12 cm 3 s −1 for a typical value of T e = 1.25 eV. The N 2 * versus p trend displayed in Figure 8b shows that the net effect of the decreases in n e , T e (and thus k e ) with increasing p more than outweigh the (linear) increase in [N 2 (X)]. The NH(A ← X) EI excitation frequency k e (NH(A−X)) × n e will also decline with increasing p, but the NH* emission is seen to increase and then plateau at p ≈ 150 Torr. This reflects the previously noted greater than linear increase of [NH (X)] (and other NH x species) due to the near quadratic dependence of X(H) with p in the hot plasma region. The Journal of Physical Chemistry A Article The foregoing discussion excludes any possible contribution to the observed N 2 * emissions from EI pumping of molecules in any state other than the ground state on number density grounds; k e (N 2 (C ← A3)) is estimated to be an order of magnitude larger than k e (N 2 (C ← X)), but this difference is overwhelmed by the concentration difference ([N 2 (A3)]/ [N 2 (X)] < 10 −5 ) in the hot plasma region. The N 2 (C ← X) excitation must be balanced by N 2 (C → B) radiative decay and collisional quenching. Probe calculations suggest that the latter must dominate in order to reproduce the observed smooth spatial N 2 * emission profiles. The only feasible quencher (on concentration grounds) is H 2 , for which Pancheshnyi et al. 41 report a suitably large N 2 (C 3 Π u ) + H 2 quenching rate coefficient k q > 3 × 10 −10 cm 3 s −1 (at 295 K).
Notwithstanding the previously noted limited agreement between the experimental data and model outputs for the MW activated NH 3 /H 2 gas mixtures, the 2-D model also succeeds in reproducing the near independence of {NH(v = 0)} with p (Figure 5b), reflecting the alternative NH x source term when using NH 3 as the nitrogen source gas, and accounts for the pdependent N 2 * and NH* emission intensities shown in Figure  8b. The observed p-dependence of N 2 * is very similar to that seen with the N 2 /H 2 plasma, for the same reasons. The NH* emission from the NH 3 /H 2 plasma, in contrast, declines with increasing p, which is as expected for the product of a (nearly pindependent) NH(X) density and an NH(A ← X) EI excitation rate coefficient that declines with increasing p.

SUMMARY AND CONCLUSIONS
Small additions of N 2 to MW-activated CH 4 /H 2 gas mixtures used in diamond CVD have been shown to enhance the material growth rate and influence the surface morphology, 2−6 but a complete mechanistic explanation for such behavior has yet to be determined. Here, we have addressed dilute N 2 /H 2 and NH 3 /H 2 microwave plasmas operating under CVDrelevant regimes of gas temperature and pressure, which have otherwise received little attention thus far. The present work can therefore be considered a prerequisite for any subsequent study of N-containing CH 4 /H 2 plasmas, such as those that are used in many diamond CVD reactors. Our investigation has involved three main aspects: (i) CRDS measurements, yielding spatially resolved absolute column densities of H(n = 2) atoms and NH(X) radicals, as functions of gas pressure p, input power P, and mole fraction of nitrogen in the source gas X 0 (N), (ii) OES measurements of the relative densities of H(n = 3) atoms, NH(A) radicals, and triplet N 2 molecules, with respect to the same process conditions; and (iii) complementary 2-D (r, z) coupled kinetic and transport modeling for the same process conditions, including consideration of variations in both the plasma parameters (e.g., T e , T, n e , and power density Q) and the overall chemistry.
Comparisons between experimental measurements and model outputs have provided refinements to the prior understanding of N/H plasma-chemical reactivity, with the proposed scheme now able to demonstrate the interconversion between NH x (x = 0−3) and N 2 H x (x = 0−4) species, and its dependence on process conditions and location within the reactor. We have highlighted the essential role of metastable N 2 (A 3 Σ + u ) molecules (formed by electron impact), and their hitherto underappreciated reactivity with H atoms, in converting the N 2 process gas into reactive NH x (x = 0−3) radical species. We have also illustrated the much more extensive NH x spatial distributions prevailing in MW-activated NH 3 /H 2 plasmas, and the importance of surface-mediated NH x loss processes in establishing the measured radical densities in the case of the NH 3 feedstock. The overall result is that we are now satisfactorily able to rationalize the observation that measured NH column densities differ by less than a factor of 2 between N 2 /H 2 -and NH 3 /H 2 -based MWPACVD processes operating under base conditions with the same nitrogen atom input mole fraction, though the difference is larger at lower p and/or P. An important additional finding in the CVD context is that N atoms are, by an order of magnitude, the dominant reactive nitrogenous species in the near-substrate region under the present conditions.

■ APPENDIX
The earlier fast discharge flow studies of reactive conversions in N 2 (A3)/H 2 /Ar and N 2 (A3)/H/H 2 /Ar gas mixtures involved monitoring relative (and, with appropriate calibration experiments in many cases absolute) H atom, N 2 (A3) molecule and NH(X) and NH 2 (X) radical concentrations downstream of the mixing region. 38 Data relevant to the current study have been simulated using the following minimalist reaction scheme (with respective rate coefficients k Ai (cm 3 s −1 ) at the experimental temperature T = 295 K): These rate coefficients were drawn from various sources: k A1 and k A2 from experimental data surveyed in the Herron evaluation, 39 k A4 from the combined experimental and theoretical study of reaction A4 by Adam et al., 42 and k A3 derived from present study. This value of k A3 does not contradict the conclusion of the Ho and Golde study, 43 given it is so much smaller than k A2 (k A3 ≈ 1.3 × 10 −5 × k A2 ). The simple mechanism (A1)−(A4) is able to replicate many of the features observed in the fast discharge flow experiments, e.g., the lack of any discernible increase in [NH] at the measurement time, t = 14 ms, upon introducing H atoms at a concentration [H] = 1.1 × 10 14 cm −3 (X(H) = 0.17%). The fact that the observations are made downstream, after a userselected time delay t, is crucial to the interpretation. As Figure  14 shows, reaction A3 leads to an initial increase in [NH], which has then declined precipitously by the time of the measurement through reaction A4 with the high concentration of H atoms.
Though appealing, this simple analysis of the prior data may well be deficient in detail. For example, we note that the present calculations return [H] concentrations in the experiments using the 0.001% N 2 (A3)/25% N 2 /2.3% H 2 /Ar gas mixture (i.e., without any deliberate H atom addition, Figure  14a