Plasma-produced NxHy radicals facilitate the removal of native oxide layers in a semiconductor wafer surface. A remote microwave excited plasma with a NH3–N2 feed gas is used commonly to produce the active radicals. We perform a three-dimensional modeling of a microwave excited plasma operating in a surfatron mode. The device consists of a rectangular waveguide intersecting a quartz tube through which the feed gas flows. We discuss the propagation of a polarized 2.45 GHz microwave from the waveguide into the quartz tube where power is deposited into the plasma. The plasma–wave interaction is found to be highly three dimensional, with a propagating surface mode of the wave established along the dielectric tube plasma interface. Significant heating occurs on the side of the tube that directly faces the incident wave. As the flow carries the plasma-produced species down the tube, species radial profiles become increasingly diffusion controlled and axisymmetric. The dominant radicals that exit the tube are H2 and NH2, with nearly complete conversion of the feed gases to product species. The gas temperature rises above this inlet feed gas temperature and increases with increasing wave power. However, the gas temperature increase is not consequential to the overall radical yield from the plasma. The parametric study with changing pressure and input power illustrates the role of specific chemical reactions in the overall remote plasma process.

Wafer surface cleaning processes are essential steps in semiconductor integrated circuit manufacturing. In the early days of large-scale integrated circuit manufacture, wet (liquid)-etch/clean techniques were widely used in the industry for surface cleaning processes, but the excess waste generated in these processes was a source of concern, although the use of wet etchants also offers some advantages. Dry (plasma) etching/cleaning can be used where wet etching faces limitations, but at the same time, it is accompanied by other problems such as residue buildup in the plasma chamber, exposure of the wafer surface to ultraviolet (UV) radiation1,2 and ion bombardment that damages the processed surface.3 Hence, the choice between wet and plasma etching will depend on the requirements of the process and process limitations.

Dry etch/clean processing using remote plasma sources (RPSs) has proven ideal for wafer cleaning processes.4 Here, a plasma is generated remotely (some distance away from the wafer surface) and long-lived radical species from this source are transported to the wafer surface where the etch/clean process is facilitated through purely chemical reactions.2,3,5,6 UV and ion-impact damage to the wafer is, therefore, avoided since there is no direct view of the process surface to the plasma. The pure chemical etch reactions also ensure high cleaning selectivity. As briefly explained above, an RPS consists of a plasma chamber (where the discharge is located) that is at a distance from the processing chamber, thus avoiding the exposure of the wafers to UV radiation. Besides, due to the physical distance between plasma and process chambers, charged particles generated in the plasma recombine rapidly leading to only active neutral species interactions with the process surface. Ion and UV induced damage is, therefore, eliminated and high cleaning selectivity is ensured through the pure neutral process chemistry (defined as the ratio of oxide removal to substrate etching).

In this work, we focus on a plasma native oxide cleaning (PNC) process for the removal of thin native oxide layers from Si wafer surfaces. The process is used extensively in the semiconductor integrated circuit manufacturing and is indispensable with the introduction of three-dimensional (3D) integration of semiconductor integrated circuits and the downscaling of their dimensions below 10 nm3. Importantly, Cho et al.7 have shown that PNC with RPS can effectively remove thin film material in the lateral direction of the 3D structure, thereby achieving a highly conformal clean step.

The RPS of interest in this work is a 2.45 GHz microwave-generated plasma that fragments a gas mixture of N2 and NH3 to produce active radical species. These NxHy radicals are transported into the batch processing reactor where NF3 gas is also introduced and reacts with the NxHy radicals to produce NHxFy radicals. The radicals can then react with SiO2 on the wafer surface to produce ammonium fluorosilicate (AFS) [(NH4)2SiF6] that is volatile at 100 °C and can be removed as a gaseous byproduct, thereby stripping the wafer of the native oxide layer.5,8

Optimization of the PNC process is critically dependent on an understanding of the chemical composition of the effluents (products) from the RPS source. This work seeks to provide a detailed, first-principles modeling and simulation-based understanding of a remote plasma feed gas activation process for the PNC process.

The plasma is initiated by a propagating electromagnetic (EM) wave with a frequency in the microwave range. The reactor is designed to produce a peak value of the electric field near the dielectric barrier so that the gas is ionized. At low ionization degrees, the wave frequency is larger than the plasma frequency, and the wave can propagate through the plasma, further enhancing ionization.9 As the electron density increases over the critical (cutoff) density, calculated as m e ε 0 ω 2 / e 2 (7.45 × 1016 m−3 for 2.45 GHz wave), where me is the electron mass, ε 0 is the vacuum permittivity, ω is the wave frequency, and e is the electron charge, shielding effects prevent the wave from penetrating into the discharge. A surface wave is then formed, which propagates along the plasma–dielectric interface at the tube wall, and helps to sustain the plasma column away from the excitation point where the microwave impinges on the plasma tube. The ability to tune the plasma column to the required length is one of the key features of microwave reactors.

Different configurations of the surface wave launchers have been discussed and characterized in the literature.10–12 Surfaguides and surfatrons are widely used for a variety of industrial and scientific applications, and each configuration has its benefits and shortcomings. Moisan et al.13 also introduced the design of the waveguide surfatron, which combines the high-power capabilities of the surfaguides and the tunability of the surfatron, which also allows for a larger plasma tube diameter. The device consists of a rectangular waveguide through which the microwave propagates and cylindrical tube that carries the working gas which penetrates waveguide structure perpendicular to the wave propagation direction in waveguide. The design includes two tunable short-circuiting plungers which can be moved to maximize the efficiency of the power transfer between the EM wave and the plasma. However, the modeling of the plungers and the optimization of power deposition are not part of the scope of this paper, and a simplified representation of the surfatron that focuses on wave propagation to the gas tube and the interaction of the wave with the plasma in the tube (see Sec. III A) is considered.

The mathematical model for the PNC device is comprised of a coupled system of governing equations for each of the physical phenomena in the plasma, i.e., plasma dynamics, electromagnetic wave, gas flow, and plasma chemistry. The description of the mathematical model is described in detail our previous work.14 

A nonequilibrium plasma model is assumed in this study. The governing equations include continuity for each individual species (see Sec. III B), electron energy, and electrostatic field equations, which are then solved in a self-consistent manner. The plasma composition, i.e., the number densities of all species, is computed by solving the continuity equations, which are formulated as
n j t + Γ j = G ˙ j .
(1)
Here, j denotes the index of a specific species and n j its number density. The source term G ˙ j is determined by the rate coefficients used for the production and/or destruction processes involving that individual species, as given by the chemistry mechanism. A zero-dimensional electron Boltzmann equation solver, BOLSIG+,15 was used to compute the rate coefficients for electron-impact reactions as a function of the mean electron energy. The drift-diffusion approximation (diffusion only for neutral species) was used to compute the flux terms, Γ j, for both charged and neutral species,
Γ j = n j u j = Z j μ j n j ϕ D j n j + n j V .
(2)
This approximation is a simplification of the species momentum equation in a collisional plasma, and it is valid under conditions in which the characteristic length scale of the problem is significantly larger than the species mean free path,16,17 e.g., in high pressure conditions. In Eq. (2), Z k, μ j, and D k are the charge number, mobility, and diffusion coefficient of jth species, respectively, u j is the species velocity of jth species, and v is the bulk flow velocity computed from the flow model. Electron transport properties are computed as a function of electron temperature, T e, using BOLSIG+, while ion transport properties are obtained from experimental data. Gauss's law was used to compute the electrostatic potential in the plasma domain,
( ϵ r ϕ ) = q ϵ 0 j Z j n j ,
(3)
where ϕ is the electrostatic potential, q is the elementary charge, ϵ r is the relative dielectric constant, ϵ 0 is the permittivity in vacuum, and Z j is the species charge number. The mean electron energy e e is defined in terms of the electron temperature as
e e = 3 2 n e k B T e ,
(4)
where n e is the electron number density and k B is the Boltzmann constant. The electron energy conservation equation is solved to compute e e,
t ( e e ) + ( ( 5 3 μ e ϕ + V ) e e 5 3 D e ( e e ) ) = q e n e u e ϕ + S ˙ + Λ e , coll + Λ in , coll .
(5)
Here,
Λ el , coll = 3 2 k B n e 2 m e m j b ( T e T g ) ν e , j b
and
Λ in , coll = q e i Δ E i e r i .
(6)
In Eq. (6), m e is the electron mass, m j b is the mass of jth species, ν e , j b is the electron momentum transfer collision frequency, q e is the fundamental charge, Δ E i e is the energy loss/gain per electron due to inelastic collisions in the ith reaction, and r i is the rate of progress of ith reaction. Λ el , coll and Λ in , coll are the elastic and inelastic collisional loss terms for the electron energy, respectively. A common temperature T g is assumed for all heavy species (ions and neutrals) and is computed from the flow model. S ˙ is the electromagnetic wave Joule heating term, which depends on the wave-induced current density in the plasma and the wave electric field. As will be discussed in Sec. II C, the wave quantities are solved in time harmonic form and the wave Joule heating term is written as
S ˙ = 1 2 R e ( j ~ E ~ m ) ,
(7)
where E ~ m is the complex conjugate of the electromagnetic wave total electric field phasor and j ~ is the electron conduction current density. Re ( ) is the real part operator for the complex number inside the bracket.
The species number fluxes are prescribed at the solid surfaces. For electrons ( Γ e ) and neutrals ( Γ n ), the fluxes are assumed to be Maxwellian with the appropriate temperatures and species densities. For ions, the flux, Γ i, is defined using the drifting Maxwellian model,
Γ e n ^ = 1 4 n e 8 k B T e π m e , Γ n n ^ = 1 4 n n 8 k B T e π m e , Γ i n ^ = 1 4 n i 8 k B T g π m i + n i max ( 0 , μ i n ^ s ϕ ) .
(8)
The flow is assumed to be laminar, and the compressible Navier–Stokes model is used. Hence, the fluid conservation equations for mass, momentum, and energy are solved,
ρ t + ( ρ v ) = 0 ,
(9)
ρ v t + ( ρ v v + p ) = . τ ,
(10)
and
t [ ρ ( e + v v 2 ) ] + ( ρ ( e + v v 2 ) + p ) v = τ . v k T + Λ g , coll .
(11)
Here, ρ is the total density, p is the total pressure, e is the total energy, τ is the shear stress, κ is the thermal conductivity, and V is the bulk flow velocity. The last term in Eq. (11), Λ g , coll, is the flow energy gain due to collisions with the electrons and is given as
Λ g , coll = 3 2 k B n e 2 m e m k b ( T e T g ) ν e , k b q e j Δ E j g r j .
(12)

Here, the summation in the second term is done over all species except the electrons. The first term represents the heating due to electron-heavy elastic collisions, while the second term corresponds to the energy losses due to inelastic collisions in heavy species reactions. Δ E j g is the energy lost/gained by the heavy species in the kth inelastic collision reaction. Note that the first term in Eq. (12) is opposite in sign, but equal in magnitude, to the elastic collision source term in Eq. (6), since the energy lost by electrons is gained by the heavy species involved in the collisions.

In this flow model [Eqs. (9)–(11)], the solution of the individual species density equations [Eq. (1)] for all species, except the background N2 and NH3, imposes mass conservation. For the feed gases, the mole fractions of N2 and NH3 are specified, and the absolute densities are computed from the pressure, p, the assumed ratio of these species in the gas mixture, and the partial pressures from all other species,
p N 2 , N H 3 = p k N 2 , N H 3 n k k b T k .
(13)
Electromagnetic waves are resolved by solving Maxwell's equations in the frequency domain. The Drude model15 is used to describe the electron conduction current associated with the electric field. The frequency domain representation of the model yields a complex plasma conductivity,
σ ~ = n e e 2 m e ( ν e + i ω ) ,
(14)
where all quantities are the same as defined above and ω / 2 π is the EM wave frequency. Then, with this expression for the plasma conductivity, the Maxwell's equation for the electric field phasor is reduced to
× μ 1 E ~ m = ( ω 2 ϵ 0 ϵ r i ω σ ~ ) E ~ m ,
(15)
where μ is the magnetic permeability. In this study, we consider the magnetic permeability to be the same as the vacuum permeability for all materials. The material permittivities are real quantities, and the complex plasma conductivity allows us to account for the phase relationships, hence ϵ r = 1 for the plasma.18 Equation (15) is coupled to the plasma equations via the electron density and the electron temperature dependence of the electron conductivity terms.

Note that in the electromagnetic wave–plasma interaction model, the effect of the electromagnetic wave on the plasma is only via the power deposition to the electrons.19 For high frequency discharges (GHz), the evolution of electromagnetic fields occurs in timescales below the nanosecond order. Thus, these are much faster than the timescales associated with the plasma evolution and do not contribute to transport effects in the plasma. However, the electrostatic fields computed in Eq. (3) are the result of the plasma formation process, as well as the resulting charge deposition on surfaces and charge separation in the plasma domain. Therefore, the evolution timescales of the electrostatic fields are comparable to the timescales associated with plasma generation, and this field is the main contributor to the transport of electrons and charged species in the plasma. This approach, where the total electric field and its contributions are decomposed based on evolution timescales has been used for simulation of microwave driven plasmas20 and capacitively coupled plasma (CCP) discharges21 and is accurate for incident waves at high frequencies.22–24 

It is essential to couple the plasma, flow, and electromagnetic wave effects in a consistent manner in order to resolve the transients associated with plasma breakdown and to capture the long timescales associated with the plasma evolution process. This coupling can be visualized in Fig. 1. The plasma affects the gas flow properties, mainly due to heating from collisional (both elastic and inelastic) processes, as given by Λ g , coll, which appears as a source term for the gas flow temperature. The flow model resolves the macroscopic properties, such as the total pressure, bulk flow velocity, and gas temperature, which are then fed into the plasma model. Here, the pressure, p, is used to impose the background species densities; T g is used to compute the electron heating collisional source terms; and the flow velocity, V , contributes to the transport of individual plasma species. In turn, the electron number density, n e, and the mean electron temperature, T e, given by the plasma model are communicated to the electromagnetic wave model, since they have a strong influence on the electrical conductivity given in Eq. (15). The electron ohmic heating, computed from the solution of the electromagnetic wave electric field and the electron current density, is a source term for the electron energy equation [Eq. (5)].

FIG. 1.

Block diagram showing the coupling in the computational model. Green-dash arrows indicate input (In) terms, and red-point arrows indicate outputs (Out).

FIG. 1.

Block diagram showing the coupling in the computational model. Green-dash arrows indicate input (In) terms, and red-point arrows indicate outputs (Out).

Close modal

Open-source program SALOME was used to create the geometry and the mesh; the apparatus used in this study consists of two main components: a rectangular waveguide and a hollow quartz ( ε = 3.8 ) tube that goes through it, following the same configuration used by Ryu et al.25 

Figure 2 shows a schematic of the apparatus being modeled. From the commercially available rectangular waveguides, the WR284 was chosen to be modeled, in accordance with the cutoff frequency of the microwave that will be used for this problem. Accordingly, the waveguide has the following dimensions: 244.80 L × 72.14 W × 36.04 H (all in mm). The gas flows through a 25 mm diameter tube, which has a wall thickness of 2 mm, from top to bottom. The tube is located at approximately 200 mm form the face where the EM wave enters and has a length of 240 mm for this study. The effects of shortening or stretching the tube in the radical exit profiles are not part of the scope of this project and are left as potential new research. To study the transient behavior of different properties, four trace points were defined along the tube as shown in Fig. 2.

FIG. 2.

Cross-sectional view of the apparatus.

FIG. 2.

Cross-sectional view of the apparatus.

Close modal

The mesh consists of tetrahedral elements only, and it was divided into three subdomains: Waveguide, Dielectric (which corresponds to the thin-walled quartz tube), and Gas (which is the space occupied by the plasma). A major refinement of the mesh was done upon the Gas subdomain, since it is the region of greatest interest. Overall, the mesh has a total of about 223 000 cells, of which 79% belong to the Gas subdomain.

1. Ammonia-nitrogen chemistry

A chemistry model consisting of 23 species and 152 reactions was used. Species considered in this study are e, NH3, NH3+, NH4+, NH2, NH2+, NH2, NH, NH+, N, N+, N2, N2+, H, H+, H, H2, H2+, H3+, N2H2, N2H3, N2H4, and NH3(v), and the details about reactions can be found in the  Appendix. According to Arakoni et al.,26 dissociative recombination of NHx+ produces NHx−1 and H, but these are also regarded as exothermic reactions and they produce thermal energy, thus increasing enthalpy of the gas mixture, elevating the gas temperature by the following mechanism:
e + N H 4 + N H 3 + H ( k = 9.0 × 10 7 T e 0.6 c m 3 s 1 , Δ H = 4.7 eV ) ,
N H 2 + H + H ( k = 1.5 × 10 7 T e 0.6 c m 3 s 1 , Δ H = 0.3 eV ) .

Surface chemistry is used to model the loss of radical species along the applicator walls in the form of recombination. Therefore, sticking coefficients on a quartz surface were defined as the following: 1.0 for ion species, 0.01 for hydrogen atoms,27 4.05 × 10−4 for nitrogen,28 and 10−4 for all radicals of type NxHy, which were assumed to be in the same order of magnitude for nitrogen. The sensitivity to these values was not tested in this study due to the high computational expense of the simulations, making it unfeasible to run a large number of simulations.

2. Radical-NF3 chemistry and production of etchants

According to Cho et al.,7 the main reaction mechanism for the removal of SiO2 has the following form:
N H 3 + HF N H 4 F ,
Si O 2 + 4 HF + 2 N H 4 F ( N H 4 ) 2 Si F 6 + 2 H 2 O ,
where the first product in the second reaction is ammonium fluorosilicate (AFS), and both products vaporize at a temperature of 100 °C.

Matsugi et al.29 expanded this reaction mechanism to include important radicals generated by the dissociation of the N2–NH3 plasma: H, NH2, NH, and N. Their study also suggests that the nitrogen present in the gas mixture is primarily responsible for radical generation. Therefore, special attention will be paid to some of these species during the discussion of the results.

The simulation time step was divided into a linear increase from 2 to 10 ns during the first 10 μs, and thereafter a constant timestep of 10 ns was used. EM equations were solved every 10 time steps, and flow equations, every 100 time steps.

Finally, a time snapshot of the outflow boundary was also obtained to quantify the radical densities at the exit of the tube.

We first perform extensive analysis of the baseline case. We discuss in detail the EM wave propagation through the waveguide and absorption of the wave energy in the plasma. The generation of the surface wave (surfatron mode) to produce a relatively large volume plasma is discussed along with the asymmetry of the wave absorption in the plasma. Next, the macroscopic flow properties are analyzed including plasma kinetics of charged and radical species. Finally, a brief discussion of the outlet conditions is provided. Results for the baseline case are followed by parametric studies where the EM power and pressure are varied.

For the reference conditions, pressure at the exit of the tube is maintained at 480 Pa (∼3.6 Torr). A gas mixture of NH3 (0.25 mole fraction) and N2 (0.75 mole fraction) enters the tube with a mass flow rate of 8 .95 times 1 0 5 kg s (corresponding to 3.9 slm of N2 and 1.3 slm of NH3) at a temperature of 400 K. A T E 10 microwave enters the waveguide with a frequency of 2.45 GHz and a setpoint power into the plasma of 2.8 kW. Finally, initial species densities for NH3 and N2 were calculated following the ideal gas law. The initial conditions for the plasma were initiated with very low seed plasma density, which was set at 109 m−3. Simulations were run to a steady state for all cases.

1. EM wave propagation in applicator tube

The electromagnetic wave was excited by applying a plane wave with a fixed amplitude of the magnetic vector potential phasor at the waveguide inlet, which was subsequently controlled throughout the simulation to achieve the specified setpoint plasma absorbed power. Figure 3(a) shows the Poynting vector magnitude through the waveguide, indicating the power flux toward the applicator tube. The wave established a standing wave pattern in the waveguide with a maxima, i.e., an antinode, in the real component of the wave electric field phasor at the location of the applicator tube, which can also be seen as a maxima for the Poynting vector magnitude. Figure 3(b) shows the wave absorbed power density in the plasma at the center of the discharge tube, i.e., the region where the electromagnetic wave impinges on the gas, while Figs. 3(c) and 3(d) show the wave power absorption along the entire applicator tube. As will be discussed in Sec. IV C, the peak electron density approaches ∼1019 m−3, which is much higher than the cutoff plasma density (∼7.5 × 1016 m−3) at the microwave frequency of 2.45 GHz. As discussed in our previous publications22–24 on the interaction of microwaves with a bulk plasma, the wave propagation is rapidly damped in the overdense plasma, with significant wave power absorption limited to a thin skin layer at the periphery of the plasma adjacent to the applicator tube inner surface. A rough ordering of the relevant frequencies in the wave–plasma interaction can be estimated as ω p e ω > ν e, where ω p e = ( e 2 n e ϵ 0 m e ) 1 / 2 is the plasma frequency estimated at about 150 GHz, ω = 2 π f is the microwave frequency of 15.4 GHz, and ν e is the electron collision frequency estimated at about 4 GHz. The much larger plasma frequency compared to the microwave frequency indicates that wave propagation is mostly evanescent, i.e., it is reflected from the bulk of the plasma.22 The electron collisions are, however, responsible for damping of the wave and absorption of the power into the plasma. The high plasma density, however, has a beneficial effect when confined by the dielectric tube, creating a sharp dielectric–plasma interface through which a surface plasmon polariton (SPP) type surface wave can propagate axially toward the applicator tube inlet and outlet. This wave is evanescent in the directions perpendicular to the interface but can propagate unhindered along the interface.23,30 Indeed, this behavior is evident from Figs. 3(c) and 3(d), where the wave absorbed power extends to significant distances away from the waveguide–tube intersection location toward the tube inlet and outlet. A much more elongated plasma will, therefore, be realized in the applicator tube than the axial distance defined by the waveguide–tube intersection. The surface wave is, however, damped gradually by the electron collisions thereby limiting overall elongation of the plasma as seen in the figures. Another important aspect of the plasma inside the applicator tube is the azimuthal asymmetry in the discharge. Power absorption is markedly higher and more elongated on the wave-facing side of the applicator tube compared to the side on the shadow of the wave propagation direction, as evidenced by Figs. 3(b)3(d). As will be discussed in Secs. IV A 2 and IV A 3, this asymmetry will have consequences on the uniformity of radical generation in the tube.

FIG. 3.

EM power deposition: (a) Poynting vector magnitude (W/m2), white arrows show the power transfer direction; (b) top view of absorbed power in plasma at center of discharge (W/m3); (c) absorbed wave power in the plasma (W/m3) for a slice parallel to wave propagation direction in the waveguide; and (d) absorbed wave power for slice perpendicular to wave propagation direction (all in the log scale). The peak values are indicated corresponding to each image. The horizontal dashed lines in (c) and (d) indicate the extent of the waveguide intersection with the tube.

FIG. 3.

EM power deposition: (a) Poynting vector magnitude (W/m2), white arrows show the power transfer direction; (b) top view of absorbed power in plasma at center of discharge (W/m3); (c) absorbed wave power in the plasma (W/m3) for a slice parallel to wave propagation direction in the waveguide; and (d) absorbed wave power for slice perpendicular to wave propagation direction (all in the log scale). The peak values are indicated corresponding to each image. The horizontal dashed lines in (c) and (d) indicate the extent of the waveguide intersection with the tube.

Close modal

2. Flow properties

Figure 4 shows the results obtained for important flow and temperature properties through the length of the applicator tube. The flow enters from the top and quickly develops into a Poiseuille flow like profile that satisfies no-slip at the tube wall and a center-peak velocity.31 This profile is disrupted as the flow enters the plasma zone owing to plasma heating that increases the gas temperature and decreases the gas density. Dilatational effects resulting from a decrease in the gas density in turn increase the axial downward flow velocity. The peak gas temperature is about 640 K, i.e., a 240 K increase from the inlet temperature of 400 K. Importantly, the gas temperature increase is confined mostly to the wave-facing side of the applicator tube, which is a direct effect of the azimuthal asymmetry of wave power deposition discussed in Sec. IV A 1. The peak axial flow velocity just prior to the flow entering the plasma zone is about 90 m/s. Once the flow enters the plasma zone, the axial flow velocity increases significantly to about 175 m/s. We also note that the maximum flow Reynolds number defined by the tube diameter, the peak flow velocity, and the viscosity of the gas is about 600, i.e., it is significantly below the critical Reynolds number for laminar-to-turbulent transitions, thus clarifying the validity of our model that precluded turbulent flow effects. The electron temperature has a peak value of about 34 000 K (about 2.9 eV) that is confined to thin regions adjacent to the tube wall, reflecting the distribution and asymmetry of the absorbed wave power in Fig. 3.

FIG. 4.

Flow properties for the baseline case: (a) slice parallel to wave and (b) slice perpendicular to wave. The wave propagates in the positive y-direction. Properties shown: (i) gas temperature (K); (ii) electron temperature (K; log scale); and (iii) axial flow velocity (m/s).

FIG. 4.

Flow properties for the baseline case: (a) slice parallel to wave and (b) slice perpendicular to wave. The wave propagates in the positive y-direction. Properties shown: (i) gas temperature (K); (ii) electron temperature (K; log scale); and (iii) axial flow velocity (m/s).

Close modal

3. Active species formation in the discharge

Figure 5 shows the density profiles for charged species (electrons and dominant ions). The peak electron density is rather high at 7.7 × 1018 m−3 and due to the asymmetric power absorption, it occurs on the wave-facing side of the tube. The H+, NH3+, and NH4+ ions remain confined to the hot region of the plasma, i.e., where the wave power is absorbed in the plasma. The azimuthal asymmetry observed in the wave absorption and the flow properties is also evident in the ion and radical species density profiles for slice parallel to the incoming wave compared to the slice perpendicular to the wave direction. H+ is the dominant ion in the plasma followed by the NH4+, NH3+, and NH+ ions. The ions of type N H x + ( x 3 ) are formed mainly by electron-impact reactions from the corresponding radical fragments NHx. This is evident from the hierarchy of ion densities where the densities of NH3+ > NH2+ > NH+, etc. The large NH4+ ion densities result from nonresonant ion charge exchange reactions of the type (NHx+ + NH3 → NHx−1 + NH4+). The H+ ions are mainly generated from the electron-impact ionization of copious amounts of H radicals that are produced from the NH3 fragmentation process. The N2+ ions are produced mainly by the electron-impact ionization of N2 feed gas in the hot regions of the plasma. With the exception of N2+, all ions are rapidly charge-neutralized once the plasma exits this hot region through recombination reaction pathways. The N2+ ions are long lived and are carried downstream with the flow to form a weak afterglow plasma that extends up to the applicator tube exit. This N2+ afterglow is charge-balanced by electrons that experience ambipolar drift along with these ions.

FIG. 5.

Charged species number densities through applicator in the baseline case. Units in m−3 (log scale; flow from top to bottom): (a) slice parallel to wave and (b) slice perpendicular to wave.

FIG. 5.

Charged species number densities through applicator in the baseline case. Units in m−3 (log scale; flow from top to bottom): (a) slice parallel to wave and (b) slice perpendicular to wave.

Close modal

Figure 6 shows the number density profiles for the dominant neutral radical species. The most dominant radical is the vibrationally excited NH3(v) molecule that results from the low vibrational excitation threshold of about 0.12 eV for the parent NH3 molecule, and the relatively low temperature of 2.9 eV in the microwave excited plasma. As mentioned above, H atoms and the NH2 and the NH molecules result from the sequential fragmentation process due to electron-impact dissociation of the parent molecule NH3 and vibrationally excited NH3(v). The H2 molecule results from several reactions including three-body recombination (2H + M → H2 + M) and conversion reactions (NH3 + H → H2 + NH2, NH2 + H → H2 + NH, and NH + H → H2 + N). Note, here “M” indicates a third body species. The dominant role of the three-body reaction is evident in the density profile of the H and H2 species, where the H is largely confined to the hot region of the plasma and with the highest density of H2 seen in the downstream recombination/afterglow region of the plasma. The heavier-than-feed gas molecules (N2H2, N2H3, and N2H4) are produced by a sequence of recombination reactions of form NHx + NHy → N2Hz + other products. The sequential buildup of the heavier radicals is again evident in Fig. 6 from the gradually increasing density in the downstream/afterglow region of the applicator tube for the heavier species.

FIG. 6.

Neutral species number densities through applicator for the baseline case. Units in m−3 (log scale): (a) slice parallel to wave and (b) slice perpendicular to wave.

FIG. 6.

Neutral species number densities through applicator for the baseline case. Units in m−3 (log scale): (a) slice parallel to wave and (b) slice perpendicular to wave.

Close modal

Figure 7 shows the distribution of some of dominant radical densities at the outlet of the tube. The dominant species at the exit are H2, followed by NH2, N2H2, N2H4, and N2H3. NH densities were negligibly small at the tube exit. Overall, the exit profiles of the species are relatively uniform with density variations across the tube cross section not varying by more than a factor of three, suggesting that recombination smooths out the spatial inhomogeneity introduced by the asymmetric power absorption present in the hot region of the plasma.

FIG. 7.

NxHy radical species number densities (in m−3) at outflow boundary for the baseline case: (a) H; (b) H2; (c) NH2; (d) N2H2; (e) N2H3; and (f) N2H4.

FIG. 7.

NxHy radical species number densities (in m−3) at outflow boundary for the baseline case: (a) H; (b) H2; (c) NH2; (d) N2H2; (e) N2H3; and (f) N2H4.

Close modal

We perform parametric studies to further analyze the radical species yield from the microwave applicator as a function of the microwave power in the plasma and the process chamber pressure (that equals the exit pressure prescribed at the applicator tube exit). Both these variables are important process parameters that can be readily optimized.

1. Effect of EM power

Here, we vary the wave input power into the plasma, with all other conditions remaining the same as in the baseline case. Two simulations were performed, one at 1.6 kW and the other at 3.5 kW. Figure 8 shows the effect of wave power input on the profiles of the absorbed wave power and the real part of the wave E-field. An increase in the total wave power absorbed by the plasma increases the peak wave input power density from 440 MW/m3 at the lowest power of 1.6 kW to 750 MW/m3 for the 3.5 kW case. The peak wave electric field, however, remains unchanged at 22 kV/m for increasing power. The important trend with increasing wave input power is an axial extension of the “hot” region of the plasma with increasing power. As is seen clearly in the absorbed wave power profiles and the wave E-field extends in both the upstream and downstream directions, thus creating an increasingly larger volume of the plasma and a corresponding larger region in which radical production can occur.

FIG. 8.

Effect of varying input power. (a) absorbed wave power density (W/m3) and (b) real part of wave E-field (V/m). All slices parallel to wave propagation and results are in the log scale.

FIG. 8.

Effect of varying input power. (a) absorbed wave power density (W/m3) and (b) real part of wave E-field (V/m). All slices parallel to wave propagation and results are in the log scale.

Close modal

The oscillatory nature of the real part of the wave E-field indicates significant wave length shortening of the wave in the microwave plasma that can occur due to the surface wave propagation along the tube dielectric–plasma interface. Note that the tube diameter is 2.5 cm and the vacuum wavelength for a 2.45 GHz microwave is about 12 cm. The wavelength discernible from the wave E-field is about 1 cm, indicating an over ten times reduction in the wavelength in the plasma. The reason for this wavelength shortening can be attributed to the surface wave dispersion relation discussed in detail by Pitarke et al.30 and in our own work.22,23 For an excitation frequency lower than the surface plasmon frequency, ω p e / 2, the surface wave is propagating and the surface wavelength rapidly deviates (shortens) from the vacuum wavelength with increasing frequency (see Fig. 2 in Pitarke et al.30). This effect resulting from the surface wave dispersion relation can possibly be explained by the subwavelength oscillatory wave E-field.

Figure 9 shows the profiles for the gas temperature, electron temperature, and the axial flow velocity for the three different wave input powers. The peak gas temperature increases from 750 K for 1.6 kW to 940 K for the 3.5 kW cases. The electron temperature increases from 2.3 eV at 1.6 kW to about 3 eV at 3.5 kW. The peak axial flow velocity at the tube outlet increases from 160 to 180 m/s for the corresponding input power changes. This axial velocity increase reflects the dilatation of the flow due to the gas temperature increase that forces high flow velocities. Overall, an approximate doubling of the input results in only a 25% increase in the gas temperature and a 30% increase in the electron temperature. This indicates that increased input wave power is increasingly coupled to the endothermic chemical reactions, i.e., to increasing decomposition of the feed gas and the resulting increasing radical yield as discussed next.

FIG. 9.

Effect of varying input power: (a) gas temperature (K); (b) electron temperature (K, log scale); and (c) axial flow velocity (m/s). All slices parallel to wave propagation.

FIG. 9.

Effect of varying input power: (a) gas temperature (K); (b) electron temperature (K, log scale); and (c) axial flow velocity (m/s). All slices parallel to wave propagation.

Close modal

Figure 10 shows the axial profiles of important radical species density along the axis of the applicator tube for the three input wave powers. Increasing absorbed power in the plasma results in an increase in all radical densities produced in the plasma. The dominant species is the H2 molecule whose density increases monotonically as the gas flows down the tube. The H radical density increases in the hot region of the plasma, and as discussed earlier, its density decreases in the afterglow region as it recombines to form the parent molecule H2 and also as it participates in the conversion/recombination of other radicals produced in the discharge. The NH2 density is the next dominant species as it is produced in the plasma and experiences a gradual decrease as it is consumed in reactions that produce heavier N2Hy species. The N2H2 species is produced by the recombination of the lighter NHy radicals but is also gradually converted to N2H3 and N2H4 through gradual recombination reactions in the afterglow region.

FIG. 10.

Axial profile for different species number densities at all three power levels (outflow is to the right).

FIG. 10.

Axial profile for different species number densities at all three power levels (outflow is to the right).

Close modal

2. Effect of pressure

The specified outlet pressure was varied to analyze the behavior of the plasma and the radical yield as function of the process pressure. The outlet pressure was about doubled from the 3.6 Torr baseline case to 8 Torr, while other operating parameters, including the mass flow rate through the tube, remained unchanged with respect to the baseline case discussed above.

Figure 11 shows results for the gas and electron temperature and the axial flow velocity for the 8 Torr case and Fig. 12 shows the wave E-field, absorbed wave power into the electrons, and the electron number density. Comparing Fig. 4(a) for the baseline case to Fig. 11 and comparing results from Figs. 3(c), 5(a), and 8(b) for the baseline case to Fig. 12, we can make observations on the effect of pressure on the plasma. As a general trend an increase in pressure is accompanied by a decrease in all molecular transport properties that in turn results in increased confinement/localization of the plasma. This is indeed seen in the absorbed wave power, electron temperature, and gas temperature hot region that is slightly thinner in the high-pressure case. Further, the absorbed wave power region also extends to less in both axial directions. For the fixed input wave power of 2.8 kW, the peak absorbed wave power density is higher (770 MW/m3) in the higher pressure case compared to 640 MW/m3 for the baseline case. The peak electron density is marginally higher (7.8 × 1018 m−3) in the high-pressure case, with greater localization in the wave-facing side of the tube. The decreased axial extent of the hot region also reflects in the axial size of the wave E-field region. The higher wave power density and localization of the plasma causes greater heating of the gas which in turn combined with the lower thermal conductivity of the gas results in a significant heating of the gas at the higher pressure. The peak gas temperature in the 8 Torr case is 1000 K compared to the 880 K for the baseline case. Finally, the axial velocity reaches a peak value of about 90 m/s at the tube exit, compared to the 175 m/s for the baseline case. This nearly halving of the axial velocity is mainly attributable to the more than doubling of pressure from 3.6 to 8 Torr, which is accompanied by proportional doubling of the mass density at the inlet which result in a near halving of the axial velocity for the fixed mass flow rate at the inlet.

FIG. 11.

Results for (a) gas temperature (K); (b) electron temperature (K); and (c) axial flow velocity (m/s) for the increased pressure 8 Torr case. Slice is parallel to the wave.

FIG. 11.

Results for (a) gas temperature (K); (b) electron temperature (K); and (c) axial flow velocity (m/s) for the increased pressure 8 Torr case. Slice is parallel to the wave.

Close modal
FIG. 12.

Results for (a) wave E-field (real; V/m); (b) absorbed wave power density (W/m3); and (c) electron number density (#/m3) for the increased pressure 8 Torr case. Slices are parallel to wave propagation (the log scale).

FIG. 12.

Results for (a) wave E-field (real; V/m); (b) absorbed wave power density (W/m3); and (c) electron number density (#/m3) for the increased pressure 8 Torr case. Slices are parallel to wave propagation (the log scale).

Close modal

Figure 13 shows the changes in radical number density as a function of the axial distance down the applicator tube for the radicals of interest, similar to Fig. 10. Overall, the higher pressure 8 Torr case provides a more chemical equilibrium like composition at the exit. This results from an increase in the residence time of the flow through the plasma and the afterglow region, resulting from about half the axial flow velocity for the higher pressure case, and the increased pressure that promotes increased collisionality and hence faster equilibration of all molecular processes. The 8 Torr case is, therefore, characterized by higher densities of the stable product species, i.e., H2 and N2H4, and lower densities for all other intermediate radicals such as H, NH2, N2H2, and N2H3.

FIG. 13.

Axial profile for different species number densities at 3.6 and 8 Torr outlet setpoint pressure (outflow is to the right).

FIG. 13.

Axial profile for different species number densities at 3.6 and 8 Torr outlet setpoint pressure (outflow is to the right).

Close modal

A 3D model of the discharge stage of a PNC process was successfully developed and simulated. The model provides a detailed description of the three-dimensional nature of the microwave interaction with plasma in the applicator tube and the consequent effect on chemical conversion of the feed gases to product species and the gas heating. Plasma formation is largely confined to the wave-facing side of the applicator tube, resulting in a highly nonaxisymmetric spatial inhomogeneity of the plasma in the tube. This nonuniformity influences the flow properties and both charged and radical species profiles in the discharge. Peak electron densities approaching ∼1019 m−3 are seen in the cases explored. The electron temperatures are of ∼3 eV for all cases. A hot region of the plasma can be identified at the location where the waveguide intersects the applicator tube, but this hot region further extends axially toward the inlet and outlet of the tube, supported by a surface wave that propagates along the dielectric tube plasma interface. This is the key mechanism that is described as surfatron mode in the literature. The dominant radical produced by the plasma is H2 followed by NH2 at the exit of the tube. Other radicals at the tube exit include N2H2, N2H3, N2H4, and H. Even though the asymmetric profile is present for all radicals in the hot region of the plasma, downstream recombination produces mostly uniform radical concentrations. The study of nonuniformities in the output profiles on the performance of the PNC process is left as potential future research. High input wave power promotes increased decomposition of the feed gases and high product species and intermediate radical densities at the tube exit. An increase in pressure promotes increased equilibrium concentration of the product species at the exit, i.e., increase in H2 and N2H4 species densities while all other intermediate radical species densities decrease. The output densities for the radicals from these studies could then be applied as initial conditions on simulations of the PNC process in the batch chamber. This, along with further refinements to the applicator model (shorting plunger in waveguide) and sensitivity analysis to different parameters (sticking coefficients, applicator tube length, modeling of a nozzle, etc.) are left as future research projects.

The authors have no conflicts to disclose.

Juan P. Barberena-Valencia: Data curation (equal); Formal analysis (equal); Investigation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Laxminarayan L. Raja: Conceptualization (equal); Formal analysis (equal); Project administration (equal); Supervision (equal); Visualization (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The full chemistry mechanism used in this study is presented in Table I. Rate coefficients are given in Arrhenius form: k i = A T B exp ( C T ), where T is either the gas temperature Tg for heavy-heavy reactions or electron temperature and Te for electron-impact collisions. Rate coefficient expressions for reactions (R1)–(R51) and (R53)–(R68) are computed using BOLSIG+ as discussed in Sec. II A. Units for rate coefficients are c m 3 s 1 and temperatures are in K, unless otherwise noted. Reactions (R27)–(R50) represent electron-impact excitation to different excited states of N2, which are represented by N2*, similarly, for reactions involving excited levels of H (R54)–(R62) and H2 (R65)–(R66). For reaction (R24), N* represents the N(2D) excited state, and in reaction (R25), N** is the N(2P) excited level. The chemistry file used in the simulations is available as a supplement if necessary.

TABLE I.

NH3/N2 plasma chemistry mechanism.

ReactionABCReference
E + NH3 ↠ −NH3 + E (R1) BOLSIG+   32 a 
E + NH3 ↠ −NH3(v) + E (R2) BOLSIG+   32 a 
E + NH3 ↠ −NH2 + H (R3) BOLSIG+   33 b 
E + NH3 ↠ −NH2 + H + E (R4) BOLSIG+   32 a 
E + NH3 ↠ −NH + 2H + E (R5) BOLSIG+   32 a 
E + N H 3 N H 3 + + 2 E (R6) BOLSIG+   32 a 
E + N H 3 N H 2 + + H + 2 E (R7) BOLSIG+   34 c 
E + NH3(v) ↠ −NH3(v) + E (R8) BOLSIG+   32 a,d,e 
E + NH3(v) ↠ −NH3 + E (R9) BOLSIG+    
E + NH3(v) ↠ NH2 + H (R10) BOLSIG+   33 b,f 
E + NH3(v) ↠ NH2 + H + E (R11) BOLSIG+   32 a,f 
E + NH3(v) ↠ NH + 2H + E (R12) BOLSIG+   32 a,f 
E + N H 3 ( v ) N H 3 + + 2 E (R13) BOLSIG+   32 a,f 
E + N H 3 ( v ) N H 2 + + H + 2 E (R14) BOLSIG+   32 a,f 
E + NH2 ↠ NH2 + E (R15) BOLSIG+   32 a,d 
E + NH2 ↠ NH + H (R16) BOLSIG+   33 b,d 
E + NH2 ↠ NH + H + E (R17) BOLSIG+   32 a,d 
E + N H 2 N H 2 + + 2 E (R18) BOLSIG+   35 c 
E + NH2 ↠ NH+ + H + 2E (R19) BOLSIG+   35 c 
E + NH ↠ NH + E (R20) BOLSIG+   32 a,d 
E + NH ↠ NH+ + 2E (R21) BOLSIG+   35 c 
E + NH ↠ N+ + H + 2E (R22) BOLSIG+   35 c 
E + N ↠ N + E (R23) BOLSIG+   36 g 
E + N ↠ N* + E (R24) BOLSIG+   36 g,h 
E + N ↠ N** + E (R25) BOLSIG+   36 g,h 
E + N ↠ N+ + 2E (R26) BOLSIG+   33 b 
E + N 2 E + N 2  (R27) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R28) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R29) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R30) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R31) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R32) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R33) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R34) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R35) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R36) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R37) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R38) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R39) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R40) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R41) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R42) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R43) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R44) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R45) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R46) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R47) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R48) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R49) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R50) BOLSIG+   37 c,h 
E + N 2 2 E + N 2 + (R51) BOLSIG+   37 c 
E + N2 ↠ 2N + E (R52) 1.959 ×106 −0.7 1.132 ×105 38  
E + H ↠ H + E (R53) BOLSIG+   39 i 
E + H ↠ H* + E (R54) BOLSIG+   39 h,i 
E + H ↠ H* + E (R55) BOLSIG+   39 h,i 
E + H ↠ H* + E (R56) BOLSIG+   39 h,i 
E + H ↠ H* + E (R57) BOLSIG+   39 h,i 
E + H ↠ H* + E (R58) BOLSIG+   39 h,i 
E + H ↠ H* + E (R59) BOLSIG+   39 h,i 
E + H ↠ H* + E (R60) BOLSIG+   39 h,i 
E + H ↠ H* + E (R61) BOLSIG+   39 h,i 
E + H ↠ H* + E (R62) BOLSIG+   39 h,i 
E + H ↠ H+ + 2E (R63) BOLSIG+   39 i 
E + H2 ↠ H2 + E (R64) BOLSIG+   40 j 
E + H 2 H 2 + E (R65) BOLSIG+   40 h,j 
E + H 2 H 2 + E (R66) BOLSIG+   40 h,j 
E + H2 ↠ H2(v) + E (R67) BOLSIG+   40 h,j 
E + H 2 H 2 + + 2 E (R68) BOLSIG+   40 j 
E + H2 ↠ 2H + E (R69) 1.2 ×108 0.0 10.0 41 k 
E + H+ ↠ H (R70) 4.0 ×1013 −0.5 0.0 26  
E + H 2 + E + H + H + (R71) 1.45 ×107 0.0 1.97 41 k 
E + H 2 + 2 H (R72) 1.0 ×107 −0.4 0.0 26  
E + H 3 + H + H 2 (R73) 4.9 ×107 0.0 0.0 41 k 
E + N+ ↠ N (R74) 4.0 ×1013 −0.5 0.0 26  
E + NH+ ↠ N + H (R75) 1.0 ×107 −0.5 0.0 26  
E + N H 2 + NH + H (R76) 1.0 ×107 −0.5 0.0 26  
E + N H 3 + N H 2 + H (R77) 1.0 ×107 −0.5 0.0 26  
E + N H 4 + N H 3 + H (R78) 9.0 ×107 −0.6 0.0 26  
E + N H 4 + N H 2 + 2 H (R79) 1.5 ×107 −0.6 0.0 26  
H 2 + + N N + + H 2 (R80) 5.0 ×1010 0.0 0.0 26  
H 2 + + H H + + H 2 (R81) 6.4 ×1010 0.0 0.0 26  
H 2 + + H 2 H 3 + + H (R82) 2.1 ×109 0.0 0.0 26  
H 2 + + N H 3 H 2 + N H 3 + (R83) 5.0 ×1010 0.0 0.0 26  
H 2 + + NH N H 2 + + H (R84) 5.0 ×1011 0.0 0.0 26  
H 2 + + N H 2 N H 3 + + H (R85) 5.0 ×1011 0.0 0.0 26  
H 2 + + N H 3 N H 4 + + H (R86) 5.0 ×1011 0.0 0.0 26  
N+ + H ↠ N + H+ (R87) 2.0 ×109 0.0 0.0 26  
N+ + H2 ↠ NH+ + H (R88) 5.6 ×1010 0.0 0.0 26  
N + + N H 3 N + N H 3 + (R89) 2.4 ×109 0.0 0.0 26  
H + + N H 3 H + N H 3 + (R90) 5.0 ×1011 0.0 0.0 26  
N H + + N H 3 NH + N H 3 + (R91) 1.8 ×109 0.0 0.0 26  
N H + + N H 3 ( v ) NH + N H 3 + (R92) 1.8 ×109 0.0 0.0 26  
N H + + N H 3 N + N H 4 + (R93) 6.0 ×1010 0.0 0.0 26  
N H + + N H 3 ( v ) N + N H 4 + (R94) 6.0 ×1010 0.0 0.0 26  
N H + + N H 2 NH + N H 2 + (R95) 1.8 ×109 0.0 0.0 26  
N H + + H 2 H + N H 2 + (R96) 1.0 ×109 0.0 0.0 26  
N H 2 + + N H 3 N H 3 + + N H 2 (R97) 1.1 ×109 0.0 0.0 26  
N H 2 + + N H 3 ( v ) N H 3 + + N H 2 (R98) 1.1 ×109 0.0 0.0 26  
N H 2 + + N H 3 N H 4 + + NH (R99) 1.1 ×109 0.0 0.0 26  
N H 2 + + N H 3 ( v ) N H 4 + + NH (R100) 1.1 ×109 0.0 0.0 26  
N H 2 + + H 2 N H 3 + + H (R101) 1.0 ×109 0.0 0.0 26  
H 3 + + N H 3 N H 4 + + H 2 (R102) 4.4 ×109 0.0 0.0 26  
N H 3 + + N H 3 N H 3 + + N H 3 (R103) 2.0 ×1010 0.0 0.0 26  
N H 3 + + N H 3 ( v ) N H 3 + + N H 3 (R104) 2.0 ×1010 0.0 0.0 26  
N H 3 + + N H 3 N H 4 + + N H 2 (R105) 2.2 ×109 0.0 0.0 26  
N H 3 + + N H 3 ( v ) N H 4 + + N H 2 (R106) 2.2 ×109 0.0 0.0 26  
N H 3 + + H 2 N H 4 + + H (R107) 4.0 ×1013 0.0 0.0 26  
N H 2 + H 2 H + N H 3 (R108) 2.3 ×1011 0.0 0.0 26  
H + H ↠ H2 + E (R109) 1.8 ×109 0.0 0.0 26  
H + N H 3 N H 2 + H 2 (R110) 8.8 ×1013 0.0 0.0 26  
H + N H 3 + H + N H 3 (R111) 3.0 ×106 0.0 0.0 26  
H + H 3 + 2 H 2 (R112) 1.0 ×107 0.0 0.0 26  
H + H 3 + H 2 + 2 H (R113) 1.0 ×107 0.0 0.0 26  
N H 2 + N H 3 + N H 2 + N H 3 (R114) 2.0 ×107 0.0 0.0 26  
N H 2 + N H 4 + N H 2 + N H 3 + H (R115) 2.0 ×107 0.0 0.0 26  
N H 2 + H 3 + N H 3 + H 2 (R116) 1.0 ×107 0.0 0.0 26  
N H 2 + H 3 + N H 2 + H 2 + H (R117) 1.0 ×107 0.0 0.0 26  
2N2 ↠ 2N + N2 (R118) 4.3 ×1010 0.0 0.0 26  
NH3 + H ↠ H2 + NH2 (R119) 9.463 ×1020 2.76 5.135 ×103 26  
NH3(v) + H ↠ H2 + NH2 (R120) 9.463 ×1020 2.76 5.135 ×103 26  
NH2 + H ↠ NH + H2 (R121) 1.1 ×1010 0.0 4.451 ×103 26  
NH2 + H2 ↠ H + NH3 (R122) 2.1 ×1012 0.0 4.277 ×103 26  
2NH2 ↠ N2H2 + H2 (R123) 1.3 ×1012 0.0 0.0 26  
2NH2 ↠ NH3 + NH (R124) 2.21 ×1021 2.79 6.6 ×102 26  
NH2 + N ↠ N2 + 2H (R125) 1.2 ×1010 0.0 0.0 26  
NH2 + NH ↠ N2H2 + H (R126) 4.33 ×108 −0.5 0.0 26  
NH2 + NH ↠ N2H3 (R127) 1.2 ×1010 0.0 0.0 26  
NH + N ↠ N2 + H (R128) 2.5 ×1011 0.0 0.0 26  
NH + H ↠ H2 + N (R129) 6.0 ×1011 0.0 1.66 ×102 26  
2NH ↠ N2 + 2H (R130) 1.2 ×109 0.0 0.0 26  
2NH ↠ N2H2 (R131) 3.5 ×1012 0.0 0.0 26  
2NH ↠ NH2 + N (R132) 9.71 ×1022 2.89 1.015 ×103 26  
N + H2 ↠ H + NH (R133) 2.7 ×1010 0.0 1.2609 ×103 26  
N2H2 + H ↠ N2 + H2 + H (R134) 1.38 ×1019 2.63 1.15 ×102 26  
2H + M ↠ H2 + M (R135) 1.4 ×1031 0.0 0.0 26 l 
2H + H2 ↠ 2H2 (R136) 2.73 ×1031 −0.6 0.0 26  
3H ↠ H2 + H (R137) 8.9 ×1033 0.0 0.0 26  
H + N + M ↠ NH + M (R138) 5.0 ×1032 0.0 0.0 26 l 
H + NH2 + M ↠ NH3 + M (R139) 6.0 ×1030 0.0 0.0 26 l 
H2 + N + NH3 ↠ NH2 + NH3 (R140) 1.0 ×1036 0.0 0.0 26  
2N + M ↠ N2 + M (R141) 7.2 ×1033 0.0 0.0 26 l 
NH + NH3 + M ↠ N2H4 + M (R142) 4.0 ×1035 0.0 0.0 26 l 
NH + NH3(v) + M ↠ N2H4 + M (R143) 4.0 ×1035 0.0 0.0 26 l 
NH + 2NH3 ↠ N2H4 + NH3 (R144) 1.0 ×1033 0.0 0.0 26  
2NH2 + NH3 ↠ N2H4 + NH3 (R145) 6.9 ×1030 0.0 0.0 26  
N2H2 + NH2 ↠ N2 + H + NH3 (R146) 1.3924 ×1023 4.05 8.1 ×102 26  
N2H3 + H ↠ 2NH2 (R147) 2.7 ×1012 0.0 0.0 26  
2N2H3 ↠ 2NH3 + N2 (R148) 5.0 ×1012 0.0 0.0 26  
2N2H3 ↠ N2H4 + N2H2 (R149) 2.0 ×1011 0.0 0.0 26  
N2H4 + N ↠ N2H2 + NH2 (R150) 1.3 ×1013 0.0 0.0 26  
N2H4 + H ↠ N2H3 + H2 (R151) 1.2 ×1011 0.0 1.26 ×103 26  
N2H4 + NH2 ↠ NH3 + N2H3 (R152) 5.2 ×1013 0.0 0.0 26  
ReactionABCReference
E + NH3 ↠ −NH3 + E (R1) BOLSIG+   32 a 
E + NH3 ↠ −NH3(v) + E (R2) BOLSIG+   32 a 
E + NH3 ↠ −NH2 + H (R3) BOLSIG+   33 b 
E + NH3 ↠ −NH2 + H + E (R4) BOLSIG+   32 a 
E + NH3 ↠ −NH + 2H + E (R5) BOLSIG+   32 a 
E + N H 3 N H 3 + + 2 E (R6) BOLSIG+   32 a 
E + N H 3 N H 2 + + H + 2 E (R7) BOLSIG+   34 c 
E + NH3(v) ↠ −NH3(v) + E (R8) BOLSIG+   32 a,d,e 
E + NH3(v) ↠ −NH3 + E (R9) BOLSIG+    
E + NH3(v) ↠ NH2 + H (R10) BOLSIG+   33 b,f 
E + NH3(v) ↠ NH2 + H + E (R11) BOLSIG+   32 a,f 
E + NH3(v) ↠ NH + 2H + E (R12) BOLSIG+   32 a,f 
E + N H 3 ( v ) N H 3 + + 2 E (R13) BOLSIG+   32 a,f 
E + N H 3 ( v ) N H 2 + + H + 2 E (R14) BOLSIG+   32 a,f 
E + NH2 ↠ NH2 + E (R15) BOLSIG+   32 a,d 
E + NH2 ↠ NH + H (R16) BOLSIG+   33 b,d 
E + NH2 ↠ NH + H + E (R17) BOLSIG+   32 a,d 
E + N H 2 N H 2 + + 2 E (R18) BOLSIG+   35 c 
E + NH2 ↠ NH+ + H + 2E (R19) BOLSIG+   35 c 
E + NH ↠ NH + E (R20) BOLSIG+   32 a,d 
E + NH ↠ NH+ + 2E (R21) BOLSIG+   35 c 
E + NH ↠ N+ + H + 2E (R22) BOLSIG+   35 c 
E + N ↠ N + E (R23) BOLSIG+   36 g 
E + N ↠ N* + E (R24) BOLSIG+   36 g,h 
E + N ↠ N** + E (R25) BOLSIG+   36 g,h 
E + N ↠ N+ + 2E (R26) BOLSIG+   33 b 
E + N 2 E + N 2  (R27) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R28) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R29) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R30) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R31) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R32) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R33) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R34) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R35) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R36) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R37) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R38) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R39) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R40) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R41) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R42) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R43) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R44) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R45) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R46) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R47) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R48) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R49) BOLSIG+   37 c,h 
E + N 2 E + N 2  (R50) BOLSIG+   37 c,h 
E + N 2 2 E + N 2 + (R51) BOLSIG+   37 c 
E + N2 ↠ 2N + E (R52) 1.959 ×106 −0.7 1.132 ×105 38  
E + H ↠ H + E (R53) BOLSIG+   39 i 
E + H ↠ H* + E (R54) BOLSIG+   39 h,i 
E + H ↠ H* + E (R55) BOLSIG+   39 h,i 
E + H ↠ H* + E (R56) BOLSIG+   39 h,i 
E + H ↠ H* + E (R57) BOLSIG+   39 h,i 
E + H ↠ H* + E (R58) BOLSIG+   39 h,i 
E + H ↠ H* + E (R59) BOLSIG+   39 h,i 
E + H ↠ H* + E (R60) BOLSIG+   39 h,i 
E + H ↠ H* + E (R61) BOLSIG+   39 h,i 
E + H ↠ H* + E (R62) BOLSIG+   39 h,i 
E + H ↠ H+ + 2E (R63) BOLSIG+   39 i 
E + H2 ↠ H2 + E (R64) BOLSIG+   40 j 
E + H 2 H 2 + E (R65) BOLSIG+   40 h,j 
E + H 2 H 2 + E (R66) BOLSIG+   40 h,j 
E + H2 ↠ H2(v) + E (R67) BOLSIG+   40 h,j 
E + H 2 H 2 + + 2 E (R68) BOLSIG+   40 j 
E + H2 ↠ 2H + E (R69) 1.2 ×108 0.0 10.0 41 k 
E + H+ ↠ H (R70) 4.0 ×1013 −0.5 0.0 26  
E + H 2 + E + H + H + (R71) 1.45 ×107 0.0 1.97 41 k 
E + H 2 + 2 H (R72) 1.0 ×107 −0.4 0.0 26  
E + H 3 + H + H 2 (R73) 4.9 ×107 0.0 0.0 41 k 
E + N+ ↠ N (R74) 4.0 ×1013 −0.5 0.0 26  
E + NH+ ↠ N + H (R75) 1.0 ×107 −0.5 0.0 26  
E + N H 2 + NH + H (R76) 1.0 ×107 −0.5 0.0 26  
E + N H 3 + N H 2 + H (R77) 1.0 ×107 −0.5 0.0 26  
E + N H 4 + N H 3 + H (R78) 9.0 ×107 −0.6 0.0 26  
E + N H 4 + N H 2 + 2 H (R79) 1.5 ×107 −0.6 0.0 26  
H 2 + + N N + + H 2 (R80) 5.0 ×1010 0.0 0.0 26  
H 2 + + H H + + H 2 (R81) 6.4 ×1010 0.0 0.0 26  
H 2 + + H 2 H 3 + + H (R82) 2.1 ×109 0.0 0.0 26  
H 2 + + N H 3 H 2 + N H 3 + (R83) 5.0 ×1010 0.0 0.0 26  
H 2 + + NH N H 2 + + H (R84) 5.0 ×1011 0.0 0.0 26  
H 2 + + N H 2 N H 3 + + H (R85) 5.0 ×1011 0.0 0.0 26  
H 2 + + N H 3 N H 4 + + H (R86) 5.0 ×1011 0.0 0.0 26  
N+ + H ↠ N + H+ (R87) 2.0 ×109 0.0 0.0 26  
N+ + H2 ↠ NH+ + H (R88) 5.6 ×1010 0.0 0.0 26  
N + + N H 3 N + N H 3 + (R89) 2.4 ×109 0.0 0.0 26  
H + + N H 3 H + N H 3 + (R90) 5.0 ×1011 0.0 0.0 26  
N H + + N H 3 NH + N H 3 + (R91) 1.8 ×109 0.0 0.0 26  
N H + + N H 3 ( v ) NH + N H 3 + (R92) 1.8 ×109 0.0 0.0 26  
N H + + N H 3 N + N H 4 + (R93) 6.0 ×1010 0.0 0.0 26  
N H + + N H 3 ( v ) N + N H 4 + (R94) 6.0 ×1010 0.0 0.0 26  
N H + + N H 2 NH + N H 2 + (R95) 1.8 ×109 0.0 0.0 26  
N H + + H 2 H + N H 2 + (R96) 1.0 ×109 0.0 0.0 26  
N H 2 + + N H 3 N H 3 + + N H 2 (R97) 1.1 ×109 0.0 0.0 26  
N H 2 + + N H 3 ( v ) N H 3 + + N H 2 (R98) 1.1 ×109 0.0 0.0 26  
N H 2 + + N H 3 N H 4 + + NH (R99) 1.1 ×109 0.0 0.0 26  
N H 2 + + N H 3 ( v ) N H 4 + + NH (R100) 1.1 ×109 0.0 0.0 26  
N H 2 + + H 2 N H 3 + + H (R101) 1.0 ×109 0.0 0.0 26  
H 3 + + N H 3 N H 4 + + H 2 (R102) 4.4 ×109 0.0 0.0 26  
N H 3 + + N H 3 N H 3 + + N H 3 (R103) 2.0 ×1010 0.0 0.0 26  
N H 3 + + N H 3 ( v ) N H 3 + + N H 3 (R104) 2.0 ×1010 0.0 0.0 26  
N H 3 + + N H 3 N H 4 + + N H 2 (R105) 2.2 ×109 0.0 0.0 26  
N H 3 + + N H 3 ( v ) N H 4 + + N H 2 (R106) 2.2 ×109 0.0 0.0 26  
N H 3 + + H 2 N H 4 + + H (R107) 4.0 ×1013 0.0 0.0 26  
N H 2 + H 2 H + N H 3 (R108) 2.3 ×1011 0.0 0.0 26  
H + H ↠ H2 + E (R109) 1.8 ×109 0.0 0.0 26  
H + N H 3 N H 2 + H 2 (R110) 8.8 ×1013 0.0 0.0 26  
H + N H 3 + H + N H 3 (R111) 3.0 ×106 0.0 0.0 26  
H + H 3 + 2 H 2 (R112) 1.0 ×107 0.0 0.0 26  
H + H 3 + H 2 + 2 H (R113) 1.0 ×107 0.0 0.0 26  
N H 2 + N H 3 + N H 2 + N H 3 (R114) 2.0 ×107 0.0 0.0 26  
N H 2 + N H 4 + N H 2 + N H 3 + H (R115) 2.0 ×107 0.0 0.0 26  
N H 2 + H 3 + N H 3 + H 2 (R116) 1.0 ×107 0.0 0.0 26  
N H 2 + H 3 + N H 2 + H 2 + H (R117) 1.0 ×107 0.0 0.0 26  
2N2 ↠ 2N + N2 (R118) 4.3 ×1010 0.0 0.0 26  
NH3 + H ↠ H2 + NH2 (R119) 9.463 ×1020 2.76 5.135 ×103 26  
NH3(v) + H ↠ H2 + NH2 (R120) 9.463 ×1020 2.76 5.135 ×103 26  
NH2 + H ↠ NH + H2 (R121) 1.1 ×1010 0.0 4.451 ×103 26  
NH2 + H2 ↠ H + NH3 (R122) 2.1 ×1012 0.0 4.277 ×103 26  
2NH2 ↠ N2H2 + H2 (R123) 1.3 ×1012 0.0 0.0 26  
2NH2 ↠ NH3 + NH (R124) 2.21 ×1021 2.79 6.6 ×102 26  
NH2 + N ↠ N2 + 2H (R125) 1.2 ×1010 0.0 0.0 26  
NH2 + NH ↠ N2H2 + H (R126) 4.33 ×108 −0.5 0.0 26  
NH2 + NH ↠ N2H3 (R127) 1.2 ×1010 0.0 0.0 26  
NH + N ↠ N2 + H (R128) 2.5 ×1011 0.0 0.0 26  
NH + H ↠ H2 + N (R129) 6.0 ×1011 0.0 1.66 ×102 26  
2NH ↠ N2 + 2H (R130) 1.2 ×109 0.0 0.0 26  
2NH ↠ N2H2 (R131) 3.5 ×1012 0.0 0.0 26  
2NH ↠ NH2 + N (R132) 9.71 ×1022 2.89 1.015 ×103 26  
N + H2 ↠ H + NH (R133) 2.7 ×1010 0.0 1.2609 ×103 26  
N2H2 + H ↠ N2 + H2 + H (R134) 1.38 ×1019 2.63 1.15 ×102 26  
2H + M ↠ H2 + M (R135) 1.4 ×1031 0.0 0.0 26 l 
2H + H2 ↠ 2H2 (R136) 2.73 ×1031 −0.6 0.0 26  
3H ↠ H2 + H (R137) 8.9 ×1033 0.0 0.0 26  
H + N + M ↠ NH + M (R138) 5.0 ×1032 0.0 0.0 26 l 
H + NH2 + M ↠ NH3 + M (R139) 6.0 ×1030 0.0 0.0 26 l 
H2 + N + NH3 ↠ NH2 + NH3 (R140) 1.0 ×1036 0.0 0.0 26  
2N + M ↠ N2 + M (R141) 7.2 ×1033 0.0 0.0 26 l 
NH + NH3 + M ↠ N2H4 + M (R142) 4.0 ×1035 0.0 0.0 26 l 
NH + NH3(v) + M ↠ N2H4 + M (R143) 4.0 ×1035 0.0 0.0 26 l 
NH + 2NH3 ↠ N2H4 + NH3 (R144) 1.0 ×1033 0.0 0.0 26  
2NH2 + NH3 ↠ N2H4 + NH3 (R145) 6.9 ×1030 0.0 0.0 26  
N2H2 + NH2 ↠ N2 + H + NH3 (R146) 1.3924 ×1023 4.05 8.1 ×102 26  
N2H3 + H ↠ 2NH2 (R147) 2.7 ×1012 0.0 0.0 26  
2N2H3 ↠ 2NH3 + N2 (R148) 5.0 ×1012 0.0 0.0 26  
2N2H3 ↠ N2H4 + N2H2 (R149) 2.0 ×1011 0.0 0.0 26  
N2H4 + N ↠ N2H2 + NH2 (R150) 1.3 ×1013 0.0 0.0 26  
N2H4 + H ↠ N2H3 + H2 (R151) 1.2 ×1011 0.0 1.26 ×103 26  
N2H4 + NH2 ↠ NH3 + N2H3 (R152) 5.2 ×1013 0.0 0.0 26  
a

Rate coefficients calculated using BOLSIG+ and the cross sections which were obtained from the Hayashi database in LxCat42; rates in units of m3 s−1.

b

Rate coefficients calculated using BOLSIG+ and the cross sections which were obtained from the Morgan (Kinema) database in LxCat42; rates in units of m3 s−1.

c

Rates obtained by integration of cross sections from reference; rates in units of m3 s−1.

d

Same cross section as NH3.

e

Reverse rates obtained by detailed balance from forward rates.

f

Cross section obtained by shifting the ground-state cross section by the energy threshold.

g

Rate coefficients calculated using BOLSIG+ and the cross sections which were obtained from the IST Lisbon database in LxCat42; rates in units of m3 s−1.

h

Reaction included for energy loss/gain, but excited state is not tracked in the model.

i

Rate coefficients calculated using BOLSIG+ and the cross sections which were obtained from the Bray (CCC) database in LxCat42; rates in units of m3 s−1.

j

Rate coefficients calculated using BOLSIG+ and the cross sections which were obtained from the Phelps database in LxCat42; rates in units of m3 s−1.

k

A in units of cm3 s−1; C units of eV.

l

M represents every species in the chemistry.

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