Optical Emission from C2– Anions in Microwave-Activated CH4/H2 Plasmas for Chemical Vapor Deposition Diamond.

: Visible emission from C 2 − (B 2 Σ u+ ) anions has been identi ﬁ ed underlying the much stronger Swan band emission from neutral C 2 (d 3 Π g ) radicals (henceforth C 2 − * and C 2 * , respectively) in MW-activated C/H/(Ar) plasmas operating under conditions appropriate for the chemical vapor deposition (CVD) of diamond. Spatially resolved measurements of the C 2 − * and C 2 * emissions as functions of the C/H/(Ar) ratio in the input gas mixture, the total pressure, and the applied MW power, together with complementary 2-D( r , z ) plasma modeling, identi ﬁ es dissociative electron attachment (DEA) to C 2 H radicals in the hot plasma as the dominant source of the observed C 2 − * emission. Modeling not only indicates substantially higher concentrations of C 2 H − anions (from analogous DEA to C 2 H 2 ) in the near-substrate region but also suggests that the anion number densities will typically be 3 − 4 orders of magnitude lower than those of the electrons and partner cations, i.e., mainly C 2 H 2+ and C 2 H 3+ . The identi ﬁ cation of negatively charged carbon-containing species in diamond CVD plasmas o ﬀ ers a possible rationale for previous reports that nucleation densities and growth rates can be enhanced by applying a positive bias to the substrate.


INTRODUCTION
Optical emission spectroscopy (OES) has found widespread use as a relatively straightforward and easy-to-implement probe of DC arc-jet 1−9 and microwave (MW) 10−59 plasmas used for the chemical vapor deposition (CVD) of diamond. Species amenable to study in this way in traditional dilute carbon/ hydrogen (C/H) plasmas include electronically excited H atoms (via the Balmer emissions), H 2 molecules (typically via lines within the Fulcher system), and CH and C 2 radicals. To this list can be added electronically excited Ar atoms (when Ar i s a d d e d t o t h e p r o c e s s g a s m i xture), 1−3,10,12 −14,16,18,21−24,26,28,31,33−37,39−42,44−48,50,54,56,57,60 B and BH (if a B-containing dopant is added), 39,44,58 CN and N 2 (when N 2 is present, either by design or as an impurity), 1,6,15,18,[24][25][26]35,41,54,59 and OH and CO (when, for example, CO 2 is used as the carbon source). 25,27,43,49,51,55,57 The emitting species are generally formed by electron impact excitation (EIE) either of the corresponding ground-state species, or of a low-lying excited state in the case of C 2 . Thus, the emission intensities are sensitive not just to the respective lower state populations but also to the electron temperature, T e , and number density, n e , and the variation of all of these quantities with changes in process conditions, e.g., in the gas composition and mixing ratio, total pressure p, applied MW power P, sign a n d m a g n i t ud e o f a n y su bs t r a t e b i a s v o l t a g e , etc., 6,7,9−11,13−16,18−24,26,27,29−31,34,36−46,48−60 and with location within the plasma volume. Several studies have investigated the correspondence (or otherwise) between measured OES intensities and absolute densities measured by absorption methods. 17,22,23,32,37,42,59 OES measurements made with high spectral resolution can provide estimates of the temperature of the emitting species, either through the measured Doppler broadening of a single spectral line (e.g., of the H Balmer-α line 14,16,17,22,28 ) or from the relative intensities of a series of rotational lines in, for example, the emission spectrum of H 2 14,17 or C 2 . 2,4,5,7,34,36,43,47,52,53,56 Given the typical pressures (and thus collision frequencies) prevailing in these plasmas, excited-state temperatures determined in this way are generally considered reliable proxies for the local gas temperature, T gas .
Electron impact excitation is the dominant, but not the sole, mechanism by which emitting species arise in MW-activated gas mixtures used for diamond CVD. Spatially resolved measurements of both the BH radical emission in MWactivated B 2 H 6 /H 2 (/Ar) gas mixtures and the CH and C 2 emissions from MW-activated CH 4 /CO 2 /H 2 plasmas 51 reveal chemiluminescence from these species, formed as products of exothermic atom−radical and radical−radical reactions, most clearly in regions of low electron density at the periphery of the plasma. Resonant collisional energy transfer from metastable triplet CO molecules in C/H/O plasmas has also been proposed as a contributor to the observed OH emission. 51 Here we report the first identification of optical emission from the electronically excited C 2 − (B 2 Σ u + ) anion (henceforth C 2 − *) in a MW-activated C/H/(Ar) plasma operating under conditions appropriate for diamond CVD. To the best of our knowledge, this is the first charged species (anion or cation) to be observed by OES in such plasmas. The finding is noteworthy for several reasons. One centers on the C 2 − * production mechanism, which we deduce to be dissociative electron attachment (DEA) to the C 2 H radical on the basis of plasmachemical modeling. This modeling is informed by spatially resolved OES measurements comparing the variation of the optical emissions from C 2 − * and from neutral C 2 radicals in their d 3 Π g state (henceforth C 2 *) with the C/H/(Ar) ratio in the input process gas mixture, the total pressure, and the applied MW power. Second, the presence of anions may have implications for the detailed modeling of such plasmas. Previous analyses of MW-activated C/H/(Ar) containing plasmas 60,61 have assumed that the negatively charged particles partnering the cations (assumed to be mainly C 2 H 2 + and C 2 H 3 + in our previous work 60 ) are exclusively electrons. Lastly, the presence of negatively charged carbon-containing species in diamond CVD plasmas offers a possible rationale for previous findings that nucleation densities and growth rates can be enhanced by applying not just a negative 62 but also a positive 31,40,63 bias voltage to the substrate.

EXPERIMENT
The experiments employ the previously described MW plasmaactivated (PA) CVD reactor 64 with a new setup for imaging the optical emission from the plasma. Base conditions were chosen as P = 1.5 kW and p = 150 Torr, with flow rates F(CH 4 ) = 19 standard cm 3 per minute (sccm) and F(H 2 ) = 300 sccm (i.e., 6% CH 4 in H 2 ). Power, pressure, and F(CH 4 ) were varied individually over the respective ranges 0.7 ≤ P ≤ 1.86 kW, 50 ≤ p ≤ 275 Torr, and 2 ≤ F(CH 4 ) ≤ 30 sccm, while keeping the other parameters at their base values. The effect of adding Ar to the process gas mixture was investigated over the range 0 ≤ F(Ar) ≤ 60 sccm, with F(H 2 ) reduced in a compensatory way so as to ensure that F(H 2 )+F(Ar) = 300 sccm. Optical emission from the plasma was coupled into a Czerny−Turner spectrograph (Newport MS127i) using a 250 mm focal length, f/16 objective lens and dispersed using an 1800 grooves mm −1 grating, yielding a spatial resolution of <0.5 mm and a spectral resolution of ≈0.11 nm (full width at halfmaximum, fwhm) when a 13 μm entrance slit is used. The effects of adding Ar were investigated at lower spectral resolution (25 μm entrance slit) wherein, under base conditions, the recorded C 2 *(0,0) and C 2 − *(0,0) emission intensities, henceforth I em (C 2 *) and I em (C 2 − *), were both increased ∼2.5-fold. The diffracted radiation was imaged onto a cooled CCD detector (Andor Newton 970) with an overall spatial magnification of ≈0.1, and each image was scaled to the equivalent of a 2048 s. accumulation for direct comparability of the intensities. The lens aperture was closed right down in these studies, so the data reported here effectively include emission from the whole thickness of the plasma.

Optical Emission Images and Spectral Analysis.
After a number of low-resolution survey scans, attention was concentrated on the wavelength range 489−566 nm, which under the present conditions is dominated by the Δv = 0 and Δv = −1 progressions of the C 2 (d 3 Π g −a 3 Π u ) transition but also includes the much weaker C 2 − (B 2 Σ u + −X 2 Σ g + ) Δv = 0 emission of current interest. The measured images comprise spatially and wavelength-resolved emission intensities I em (λ, z). Figure 1 shows an illustrative image recorded under base conditions, after postprocessing to correct for vertical skew in the raw image. The height scale spans the range −3 ≤ z ≤ 27 mm, where z = 0 corresponds to the substrate surface and the scale is calibrated by imaging a test target placed at the substrate center position. The spectroscopic parameters for the d 3 Π g and a 3 Π u states of C 2 65 are known to sufficient precision that fitting to the C 2 (d−a) line positions calculated using PGOPHER 66 constitutes the best means of calibrating the wavelength scale. From the I em (λ, z) images we can extract for further analysis one-dimensional (1-D) profiles showing I em (λ) at chosen z, or I em (z) for given λ. In doing so, we typically sum (i.e., bin) multiple rows or columns of the image, both to reduce the influence of noise in the resulting profile and limit the total number of profiles requiring to be analyzed. Figure 2a shows the I em (λ) plot obtained by binning all intensity values measured for the range 9 ≤ z ≤ 12 mm in the image shown in Figure 1, along with a best-fit simulation of the relevant part of the C 2 (d−a) spectrum that assumes that each spectral feature is broadened with a Gaussian line shape having 0.11 nm fwhm. The fit returns a rotational temperature T rot = 2900 K, in good accord with previous studies of such plasmas in this reactor, 42,59,64 and supports the assumption that the rotational population distribution in the emitting state is in local thermodynamic equilibrium. The (observed − calculated) difference plot over the limited wavelength range shown in Figure 2b highlights an obvious feature around 541.5 nm, which matches with the P-branch band-head of the C 2 − (B 2 Σ u + − X 2 Σ g + ) (Herzberg−Lagerqvist system 67 ) (v′ = 0 → v″ = 0) transition. The PGOPHER simulation of both this and the overlapping (1,1) band using the appropriate spectroscopic constants 68 and T rot = 2900 K is shown in Figure 2c  The Journal of Physical Chemistry A Article in this spectral region from similar MW activated gas mixtures but, as far as we can see, none have been recorded with sufficient spectral resolution/signal−to−noise ratio or analyzed in sufficient detail to reveal the weak C 2 − * features. Clearly, the difference plots are very sensitive to the high-v and high-J tail of the overlapping C 2 (d−a) Δv = −1 progression, the appearance of which depends on T rot (which, as before, is assumed to be a reliable measure of T gas 60 ). T gas peaks in the core of the plasma and decreases both with increasing z and, more steeply, as z → 0. 60 Much of the following analysis is based on the relative emission intensities I em (C 2 − *) and I em (C 2 *), and their variation with spatial position and changes in process conditions. As it is important to separate the relative contributions from the two species as reliably as possible, we analyze the I em (λ) data using either Δz = 1.5 mm (higher spatial resolution) or Δz = 3 mm (lower resolution) vertical strips, each with its own best-fit T gas . Under base conditions, for example, the higher resolution analysis shows T gas ≈ 2750 ± 20 K at z ≈ 2.25 mm, rising to a maximum of ≈2900 ± 20 K at z ≈ 11.25 mm and declining again to ≈2640 ± 30 K at z ≈ 24.75 mm. The comparative intensities presented below are normalized against the respective (0,0) bands in the best-fit PGOPHER simulations, with all other band intensities given by their relative transition probabilities and the vibrational partition function with T vib = T gas . To convert these intensities to relative excited-state populations requires scaling by the respective Einstein A-coefficients, for which we take 7.63 × 10 6 s −1 for the C 2 (d−a) (0,0) band 65 and 9.1 × 10 6 s −1 for the C 2 − (B−X) (0,0) transition. This latter value was derived using literature values for the radiative lifetime of the B(v′=0) level 68,69 and the relevant Franck−Condon factor. 70 Thus, if we consider the emission intensities as indicative of relative number densities, the values for I em (C 2 − *) given here should be reduced by a factor of 1.2 to obtain the relative excited-state number densities.
3.2. Trends in C 2 * and C 2 − * Emission Intensities with Changes in Process Conditions. Figure 3 illustrates the similarity of the I em (C 2 *) and I em (C 2 − *) profiles, analyzed at the higher spatial resolution, measured at pressures p = (a) 75, (b) 150, and (c) 225 Torr and otherwise base conditions. The respective profiles at any given p are similar, declining to near zero at small and large z. The maxima of both distributions shift to smaller z with increasing p, more noticeably in the case of  , and the profiles visibly narrow. Closer inspection reveals that the ratio of emission intensities is a sensitive function of pressure. As Figure 4 shows, the C 2 * emission intensity observed from the z = 10.5 ± 1.5 mm strip exhibits an approximate p 3 dependence, similar to that observed previously over a smaller range of pressures, 42 whereas I em (C 2 − *) scales near-linearly with p. These data have been derived using the lower (Δz = 3 mm) spatial resolution, to minimize any effects from the peaks of the respective distributions shifting with p. The binned intensities so derived have then been halved prior to display to allow direct comparison with the intensities in the higher resolution (Δz = 1.5 mm) profiles shown in Figure 3b.
Panels a and b of Figure 5 show I em (C 2 *) and I em (C 2 − *) profiles measured at P = 0.9 and 1.85 kW, respectively, with all other parameters maintained at their base values and analyzed at the higher (Δz = 1.5 mm) spatial resolution. As expected, reducing (increasing) P results in a smaller (larger) emitting volume, and again, the spatial distributions of the two emissions appear similar. Nonetheless, the I em (C 2 *)/I em (C 2 − *) ratio determined by (lower resolution) analysis of the z = 10.5 ± 1.5 mm strip exhibits a marked P-dependence. This is quantified in Figure 6, which shows that (as with p, Figure 4) increasing P results in a near-cubic growth in I em (C 2 *), whereas I em (C 2 − *) shows only a roughly linear increase. Again, the binned intensities have been halved prior to display for direct comparability with the intensities shown in Figures 3 and 5. The spectra also reveal a modest increase in T gas , from ≈2830 K at P = 0.7 kW to ≈2920 K at P = 1.85 kW.
The final variables investigated were F(CH 4 ) and F(Ar). Figure 7 shows the variations in I em (C 2 *) and I em (C 2 − *) determined by (lower resolution) analysis of the z = 10.5 ± 1.5 mm strip when (a) F(CH 4 ) varies across the range 2−30 sccm (or, in terms of input mole fractions, 0.66 ≤ X 0 (CH 4 ) ≤ 9.1%) with all other parameters held at their base conditions, and (b) F(Ar) varies over the range 0−60 sccm (input mole fractions 0 ≤ X 0 (Ar) ≤ 18.8%), with F(CH 4 ), p and P fixed at their base values. As Figure 7a shows, both emissions increase linearly at small F(CH 4 ) and then somewhat less steeply at higher F(CH 4 ). Figure 7b shows that adding Ar also results in (modest) increases in both I em (C 2 *) and I em (C 2 − *), more so in the former case, such that the I em (C 2 *)/I em (C 2 − *) ratio increases from ≈40 at X 0 (Ar) = 0% to ≈56 when X 0 (Ar) = 18.8%.
3.3. C 2 − * Formation Mechanism. We start by reprising some of the plasma characteristics established in our previous optical diagnosis and modeling studies of dilute CH 4 /H 2 plasmas produced in this same CVD reactor at equivalent (base) power and pressure. 42,60,64 The supplied MW power is expended mainly on gas heating by rotational and vibrational excitation of H 2 and C x H y species by electrons driven in the MW field, with subsequent vibrational-and rotational-totranslational (V → T and R → T) energy redistribution, and by elastic collisions of electrons with atoms and molecules. 60,71 The gas temperature in the plasma core is T gas ≈ 2900 K, resulting in an [H](r,z) distribution as shown in Figure 8a

The Journal of Physical Chemistry A
Article numerous H addition and abstraction reactions, summarized as a family of H-shifting equilibria that rapidly redistribute the input CH 4 into a whole range of CH x (x = 0−4), C 2 H y (y = 0− 6) and larger species, depending on the local T gas and X(H). C 2 H 2 is the most stable carbon-containing species in the hot plasma region, and >97% of all the carbon in this region is predicted to be in the form of C 2 H 2 . Figure 8b shows the calculated electron density (n e (r,z)) distribution; the peak electron density and temperature are, respectively, n e ≈ 1.8 × 10 11 cm −3 and T e ≈ 1.26 eV. Both of these values are relatively flat across the plasma volume but fall steeply very close to the substrate and at large z and r. The radical species C 2 H and, particularly, C 2 are concentrated in the hot plasma region, as illustrated by the 2-D(r,z) model outputs in Figure 8c,d. The dominant cations ensuring quasi-neutrality for our assumed ion chemistry are C 2 H 2 + and C 2 H 3 + . The presence of anions has not been considered hitherto.
Several possible mechanisms for forming C 2 − * anions are now considered. The first involves electron attachment to neutral C 2 , stabilized by the presence of a third body (M), i.e.
The C 2 radical has a sufficiently large electron affinity (E ea = 3.269 ± 0.006 eV 72 ) to support bound excited states of the resulting anion, and the B state of C 2 − has a term value T 00 (B− X) = 18484.03 cm −1 (2.29 eV). 68 Purely on energetic grounds, therefore, one could envisage that the emitting C 2 − * species observed in the present work arise directly from process 1. Such a mechanism might at first sight appear to be consistent with the similar spatial distributions of the C 2 * and C 2 − * emissions reported in Figures 3 and 5, but the very different p ( Figure 4) and P ( Figure 6) dependences of the respective emission intensities allow us to rule out reaction 1 as a major contributor to C 2 − * formation. Given the present plasma conditions, and even assuming a rather high value for the third-order recombination rate coefficient k 1 > 10 −29 cm 6 s −1 , reaction 1 would only be expected to make any discernible contribution to C 2 − * production for p > 150 Torr. The reverse collisional detachment reaction, with typical coefficient k −1 = 7.5 × 10 −10 × exp(−11605/T gas ), 73 is also not the main loss process for C 2 − *, as shown below. Electron impact processes involving C 2 − and C 2 − * anions, i.e., the excitation/de-excitation reactions with rate coefficients k EIE (C 2 − ) < k EIE (C 2 ) ∼ 10 −9 cm 3 s −1 (ref 51), and the detachment/attachment reactions 74 2 2 are too slow to be important. The photoattachment process (2)  The Journal of Physical Chemistry A Article can be excluded for similar reasons. Its estimated rate coefficient, k 2 < 2 × 10 −15 (T e /300) 0.5 cm 3 s −1 , 75 is too small for this reaction to be significant under the present process conditions.
As noted above, C 2 H 2 is the dominant carbon-containing species in the hottest part of the plasma, so it is logical to consider possible C 2 − * production routes starting from C 2 H 2 .
Although T e ≈ 1.22 ± 0.04 eV under base conditions, the electron energy distribution function (EEDF) is not identically Maxwellian and possesses a heavy high-energy tail extending to >10 eV, as evidenced by the ubiquitous H Balmer emissions, which are excited by electron impact. 22 The calculated threshold energy for the three-body fragmentation process (3) is 7.4 eV, but the first resonance in the DEA spectrum of C 2 H 2 that yields C 2 − as the dominant product is centered at ≈8.1 eV, with a cross-section of 4.1 ± 1 pm 2 . 76,77 Reaction 4 has a calculated threshold of 2.7 eV and a reported DEA cross-section of 3.6 ± 0.9 pm 2 at 2.95 eV, with C 2 H − as the dominant product. Combining the literature cross sections 76 with the EEDF calculated in our modeling allows estimation of rate coefficients for reactions 3 and 4, as functions of T e under the present plasma conditions, as shown in Table 1. 2-D(r,z) coupled kinetic and transport modeling employing the previous C/H/(Ar) reaction mechanism, 60 supplemented by the additional reactions in Table 1, shows that reaction 3 is the main source of C 2 − close to the substrate (0 < z < 5 mm) and that reaction 4 is the main source of C 2 H − in the entire plasma region. Further processing of C 2 H − via H abstraction, followed by EIE, could then be envisaged as a means of generating the observed C 2 − * species, but the work of Barckholtz et al. 78 suggests that the reaction is rather slow (k < 10 −13 cm 3 s −1 ). Thus, we conclude that Hshifting from C 2 H − cannot be an important source of C 2 − . Processes 3 and 4 can also be ruled out as (indirect) sources of C 2 − * through consideration of the observed spatial distributions. The C 2 H 2 number density (indicated using [ ] brackets, i.e., [C 2 H 2 ]) increases at small z as an inevitable consequence of the fall in T gas upon approaching the substrate. 60 The spatial distributions of the products of reactions 3 or 4 will closely resemble the product of the [C 2 H 2 ] and n e distributions, and the C 2 H − and C 2 − column densities (indicated using { } brackets) predicted on this basis peak close to the substrate and decline with increasing z as a result of the fall in, first, [C 2 H 2 ] and, at larger z, n e . Consequently, this predicted {C 2 − (v″=0)} distribution bears no resemblance to that of the C 2 (v″=0) neutrals, {C 2 (v″=0)}, formed by the well-established 60 sequence of thermally driven H-shifting reactions. We emphasize that the contributions from reactions 3 and 4 still outweigh those from reactions 1 and 2 and are non-negligible C 2 − sources under the present conditions, but the observed spatial distributions allow us to exclude electron impact with the ground-state anion as the progenitor of the observed C 2 − * species. Similar arguments will apply to any other formation processes starting from a stable precursor. For example, we have investigated the possible direct formation of C 2

Article
From here on, we therefore focus on electron-driven processes involving transient species−particularly the C 2 H radical, which sits between C 2 H 2 and C 2 in the sequence of Hshifting equilibria involving the C 2 H y (y = 0−6) family. As Figure 8c shows, its number density is predicted to peak at [C 2 H] ≈ 5 × 10 13 cm −3 in the hot plasma region (i.e., to be ≈40-fold higher than [C 2 ]) and to adopt a more spatially extensive distribution than that of C 2 (a), which is given in Figure 8d. As we now show, adding the set of negative ion reactions listed in Table 1 to the C/H reaction mechanism used in our previous 2-D(r,z) coupled kinetic and transport modeling 60 enables near-quantitative replication of the measured I em (C 2 − *) and I em (C 2 *) distributions, their relative intensities, and their respective variations with process conditions.
The dominant source of C 2 − * is deduced to be with DEA also being the main source of ground-state C 2 − in the hot plasma core according to The balance of reactions 5 and −5 and the radiative decay largely determine the C 2 − * concentration and thus the emission intensity, I em (C 2 − *). Other possible quenching processes, e.g., C 2 − * + H 2 → products, are unimportant relative to the reactive quenching process −5 under the present conditions.
In the quenching of C 2 * species, however, the roles of H and H 2 are completely different. I em (C 2 *) is modeled simply as the balance between EIE 51 radiative decay and the quenching process C 2 * + H 2 → products, e.g.
where C 2 H † represents C 2 H products possessing some, but undefined, internal excitation. We have not found information on either the rates or the major products of reaction 10, which, as written, is exothermic by ≈3 eV. Pasternack et al. 80 reported a rate constant k −12 [cm 3 s −1 ] ≈ 1.5 × 10 −11 exp(−3012/T gas ) for the corresponding reaction of C 2 (a) radicals with H 2 (reaction −12 below) and, lacking alternative information, we have adopted a similar form for k 10 (T gas ) in Table 1. The C 2 H † products are assumed to be rapidly quenched by H 2 and C 2 H 2 with rate coefficients in the range (0.5−1.5) × 10 −10 cm 3 s −1 (ref 81), so reaction −10 is not considered to be a source of C 2 *. Other possible C 2 * loss processes such as the reactive quenching reaction for which we deduce a rate coefficient k(T gas ) < 3.7 × 10 −12 cm 3 s −1 from the coefficient of the reverse chemiluminescent reaction, 51 is too slow to be important under the prevailing plasma conditions. So, too, is the quenching of C 2 * by CH 4 (with a reported rate coefficient 3.7 × 10 −11 cm 3 s −1 at T gas = 298 K) and other hydrocarbons. 82 The rate coefficient for the associative detachment reaction − 4 is due to Barckholtz et al. 78 We have not found reported DEA cross sections for reactions 5 and 6. The expression for k 5 was chosen to provide a value k 5 ≈ 1.5 × 10 −12 cm 3 s −1 in the hot plasma region. Such a value, along with the appropriate rate coefficients k 8 and A 9 (Table 1) Figure 9a. The respective profiles and the ratio of these column densities all match well with the measured I em (C 2 *) and I em (C 2 − *) profiles and I em (C 2 *)/I em (C 2 − *) ratios. Changing the activation energy in the expression for k 5 has little impact on the predicted {C 2 − *(v′=0)} profile. The rate coefficient k 6 is also not known, but its value is unimportant from the viewpoint of C 2 − * emission. Reaction 6 will contribute to C 2 − production but, as discussed above, C 2 − is not a significant source of the observed C 2 − * in the proposed mechanism. One other aspect of the present data and its interpretation requires comment. The C 2 − * species are deduced to be formed directly by DEA to C 2 H. The radiative lifetime of the C 2 − (B) state is short (≈77 ns 69,70 ), but more than an order of The Journal of Physical Chemistry A Article magnitude longer than the interval between collisions under the prevailing plasma conditions. Thus, the conclusion, from the spectral simulation (Figure 2b), that the C 2 − * species are in local thermodynamic equilibrium (LTE) is not wholly surprising. Rate coefficients for vibrational and, particularly, rotational relaxation of electronically excited molecules are typically higher than those for the corresponding ground-state species. 83 In our particular case, rotational-to-translational (R → T) energy relaxation of C 2 − *(v′,N′) on H 2 is likely to be efficient. The fact that the light departing H atom formed in the DEA process is unlikely to generate a significant torque on the C 2 − * partner provides further reason why these anions show a rotational-state population distribution consistent with the rotational excitation of the C 2 H precursor and thus the local T gas . The C 2 − * vibrational-state population distribution (C 2 − *(v′)) also appears to be in LTE. This may simply reflect a large (>10 −10 cm 3 s −1 ) V → T relaxation rate coefficient for C 2 − * in collision with H 2 but may also be a reflection of the very similar equilibrium C−C bond lengths in the C 2 H(X) radical (1.210 Å 84 ) and in the B state of C 2 − (1.223 Å 67 ), thereby ensuring only a vertical Franck−Condon contribution to the vibrational excitation.
The conclusion that reaction 3 is a dominant source of C 2 − near the substrate (Table 1) is key to explaining the very different profiles for C 2 − * and C 2 − , which are reflected in the respective calculated column densities (Figure 9a,b, respectively). In contrast, the spatial similarity of I em (C 2 − *) and I em (C 2 *) (recall Figure 3) is understandable given the similar zprofiles calculated for {C 2 H}, Figure 9c, and {C 2 (v=0)}, Figure  9b, these being the dominant sources of the respective electroninduced emissions (i.e., DEA to C 2 H (5) and EIE of C 2 (8), respectively). Reactive quenching of C 2 − * by H atoms, reaction (−5), and of C 2 * by H 2 molecules, reaction 10, also influences the calculated {C 2 *(v=0)}/{C 2 − *(v=0)} ratios and, as we now show, can account for the major p-and P-dependent variations in the measured I em (C 2 *)/I em (C 2 − *) ratio.

Explaining the Process Condition Dependent
Trends in I em (C 2 − *) and I em (C 2 *). Analysis of the main C 2 * and C 2 − * production/loss reactions provides a rationale for the quite different dependences of I em (C 2 − *) and I em (C 2 *) on both pressure and power (Figures 4 and 6).
I em (C 2 *). As noted above, C 2 * is produced by EIE of C 2 (a) (reaction 8), balanced by radiative decay (9) and reactive quenching (10); its number density will be given by an expression of the form    8 and 2, respectively, and the P = 0.7 and 0.9 kW data in (d) have been multiplied by factors of 4 and 3, respectively, prior to display. To compare with the observed I em (C 2 *) and I em (C 2 − *) intensities (Figures 3 and 5), the column densities in (a) and (d) must be multiplied by the respective Einstein coefficients A 9 (v′=0→v″=0) and A 7 (v′=0→v″=0) (as in Figures 4 and 6 and described in section 3.4 and Table 2).
The aforementioned rate coefficient k −12 (T gas ) 80 and thermochemical data were used in calculating the forward reaction coefficient k 12 (T gas ) ≈ (7.05 × 10 −8 /T gas ) × exp(−8180/T gas ). Balancing the direct and reverse H-shifting reactions 11 and 12 gives the following relation for [C 2 (a)]: The calculated intensity I em (C 2 *) calc (with units of cm −2 s −1 ) is then the product A 9 (v′=0→v″=0) × {C 2 *}, where A 9 (v′=0→ v″=0) = 7.63 × 10 6 s −1 (ref 65) and the column density {C 2 *} ∼ [C 2 *] × 2R pl (where R pl (z) is the plasma radius) has the following dependence as a result of reactions 8−12: The 2-D model calculations show that the [H]/[H 2 ] ratio in the plasma region is roughly proportional to both pressure and power, whereas the electron density n e and temperature T e depend only weakly on p and P. The maximal gas temperature T max increases by a few percent with increasing p (the calculated T max ≈ 2825, 2890, 2920, and 2970 K at p = 75, 150, 225, and 275 Torr, respectively, at P = 1.5 kW) and P (T max ≈ 2765, 2890, and 2930 K at P = 0.7, 1.5, and 1.85 kW, respectively, at p = 150 Torr). [C 2 H 2 ] dominates the total carbon content and is thus proportional to the gas concentration and thus to p (if we neglect the weak variations in T max ). Radiative decay is dominant under the present conditions (A 9 /(k 10 [H 2 ]) > 4 under base conditions, Table 1 59,85 ) and in the product (k 11 /k −11 ) × (k 12 /k −12 ) (which increases with p) largely compensating one another.
The 2-D modeling also rationalizes the observed near cubic power dependence of {C 2 *}. [C 2 H 2 ] is essentially independent of P. The {C 2 *} ∼ R pl × (k 11 /k −11 ) × (k 12 /k −12 ) × ([H]/ [H 2 ]) 2 ∼ P 3 dependence in this case relies on the same ([H]/ [H 2 ]) 2 ∼ P 2 contribution as above, supplemented by weaker, less than linear, increases in the ratio of the reaction coefficients (k 11 /k −11 ) × (k 12 /k −12 ) (which increases as a result of the Pinduced increase in T gas ) and in R pl (which scales as ∼ P 0.5 due the increased plasma volume, V pl ∼ P. 59 *} should show a (more than) linear increase with p at low p, but that the gradient of any such plot should decline to less than linear at higher p, in almost quantitative accord with the I em (C 2 − *) data shown in Figure 4 over the range 50 ≤ p ≤ 200 Torr. Figure 4 suggests a further rise in I em (C 2 − *) at p > 200 Torr, though we caution that these data points carry progressively larger error bars. The present 2-D model calculations could accommodate such a trend by assuming a value k 1 ≈ 3 × 10 −29 cm 6 s −1 for the three-body reaction 1. Further speculation is unwarranted at this time, but we note that such a value lies well within the range (∼10 −31 −10 −28 cm 6 s −1 ) reported for many other three-body electron attachments. 73,87 We also highlight that inclusion of the quenching reactions −5 within the overall mechanism is crucial for reproducing the diverse dependences of I em (C 2 − *) on p and P. Comparisons between I em (C 2 − *) and I em (C 2 *).  (Table 1) also reproduces the measured p-and Pdependent variations in the I em (C 2 *)/I em (C 2 − *) ratio well, as can be seen from the ratios of the calculated intensity maxima shown in Table 2.
Effects of Varying F(CH 4 ) and F(Ar). The functional dependences (13) and (14) derived above and our previous OES/actinometry, 42,51 CRDS, 42,64 and 2-D modeling studies 51,60 also enable explanations of the measured dependences of I em (C 2 − *) and I em (C 2 *) when the input mole fractions of both methane, X 0 (CH 4 ), and argon, X 0 (Ar) are varied ( Figure  7). Equations 13 and 14 show that {C 2 *} and {C 2 − *} are both linearly proportional to [C 2 H 2 ] which, in turn, is proportional to X 0 (CH 4 ). 60 The other terms in eqs 13 and 14, e.g., [H], the [H]/[H 2 ] ratio, and T e (which appears in k 5 and k 8 and has less direct influence on other plasma parameters like n e ), are barely changed by increasing the methane fraction in the range 0.66 ≤ X 0 (CH 4 ) ≤ 9.09% (as shown, for example, in Figure 3b of ref 42). Thus, we should predict a broadly linear increase in I em (C 2 − *) and I em (C 2 *) (and a constant I em (C 2 − *)/I em (C 2 *) ratio) with increasing X 0 (CH 4 ), as observed (Figure 7a). Figure 7b showed the corresponding trends observed when X 0 (Ar) varies in the range 0 ≤ X 0 (Ar) ≤ 19%. [ 3.5. Further Implications for Plasma Activated Diamond CVD. C 2 is not the only radical species present in C/H plasmas that has a large electron affinity (E ea = 3.269 ± 0.006 eV 72 ). The electron affinity of C 2 H is almost as large (E ea = 2.969 ± 0.006 eV 72 ), and that of the CN radical (which will be present if the plasma includes, whether by design or by accident, any nitrogen-containing precursor) is even larger (E ea = 3.862 ± 0.004 eV 88 ). Of the resulting anions, only C 2 − is an open-shell species, with bound excited electronic states capable of supporting OES in the visible spectral region. C 2 H − and CN − are isoelectronic with N 2 ; their excited electronic states all lie at much higher energies, above the respective E ea values. As Table 1 shows, the steady-state concentrations of anions like C 2 − and C 2 H − in a MW-activated C/H plasma are largely determined by DEA reactions 3, 4, and 6, balanced by associative attachment reactions −4 and −6. The rates of all other anion production and loss mechanisms (e.g., photoattachment, recombination with positive ions, electron detachment by electron impact, etc.) are orders of magnitude lower. As panels a, c, and d of Figure 9 show, the spatial profile of the C 2 − * anions revealed by OES is not representative of the majority anions. These are predicted to be C 2 H − (X), from reaction 4, supplemented by ground-state C 2 − anions from reactions 3 and 6. The column densities of these ground-state anions are predicted to peak at small z ≈ 1.5 mm, as with the main cations (C 2 H 2 + and C 2 H 3 + ), but to be 3−4 orders of magnitude smaller than those of the cations under base conditions.
We can also predict (perhaps surprisingly) high abundances of CN − anions in the case of N-containing C/H plasmas. As shown in our recent combined experimental and modeling studies of MW and DC activated CH 4 /N 2 /H 2 plasmas, HCN is by far the most abundant N containing species (besides N 2 ) in the near substrate region. 59 59 Extrapolating to lower N 2 input mole fractions, even with X 0 (N 2 ) = 100 ppm, we predict that CN − anions from process 15 could account for ∼5% of the total near substrate anion concentration (which will then be dominated by [C 2 H − ] < 3 × 10 7 cm −3 from process 4). We reiterate, however, that this anion number density is still 3 or more orders of magnitude lower than the concentrations of electrons and the positive ions n e ∼ ∑[C x H y + ] ∼ 10 11 cm −3 . Negative bias enhanced nucleation (BEN) has long been recognized as a route to accelerating diamond film growth on silicon substrates 62 and is generally rationalized in terms of impacting C/H-containing cations yielding an interfacial SiC layer that facilitates subsequent diamond growth. 91−94 The present identification of C 2 − * anions in a MW activated C/H plasma typical of those used for diamond CVD, and the deduction that other anions (e.g., C 2 H − , and CN − in the presence of adventitious N 2 ) must also be present in the near substrate region, offer a plausible explanation for the (fewer) previous reports 31,40,63 that the application of a positive bias voltage to the substrate can also lead to enhanced nucleation densities and growth rates. Negative BEN exploits the majority ions: as shown above, the cation densities in these plasmas are several orders of magnitude higher than those of the anions. But the dominant anions identified in the present work have much higher average C:H ratios, which may be beneficial for developing a carbon-rich seed layer.

CONCLUSIONS
Electronically excited C 2 − * anions have been identified, by spatially resolved imaging of their optical emission, in a MWactivated C/H/(Ar) plasma operating under conditions appropriate for diamond CVD. Various possible formation mechanisms have been modeled, only one of which (DEA to C 2 H resulting in direct formation of the observed C 2 − * anions, balanced by the inverse associative detachment process) is consistent with the observed spatial distributions and the measured variations in emission intensity with the C/H/(Ar) ratio in the process gas mixture, the total pressure, and the applied MW power. The same 2-D(r,z) plasma-chemical modeling predicts DEA to C 2 H 2 as a yet more important source of (C 2 H − ) anions in such plasmas, and DEA to HCN as an efficient route to forming CN − anions when a nitrogencontaining precursor is present. This work thereby extends previous analyses of such MW-activated diamond CVD plasmas that assume the charged particles to be exclusively cations and electrons. Although the predicted anion densities never exceed 0.1% of the cation density under any conditions investigated, their newly confirmed presence may offer some rationale for Table 2. pand P-Dependent Variations in the I em (C 2 *)/ I em (C 2 − *) Ratio Measured for the Strip Centered at z = 11.25 ± 0.75 mm Compared with the Corresponding Ratios of the Respective Maximum Intensities Calculated Using the Reaction Mechanism in Table 1 *