JfPtys. D: Appl. Phys. 28 (1995) 1856-1868. Printed in Hie UK CspvclJ On the use of actinometry to measure the dissociation in 02 DC glow discharges: determination of the wall recombination probability D Pagnon, J Amorim, J Náhorný, M Touzeau and M Vialle Laboratoire de Physique des Gaz et des Plasmas, CNRS, Universitě Paris XI, 91405 Orsay Cedex, France Received 20 April 1995 Abstract. A study has been performed to re-investigate the actinometric technique used to determine the absolute concentration of O atoms in DC 02 flowing glow discharges for pressures ranging from 0.36 to 2 Torr and discharge currents ranging from 5 to 80 mA in Pyrex tubes of three different diameters (16, 7 and 4 mm). Actinometric measurements using 0(3P - 3S) 844 nm, 0(SP - 5S) 777 nm and Ar(2pi - 1s2) 750 nm transitions are compared to VUV absorption spectrometry. The choice of the excitation cross sections for the calculations of atomic excitation rates as a function of the reduced electric field using a Boltzmann code and the contribution of the quenching processes of the excited states are discussed. The dissociation ratio [0]/[02] can be determined from the ratio of intensities lM*lhsa by the re|ationXQ]/[02] rZp\ WW We have found that C^ remains constant (C*p = 2.6 x 10~3) throughout the range of experimental conditions investigated. The recombination probability y of the O atoms at the wall is calculated and correlated to the wall temperature of the Pyrex tubes. The variation of the recombination probability as a function of the wall temperature is fitted by the relation y = 0^94expJrl1780/J4«aÄlfor 300 < T„a„ < 500 K. 1. Introduction Oxygen discharges have been extensively used as sources of oxygen atoms for basic studies in atomic and molecular physics [1,2], etching and surface treatment [3,4]. More recently oxygen atom sources have been used in oxidation of high-temperature superconductor thin films in molecular beam epitaxy devices [5,6] and in the oxidation of YSZ thin films obtained by pulverization [7]. The aim_of this work is to investigate the validity of actinometry in the positive column pfjrnall diameterO-> DC glow discharges in order to .monitor the flux of atoms in oxygen atom plasmaLSOUtses Qf^is.JdndJl-j_Ô]7"" Optical emission actinometry is a widely utilized diagnostic for in situ monitoring of spatial and temporal variations of atomic and molecular concentrations [11,12]. It is easier to handle than optical absorption spectroscopy or laser-induced fluorescence. OnjhejDther hand, the validity of actinometry is somewhat controversial and the criteria for the utilization of the technique and its limits of validity must be verified in each case. The validity of actinometry using 0*(3s 3S-3p 3P) 844 nm and Ar*(4s-4p) 750 nm transitions was investigated by Walkup et al [13]. They found that the actinometric determination was well correlated with the variation of atom concentration in 0.4 Torr RF O2-CF4 plasmas, but discrepancies occurred in pure O2 plasmas. Booth et al [14] have shown that the ratio of the intensities of the oxygen line to the argon line, Io* (844 nm)/I,4r* (750 nm), was poorly correlated to the oxygen atom concentration in ECR low-pressure (1-6 mTorr) plasmas containing O2. The fact that the ratio of intensities was well correlated with [O2] was interpreted by considering that the most important mechanism of production of the 844 nm line is dissociative excitation when dissociation rates are lower than 0.1. Breithbarth etal [15] proved the validity of actinometry in RF O2-CF4 plasmas with an applied electric field. Granier et al [16] have shown that actinometry can be used to monitor the atom concentration in O2 and O2-N2 low-pressure (0.5-2 Torr) microwave plasmas^ A new method, time-resolved actinometry has recently been developed in modulated plasmas to study the kinetics of hydrogen-argon plasmas [17] or fluorinated plasmas [18]. This technique has been applied to O2 and O2-SF6 or F2 ECR plasmas by Booth and Sadeghi [19], who concluded that the determination of oxygen atom concentrations was impossible from observation of the 844 nm line because the production of emitting atoms 0(3p3P) (844 nm) is principally due to dissociative excitation of O2. The same 0022-3727/95/091856+13$19.50 © 1995 IOP Publishing Ltd '*. Actinometry in 02 ÖC glow discharges conclusion was obtained in pulsed RF low-pressure O2 plasmas by Collart et al [4], who suggested that highly energetic electrons are responsible for the dissociative excitation of O2. It_ appears then that the validity of actinomejr^technjgue jtron&ly dependsjpn the experimental conditions. In the present work, we have determined the concentration of oxygen atoms in the positive column of a glow discharge created in Pyrex tubes of three different diameters (16, 7 and 4 mm). The actinometric technique using the classical 0(3P-3S) 844 nm, 0(5P-5S) 777 nm and Ar(2pi-ls2> 750 nm transitions is discussed in detail for these experimental conditions in section 2. The values of the excitation rate of the 0(5P), 0(3P) and Ar(2pi) states are calculated as a function of the reduced electric field E/N using a Boltzmann code which had been developed previously [20]. The contribution of the dissociative excitation of the O2 molecules which can contribute to an inaccuracy in the determination of the oxygen atom concentration is evaluated. The importance of the quenching processes of the excited states is also discussed. In section 3, we present a comparison of the dissociation ratio determined by actinometry and by VUV absorption and we show that we obtain a good agreement between these two techniques. The actinometry technique was used to determine the dissociation ratio in small-diameter tubes for which the VUV technique is difficult to utilize. The results of the dissociation ratios obtained in the tubes of three different diameters are compared in section 4. These measurements show that a saturation of the dissociation ratio is obtain in small-diameter tubes when the discharge current increases. This behaviour is interpreted in section 5 as the result of the balance between the production of atoms by dissociative electronic impact and their loss by recombination at the wall. 2. Determination of the concentration of ground state oxygen atoms by actinometry 2.1. Principles In order to determine the concentration of ground state oxygen atoms, we have used the classical technique which consists of comparing the emission of the 0(3P-3S) 844 nm and 0(5P-5S) 777 nm transitions to the emission of the Ar(2pi-lS2> 750 nm transition (figure 1). We suppose that these X* states are mainly populated by electron impact from the ground state X: *,"' e + X ^-» X* + e. (1) The de-excitation of excited states X* is either radiative: X*-^X*+hvu (2) or non-radiative by quenching with species Q (Q = O2, O or Ar): Xf + Q-A-X + Q. (3) The emission intensity /*. of a transition X,* -> X* is then written as the ratio between production and loss processes: hVijAuk*ne /*• = c- ■[X] (4) (XMy+*ôtQ]) where ne is the electronic density, ftvy is the energy of the emited photon (relation (2)), Ay is the Einstein coefficient for the observed transition (i -*• j), EA,y is the sum of all radiative de-excitation processes of the /th level, and C represents a constant dependent on the detection system (in the following, we take the same C value for all emission lines because the volume observed by the optical system is the same). The coefficient £*•' can be expressed by the following relation: m ) "-en:- (e)or( (e)/(<0 de (5) where v(e) is the electron velocity, at(ß) is the collision cross section with threshold energy eth for excitation of level í (relation (1)) and /(e) is the electron energy distribution function (EEDF) normalized by ľ Jo /(e)e1/2de = l. With the relation (5), relation (4) becomes ».[X] l-OO Ix. = Ch vu Au / v(e)ff/ (r)/(e) de -Jen, (6) (7) SAy+*fl[Q] As we can see, the intensity relies on the electron density and the electron distribution function. It is possible to compensate the variations in ne by dividing the emission intensity of an oxygen line by the intensity of the actinometer line (in our case the 750.4 nm line of argon), thus Í21 = hv°A° k? (s^ + fflQJHQdtO] hr> hvffAfí k? CEAfj + JfcgíQ]) [Ar] f02] 1 [O] C*r [02] (8) where C Ar __ 0 — hvffAtfkf SAg+*g[QI [Ar] hv°A° k° SAíV + *á'[Q][02]' Hence the ratio of the intensities loll Ar is proportional to the [0]/[C>2] concentration ratio if the coefficient Cpr remains constant throughout the experimental range. 2.2. The influence of the dissociative electronic excitation of 0(3p 3P) and 0(3p 5P) Under our experimental conditions the Ar(2pi) excited state of argon is populated by direct electronic impact from ground state: *,2" e + Ar(lpo) -!■♦> Ar(2p,) + e. (9) The stepwise excitation by metastable Ar states can be neglected because the metastable states are destroyed by collision with the oxygen molecules [21]. To yield oxygen excited states 0(3p3P) and 0(3p5P), two channels have to be taken into account: 1857 v______ O Pagnon etat O (2p4 3P) Ar-(lpo) Figure 1. A schematic diagram of the excited levels involved in the determination of the concentration of ground state atoms by actinometry. 10u 10 1 :• > ~ 10 2 - IQ"3 10' -J----------1-------1—ll 11 . .1 30 Td ľ • ľ ti "i n 10" 10' E u 10 (O 2 10 10 r* 10 [eV] 100 Figure 2. The electron energy distribution function calculated for EfN = 30 (full line) and 100 Td (broken line) versus the electron energy. The cross sections for direct excitation of Ar(2p0, ' e + 0(2p4 3P) -^ 0(3p 3P) + e tf e + 0(2p4 3P) -i* 0(3p 5P) + e (10) (H) (ii) dissociative excitation by electronic collisions from the ground state molecules: e + 02 —► 0 + 0(3p3P) + e (12) tíľ e + 02-^0 + 0(3p5P) + e. (13) The excited states are depopulated by radiative de-excitation: 0(3p 3P) -A. 0(3s 3S) + h v(844.6 nm) (14) A,r 0(3p5P) -A- 0(3s5S) + Av(777.4 nm) (15) A*1 Ar(2pi) -A- Ar(lpo) + M750.4 nm) (16) 1858 and by quenching with oxygen molecules: 0(3p3P)+O2-^»0 + 02 0(3p5P) + 02-^*0 + 02 Ar(2p0 + 02 -^-k Ar + 02. (17) (18) (19) From the relations (9>-<19), the intensities of the oxygen and argon lines can be written as follows: /g44 — ^777 = nehVs44Atf(klP[0] + k^[02]) nehvniA5J{klP[Q}+kYe{02}) LAlf+k5Qp[02] nthvysoA^k^lAr] ^750 = i2P 2pii XMJf+^'iOj] (20) (21) (22) The ratio of the intensity of one oxygen line, 844 nm for example, to the argon line is h» hv8A4AlP EaJ" +k2QPl[02)klP[0] + k%[02] '750 hvysoAl1" XAlP + k3Qp[02] *2"[Ar] (23) and it can be written in the simple form described in relation (8): hZ^JLEi (24) /750 C2/p'l02] only when the yield of oxygen excited states 0(3p 3P) or 0(3p5P) by dissociative excitation (relation (12) or (13)) is negligible: k3P klp or k5/ ^[o2y (25) Then, the concentration ratio [0]/[02] is proportional to the ratio of the intensities when the following coefficients remain constant: SP ÄV844A3/ e A J" +kf[02] klp [02] (26) ,2„ ^soAy-' SAf/ +4/'[02] klPl [At] '5P hvnmA^ eaJ" + kf{02) k\p [02]' So, in order to discuss the validity of the actinometric method, we have calculated the coefficients c\Pp and C5p and the ratios k^/k]p and k^p/klP. We have then calculated the electron energy distribution function under our experimental conditions. With this EEDF, we have determined the different rate coefficients (k]p, k\p, k3dp, &Jf and k/'), using relation (5) and different sets of collisional cross sections for each excited state in order to evaluate the importance of the choice of a cross section. The influence of the quenching processes (relations (17)—(19)) is also discussed in the following. I Actinometty in 02 DC glow discharges 2.3. Calculation of the excited states rate coefficients The plasma of the positive column is a homogeneous medium in which the electric field, the gas temperature and the concentration of the main active species have already been measured with a good accuracy [22]. For oxygen pressures ranging from 0.1 to 5 Torr and discharge currents ranging from 5 to 80 mA, reduced electric fields from 30 to 100 Td and electronic density of the order of 10I0-10" cm"3 have been measured in Pyrex discharge tubes of 16 mm inner diameter. Relative concentrations of oxygen atoms [0(3p3P)]/f02(X)] and singlet molecules [02(a' A)]/[02(X)] of the order of 10% have been measured by VUV absorption spectroscopy. A kinetic model has been developed which solves simultaneously the Boltzmann equation and the rate balance equations for the dominant heavy particles and describes the experimental results reasonably well [20,23]. As a result of the large quenching of vibrationally excited 02 molecules by oxygen atoms, we have assumed in this model that the vibrational temperature is equal to the gas temperature. This assumption has been verified under our experimental conditions by coherent anti-Stokes Raman spectroscopy (CARS) measurements [24]. The presence of vibrationally excited 02 molecules has, then, an almost negligible effect on the dissociative excitation. The EEDF has been calculated by solving the ^2^™^BĽl.^QMÉ5SlPiJ^ n^SÜElS^^SI9^E} dejreloped in [20]. The processes taken into account in the Boltzmann code are listed in table 1. In figure 2 are reported the EEDFs calculated for reduced electric fields E/N = 30 and 100 Td, for relative atomic concentration [0]/[02] = 10% and singlet molecule relative concentration [02(a'A)]/[02] = 10%, versus the electron energy. In figure 2 are also reported the cross sections for direct (Laher [25]) and dissociative (Schulman [26]) excitation of 0(3p3P) and 0(3p5P) oxygen states and for excitation of the Ar(2pi) state (?uech [27]). In figure 3 are reported the results of the calculation of the reaction coefficients (according to relation (5)), for direct and dissociative excitation of 0(3p 3P) and 0(3p SP) states and direct excitation of Ar(2pi) state. Throughout the range of E/N studied, the coefficients for direct electronic excitation of 0(3p3P) and 0(3p5P) states are two orders of magnitude larger than those for dissociative excitation. It can be observed in figure 3 that the values of the excitation rate are very sensitive to the shape of the cross sections near the threshold energy. In order to estimate the uncertainties due to our choice of cross section, we have calculated each rate coefficient with two different cross sections from the literature. The comparisons between the cross sections from Laher et al [25] and Julienne et al [34] for excitation of 0(3p3P) or 0(3p 5P) and of the cross sections from Puech et al [27] and Ballou etal [35] for excitation of Ar(2p0 are reported in figure 4. Calculations of the argon to oxygen excitation rate coefficients ratios kepl/k*p and k/x/k]p lead to results presented in figure 5 for reduced electric field E/N ranging from 30 to 100 Td. In figures 4 and 5, the following two facts are evident. 1859 D Pagnon er al Table 1. Inelastic and superelastic collision processes considered in the Boltzmann equation, and corresponding references to the cross section data. Electron processes Reference Molecular oxygen (R1) e + 02(X, v) *± e + 02(X, w) 128) (R2) e + 02(X, v = 0)r=*e + O^a1 A) [28] (R3) e + 02(X, v = 0) *± e + OsKb1 £) [28] (R4) e + 02(X, v = 0) -> e + 02(4.5 eV) [28] (R5) e + 02(X, v = 0) -*■ e + O2{6.0 eV) [28] ■ e + e + Oí e + 02(X, v * 0) -»■ 0(3pV) + 0(3P) + e (R13) (R14) e + 02(X, v = 0) -> 0(3p 5P) + 0(3P) + e Atomic oxygen (R15) e + 0(3P);=*e + 0(1D) [30] (R16) e + 0(3P)f=se + 0(1S) [30] (R17) e + 0(3P) -*■ e + 0(3S) [31] (R18) e + 0(1D)?=*e + e + 0(1S) [30] (R19) e + 0(3P)-+ e + e + 0+ [32] (R20) e + 0(1D)-*e + e + 0* [33] (R21) e + 0(1S)-> e + e + O* [33] (R22) e + 0(3P)-*0(3p3P) + e Text (R23) e + 0(3P)-> 0(3p5P) + e Text Argon (R24) e + Ar(1 po) -* e + Ar(2pT) Text «-11 30 40 50 60 70 80 90 100 E/N [1.10"17V.cm2] Figure 3. Reaction rates for direct and dissociative electronic excitation of 0(3p3P) and 0(3p5P) and direct electronic excitation of Ar(2pi) states. (i) At low E/N (30-40 Td), the large difference between calculated ratios kepi/k*p or k1/ lk\p can be explained in terms of different rising fronts in the cross sections near threshold energies. At high E/N (90-100 Td) we also obtain a large difference due to different shapes of the various cross sections. At medium E/N (50-80 Td), the two causes of difference compensate each other and the resulting difference is minimized. We will see in the following that the best fit between VUV and actinometric [0]/[02] concentration ratio measurements is obtained with the Ar(2pi) Puech cross section and 0(3p3P) and 0(3p5P) Laher cross sections. (ii) An uncertainty in the determination of reduced electric field E/N, which is principally due to the determination of gas temperature, introduces an error into the determination of ratios keP'/k^p or klpX /k]p'. An error of ±10% in the reduced electric field E/N leads to an error of ±20% in the ratios for E/N > 70 Td and of ±35% for E/N < 60 Td. For values of E/N < 40 Td the calculation is imprecise because it only uses the rising front of the cross section near the threshold. 2.4. Quenching of the excited states In order to express the ratios Im/hso and Im/hso versus [0]/[02] (according to relations (23) and (24)) with coefficients C|^ and C\p expressed in relations (26) and (27), we have also evaluated the quenching of excited atomic states by oxygen molecules (relations (17)—(19)). For the 0(3p3P) excited state, Dagdigian et al [36] obtained by laser-induced fluorescence emission of the 3P state upon two-photon excitation a radiative decay rate T,A]f s= 2.98 x 107 s_1 which agrees well with other determinations (for example by Bamford [37] and Bittner 1860 Actinometry in 02 DC glow discharges («) £ u c o u e 10 17 10 18 S 10"1! O -------------_■:--------------y--~ -raaa — r = --"=s-: .________£_:!: "IZ" (B) Ballou: . _..,_____...... .......p. n. ™ .L. t-ŕ— """tk, _.____ (P) Puech . ,____._ -+:_-:_ ... i j r í rí f T T r j............ Ar(2Pi) - "Tit 11 r i * —i—i—i—i——[j\—(—i—i— 3d:±±:::t: (6) E o (A e o «-i o « j"t"~' i vj>. •,9- = .4)z = :: (L) Laher v * 40 50 1.0 20 30 Energy [eV] 40 50 ■(c) 10 -17 E u 0) e o u o M W m 10 18 10" ; :::Tľ: :q:.....™ :~ -: — isí ".. _.. j| JU||enne:: L' "*" Dat^» -L *JiÍ— — -r .__„_! ^ "i ■-L-r—.....~L|i........------- .....---rFJ=mTff- —t~ (L) Laher « ......T"........—r*4" o [3p3P)" f +^ ■ • ■•»• -.....---------- -------------.....-j;......- —.........JEiE------........:----- • - -4---------------------...............- .........—+- •----------------------------- 10 20 30 40 50 Energy [eV] Figure 4. A comparison of the cross sections for direct electronic excitation of Ar(2pi) (a), 0(3psP) (b) and 0(3p3P) (c) versus energy given by Ballou [34], Puech [26], Julienne [33] and Laher [24]. [38]). This is also the value of the transition probability at 844 nm since the 0(3p 3P) state has only one electric-dipole-allowed decay pathway. These authors deduced a quenching rate of the 0(3p3P) state by O2 molecules, k^ = 7.8 x 10-!0 mol-1 cm3 s_1, and surmise that the bulk of 3P quenching collisions occur by excitation transfer to the O2 molecule partner rather than collision-induced transitions to lower lying oxygen atom states. By taking the quenching rates kQř and kg" of Dagdigian, and comparing the actinometric and" the VUV measurements (section 3), we have found that the best fit is obtained throughout the range of pressure and current when *ö'iOiJ = 2.6 x 107p (Torr s"1) k5QPí02] = 3.5 x Í07p (Torr s"1) (28) namely with a quenching rate constant that increases linearly with the gas temperature. The quenching rate constant k2Q of the argon excited state Ar(2pi) by O2 molecules has been measured by Belikov et al [39] for gas temperatures ranging from 95 to 210 K. They obtain a quenching rate constant kQpX = 0.9T~063 x 10-10 cm3 s"1. Insofar as we can extrapolate this temperature law under our experimental conditions, we obtain for 300 < T < 600 K 8.1 x 106p (Torr s"1) > kQpl[02] > 2.6 x l<ŕp (Torr s"1). 21 (29) Because these kg [O2] values are lower than the uncertainty in the radiative decay rate DA3/ = 4.4 x 107 s~', we have neglected the quenching of the argon excited state Ar(2pi) by O2 molecules in our calculations. 1861 D Pagnon eŕ a/ 30 40 50 60 70 80 90 100 E/N (Td) Figure 5. Values of *f1 /k*" (a) and *** fkf (b) calculated using the cross sections of Puech and Laher (P/L), Ballou and Laher (B/L), Puech and Julienne (P/J) and Ballou and Julienne (B/J). The values of Cjp and C*p coefficients calculated (relations (26) and (27)) with these quenching values under our experimental conditions are reported in table 2. 3. Comparison with VUV absorption measurements The experiments were performed by measuring the emissions of 0(3p3P) and 0(3p5P) excited oxygen atoms and Ar(2pi) argon lines in the positive column of a DC discharge. The experimental device reported in figure 6 allows simultaneous measurements by VUV absorption spectrometry and by actinometry. The light emitted by the discharge is focused at the entrance slit of an 1862 optical multichannel analyser (OMA). The VUV absorption technique has been described in detail elsewhere [22,23]. The DC discharge is excited in a 16 mm inner diameter Pyrex tube containing an 02-Ar mixture ([Ar]/[02]) = 10~2. The pressures range from 0.3 to 2 Torr and the discharge currents from 5 to 80 mA. The reduced electric field E/N is determined by measuring the sustained electric field E using two Langmuir probes and the gas temperature is deduced from the rotational emission distribution of the 760 nm atmospheric band 02(b'£-X3E) by the method described in detail in [40]. In figure 7 are reported the values of the dissociation ratio [0]/[02] measured by VUV absorption spectroscopy and actinometry versus the discharge current for 0.36 and 0.56 Torr. We obtain a good agreement with VUV measurements for the two sets of determinations using 0(3p 3P) (±30%) or 0(3p 5P) (±20%) throughout the range of pressure investigated. As shown in figure 8, the values deduced from actinometric measurements are larger than those obtained from VUV absorption. This discrepancy is important at low current and low pressure because under these conditions the reduced electric field is high, yielding energetic electrons able to induce dissociative excitation and the concentration [0]/[02] is below 1%. We have thus to take into account the production of atomic excited states 0(3p5P) by dissociative excitation (relation (13)). For this excited state the intensity ratio is /777 hvrnA» S A2/' *."[()] +iff [fr] '750 ■ A^soA^SA^+^tOal *e2"'[Ar] Using this relation, we can express the concentration ratio [0]/[02] versus the intensities ratio by [O] _c2Pl(Im\ *% where the C2£' coefficient is- defined by relation (27). Calculations of the ratio k^fk^p are performed using the calculated EEDF and the cross sections from Schulman [26] for dissociative excitation and Laher [25] for direct excitation of the 0(3p5P) excited state (figure 9). Taking into account this correction, it can be shown in figure 8 that the discrepancy is then lower than 30%. We can conclude, from this study of a DC glow discharge in 02 (1% Ar) in a 16 mm diameter Pyrex tube, that actinometry can lead to absolute [0]/[02] concentration ratios with a good accuracy for current ranging from 5 to 80 mA and pressure from 0.36 to 2 Torr. Perturbation due to dissociative excitation can be minimized by choosing the 0(3p3P) state instead of 0(3p5P). In fact, as we can see in figure 9, the ratio kde/ke for 0(3p3P) is one order of magnitude smaller than that for 0(3p 5P). Because the quenching rate is also better determined for 0(3p 3P) than for Q(3p5P), and the coefficient C2£' (2.10 x ÍO-3 ± .7%) is constant throughout the range of our experimental conditions, it is preferable to choose the 0(3p3P) -»■ 0(3sJS) transition (844 nm) to determine the absolute concentration ratio [0]/[02] by actinometry. Actinometry in 02 DC glow discharges Table 2. Variation of C*p and cl^ versus the pressure. Pressure (Torr) Coefficients 0.36 0.56 1 Mean value 2.09 x 10-3 2.24 x IQ"3 1.98 x 10-3 1.86 x IQ-3 2.09 x 10-3 1.75x10-3 2.25 x 10-3 1.63x10-3 2.10 x 10-3 (±7o/o) 1.87 x IQ"3 (±20%) optical fiber O.M.A. MgF2 window Lamp Source 1 Pump SS U. Sä a. Pump 0? + Ar 0, Lock-in Amplifier Recorder Microwave Generator 100 W 2,45 GHz Figure 6. The experimental set-up for actinometry and VUV absorption spectrometry. Table 3. A comparison between measured and 'calculated' reduced electric field in a 7 mm diameter tube for a pressure of 1 Torr. /«, (mA) Calculated E/N (Td) Measured E/N (lá) 93.0 87.3 96.8 96.1 102.3 103.7 10 95.0 20 87.0 30 84.6 40 88.1 50 86.3 60 88.5 70 84.6 80 83.2 100 83.4 4. Actinometry in 7 and 4 mm diameter tubes In order to design sources of atomic species (O, H and N), we have used small-diameter tubes. Because we are in this case principally interested in the yield of oxygen atoms, and VUV absorption measurements are difficult to perform in these tubes, we have used the actinometric method to determine [OJ/Í.O2] concentration ratios in 7 and 4 mm inner diameter discharge tubes, for a pressure of 1 Torr and currents ranging from 10 to 100 mA. For these small-diameter tubes, the reduced electric field E/N has been deduced from the intensities of the 844 and 777 nm lines. From relations (20) and (21) describing these intensities, we can write the intensities ratio as lm = hvmAlf SA?/ + k5Qp[02] k)p hn hvmA" E A?' + fc3/[02] **' (32) On taking into account the quenching for 1 Torr of the two excited states as discussed previously, we obtain 7*-'■"■<£ /777 k5/ (33) and so, from the measurement of the intensities of 844 and 777 nm emission lines, we can determine the ratio k]p /k*p and deduce the reduced electric field E/N leading to this ratio. From the values of E/N obtained, we have calculated the kepl, k\p and k5ep rate coefficients and then the ratios kl,x/k\r and rtpX/k\p involved in the C\pp and c\ppx coefficients (relations (26) and (27)). Concentrations [OMO2) are obtained using relation (24) for the 0(3p3P) ->• 0(3s3S) transition and a similar relation for the 0(3p5P) -> 0(3s5S) transition (844 and 777 nm respectively). In order to validate this method, we have tested it on the 7 mm diameter tube in which the reduced electric field E/N has been measured. In table 3 the values of the reduced electric field measured in the 7 mm tube are compared to that deduced from relation (33) for discharge currents ranging from 10 to 100 mA. The error in the measured E/N values is of the order of 20%. 1863 D Pagnon ef al (a) 0.25 0.2 0.15 O - 0.1 0.05 —Ill—I—II 1 ,1 1—1—1— ■ * ■ ! 1 / ----&----LmI-----~ 1 - o Act5P(0.36 Torr) ° Act5P(0.56 Torr) • VUV(0.36 Torr) ■ VUV(0.56 Torr) - • ■ • - Á ( i i • ■ 1 i ' i: i i i i 11 1 ■ (b) 20 40 60 80 100 Discharge current (mA) 0.3 0.25 "- 0.2 O" S 0.15 O ■m* 0.1 0.05 . "I"1 , Im li lil i -.. i........i,., l..... —.-t.—.*..—1^_ _ -— ° Act(3P)-o Act(5P)-* VUV 344 -_X£Ž_. S f . ■ ■ /^X' \ • • Z /1 : 1 Torr H f' 'i ' ").....!"■-■■■ —i—-t—r— ......i.....i« «-'ľ " ■ ""»"•'"T—T"""" --------1—1 ' l " 1 ,IM 0 20 40 60 80 100 Discharge current (mA) (c) 0.3 0.25 0.2 O" S 0.15 O 0.1 0.05 '. ' 1 ,1 , ' ' ' ' I A—-A,.,-t...... 1 i 1-----L_ _ • ° Act(3P) ° Act(5P) * VUV ■ 1 • • 1 ■ z Í • ! v 2 Tc >rr Q/* H 1 ' i "| ' |" ' 1 '1 " '1.......I"""1 i ii 1 ""i "' 'ľ " i......- 20 40 60 80 100 Discharge current (mA) Figure 7. A comparison of the dissociation ratio [0]/[02] determined by actinometry (Act3P using the 844 nm line, Act5P using the 777 nm line) and VUV measurements for 0.36 and 0.56 (a); 1 (b) and 2 Torr (c). The reduced electric fields E/N deduced from relation (33) compare well with the measured values with discrepancies lower than 20%. The ratios klp{/k]p and k/llk5/ are then deduced from the values of E/N corresponding to each discharge current. The [OMO2] concentration ratios are deduced from relation (24) using the coefficients C5p and C3£ calculated from relations (26) and (27) and listed in table 4. In figure 10(a) are represented the [0]/f_02] concentration ratios resulting from measured E/N and from E/N deduced from relation (33). If we calculate the mean value between the two determinations, we obtain an accuracy of ±20%. This method has then been used to determine the atomic concentration ratios [OMO2] in the 4 mm diameter tube from the measurements of the intensities of the 844 and 777 nm lines and the values of C/P and CJp1 given in table 4. Results are represented in figure 10(b). 5. Recombination of oxygen atoms at the wall In figure 10(c), we can observe a saturation of the [OMO2] concentration ratio with increasing discharge currents for values above 50 and 20 mAfor 7 and 4 mm diameter tubes respectively. We surmise that this saturation is due to the increase in the losses of oxygen atoms by recombination at the wall with increasing wall temperature. We have thus measured the temperature of the external wall of the tubes of different diameters and related the wall temperature to the recombination coefficient. 1864 Actinometry in 02 DC glow discharges Table 4. Values of Cs2£1 and C^1 calculated for the tubes of three diameters. Diameter (mm) 4 7 16 Mean value C^p 3.35 x 10"3 3.44 x 10~3 1.87 x 10"3 2.78 x 1Q~3 ±55% C$' 2.78 x 10-3 2.83x10-3 2.10 x 10~3 2.60 x 10~3 ±20% 0.06" „ 1 1 , I..I j > lil i 1 1 II 1, Inj .1, * j—1_ ■ ' ' ■ i «i i i------ ■ ■ Act5P(0.36 Torr) • VUV(0.36 Torr) " —b— fit+dls(0.36 Torr) cos: S ' ' . 0.04: 1 __ yíi 1 / \__ __ ■ 0.03: 1.. _ ______ / 1 i ■ 0.02: i /i i S i 1 1 ■ 0.01: 0 H I'll"! —t—i—i—r- —i—r—i—r- —1—III —r—i—i—r— "T—T.....1-T" - 5 10 15 20 25 Discharge current [mA] 30 Figure 8. A comparison of [0]/[02J measured by VUV absorption at 0.36 and 0.56 Torr and by actinometry taking into account the contribution of dissociative excitation of CfP). In the discharge, the production of oxygen atoms in the ground state 0(2p4 3P) is principally due to the dissociation of the molecule 02(X3I!~) by electronic impact, according to the reactions e + 02(X3Ep KDisi 0(3P) + 0(3P) + e (34) e + 02Qty?;;)-^0??) + 0{xD) + t. (35) Calculations of the kDpiss and kDDixs rate coefficients are performed using EEDFs and cross sections from Phelps [28] as indicated in relation (5). The total creation rate coefficient can be written t„. _ rýp 4-kl° "■Diss — *-KDiss ^ KDiss- (36) The loss of oxygen atoms in the ground státe 0(2p4 3P) is mainly due to atomic recombination at the wall {23]: 0(2p43P) + wail —"► 2°2 Kwall — VT h Y 2R (37) where R is the discharge tube radius, y the recombination probability and ur* the thermal velocity of the oxygen atoms. 10 10 10 10 10 -1-■7 , i i i i ■_ 0(3pSP) i i i, i , ___ ' ■ ■ _ *=£____ . ., _ ■ -3 0(3p3P) : --4 / • ': -5_ // ,— T„- ,. ..y.— t-— - 50 100 E/N [Td] 150 200 Figure 9. The ratio k^/ke of dissociative to direct excitation calculated for 0(3p3P) and 0(3p5P) states versus E/N. The radial profile of the gas temperature has been measured previously by CARS (coherent anti-Stokes Raman spectroscopy). It has been shown that the gas temperature near the wall is approximately the same as the wall temperature measured by a thermocouple [40]. We have then calculated vtk assuming that the atom temperature is equal to the gas temperature at the wall. The balance between atomic oxygen production and loss is [0(2p43P)] = ^nď[02]. (38) V-wall If we express the mean value of electronic density ne versus discharge current: n. = TcR2evp (39) where vp is the electron drift velocity calculated as an electron transport parameter in the kinetic model of [20], then we can write the recombination probability as Y - 2Idkpiss [Q2] n RevThVD [O] ' (40) From the results of [0]/(02] concentration ratios previously obtained by actinometry in the 4, 7 and 16 mm diameter tubes, we have calculated the values ( 1865 D Pagnon eŕ a/ (a) 0.5 0.4 0.3 £ 0.2 0.1 n. .Im.ü,,-!,,-,. 7 n 1 T i......*....* ...... í nm orr ill ti ill ■ ■ ■ ' 1 i r / 1 i a i L < 7 i /a 1 • o/ , ■ * E/N measured ° E/N "calculated" • • E—,—11- 11 m —1—1—I— ■ 1 " i.....i" " 1.......i"" i" ■ ť"' ■—IT„,lwr—r— • 4 mm 1 Torr o rpj/f.02] 777 nm o [0]/[021 844 nm Discharge current [mA] ..... i ■'■ '■■ ' 60 80 Discharge current [mA] 100 O" o 0.5 . 1 1 řorr ■ m-lt-l. ,.!„......1 ,■■„,. M, ■■ . Ill......k....., 7 mm - 0.4 . • 0.3 . 16 mm • 0.2 . 4 mm 0.1 . - 20 40 60 80 100 Discharge current [mA] Figure 10. The [O^Cfe] dissociation ratio in 7, 4 and 16 mm diameter tubes versus discharge current for a pressure of 1 Torr. (a) For a 7 mm diameter tube: (■), values determined using the values of E/N measured by probes; and (O), values determined using E/N calculated from optical measurements. (o) For a 4 mm diameter tube, dissociation ratio determined using E/N calculated from optical measurements: (O), using the 777 nm line; and (D), using the 844 nm line, (c) A comparison of the results obtained in 4, 7 and 16 mm diameter tubes. of y under our experimental conditions of current and pressure for the three tube diameters. The results are represented in figure 11 versus 300fTwau, where Twau is the wall temperature measured under the same experimental conditions. The variation of y versus Twau for the tubes of the three diameters can be fitted by the relation y = 0.94 exp 1780 \ wall) (41) It should be noted that the recombination of the oxygen atoms at the wall leading into the discharge Pyrex tube is larger than the values of y ranging between 0.2 x 10-4 and 5 x 10~4 measured downstream of the discharge [41,42]. This effect was first pointed out by Sabadil, who determined a recombination coefficient of y — 4.6 x ÍO-4 within the discharge and y = 2.2 x ÍO-4 outside the discharge. The values of y measured in this work are five times larger. Nevertheless it is interesting to mention that the value y — 2.4 x 10~3 measured at 300 K is in good agreement with the value determined by Magne [43] from the measurement of the atom concentration's time-dependence during the afterglow in a similar discharge tube. An explanation of this effect is proposed by the authors. 6. Conclusions The validity of actinometric technique as a diagnostic tool for determination of absolute concentrations of atoms 1866 Actinometry in 02 DC glow discharges I c o «9 C 3 E o u a> (C 0.1 ■; ■ J...1 l„.I...ĽA-JMi.„i.„,fi 1 1 I ,t,i-t..l,,l,.l,-i-JU 1.1,1 o 16mm tube ■ 7mm "calculated" ° 7mm measured * 4mm tube • Magne [42] —. - J ä — - Ä ""'- M____™ 0.01 " "■ "** * " -s. "»' Ä . .^*...,....a s a n ""o""*'"-" ■«e o — ......."ä ' T..... í.-...............j . ~-n .001 - ■" '"''■ 111 ' ■I'T'ťT r-r-rr-r- 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 300/Tw [K'1J Figure 11. The variation of the recombination probability y with the wail temperature Tyuhh for a 16 mm internal diameter tube (O), 7 mm internal diameter tube (□) and 4 mm internal diameter tube (a); (•), the value measured by Magne et a! [42]. has been investigated. We have deduced the absolute concentration of oxygen atoms from the measurement of 0*(3P)/Ar*(2p,) and 0*(5P)/Ar*(2pi) emission intensity ratios. For this purpose we have calculated the rate coefficients for excitation of O* and Ar* versus reduced electric field using the calculated EEDF under our experimental conditions and several sets of cross sections. We have also studied the quenching of the emitted lines. By comparing the actinometric measurements to the results of VUV absorption spectrometry, we have demonstrated that the best choice of cross sections is the cross section of Puech [27] for Ar*(2p,) and those of leaner [25] for 0*(3P) and 0*(5P). Under these conditions, it has been shown that dissociative excitation can be neglected, except at low pressures and low currents. Under these experimental conditions in which [OMO2J is lower than 1% and the reduced electric field E/N is higher than 90 Td, dissociative excitation is a significant source of excited oxygen atoms, especially in the 0(5P) state. However, it is possible to use actinometry for small concentrations of oxygen atoms if the contribution of dissociative excitation is taken into account in the calculations. When a large population of energetic electrons is present in the discharge, as in an ECR discharge, the contribution of dissociative excitation becomes too large to be corrected. Furthermore, it has been shown that the reduced electric field can be deduced from the measurement of the intensity ratio. This allows a direct determination of the absolute concentration of oxygen atoms in discharge tubes of small diameter, where VUV absorption measurements are difficult to perform. It is to be noted that the transition 0(3P-3S) at 844 nm is a better choice for actinometric measurements because it can be used for a wide range of reduced electric fields (4O-110 Td) and because the calibration factor C^' = 2.6 x 10~3 ±20% remains constant when the pressures, the discharge currents and the tube diameters are varied. In addition, we have shown that the concentration of oxygen atoms first exibits a linear variation with increasing discharge currents and then tends towards a saturation value. This saturation has been explained by the increase in the recombination of oxygen atoms at the wall, due to the increase in the Pyrex tube walľs temperature. A variation in the recombination probability y = 0.94 exp(—1780/7") has been determined for 300 < T < 500 K. Work is in progress to determine the surface kinetics of oxygen atoms at the discharge tube wall. This study allows one to conclude that the largest dissociation ratio is obtained in a 7 mm diameter discharge tube. Such a discharge tube has been used to build a source of oxygen atoms inserted into molecular beam epitaxy devices. The characteristics of this source will be published in the near future. Acknowledgments The authors would like to thank C M Ferreira, L Loureiro and V Guerra for providing the code for calculation of the EEDF, V Puech, J Bretagne and W Trennepohl for providing the cross sections for the excitation of argon and all of the above for helpful discussions. J Amorim and J Nahorny are supported by the CNPq, Brazil. References [l] [2] [3] W [5] [6] [7] [8] [9] [10] HI] Brink G O, Fiuegge R A and Hull R J 1968 Rev. Sei. Instrum. 39 1171 Samson J A R and Pareek P N 1985 Phys. Rev. A 31 1470 Cuthbertson J W, Langer W D and Motley R W 1990 Mater. Manufacturing Processes 5 387 Collart E 1 H, Baggerman JAG and Visser R J 1991 J. Appl. Phys. 70 5278 Touzeau M, Schuhl A, Cabanel R, Luzeau P, Barski A, Pagnon D, Hirtz J P and Creuzet G 1989 MRS Fall Meeting, Boston Kwo J, Hong M, Trevor D J, Fleming R M, White A E, Farrow R C, Kortan A R and Short K T 1988 In-situ epitaxial growth of YiBajCusO?-;, films by molecular beam epitaxy with an activated oxygen source Appl. Phys. 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