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Gas Phase Model of Surface Reactions for N2 Afterglows
V. Marković, Z. Petrović, M. Pejović
To cite this version:
V. Marković, Z. Petrović, M. Pejović. Gas Phase Model of Surface Reactions for N2 Afterglows.
Journal de Physique III, EDP Sciences, 1996, 6 (7), pp.959-973. �10.1051/jp3:1996165�. �jpa-00249502�
Gas Phase Model of Surface Reactions for N2 Afterglows
V. Lj. Markovid (~~*), Z. Lj. Petrovid (~~**) and M. M. Pejovid (~)
(~) Department of Physics, University of Nil, P-O- BOX 91, 18001 Nib, Yugoslavia (~) Institute of Physics, P-O- BOX 57, 11001 Belgrade, Yugoslavia
(~) Faculty of Electronic Engineering, P-O- BOX 73, 18001 Nil, Yugoslavia
(Received 15 September 1995, revised 30 January 1996, accepted 28 March 1996)
PACS.52.80.-s Electric discharges
PACS.52.20.-j Elementary processes in plasma PACS.82.65.-I Surface and interface chemistry
Abstract. The adequacy of the homogeneous gas phase model as a representation of the surface losses of diffusing active particles in gas phase is studied. As an example the recent data obtained for the surface recombination coefficients are reanalyzed. The data were obtained by the application of the breakdown time delay technique which consists of the measurements of the breakdown delay times td as a function of the afterglow period T. It was found that for the
conditions of our experiment, the diffusion should not be neglected as the final results are signifi- cantly different when obtained by approximate gas phase representation and by exact numerical
solution to the diffusion equation. While application of the gas phase effective coefficients to represent surface losses gives an error in the value of the recombination coefficient, it reproduces correctly other characteristics such
as order of the process which can be obtained from simple fits to the experimental data.
R4sum4. Dans cet article, nous 4tudions la validit4 du modAle approximatif repr4sentant les pertes superficielles des particules actives qui diffusent de la phase gazeuse comme pertes dans la phase homogAne du gaz. Les donn4es actuelles du coefficient de recombinaison en surface sont utilis4es pour cette v4rification. Les donn4es exp4rimentales sont obtenues en utilisant la
technique qui consiste en la mesure du temps de retard du d6but de la d6charge en fonction de la p6riode de relaxation. Nous avons trouv6 que, pour
nos conditions exp6rimentales, la diffusion
ne peut pas Atre n6glig6e. Aussi, les r4sultats finals sont consid6rablement diff6rents quand ils sont obtenus en utilisant le modAle approximatif par comparaison avec les r6sultats obtenus par la solution num6rique exacte de l'6quation de la diffusion. L'application des coefficients effectifs dans la phase gaseuse pour la prdsentation des pertes superficielles donne, pour les
coefficients de la recombinaison, des valeurs qui diffArent en ordre de grandeur mais la m6thode donne Agalement correctement les autres caract6ristiques par exemple l'ordre des processus en
tragant simplement la courbe des donn6es exp6rimentales.
(*) Author for correspondence (e-mail: vmarkovic©ban.junis.ni.ac.yu)
(**) also at Faculty of Electrical Engineering, University of Belgrade and MTT INFIZ
© Les #ditions de Physique 1996
1. Introduction
Diffusion of active particles through gas to surfaces where those particles are either reflected,
deactivated or physisorbed is often treated by neglecting diffusion or in other words the spatial
variation of the active particle density. In such an approach, effective gas phase loss terms are defined which represent the surface losses. The representation of surface processes by effective gas phase coefficients is deafly applicable at lower pressures.
The surface processes play a major role in the kinetics of active particles in gas discharges for plasma deposition iii, plasma etching [2], sputtering [3], surface nitriding [4], gas purification [5]
and also in studies of electronic and vibrational energy relaxation in gas discharges [6-8]. Quite often gas phase approximation is applied [9-14] eventhough it is not clear whether it is justified
or not. Even more often effective representation of the diffusion losses with assumed zero- order mode and characteristic diffusion length is applied without paying much attention to the questions of reflection and the presence of the higher modes [15,16]. When the attention is
addressed to the latter, a loss process on the wail linear in number density is assumed II?].
The most serious situation occurs when gas phase approximation of the surface processes has been used to obtain the rate coefficients for those surface processes. Such results should be
applicable under the conditions similar to the original experiment and could be questionable
under significantly different conditions unless precautions were made to check for the adequacy
of the inherent approximation of negligible gradients and fixed reflection. Testing the adequacy
of such a model would require a solution of the diffusion equation with realistic surface terms which if available makes the simpler gas phase representation redundant. Numerical procedure also makes it more difficult to make a graphical representation of the processes which can be used to visualize the process of fitting and adequacy of different physical assumptions.
In this paper we make a comparison of the results for the surface recombination coefficients obtained by assuming the homogeneous gas phase reaction as a representation of surface prc-
cesses and the results obtained by fitting the experimental data with the aid of numerical
solution to the diffusion equation with proper representation of diffusion terms. We discuss the results obtained by the two methods and the adequacy of the similar data available in the literature. Further on we try to shed some more light on the breakdown time delay method for
obtaining the surface recombination coefficients and the kinetics of excited states of nitrogen
in the very late afterglows.
The memory curves are the plots of the breakdown delay times as a function of the afterglow
time or inversely the plots of the electron yield Y o~ Ill on the same afterglow time scale.
Memory effect is the fact that the electron yield and therefore the delay time for the gas
discharge breakdown changes with time at long afterglow times indicating the presence of active species whose decay determines the time dependence of the memory effect. Once the
breakdown time becomes determined by the natural radioactivity andfor cosmic ray ionization,
the curve will be saturated I.e. independent of the afterglow time.
Bo§an and coworkers [18,19] were the first to observe the memory effect in the late nitrogen afterglows. The effect was attributed initially to the unidentified metastable nitrogen molecules
remaining after the discharge in the gas phase. More recently it has been suggested that the weir known N2 (A~Et state [20] could be the particle storing the energy in the gas phase which later on facilitated the breakdown and created the memory effect. It has been observed that the removal of the gas in gas flow systems [21] removed the effect too. The basis of the assumption that the N2(A~Z$) state could be the state contributing to the memory effect was its very
long lifetime in pure nitrogen [22-24]. However in the modeling of the afterglow unrealistic assumptions had to be employed to fit the experimental data which included neglecting the
quenching by impurities and nitrogen atoms [20]. Such models failed however to explain
the similar effects observed at higher pressures and/or in nitrogen with a large quantity of impurities [25,26] where even without the quenching by nitrogen atoms the two body quenching by nitrogen molecules [27-29] and impurities [30,31] reduce the lifetime of the metastable states
several orders of magnitude below the observed lifetimes.
Therefore Markovid et at. proposed that the energy stored in the nitrogen atoms and released upon recombination was the source of energy for the long afterglow time memory effects [32,33].
It turned out, that the gas phase processes could not account for the observed effect, the quenching is too large and therefore the surface recombination of two atoms leading to the
ejection of a secondary electron gives initiation to the discharge [33]. As it also turned out, the main loss of the nitrogen atoms remaining in the gas phase after the discharge is the surface recombination. The memory effect dependencies were used to establish the characteristics and obtain coefficients for the surface recombination on the molybdenum glass [33]. Results were
obtained by applying a detailed two dimensional diffusion calculation with proper inclusion of surface processes. When compared with the data from the literature, it was found that
large differences can be partly accounted for by the different surface material which in the
case of our experiment was not specially prepared and cleaned. However, in this paper we
analyse a possibility that partly, the differences could be due to the different type of analysis,
The present case represents a very good example to test the adequacy of the gas phase loss representation of the surface processes since the gradients are significant yet not too large and the pressures are approximatively as that used in most glow discharges. Thus in the case of the present experiment one could be tempted to use the gas phase approximation. At the same
time experiment gives dependence over two orders of magnitude in time of the process which is dominated by the surface loss of the active particles and thus there is enough dynamic range
to perform the test.
We may also add that the memory effect has been observed in other gases such as hydrogen [34] and different configurations including the hollow cathode pseudo spark discharges [35]
and spark gaps [21].
In Section 2 we give a very brief summary of the experiment used to obtain the basic data.
In the third section we first present the details of the active species kinetics pertinent to the
application of models and discuss the gas phase model of surface losses in its standard mode of application, than we proceed to make the comparison with more detailed numerical calculations in the forth section. In the concluding section a resume of the discussion is given together with
some further comments on the application of both methods and kinetics of active nitrogen molecules.
2. Experimental Details
The experimental data analysed in this paper have already been published together with a
more detailed analysis [32,33]. Here we give just a brief review of the experimental technique
which is required to understand the nature of the data.
The time delay dependencies were performed for a gas tube made of molybdenum glass
with volume V
= 160 cm~ and
area Sw
= 180 cm~. Radius of the tube is R
= 2 cm,
length 12.5 cm. The electrodes are rounded and polished copper rods with 99.98Sl purity.
The electrode diameter was D
= 5 mm, area SE
" 1.3 cm~ and gap d
= 2 mm. The static breakdown voltage was Us
" 307 V. Ratio of the discharge radius r
= 0.2 cm to the radius of the tube R
= 2 cm is 0.I, and ratio between the volume of the interelectrode space to the volume of the tube is VcIV
-J lo~~. The tube was baked out at 600 K and evacuated down to
10~6 mbar, then filled with Matheson research grade nitrogen at 6.6 mbar pressure with the claimed abundance of impurities such as 02 below I ppm.
o 50
o40
o ao
j
~
~~020
'
o lo
o.oo
O 2 4 5 B lo 12
~ Is)
Fig. 1. The time delay dependence on the afterglow period G
" f(r) (the memory curve) fitted
by a straight line according to equation (6)
A series of high voltage pulses is applied to the discharge tube. Each pulse cycle consists of the breakdown time delay td, the glow time tg, long enough for the stationary glow conditions to be reached, and the afterglow period T, during which there is neither voltage on the tube, nor
current flow. For each experimental point the afterglow period T (time between the voltage pulses) is kept constant and the breakdown time delay td were measured. The voltage of
the pulse is U~V
= Us + /hU, where /hU/Us is the fractional overvoltage given in percents and Us is the static breakdown voltage. The experiment consists of series of100 cycles for each experimental point. Each pulse is used in two ways, to determine the breakdown time
delay after the previous afterglow and also to establish a stationary glow conditions before the
beginning of the subsequent afterglow. Thus, the mean values of the breakdown time delay
were established from series of100 measurements, under the same other conditions.
The time delay dependence on the afterglow period [
" f(T) (the memory curve) was
obtained for
T in interval (0.1 10) s, at glow current of Ig = 0.5 mA, glow time tg = I s, and overvoltage of /hU/Us " 50Sl (Fig. I). The memory curve is linear up to the afterglow time of the order of
-J
10~ s, then a plateau of the memory curve (the saturation range) is induced by
the cosmic rays and the natural radioactivity [33]. It should be noted that with overvoltages
as used in the present experiment, the unit probability of starting the discharge is achieved
once the electron is released to the interelectrode space close to the cathode surface [33].
3. Homogeneous Gas Phase Model of Surface Reactions
3.I. KINETICS oF ACTIVE NITROGEN SPECIES IN THE LATE AFTERGLOW If one assumes
that the breakdown time delay is inversely proportional to the number density of active particles
in the inter-electrode space, [ o~ II [N], and represent [N] in a relative manner [N] o~ II [ as
a function of T in a semi-log scale, the dependence is not linear. This means that the temporal decay of our active particle is not exponential, thus its decay is not governed by the first order processes. On the contrary, the experimental data when plotted in the (I/[N] us. T form, I.e. &
us. T in a linear-linear scale indicate a second order process (Fig. I). Since the N2(A~Et decay
is the first order process with very small effective lifetime it is not possible to explain the long
time behavior of breakdown time delay by the temporal decay of N2(A~Z$) population [32].
Also, for the technical purity nitrogen and for the pure nitrogen at high pressures similar memory effect has been found as mentioned in the introductory section. Model of Markovid et at. gives a good agreement with such data while two body quenching by nitrogen molecules or
impurities reduces the lifetime of metastable states to well below the observed lifetimes [25-30].
Therefore it is obvious that some other active state of nitrogen should be the carrier of the
"memory effect". The equations listed below can be used efficiently to perform fits to the
experimental data directly on the graph or by simple calculations. Whatever one decides to use, the results have a built in uncertainty due to the neglect of the density gradients which will be different for different geometries, surface conditions, pressures and other conditions.
It is reported in the literature that the long lived Lewis-Rayleigh afterglow lasts up to several hours [10,36]. It has also been established that the source of the energy for the glow is the gas
phase recombination of the ground state nitrogen atoms [10, 36]. Thus, N(~S) are present a
very long time after the glow is turned off and decay by the surface recombination on container walls. There is some doubt about order of that process [10]. If it is the second order process in the number density, N(~S) is a possible carrier of the "memory effect" in nitrogen, as sho1A~n
by Markovit et al. [32,33].
The volume recombination of nitrogen atoms produces N2(A~Et as a final product
110,36],
but the first order quenching processes cannot fit the slope of the experimental data. The
possible solution is that nitrogen atoms recombining on the surface of cathode and forming N2(A~Z$) by the surface-catalyzed excitation [37], provide initial secondary electrons that
determine the breakdown time delay in the late afterglow.
In our model, N(~S) is responsible for the observed memory effect in nitrogen. Its de- cay is governed by the second order recombination process on the container wails, and the inter-electrode space is very sensitive for its detection through the mechanism of the surface excitation. The shape of the memory curve represents a joint effect of a gas, and a surface of the tube and cathode, but recombination on the surface of the tube is the predominant
loss channel which determines the time dependence of the atom number density, while re- combination on the cathode surface make negligible contribution to the total loss of nitrogen
atoms because SE < Sw [33]. When realistic data from the literature for collision rate coeffi- cients are used, the predictions of our model fit the experimental data both qualitatively and quantitatively [32, 33].
Independently to our work the recombination of nitrogen atoms on the surface of the elec- trodes has been proposed as a source of secondary electrons that may induce the breakdown in the experiments of Haydon and coworkers [38].
3.2. ANALYTICAL SOLUTION. In the homogeneous gas phase representation of surface
losses, the loss rates of the density of nitrogen atoms [N](r,T) during the afterglow are given by equation:
~~~
=
-k~~ (N]~ [N2) ~(N]~. (l)
dT
The first term on the right-hand side is the volume recombination loss of N, resulting in
the Lewis-Rayleigh afterglow [10,36]. With the volume recombination rate coefficient k~~
=
2.25 x10~~~ cm6 s~~ [9] the influence of the volume loss process of N on the rate of nitrogen atom loss is negligible under our conditions. The same refers to the recombination on the electrode surface [33] and to the reaction of quenching N2(A~Z$) by N(~S) in which metastable states
N(~P,~ D) are formed (Sect. 4). Here [N2) is the number density of nitrogen molecules.
Some authors have concluded that the nitrogen atom recombination process at the surface is the first order in the atom density at the room temperature ill,39]. However, other authors
