Imaging and Modeling C₂ Radical Emissions from Microwave Plasma-Activated Methane/Hydrogen Gas Mixtures: Contributions from Chemiluminescent Reactions and Investigations of Higher-Pressure Effects and Plasma Constriction

Abstract

Wavelength and spatially resolved imaging and 2D plasma chemical modeling methods have been used to study the emission from electronically excited C2 radicals in microwave-activated dilute methane/hydrogen gas mixtures under processing conditions relevant to the chemical vapor deposition (CVD) of diamond. Obvious differences in the spatial distributions of the much-studied C2(d3Πg–a3Πu) Swan band emission and the little-studied, higher-energy C2(C1Πg–A1Πu) emission are rationalized by invoking a chemiluminescent (CL) reactive source, most probably involving collisions between H atoms and C2H radicals, that acts in tandem with the widely recognized electron impact excitation source term. The CL source is relatively much more important for forming C2(d) state radicals and is deduced to account for >40% of C2(d) production in the hot plasma core under base operating conditions, which should encourage caution when estimating electron or gas temperatures from C2 Swan band emission measurements. Studies at higher pressures (p ≈ 400 Torr) offer new insights into the plasma constriction that hampers efforts to achieve higher diamond CVD rates by using higher processing pressures. Plasma constriction is proposed as being inevitable in regions where the local electron density (n e) exceeds some critical value (n ec) and electron–electron collisions enhance the rates of H2 dissociation, H-atom excitation, and related associative ionization processes relative to those prevailing in the neighboring nonconstricted plasma region. The 2D modeling identifies a further challenge to high-p operation. The radial uniformities of the CH3 radical and H-atom concentrations above the growing diamond surface both decline with increasing p, which are likely to manifest as less spatially uniform diamond growth (in terms of both rate and quality).

Self-consistent modeling of microwave activated N2/CH4/H2 (and N2/H2) plasmas relevant to diamond chemical vapor deposition

“…The reasons for this (particularly the deduced relation [CHx] ~ (X0(CH4)) 0.5 ) have been detailed previously [51,62]. The rates of fast and critical reactions (39) and (40) are in near balance (Table 2), with the mis-balance (less than 10%) accommodated by the 1 CH2 + H ↔ CH + H2 reaction (which is not of sufficient importance under the present conditions to merit inclusion in Table 2). Similar to {CN}max(p), the calculated pressure dependence {CH}max ≈ 3.4×10 12 ×(p/150) 2.25 cm -2 (with p in Torr, Table 3) is induced by the complex p-dependences of all three terms in the relation…”

“…The predicted maximal C2(a 3 Πu) radical column densities, {C2(a),(v=0)}max, included in Table 3 clearly show such a linear dependence on X0(CH4). This can also be expressed via the 2 , which reflect the partitioning between the various C2Hy species as a result of the fast H-shifting reactions [40]. Such relationships are also revealed by the stronger than linear dependence of {C2(a),(v=0)} on pressure p and by its insensitivity to N2 additions, as shown in Table 3.…”

“…The main contribution to substrate heating is conduction from the hot gas, but H atom adsorptions at C* sites become increasingly important at higher p. The present modelling suggests that the latter process contributes, respectively, 13, 21, 27, 32% to Ps at p = 100, 150, 200, 350 Torr. Sources of substrate heating and typical gas-surface loss probabilities of ~0.1 for incident H atoms (from H addition and H abstraction reactions at the substrate surface) have been discussed previously (e.g., [62] and [64]), as has the reduction of gas phase [H] (along with the much smaller drop in [CH3]) from such gas-surface processes (section 3.4.2 of [40]).…”

“…The uncertainty in these rate coefficients hampers interpretation of the measured {CH} column densities. That the forward and reverse reactions proceed via an intermediate CH3* complex ensures that their rates are p and Tg dependent [79], suggesting that it may be inappropriate to treat reactions (39) and (40) in Table 2 as a simple reversible 3 CH2 + H ↔ CH + H2 conversion or to estimate the k39/k40 ratio from thermochemical data, as in [67]. The present modeling confirms that these conversions should be treated as two separate reactions (39) and ( 40), with associated rate coefficients measured under similar high Tg conditions.…”

Nongrowth regime in microwave chemical vapor deposition reactor due to formation of plasma nonhomogeneity

“…[ 17,18 ] In addition, in a mixture of gases H 2 + CH 4 , with increasing pressure, the dominant ion in the plasma can change to one that has a significantly higher recombination coefficient and lower mobility. [ 31,32 ] An increase in recombination rate and a decrease in diffusion provide volumetric electron losses. Estimates show that the diffusion loss length due to recombination $$\sqrt{{D}_{a}/(\alpha {N}_{{\rm{e}}})}$$, where D a is the diffusion coefficient, α is the recombination coefficient, and N e is the electron concentration, is about 1–2 mm.…”