Pressure dependence of dissociation fraction and optical emission characteristics in low-pressure inductively coupled N2-Ar plasmas

A diagnostics study of low-pressure inductively coupled N2-Ar plasmas was performed by using optical emission spectroscopy (OES) and an rf-compensated Langmuir probe under the conditions of pressures of 1 30 mTorr and powers of 300 600 W. In the OES experiments, the argon was used as an actinometer and as an adding gas. The effect of the argon content in the gas mixture was examined in the range of 5 30%. The investigation of the effects of pressure on the dissociation fraction of nitrogen molecules and on the optical emission characteristics were carried out. The correction factors for estimating the dissociation fraction by OES actinometry accounting for argon effect were formulated and calculated. It was found that the dissociation fraction increased with increasing power and Ar content, while it decreased with increasing pressure. In addition, the electron energy probability function (EEPF), the electron density, and the electron temperature were obtained by using a Langmuir probe to investigate the effects of the plasma parameters on the optical emission characteristics and the dissociation fraction. Copyright 2011 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License. [doi:10.1063/1.3628670]


I. INTRODUCTION
There has been a growing interest in the study of N 2 plasmas because of their potential use in the synthesis of nitride thin films and in the surface modification of various materials. Since atomic nitrogen plays an important role in the plasma processes, the determination of the absolute concentrations of N atoms in N 2 molecular discharges is crucial for understanding plasma process at the surface. [1][2][3] Electric discharges produced either by microwaves, helicon waves or radio frequency (rf) power are commonly used for generating nitrogen atoms. 2,[4][5][6] Recently, there has been a steadily growing interest in the application of inductively coupled plasma (ICP) sources for numerous plasma-enhanced materials processing. It has been known that most of these plasma systems are characterized by high nitrogen atom content. 7 The dissociation fraction in an inductively coupled nitrogen plasma is important for understanding and improving the nitridation processes because the number density of N atoms is deducible from the dissociation fraction. Generally, it is difficult to achieve a high dissociation efficiency of N 2 due to its extremely high bonding energy. 8 The dissociation of N 2 molecules in nitrogen plasmas has been diagnosed by using several techniques, such as mass spectrometry 9, 10 and optical emission spectroscopy. 6,11,12 Nakano et al. measured the dissociation degree of N 2 in an inductively coupled plasma by using vacuum ultraviolet emission spectroscopy. 13 They observed that the dissociation fraction increased with the rf power when the N 2 pressure was kept at 4.98 mTorr. 13 In contrast, no large increase in the degree of N 2 dissociation with pressure was observed for a fixed rf power (1 kW) condition even when electron density increased sharply in the pressure range of 0.09 -4.98 mTorr. Czerwiec et al. measured the dissociation fraction for an ICP sustained in a long cylindrical tube with a small radius specially designed for radical beam generation. They obtained a dissociation fraction from 0.1 (evaluated by using optical emission actinometry) up to 0.7 (by using mass spectrometry) for N 2 discharges at 50 mTorr. 9 In other articles, the degree of dissociation was found to be 1 -4.9 %, 13 0.58 -4.4%, 8 1 -7%, 2 and 1% or below. 3,5,6 One of the promising ways to enhance the dissociation of molecular nitrogen is to introduce another gas such as hydrogen and argon in the plasma. 2 Tabbal et al. evaluated the nitrogen molecular dissociation level in N 2 -Ar surface-wave plasma and observed the dissociation enhancement factor of 4.1 -8.5 with the introduction of Ar to pure nitrogen discharges at the power of 60 -120 W and the pressure of 7.6 Torr. 4 In this study, N 2 -Ar plasmas are produced with ICP sources. The production and loss mechanisms of N atoms in N 2 -Ar discharges are very complex due to a huge set of reactions between charges species and neutrals (atomic and molecular nitrogen and argon atoms) including the wall interactions. 14,15 In our previous work, 16 we have shown that increasing the Ar content causes significant changes in the properties of discharge such as gas temperature, rovibrational excitation, electron energy distribution function, and dissociation fraction of N 2 molecules. A higher Ar content caused an enhancement of the dissociation fraction. It was found out that the calculated density of nitrogen atom was maximum at the Ar content of 30%. 16 A simple actinometry for N 2 -Ar discharges with larger portion of Ar would give an overestimated value for dissociation fraction because the Penning excitation and/or dissociative excitation of nitrogen molecules due to all the excited states of Ar is usually neglected. In this work, we will determine the dissociation fraction more accurately by estimating the contributions from Ar excited states in more detail.
Another emphasis is placed on the effect of pressure on the dissociation fraction and discharge characteristics. For that purpose, the Ar content in the gas mixture is kept constant at 5% otherwise mentioned. This amount of Ar content allows us to apply the optical emission actinometry. But, as the pressure increases the amount of Ar gets larger, thus the interactions of the Ar atoms with neutrals and ions of atomic and molecular nitrogen become important. Especially, argon metastable atoms play an important role in the discharge kinetics, thereby influencing the dissociation of nitrogen molecules as well as rovibrational temperature. In this study, the density of argon metastables is calculated using a simple kinetics. This quantity is used to make a correction for determining the dissociation fraction by the optical emission actinometry.
The total pressure is varied in an attempt to fully characterize the optical emission characteristics of inductively coupled N 2 -Ar discharges. We obtain the dissociation fraction by using optical emission actinometry at various powers (300 -600 W) in the pressure range 1 -30 mTorr, which is different from the range of similar studies. 3,4,8,13 A physical explanation of the variations of the dissociation fraction with pressure is given with a discussion of the particle balance and of plasma properties, such as the electron density, the electron temperature, and the electron energy probability function measured by using a rf-compensated Langmuir probe.

II. EXPERIMENT
A schematic diagram of the experimental setup with the diagnostics system (optical emission spectroscopy (OES), and rf-compensated Langmuir probe) is shown in Fig. 1. The plasma chamber consists of a stainless-steel cylinder with a 28-cm diameter and a 34-cm length. A 1.9-cm-thick by 27-cm-diameter tempered glass plate mounted on one end separates the planar one-turn induction coil from the plasma. The induction coil is made of copper (with water-cooling) and is connected to an L-type capacitive matching network and a rf power generator.
The plasma chamber is evacuated by using a diffusion pump backed by rotary pump giving a base pressure of 5 × 10 −6 Torr. The equilibrium gas pressure in the chamber is monitored with a combination vacuum gauge (IMG 300). The operating gas pressure is controlled by adjusting the mass flow controller. The nitrogen gas pressure is varied in the range of 1 -30 mTorr, and a 13.56 MHz generator (ENI OEM 12) drives an rf current in a flat one-turn coil through the rf power generator and matching network. The source gas is N 2 gas. We introduce Ar as an actinometer and as an adding gas for all cases. An rf-compensated cylindrical single Langmuir probe was mounted through one of the ports on the vacuum chamber. The probe tip was located on the axis of the cylinder at 14 cm below the tempered glass plate. To measure the plasma parameters, the harmonic technique, which exploits the generation of harmonics resulting from excitation of the nonlinearity of the single Langmuir probe characteristics, combined with Druyvesteyn method was used. In the harmonic method, the voltage applied to the probe consists of the sweep voltage and the sinusoidal voltage v 0 of the frequency ω. Two signal generators were used to make 10 kHz of a small sinusoidal wave (v 0 = 1.0 V) and 1 Hz of a sawtooth wave. After being amplified by operational amplifiers, the sinusoidal signal was superimposed on the sawtooth signal swept from −30 V to 30 V. The superimposed signal was amplified by a power amplifier, and then applied to the probe tip though a resonance filter for 13.56 and 27.12 MHz to remove the rf fluctuation from the plasma potential. A cylindrical probe tip made of tungsten which is 0.1 mm in diameter and 10 mm in length was used. The current was obtained by measuring the voltage difference across the sensing resistor (100 ) using the differential amplifier. After data processing in the analog-to-digital converter, the fast Fourier transform was performed to find the second harmonic of the I-V characteristic. The second harmonic term I 2ω of the measured probe current is proportional to the second derivative as I 2ω ≈ (1/4) v 2 0 d 2 I /dV 2 cos 2ωt, which is related to the electron energy distribution function(EEDF), f ( ), where e is the electron charge, S is the probe area, m is the mass of electron, V is the probe potential referenced to the plasma potential (V p ), and is measured in units of eV. The electron density (n e ) and the effective electron temperature (T e ) are calculated with the measured EEDF as follows: where max is determined by the dynamic range of the EEDF measurement. The electron temperature can also be determined from the slope of the probe I-V curve in the exponential region (from the point where the probe current is zero to where the slope of the curve begins to decrease). We observed that both methods yield almost same values of the electron temperature. The EEDF integral method has been used to obtain plasma parameters for many processing plasmas utilizing molecular gases. [17][18][19][20] The light intensity of emissive molecules and radicals in the plasma was focused by means of optical fiber into entrance slit of 0.75 m monochromator (SPEX 1702), equipped with a grating of 1200 grooves per millimeter and slit width of 100 μm. The light was collimated at the exit slit where a photomultiplier tube (Hamamatsu R928) converted photons into an electric signal. Optical emission spectra were recorded in the wavelength range of 250 -850 nm with a resolution of 0.1 nm. The measured emission spectra should be corrected for the spectral response of the detection system which includes optical fiber, monochromator, and photomultiplier tube. The detection system had to be calibrated in intensity between 250 to 850 nm using a quartz halogen lamp with a known spectral radiance.The dependence of the emission intensities on the plasma parameters is investigated. In plasma processing, actinometry is a frequently-used and well-developed technique to estimate the density of neutrals. In this method, a known concentration of an impurity is introduced, and the intensities of two neighboring spectral lines, one from the known gas and one from the sample, are compared. Since both species are bombarded by the same electron distribution and the concentration of the actinometer is known, the density of the sample can be calculated.
A kinetic analysis of a nitrogen discharge under the assumption of quasi-static equilibrium gives where n e is the electron density, [N], [N * ], and [N m ] are the population densities of the ground state, the excited state, and of the metastable state form of species N, respectively. And k dir N is the rate coefficient for electronic excitation of the ground state, k exc N m is the rate coefficient for electronic excitation of the metastable state, k diss−exc N 2 is the rate coefficient for electronic excitation through dissociation of molecule N 2 , k Penn N is the rate coefficient for Penning excitation of the ground state N due to the excited states of Ar, k Penn−diss N is the rate coefficient for Penning dissociation of N 2 due to the excited states of Ar, τ N is the lifetime of the excited state and k Q N * is the rate coefficient for quenching by argon. Usually, at low-pressure discharges, k Q N * [Ar] is much less than 1/τ N thus the quenching term can be neglected. The Ar metastables, 1s 5 and 1s 3 , are at energy levels of 11.55 and 11.72 eV, respectively. 3 These metastables have significant interactions with nitrogen molecules through resonant energy transfer called Penning excitation and dissociation.
The emission intensity due to a transition from an excited level to a lower state is where K N is a factor depending on plasma volume, solid angle and spectral response of the spectrometer, h is the Planck's constant, ν N is the frequency of the transition, and A N is the optical emission probability for the transition. and k Q N * are ignored, equation (4) can be expressed as where c 1 is the correction factor accounting for various contributions to the formation of excited nitrogen atoms rather than the direct excitation by electron impact. From equations (3) and (5), we have The rate coefficients k exc N m , k diss−exc are less than k dir N by one order of magnitude. Unless the densities of metastable N and Ar atoms are large, the factor c 1 is small.
Similarly, the emission intensity from excited Ar atom is written as where c 2 is the correction factor accounting for the excitation from the metastable Ar, where k exc Ar m is the rate coefficient for the excitation of Ar m (1s 3 ) to a specific higher (2p 1 ) state. Density of metastable atoms is determined from the balance of the production (mainly by electron-impact excitation from the ground state (k Ar m e )) and various loss mechanisms (excitation and ionization from metastable state, quenching, and diffusion induced wall loss). 21 where k exc e , k i e , and k Q e are the rate coefficients for excitation and ionization from metastable state, and for electron-quenching of metastables, respectively. Here k Q N 2 is the quenching rate coefficient of Ar m in N 2 , and k di f f is the rate coefficient for diffusion induced wall losses expressed by k di f f = D Ar /( 2 [Ar]) where D Ar is the diffusion constant of Ar m in Ar (D Ar = 1.8 × 10 18 cm −1 s −1 is used) and is the effective diffusion length of a cylinder of radius R and length L (1/ 2 = (π/L) 2 + (2.405/R) 2 ). The rate coefficients are calculated using the cross section data as where σ j is the electron-impact cross section of the collision type j. Utilizing the cross section data in the literature, 22-25 the rate coefficients for the direct excitation of the ground state Ar to 1s 5 (k Ar m e ), the direct excitation of Ar metastables to 2p 1 state (k exc Ar m ), and the total direct excitation and ionization of Ar metastables (k exc e and k i e ) are computed and presented as a function of T e in Fig. 2. In the operating region of this study, the values of k Q N 2 and k Q e are 3.6 × 10 −11 cm 3 /s, 26 and 4 − 7 × 10 −8 cm 3 /s, respectively. 24 For the optical emission actinometry for N 2 -Ar plasmas, the emissions of the N line at 746.68 nm ( 3p 4 S 3/2 → 3s 4 P 5/2 ) and the Ar line at 750.4 nm (2p 1 → 1s 2 transition) are selected because they are not sensitive to two step excitation.
From equations (5) and (7), Then the dissociation fraction is derived as by 9,11 [N] where x Ar and x N 2 are the percentages of argon and nitrogen in the gas mixture with the discharge off. However, quantitatively accurate results can only be obtained if excitations via dissociative channels, Penning effect, and the quenching of excited states are accounted for. In this experiment, using OES, we obtain the dissociation fraction for an inductively coupled N 2 -Ar discharge as functions of Ar content, pressure, and applied ICP power. In order to better understand the effects of these parameters on the dissociation fraction, we measured EEPF (electron energy probability function), and the electron density, and the electron temperature by using a Langmuir probe.

III. RESULTS AND DISCUSSION
).
Here v and v are the vibrational quantum numbers of the upper and lower states and the vibrational transition is denoted simply as (v , v ). The spectra are dominated by strong molecular features, which peak around 300 -400 nm and 600 -800 nm. The total intensities of emission, from state C 3 u , and from state B 3 g , are changed as the pressure and ICP power vary. The emission intensities of all peaks significantly increased with power, while they overall decreased with pressure. The most intense emission intensities from N 2 second positive system are caused by many excitation and quenching processes such as the electron impact excitation from the ground state, the excitation from the first metastable state N 2 (A 3 + u ) due to collision with metastable state Ar m , which indicate the overpopulation of N 2 (C 3 u ). 13,27 Therefore, it is observed that the most intense peak of the second positive system is large compared with the most intense peak of N 2 first positive system and N + 2 first negative system. The reason for this phenomenon is the energy pooling reaction caused by effective lifetime of the first metastable state N 2 (A 3 + u ) which has the lowest threshold energy (6.2 eV) and a long lifetime (about 2 s). 28 The Ar content in the gas mixture does not make a noticeable influence on the emission intensities of the typical lines of N 2 first and second positive systems and N + 2 first negative system. By decreasing the amount of molecular N 2 with increasing the Ar content, excited atomic N and N + 2 would also decrease. However, with the addition of Ar, Penning excitation and Penning dissociation due to Ar m increase the densities of the excited states of N, N 2 , and N + 2 trading off the decrease in the amount of N 2 . An increase in the Ar content results in a slight increase of the emission intensity from N atoms. Figure 4 shows the emission spectra with the wavelength range of 250 − 450 nm from N 2 -5%Ar plasmas at different pressures. Many SPS bands ( v = −2, −1, 0, +1, +2, +3, +4) and FNS bands ( v = 0, +1) are clearly observed. Although not shown in the figure, the intensities from SPS at 5 mTorr increased compared to those at 1.4 mTorr. But, as the pressure further increases, the emission intensities of these bands decrease. The relative intensity of each bands vary depending on the pressure. For instance, in the plasma at 11 mTorr, the relative intensity from the SPS v = +2 transition is larger than that from the SPS v = +1 transition. With increasing pressure, the emission intensities of FNS (0,0) at 391.4 nm exhibits a significant change. The intensity ratio of I 391.4 to I 337.1 (SPS (0,0)) is decreased drastically at 11 mTorr, but rises at 22 mTorr and then decreases again at 30 mTorr. This complicated variations result from the changes of n e , T e , and neutral particle densities with pressure. Also the intensity from the SPS v = +2 sequence follows a similar change to those of FNS at 391.4 nm. These can be explained by the effects of N 2 supply and a subsequent decrease in T e with pressure. These two effects act oppositely. As pressure increases, T e decreases, thus the electron-impact vibrational excitation to higher levels are reduced. However, the number density of N 2 molecules is increased with pressure, thus the event of vibrational excitation (and       (4,2), (3,1) and (2,0) are also observed. In addition, the N peaks appear at 746.8 nm (3p 4 S → 3s 4 P 5/2 ), 744.2 nm (3p 4 S → 3s 4 P 3/2 ), and 742.3 nm (3p 4 S → 3s 4 P 1/2 ). As shown in the figure, as the pressure increases, the overall intensities of these lines decrease. The optical spectrum from the 11 mTorr discharge shows a significant change compared to that of the 5 mTorr discharge. The argon peaks except some dominant ones are almost smeared out. This can be explained by that the 2p → 1s transitions are suppressed since the excitation of the ground state Ar to 2p levels is diminished due to the decrease in T e with increasing pressure. However, when the gas pressure increased to 22 mTorr, with an abundant supply of nitrogen molecules, the emission from nitrogen atom is clearly seen. At the pressure of 30 mTorr, the N peaks diminish again while the Ar 811.5 nm line becomes high. Figure 6(a) and 6(b) show the electron density and the electron temperature obtained by a Langmuir probe measurement as a function of the Ar content. With an increase in the Ar content, the electron density increases and the electron temperature decreases. For a fixed power, with an increase of Ar content, the total energy loss per electron-ion pair decreases, hence the electron density increases due to the power balance. This trend is in agreement with the modeling and the experimental works. 16,29,30 Figure 6(c) shows the electron energy probability function (EEPF) for the Ar content of 10 -30 % at the ICP power of 500 W and the pressure of 1.4 mTorr. In this work, the electron energy probability functions were found to be Maxwellian. The population of electrons with energy greater than 15 eV exhibits an unstable behavior, which might be caused by noise. For nitrogen, the threshold for dissociation is at 9.8 eV; however, the cross section function does not rise significantly until after 15 eV. From there, it rises gradually to a value of 6.74 × 10 −17 cm 2 at 20 eV. 3 Generally, very little N 2 is dissociated because of the high threshold and the peak energy well above 20 eV. However, ICP discharges show a considerable amount of high energy electron, and this may promotes the dissociation of N 2 . These electrons contribute to an increase in the electron-impact dissociation. In our previous work, 16 it was observed that higher Ar contents resulted in a higher dissociation fraction. This is also related to an increase in the relative production of Ar metastables.
In order to investigate the pressure dependence of n e , T e and EEPF, the pressure was varied from 1.4 to 22 mTorr with a fixed power of 500 W. As shown in Fig. 7, the electron density increases first and has a maximum at 11 mTorr, and then slightly decreases with increasing pressure, which is due to the increased collision frequency between electrons and neutral molecules or atoms. The electron temperature decreases with increasing pressure: for the ICP power of 500 W, T e is about 3.6 eV at 1.4 mTorr, while about 1.7 eV at 22 mTorr. Figure 7(c) shows the measured EEPF with different gas pressures at the ICP power of 500 W. The population of electrons with high energy exhibits an unstable fluctuation. As pressure increases, an easy heating due to a frequent electron-impact rovibrational excitations of nitrogen molecules is thought to contribute to the fluctuation of the probe currents. However, the shape of EEPF roughly remains the Maxwellian distribution. At the pressure of 22 mTorr, there is a significant decrease of the electron energy in the high energy electron region, while the electron density in the low energy electron region does not change much compared to that of 11 mTorr. This can be explained by that the depletion of the high energy electrons around the excitation threshold becomes dominant at the pressure of 22 mTorr.
In order to calculate the dissociation fraction using Eq. (12), the correction factors c 1 and c 2 should be determined. The density of N-metastable, [N m ( 2 D)], is about 0.1 − 0.3 times the density of the ground state species and [N m ( 2 P)] is smaller than [N m ( 2 D)] by one order of magnitude. 3,31 The excitation rate coefficient k exc N m is less than k dir N by a factor of 10 at T e = 3 -5 eV. 9 Therefore, the excitation from N m ( 2 D) to N * (3p 4 S) is small. However, introducing Ar into the nitrogen plasma causes the generation of N 2 (B), N 2 (C), N + 2 (X) and N + 2 (B). 32 The content will not be considered in the analysis of this study. Dissociative excitation rate coefficient is less than k dir N by a factor of 1000 at T e = 3 -5 eV. 9 Then the factor c 1 is written as represents the Penning dissociation followed by the Penning excitation due to Ar excited states. 33 The rate coefficient for this reaction is hardly found in the literature. The rate coefficients k Penn In this calculation, the neutral particle densities are obtained using the relation [N 2 ] = p x N 2 /k B T rot . 16 Figure 8(a) represents the ratio of rate coefficients k dir Ar /k dir N used in this work. The values of the electron impact excitation cross sections are obtained from the literature. 34,35 In deriving the rate coefficient, a Max-well-Boltzmann energy distribution of electrons was assumed. The determination of dissociation fraction via actinometry is convenient because the necessary parameters are the electron temperature and the emission intensity ratio of nitrogen atom peak and argon peak. However, the actinometric method has some drawback in providing accurate results because of the larger errors on the excitation cross section data [34][35][36][37][38] and of the assumption of Maxwell-Boltzmann energy distribution of electrons. All these factors contribute to a limited accuracy of the actinometric method. Figure 8(b) shows the estimated dissociation fraction of N 2 as functions of power at the pressure 1.4 mTorr for the Ar content of 5%. The dissociation fraction increased with increasing power from 1.92 % at 300 W to 2.28 % at 500 W. The dissociation fraction versus the Ar content is shown in figure 8(c), where the uncorrected and two kind of corrected estimations are presented. As was shown in the previous works, the dissociation fraction increases with the Ar content. As expected, the correction factor reduces the value of dissociation fraction and becomes more important at higher Ar contents. If one utilizes the larger value of k Penn−diss N (that is, the Penning dissociation followed by the Penning excitation due to Ar excited states is fully considered), one can obtain a lower dissociation fraction (designated as correction 2 in Fig. 8(c)). The pressure dependence of the dissociation fraction is represented in figure 8(d). The dissociation fraction decreased with increasing pressure. The values of dissociation fraction were well comparable to those obtained by vacuum ultraviolet emission spectroscopy performed by Nakano et al. 13 and to the result of global modeling. 31 The pressure dependence of the dissociation fraction was similar to the results of earlier works. 6,31 The observed decrease in dissociation fraction with pressure is expected to be due to increased wall recombination and also potentially due to the decreased electron-neutral collisional frequency at higher pressures. 3 To explore the dependence of dissociation fraction on plasma parameters, a simple scaling relation can be utilized. Neutral nitrogen atoms are assumed to be generated mainly by electronimpact dissociation of N 2 (and partly by the Penning dissociation due to the excited Ar), and to be lost by diffusion to and recombination at the reactor wall and by the electron-impact ionization of N. There is also another contribution to N-atom production: charge exchange between nitrogen molecules and argon ions followed by dissociative recombination. 9 But this can be neglected in nitrogen-rich plasmas. In addition, the creation of nitrogen atoms resulting from the dissociation of vibrationally excited N 2 (X, v) molecules past a threshold vibrational level (v = 45) and the loss due to the volume recombination occurring through a three-body collision process involving molecular nitrogen should be also considered. 14,15 These addition terms are especially important for higher pressure plasmas such as microwave-sustained discharges. Then we have where K diss is the rate coefficient for electron-impact dissociation of N 2 , K V −V for dissociation from vibrationally excited N 2 (X, v) molecules, k N iz for the electron-impact ionization of N, K d for the diffusion to and recombination at the reactor wall of N atoms, and K rec for recombination through a three-body collision process. Assuming that metastable Ar plays an important role, the dissociation fraction is approximated by If K diss and k N iz are assumed to have Arrhenius forms K diss = K diss0 e −ε diss /T e , k N iz = k iz0 e −ε iz /T e (ε diss (= 9.8 eV) and ε iz (= 14.5 eV) are the threshold energies for dissociation and ionization reactions), 39 then K diss and k N iz decrease with decreasing electron temperature (k N iz has a steeper variation). It is worth noting that if we look into the electron energy dependence of the cross section of nitrogen dissociation, ε diss should be replaced by the real activation energy which is a little higher than the threshold energy (but lower than ε iz ).
It is observed that as pressure is increased, n e increases first and then slightly decreases, while T e decreases. The electron impact reaction rates show an exponential dependence on T e and generally exhibits linear variations in n e . The k N iz n e decreases dominantly over K diss n e with a decrease in T e (indicated as ⇓ below). An increase in pressure decreases the diffusion to and recombination at the walls. 3 The contribution from vibrational excitation of N 2 (X, v) followed by dissociation to N atoms is enhanced with increasing pressure due to an increase in the vibrational temperature. Therefore, with an increase of the pressure at a fixed Ar percentage, we have a simple scaling: The dissociation fraction was observed to decrease slightly with pressure. The nitrogen atom densities increase with pressure because the initial density of molecular species is increased with pressure.
In the pressure range of 1.4 -30 mTorr, the dissociation fraction decreased. The observed decrease in dissociation fraction with pressure is mainly due to a decrease in T e in addition to the increased wall recombination and due to the decreased electron-neutral collision frequency. As the power is increased, the dissociation fraction is observed to increase. From the global balance of the discharge kinetics, the dissociated neutral atom density is expected to be proportional to the power. 31,39 The trend of change in the dissociation fraction correlates well with the n e , T e , and the EEPF.

IV. CONCLUSION
A detailed diagnostic study of low-pressure inductively coupled N 2 -Ar plasmas by using OES and Langmuir probe was performed under the conditions of nitrogen pressures in the range of 1.4 -30 mTorr and ICP powers of 300 -600 W. The effect of gas pressure on the characteristics of optical emission from discharges was investigated. The complicated variations in the emission intensities of atomic lines and molecular bands resulted from the changes of n e , T e , and neutral particle densities with pressure. The electron density was found to increase and the electron temperature decreased with increasing Ar content. With increasing pressure, the electron density increased first and had a maximum at 11 mTorr, and then slightly decreased. As expected, the electron temperature decreased with pressure. The EEPFs were roughly Maxwellian over the operating parameter range of this study. The correction factors for the dissociation fraction of nitrogen molecules accounting for Ar effect was formulated and calculated. The correction factors became important as the Ar content increased. The dissociation fraction measured by using OES actinometry increased with increasing Ar content and power as expected. For the pressure range of 1.4 -30 mTorr in the Ar 5% -N 2 discharge, the dissociation fraction decreased with pressure and had values ranging 0.86 -2.12%. The formulated correction factor can be utilized to provide a reasonable value of dissociation fraction for various N 2 -Ar plasmas in broad operating conditions.