Fast processes in a N2O-modulated hollow cathode discharge: Excitation and diffusion

Article abstract of DOI:10.1021/jp0010177

In this work the changes in the infrared absorption of N₂O observed in a hollow cathode discharge modulated by a 45 Hz square wave are studied by time-resolved infrared absorption spectroscopy, with a Fourier transform infrared (FTIR) spectrometer working in the step-scan mode. These variations are attributed to alternative population and depopulation of the ground state of N₂O; on the other hand, no changes are observed in the total concentration of N₂O and the major products of the discharge. The experimental results are explained by means of a simple kinetic model: vibrational excitation processes are assumed to be the main cause of the observed effects, but an inhomogeneous distribution of the stable species and the incorporation of diffusion terms between the plasma volume and the rest of the discharge cell are shown to be crucial in order to justify the quick and sharp variations in the N₂O ground-state population seen along the path of the IR beam. The influence of these effects has been verified also by mass spectrometric measurements of the temporal behavior of the concentration of the major products N₂O, N₂ and O₂ at one end of the discharge cell and at different frequencies.

Full text of DOI:10.1021/jp0010177

J. Phys. Chem. A 2000, 104, 8183-8193
8183
Fast Processes in a N2O-Modulated Hollow Cathode Discharge: Excitation and Diffusion
T. de los Arcos,† M. Castillo,† C. Domingo,† V. J. Herrero,† M. M. Sanz,‡ and I. Tanarro*,†
Instituto de Estructura de la Materia (CSIC), Serrano 123, 28006 Madrid, Spain and Departamento de F´ısica
Aplicada, UniVersidad Alfonso X el Sabio, VillanueVa de la Can˜ada, 28691 Madrid, Spain
ReceiVed: March 16, 2000; In Final Form: May 31, 2000
In this work the changes in the infrared absorption of N2O observed in a hollow cathode discharge modulated
by a 45 Hz square wave are studied by time-resolved infrared absorption spectroscopy, with a Fourier transform
infrared (FTIR) spectrometer working in the step-scan mode. These variations are attributed to alternative
population and depopulation of the ground state of N2O; on the other hand, no changes are observed in the
total concentration of N2O and the major products of the discharge. The experimental results are explained
by means of a simple kinetic model: vibrational excitation processes are assumed to be the main cause of the
observed effects, but an inhomogeneous distribution of the stable species and the incorporation of diffusion
terms between the plasma volume and the rest of the discharge cell are shown to be crucial in order to justify
the quick and sharp variations in the N2O ground-state population seen along the path of the IR beam. The
influence of these effects has been verified also by mass spectrometric measurements of the temporal behavior
of the concentration of the major products N2O, N2 and O2 at one end of the discharge cell and at different
frequencies.
1. Introduction
As a result, the progress in the applications of these plasmas is
largely empirical. A theoretical modeling of these systems
The cold plasmas occurring in glow discharges are nonequi-
librium systems characterized by a comparatively hot (several
electronvolts on average) electron energy distribution and much
colder (close to room temperature) energy distributions for the
heavier neutrals. Electronic collisions within these plasmas
unleash a series of processes giving rise to a rich physico-
chemistry with practical applications in many fields and most
notably in the processes of deposition of chemical vapors and
surface conditioning. Plasma-enhanced chemical vapor deposi-
tion (PECVD) and plasma assisted surface modification are
nowadays well-established technological tools1 offering an
advantageous alternative to the higher temperature thermal
procedures. Till now, PECVD has been used mainly with RF
and MW discharges, but recently, an increasing growth in papers
reporting DC or low-frequency plasmas for PECVD is found,2-5
since particle formation can be largely avoided, even with room-
temperature substrates.2 On the other hand, with DC plasmas,
larger surfaces can be coated in a simpler way, as needed for
example in the conditioning of nuclear fusion vessels6 and in
the cleaning and hardening1 of large surfaces. In that cases,
diffusion effects may be critical in determining the homogeneous
distribution of the films, depending on the geometry of the
discharge and, specially, when the input of the precursor is
localized at a single point and high dissociation rates are present.
The undeniable practical advantages of cold plasmas are not
paralleled by a corresponding ease for the analysis of the
mechanisms ultimately responsible for their properties. The
complex kinetics taking place in them, which includes electron
impact dissociation, ionization and excitation, nonreactive
quenching, gas phase homogeneous chemistry, heterogeneous
wall reactions, diffusion, etc., is extremely difficult to unravel.
providing a clear insight into the atomic and molecular
mechanisms, though highly desirable, is usually far from
satisfactory. Because of the scarcity of data on cross sections
and rate constants, either from experiment or theory, for many
of the relevant elementary processes, plasma models are often
plagued with daring hypothesis and dubious assumptions. As a
rule, a thorough experimental diagnostics is the only way to
make sound advances in the modeling.
Nitrous oxide is often used, together with different silicon
compounds, in the PECVD of SiO2 and thus, its glow discharges
have deserved some attention and reliable information about
its kinetics is already available. Former studies have concen-
trated on the diagnosis and modeling of steady-state glow
discharges of N2O and of its mixtures with inert gases.7-12 In
a previous work,12 we extended the studies of Cleland and Hess7
and of Kline et al.8 on rf discharges of pure N2O by using a
DC hollow cathode discharge and combining various analytic
tools (namely double Langmuir probes, Fourier transform
infrared spectroscopy and mass spectrometry) for the diagnosis
of the steady-state plasma. Our data could be essentially
described with a relatively simple set of kinetic equations based
on the former models of refs 7 and 8 except for the appearance
of NO2, a minor but clearly identifiable component of our
plasma that was not detected in the previous rf works. To justify
the presence of NO2, we had to introduce in the model an
heterogeneous reaction at the steel walls of the cathode.
Plasma modeling is not only hampered by the lack of reliable
data about many of the relevant elementary processes, but also
by the difficulties for an experimental observation of many of
the species involved, specially the most reactive and unstable
ones. However, even restricting the observations to a reduced
set of species, one can still take advantage of the hierarchy of
characteristic dynamical times involved in the global kinetics
of the discharge and perform measurements with different time
* Corresponding author. Fax: +34.91.5855184; e-mail: itanarro@
iem.cfmac.csic.es.
† Instituto de Estructura de la Materia (CSIC).
‡ Universidad Alfonso X el Sabio.
10.1021/jp0010177 CCC: $19.00 © 2000 American Chemical Society
Published on Web 08/08/2000

8184 J. Phys. Chem. A, Vol. 104, No. 35, 2000
de los Arcos et al.
resolution. A suitable way of doing it is the use of modulated
discharges of different frequencies.
In a recent work13 we analyzed the transients associated with
the ignition and extinction of the discharge with a time resolution
in the order of the second and disclosed the role of new electron
impact dissociation processes that were not apparent in the
steady-state measurements; besides, previous assumption of an
heterogeneous wall reaction as the main source of the observed
NO2 was not born out by the time-resolved measurements and
a reaction of vibrationally excited nitrous oxide was invoked.
The significant presence of N2O (001) in the plasma was
demonstrated by emission spectroscopy, but the process of
electron impact vibrational excitation of N2O, assumed to be
the origin of the N2O (001) found in the plasma, is too fast14 to
be directly detectable with the time resolution of this experiment.
Figure 1. Scheme of the hollow cathode discharge cell, showing the
focusing and the optical path of the IR beam of the FTIR spectrometer
across the cell, as well as the location of the plasma region, VP, and of
the rest of the volume without electrical charge, VA, assumed in the
present theoretical model. Mass spectrometry is performed in this cell
by replacing one of the IR windows by a flange supporting a central
diaphragm with a diameter of 100 µm. Another flange holding the
double Langmuir probe can be used in order to measure the charge
density and mean electron energy.
To evince in a more clear way the role of the faster processes,
we present in this study the diagnosis and modeling of a 45 Hz
modulated hollow cathode discharge with a time resolution of
the order of a millisecond, appropriate for the investigation of
the effects of diffusion and electron impact excitation under
our experimental conditions. These phenomena are so fast for
populating and depopulating the ground state of species such
as N2O, that their effects in the stationary state of a continuous
discharge or during the transients of a very low frequency
modulated one, can go unnoticed in comparison with the
remarkably slower but larger changes originated by dissociation,
ionization, homogeneous or heterogeneous processes. The
experimental upgrading needed for these faster measurements
is described and the validity and limitations of the previous
kinetic model13 is checked against the new data.
of the slow transients happening during this time until the
attainment of the “stationary” state, which were studied in detail
in ref 13.
The concentrations of the major stable species involved in
the discharge, N2O, N2 and O2, were studied with the mass
spectrometer at different modulation frequencies, and no
modulation at all was observed above 20 Hz for any of these
species. Their steady-state concentrations, as well as their
evolution during the turning on and off of a DC discharge, were
studied in detail in refs 12 and 13 for various physical
conditions. Extraction of the gas sample was performed at the
center of one end of the cell through a holder with a 100 µm
diaphragm, located in place of one of the IR windows, in the
same way as in refs 12 and 13. The time constant of the mass
spectrometric system was determined by the gas residence time
in the quadrupole vacuum chamber, which was 12 ms, since
the temporal response of the electronics was considerably
smaller (2 ms with the amplification factor employed in this
work).
The dependence of charge density and mean electron energy
on longitudinal and radial position along the discharge cell were
measured with a double Langmuir probe and a digital oscil-
loscope with special probes isolated from ground, in a similar
way to that used in refs 12 and 15, with the discharge operating
in the DC mode. To verify the speed with which the charge
density is established or disappears following the square wave
modulation of the discharge, the temporal response in electrical
current of the Langmuir probe was collected for a constant value
of the floating potential applied between the two wires. Once
the discharge was turned on or off, the current intensity reached
a constant value or disappeared respectively in less than 10 µs.
This is in good agreement with other estimates found in the
literature16 and indicates that for the time scales of the present
work the appearance of ions and electrons may be assumed to
be instantaneous.
2. Experimental Measurements
The experimental measurements carried out in the present
work were obtained with a hollow cathode discharge cell
specially designed for both absorption and emission spectros-
copy, and mass spectrometry. Time-resolved absorption mea-
surements were taken by means of a Fourier transform infrared
spectrometer (FTIR) Bruker IFS66, used in the step-scan mode.
Charge density and mean electron energy were measured with
a double Langmuir probe built in our laboratory. Besides, a
quadrupole mass spectrometer Balzers QMG112 was employed
to study the temporal behavior of the concentration of the major
products of the N2O discharge.
A scheme of the hollow cathode discharge cell is shown in
Figure 1; it is just the same one used in references 12, 13, and
15. In Figure 1, the focusing and the optical path of the IR
beam of the spectrometer across the cell are indicated, the length
of the cell is the maximum one compatible with the dimensions
of the absorption sample chamber of the FTIR spectrometer.
For time-resolved absorption spectroscopy measurements, the
discharge was modulated with a 45 Hz square wave electrical
signal and a current of 80 mA. This frequency was selected in
such a way that it was low enough to allow an efficient
modulation of the IR absorption signal due to the N2O excitation
and relaxation processes to be studied here, but high enough to
distinguish these processes from the slower but more intense
ones studied in the previous work.13 The measurements were
taken at a 2 mbar pressure with two different gas flow rates of
pure N2O (99.5%): 3 and 108 sccm, coincident with those
employed in the previous paper. The cell was refrigerated by a
continuous flow of water. A time interval of some 10 s was let
between the ignition of the modulated discharge and the
beginning of the acquisition process, to avoid the interference
In a previous paper devoted to the study of the ignition and
extinction slow processes of the discharge,13 a single cycle of
modulation lasting for several seconds was recorded for each
whole measurement, and temporal resolution during this cycle
was achieved with the FTIR spectrometer working in the
continuous scan mode, in such a way that each interferogram
was acquired completely before the next one, some 100 ms later.
This temporal resolution is not sufficient at all to study by FTIR
spectroscopy the transients corresponding to a 45 Hz discharge,
so the interleaving-sampling technique based on the continuous-

N2O-Modulated Hollow Cathode Discharge
J. Phys. Chem. A, Vol. 104, No. 35, 2000 8185
scan mode of operation or, alternatively, the step-scan technique
(without phase modulation), can be selected to be used with
this instrument under the present conditions. Both techniques
are described in detail elsewhere.17-19 Although the final data
arrays produced by each option are similar, the differences in
the methods imply substantial differences in the kind of
measurements for which the two techniques are suited, and also
in the potential noise sources to which they are subject.
Basically, for short transients, which can be repeated at high
rates, the interleaving methods are preferable, since step-scan
techniques lead usually to more noisy spectra.19 The main
advantages of the step-scan technique are found in measurements
where the maximum repetition rate of the experiment is
relatively low (e.g., less than 100 Hz), because in the continuous-
scan version there is a maximum time between initiations of
the transients, imposed by the fact that the mirror has a minimum
velocity, below which its movement becomes unstable.20
In the step-scan technique, the interferometer mirror is held
at a fixed position during the time course of the process while
the transient is digitized. In this way, by moving the mirror
stepwise, one obtains the time courses of the change of the
interferogram at each sampling point, and from the data set,
the spectral changes can be obtained by performing the Fourier
transform at each time of interest.
Figure 2. (a) Absorbance spectra of the ν3 band of N2O with a spectral
resolution of 40 cm-1, at two different moments, with discharge “on”
and “off”, and at the two different values of N2O gas flow rates (3 and
108 sccm). Integration of the band was performed between 2100 and
2300 cm-1 for obtaining the concentration. (b) FTIR rapid-scan
spectrum of a DC, 40 mA, 3 sccm, N2O discharge between 1500 and
2700 cm-1 with a spectral resolution of 2 cm-1. Some weak bands of
NO and NO2, as well as the 2ν1 and ν1 + 2ν2 bands of N2O can be
observed.
As far as we know, since the pioneering works of Murphy et
al.21,22 describing the step-scan time-resolved Fourier Transform
spectroscopic method, this technique has been used for very
few absorption measurements.23,24 In contrast, a lot of references
about time-resolved emission measurements can be found in
the literature employing step-scan FTIR spectroscopy (see for
example refs 17-19, 21, 22, and 25). This lack of absorption
measurements is probably due to the difficulty associated with
the huge difference, of some orders of magnitude, between the
large intensity of the continuous infrared source (a Globar in
our case), specially near the maximum of the interferogram,
and the small amplitude of the modulated absorption signal.
Small mechanical vibrations of the optical bench of the FTIR
instrument, produce undesired displacements of the moving
mirror; if these mirror shifts happen when it is located near the
maximum of interference, they can cause oscillations in the
amplitude of the signal (identified as noise) much larger than
the amplitude of the true modulated absorption signal, even if
the displacement is only of a few nanometers. Besides, time-
resolved Fourier transform spectroscopic techniques require in
general a much wider bandwidth than the non-time-resolved
procedure, because the transients to be measured have usually
high-frequency components, and this eliminates one of the great
advantages associated with FTS: the ability to convert a wide
range of optical frequencies into a relatively narrow band of
lower frequencies and achieve noise rejection by the application
of narrow band-pass electronic filters.26 Furthermore, in the case
of step-scan techniques and when no phase modulation is
employed27 this band of frequencies is located at the lowest
end of the spectra, where electrical noise is highest.
typical time constant is of the order of 1 ns. Its preamplifier
was coupled in the DC mode. The cutoff frequency of the
preamplifier was above 20 MHz. To increase the signal/noise
ratio, each measurement, which covered a time interval of two
discharge modulation periods, was averaged 32 times (i.e., ∼1.4
s) with the mirror held at a constant position. Globally, a total
duration of some 25 minutes was necessary to perform a whole
set of time resolved single-sided interferograms with a spectral
resolution of 40 cm-1 (932 data points, with the origin of the
scan slightly advanced in relation with the maximum of the
interferogram for phase adjust purposes). Before acquiring the
interferograms of the modulated discharge, the reference inter-
ferogram needed to transform transmittance spectra into absor-
bance spectra was taken with the empty cell. Despite the
averaging procedure, the signal/noise ratios reached in the
present measurements are notably worse than those obtained
with the rapid scan technique for the continuous or the low
frequency modulated discharge. As a consequence, only the ν1
and ν3 bands of the N2O could be obtained with sensitivity
enough to characterize the temporal evolution of the ground
state of N2O; the temporal behavior of NO and NO2 could not
be studied at this modulation frequency. To obtain absolute
concentrations of N2O, the absorbance of the ν3 band at a
spectral resolution of 40 cm-1 was calibrated at different N2O
pressures. A slight widening of the bands was observed for the
case of the highest N2O flow rate during the discharge, thus,
absolute concentration measurements performed with the N2O
discharge operating at 3 sccm flow rate are more reliable and
precise than those performed at 108 sccm. Figure 2 a shows
some of the time-resolved absorbance spectra of the ν3 band of
N2O used for these measurements, with a spectral resolution of
40 cm-1. A series of ∼40 spectra was recorded during each
modulation cycle (sampling time: 0.55 ms). For clarity, only
two of these spectra (with discharge “on” and “off”) are
In the present case, the hollow cathode discharge cell was
installed in the sample compartment of the FTIR instrument,
and the joints between the cell and the spectrometer were sealed
with an elastomer material that prevented the entrance of wet
air inside the interferometer. To reduce as much as possible
the noise in the interferograms, it was necessary to isolate
carefully the mechanical vibrations transmitted to the cell
through the vacuum tubes coming from the rotary pump, and
any other kind of mechanical instability. The IR detector
employed in the present work was an MCT (HgCdTe), whose

8186 J. Phys. Chem. A, Vol. 104, No. 35, 2000
de los Arcos et al.
Figure 3. Temporal evolutions of the N2O ground state concentration experimentally obtained by FTIR absorption spectroscopy with the hollow
cathode discharge cell operating at 45 Hz, 80 mA (maximum current) and 2 mbar, for two gas flow rates, 3 and 108 sccm. The theoretical predictions
of the present model, as well as the results of the model of ref 8 are also shown. For a better comparison of the temporal behavior, Figure 2b shows
the experimental results and the theoretical predictions with equivalent amplitudes.
displayed for each of the two gas flow rates (3 and 108 sccm).
Integration of the band was performed between 2100 and 2300
cm-1 in order to obtain the concentration. A Blackman-Harris
function of 3 terms was used for apodization and phase
correction was of the Mertz type. To compare, Figure 2b shows
a 2 cm-1 spectrum of a DC, 40 mA, 3 sccm, N2O discharge
between 1500 and 2700 cm-1, obtained with the FTIR spec-
trometer working in the rapid scan mode; in this figure, the
weak NO and NO2 bands, as well as the 2ν1 and ν1 + 2ν2 N2O
bands can be observed too.
3. Kinetic Model
The kinetic model used here was first developed in an attempt
to explain the processes involved in a DC hollow cathode N2O
discharge,12 and was subsequently upgraded in order to predict
also the slow transient effects, with characteristic times of some
seconds, that could be observed experimentally during the
ignition and the extinction of that discharge.13 Nevertheless
further improvements have been required in this work, to
reproduce, at least qualitatively, the variations suffered by the
ground-state population of the precursor N2O, with characteristic
times of some milliseconds, that can be observed when the
discharge is periodically modulated at higher frequencies. As
explained briefly in the previous section, these transients cannot
be attributed to the relatively slow dissociation processes by
electronic impact, which initialize the whole chemistry of the
discharge, or to chemical reactions, but are found to be
attributable fundamentally to faster processes that do actually
happen in the discharge too: the excitation of the N2O ground
state by electronic impact which was already included in the
kinetic model, followed by quick de-excitation processes, and
the very significant diffusion effects, which could be overlooked
when considering slower transients, but are found to be crucial
in the present case. Because of this fact, the former assumption
that the stable species were homogeneously distributed along
the whole cell volume can be no longer maintained.
The kinetic model has been kept as simple as possible, both
in the number of chemical reactions and in the physical
phenomena considered. The set of relevant differential equations
has been numerically integrated, like in the former papers.12,13
Diffusion effects have not been incorporated actually as a three-
dimensional problem depending locally of each position; instead,
two different volumes have been distinguished: the plasma
volume, and the rest of the cell. In each of the two volumes the
concentrations of the stable products may be different, but are
assumed to be homogeneously distributed; in the kinetic model
the two volumes are inter-communicated just by diffusion
processes. Furthermore, an elementary geometry with cylindrical
In Figure 3 the temporal evolutions of the ground-state N2O
concentration experimentally obtained with the hollow cathode
discharge operating at 45 Hz and 2 mbar are shown at the two
gas flow rates, 3 and 108 sccm, as well as the excitation signal.
The data acquisition began in both cases once the ignition
transient of the modulated discharge had finished and a pseudo-
stationary state had been reached (i.e., ∼10-20 s after the
turning on of the plasma). As can be seen, very different values
of the mean N2O concentration in the ground state were obtained
with each value of the gas flow rate. This difference is mainly
due to the influence of the slow dissociation and chemical
processes happening in the discharge;13 in this sense the 45 Hz
square wave modulated discharge could be considered on
average like a DC discharge with half the current intensity. On
the contrary, the modulated components of the signals reveal
the existence of much faster processes and are very similar for
both flow rates, with rise and decay responses approximately
exponential, and characteristic times of the order of one or two
milliseconds. In Figure 3, the simulation of the discharge with
the model developed in ref 13 is also shown. As can be seen,
the appearance of the rapid and relatively large amplitude
transients experimentally observed cannot be explained with that
model. Improvements in the theoretical treatment of the
modulated discharge are thus needed in order to obtain a better
description of its behavior. Figure 3 also includes the results of
the improved kinetic model used finally in the present work,
which will be described in the next section.

N2O-Modulated Hollow Cathode Discharge
J. Phys. Chem. A, Vol. 104, No. 35, 2000 8187
TABLE 1: Reactions Included in the Kinetics Model of the
N2O Hollow Cathode Dischargea
symmetry has been assumed and diffusion has been considered
to take place effectively just along the direction of the symmetry
axis of the cylinder.
reaction
rate constant
ref
In a previous paper,12 the set of kinetic reactions considered
in the modeling of the N2O discharge was evaluated in detail;
therefore, only a brief description of the individual processes
taken into account in both cases will be given here, with a more
extended explanation of the improvements needed to simulate
suitably the 45 Hz modulated discharge.
Dissociation by Electronic Impact
D1
D1
D1
D2
D2
D2
D3
D3
D3
D4
D5
D6
D7
N2O + e- f N2 + O(3P) + e-
8.0 × 10-10
b
N2O(001) + e- f N2 + O(3P) + e-
N2O(100) + e- f N2 + O(3P) + e-
N2O + e- f N2 + O(1D) + e-
N2O(001) + e- f N2 + O(1D) + e-
N2O(100) + e- f N2 + O(1D) + e-
N2O + e- f NO + N + e-
3.7 × 10-10
1.2 × 10-10
b
b
Excitation Processes. In the present model, vibrational
excitation by electronic impact of the fundamental, the sym-
metric (100), and asymmetric (001) vibrational stretching modes
of N2O are found to be the main cause of the rapid variations
of the N2O ground-state population observed in the modulated
hollow cathode discharge. In the previous work13 the rate
constants for the vibrational excitation of these levels were
already included in the global kinetics, but the effect of these
fast processes could not be observed directly. These rate
constants, remarkably large, are 2 orders of magnitude higher
than the dissociation ones due to resonances in the excitation
cross sections for electron energies close to the electron mean
energy found in the present discharge14 (see Table 1).
N2O(001) + e- f NO + N + e-
N2O(100) + e- f NO + N + e-
NO + e- f N + O(3P)
8.5 × 10-10
8.5 × 10-10
4.8 × 10-11
7.2 × 10-11
b
b
b
b
NO2 + e- f NO + O(3P) + e-
O2 + e- f 2 O(3P) + e-
O2 + e- f O(3P) + O(1D) + e-
Electronic Impact Excitation
N2O + e- f N2O(001) + e-
E1
E2
1.4 × 10-8
1.4 × 10-8
c
c
N2O + e- f N2O(100) + e-
Quenching of Excited States
N2O(001) + N2O f 2N2O
Q1
Q2
Q3
Q4
2.44 × 10-14
5.26 × 10-13
2.6 × 10-11
1.5 × 10-10
10
30
31
32
N2O(100) + N2O f 2N2O
O(1D) + N2 f O(3P) + N2
O(1D) + NO f O(3P) + NO
Vibrational excitation to the bending mode (010) of N2O has
not been incorporated, since its cross section by electronic
impact is ∼50 times smaller than that of the (100) state14 at the
electron energies found in the N2O hollow cathode discharge
(measured mean value ∼3 eV, assuming a Maxwellian distribu-
tion15). The excitation cross section of this (010) level increases
by decreasing electron energy down to 0.1 eV, but it is in any
case at least 10 times smaller than that of the (100) stretching
mode. Excitations by electronic impact to overtone vibrational
modes or to excited electronic levels of N2O have not been
considered, since, to our knowledge, there is no information
about these processes. Rotational excitation is efficient in
collisions with low energy electrons but it has not been included
either because the collisional relaxation of the N2O rotation at
the working pressure of 2 mbar is very fast28 (<1 µs) in
comparison with the vibrational one13 (>1 ms for the (001)
mode). In fact, an approximate Boltzman distribution of the
rotational levels corresponding to the ambient temperature can
be assumed, as it was shown experimentally in Figure 3 of ref
12, where the absorbance spectrum of N2O during a 40 mA
DC hollow cathode discharge displays a population distribution
corresponding to a temperature lower than 325 K. In contrast,
emission spectra of the same discharge showed vibrational
temperatures of ∼1300 K for the (001) asymmetric stretching
mode. In any case, the inclusion of additional excitation terms
of N2O into the kinetic model would lead to an increase of the
predicted amplitude of modulation of the N2O ground-state
population with the modulated discharge, in better agreement
with the present experimental results; the same effect would be
obtained with excited levels of the other products of the
discharge, provided they could couple efficiently with the N2O
excitation or with the physicochemical mechanisms considered
in the model.
Homogeneous Reactions
N2O + O(1D) f 2NO
G1
G1
G1
G2
G2
G2
G3
G4
G5
G6
G7
G8
7.2 × 10-11
N2O(001) + O(1D) f 2NO
N2O(100) + O(1D) f 2NO
N2O + O(1D) f N2 + O2
N2O(001) + O(1D) f N2 + O2
N2O(100) + O(1D) f N2 + O2
N2O(001) + O(1D) f NO2 + N
NO + O(3P) + M f NO2 + M
NO2 + O(1D) f NO + O2
NO2 + O(3P) f NO + O2
NO + N f N2 + O(3P)
31
31
4.4 × 10-11
1.0 × 10-10
1.0 × 10-31
3.0 × 10-10
9.7 × 10-12
3.0 × 10-11
8.5 × 10-11
b
31
b
31
33
33
NO + O(1D) f O2 + N
Heterogeneous Reactions
O(1D) + wall f O(3P)
O(3P) + wall f O(S)
W1
W2
W3
W4
W5
W6
W7
2200
2200
180
16.1
222
d
d
7
d
d
d
b
O(3P) + O(S) f O2
N + wall f (1/2)N2
N2O(001) + wall f N2O
N2O(100) + wall f N2O
NO + O(S) f NO2
222
2.75 × 10-3
Radiative Deexcitation
N2O(001) f N2O (τ1 ∼ 4 ms)
N2O(100) f N2O (τ2 ∼ 83 ms)
R1
R2
258
12
15
34
Diffusion Coefficients
DN O
DO
DN
DNO
71.5
84.0
79.0
84.0
71.0
e
e
e
e
e
2
2
2
DNO
2
a Rate coefficients are in units of cm3 molecule-1 s-1 for dissociation
by electronic impact and bimolecular reactions; cm6 molecule-2 s-1
for trimolecular reactions and s-1 for heterogeneous reactions. The
diffusion coefficients are included as well in units of cm2 s-1
.
b Estimated in this work. c Calculated from ref 14. d Calculated in our
cell geometry assuming γ ) 1 (see text). e The diffusion coefficients
have been estimated by using the approximation of rigid spheres35 for
a temperature of 300 K and a pressure of 2 mbar. The diffusion
coefficients have been estimated for all gases in N2O, the main species
in the discharge. Molecular diameters have been taken from ref 35.
The value of the molecular diameter for NO2 has been assumed to be
the same as that for N2O.
Dissociation. Electron impact dissociation of N2O is the key
process in the chemical kinetics of the hollow cathode discharge
and it is responsible of the partial disappearance of this
species,12,13 once the steady state has been reached, in a typical
time scale of a few seconds. This long-term depletion can be
observed in Figure 3, where the value of the initial N2O
concentration, which can be assumed to correspond essentially
to the ground vibrational state, is shown together with the value
of the ground-state N2O population recorded with the FTIR
spectrometer, once the steady state of the modulated discharges
has been reached. Note specially the small value of the mean
ground-state N2O concentration left in the discharge at the lower
gas flow rate (∼1.5 × 1016 cm-3) as compared to the initial

8188 J. Phys. Chem. A, Vol. 104, No. 35, 2000
de los Arcos et al.
value (∼5.3 × 1016 cm-3). Nevertheless, the dissociation rate
constants of N2O, notably smaller than the excitation ones,
combined with the low electron concentrations in the plasma,
cannot justify the fast variations observed in the ground-state
N2O concentration, which correspond to the modulation of the
discharge. In this work, the same three N2O electron dissociation
channels assumed in ref 13 have been considered, each one with
the same rate constants when applied to the ground state and to
the (100) and (001) vibrationally excited N2O levels (see Table
1).
De-excitation. In the former works12,13,15 it was seen that the
most significant excited species involved in the chemical kinetics
of the discharge was the O(1D), and consequently, the same
de-excitation and reaction channels involving this species, with
the same rate constant values, have been taken into account in
the present work. Chemical reactions and quenching of the
excited oxygen atoms have relatively large rate constants.
Nevertheless, O(1D) elementary processes turn out to be too
slow, as compared with the vibrational excitation and de-
excitation of the nitrous oxide, to justify the experimental results
studied here. In the present work, the same vibrational de-
excitation processes involving the (100) and (001) levels of N2O
considered previously have been included: spontaneous emis-
sion, quenching with N2O in its ground state, and diffusion
outward the plasma volume with possible de-excitation by
collision on the wall, all of them with the same lifetimes or
rate coefficients assumed previously. In general, they are
relatively fast processes, which happen in time scales of
milliseconds.
coefficient DX of each one of them in a medium where the main
species is the precursor N2O. The diffusion area A and the
diffusion length L do not participate in the differential equations
separately but as a single parameter A/L, whose value, which
should be selected properly, supplies an estimation of the speed
or facility of mixing of matter between both volumes.
O(1D) and N atoms and excited N2O molecules recombine
or de-excite too quickly in the gas phase through homogeneous
reactions or quenching, and they do not diffuse appreciably
outside the plasma volume Vp; therefore, differential equations
for these species corresponding to the volume VA are not
included. The O(3P) atoms are formed by dissociation of N2O
or by quenching of O(1D) and do not experience gas phase
recombination but disappear exclusively by adsorption and
recombination in the cathode wall. This disappearance processes
are very efficient, with a probability γ ) 1, and wall adsorption
of O(3P) atoms is actually limited by diffusion. This fact implies
that the O(3P) concentration may be considered to have a
constant value inside the plasma volume and to decrease
smoothly out of Vp and toward the neighborhood of the cathode
wall until it gets to zero at the stainless steel surface.29
Nevertheless, in the present model, the cylindrical limits of the
plasma volume are very near the cathode walls, and for the sake
of simplicity we have just considered O(3P) atoms confined to
the plasma volume, although adsorption and wall recombination
to produce oxygen molecules are taken explicitly into account
through reactions W1 and W2 of Table 1.
The whole set of differential equations has been numerically
solved by means of a fourth order Runge-Kutta method. The
solution of these equations yields the time evolution of the
concentrations of each species in the volumes VA and VP, from
the beginning of the experiment until the attainment of the quasi-
stationary state of the modulated discharge, which is reached
in a time interval of a few seconds and can be compared with
the experimental results.
Homogeneous Reactions. As it is shown in Table 1, for the
sake of coherence all the homogeneous reactions included in
ref 13 have been considered in the present work.
Heterogeneous Reactions. The set of heterogeneous reactions
included in the current work and shown in Table 1 is also the
same included in ref 13, although only wall deactivation of
vibrationally excited N2O, may be of significance. On the
contrary, processes affecting mainly the concentrations of the
minor products do not influence notoriously the changes in the
populations of the N2O ground state and its excited vibrational
levels.
In the same way as in the DC mode of operation, the long-
term pressure increase experienced by the cell when the present
modulated discharge is turned on determines a variation in the
output conductances of the experimental system, which were
previously calibrated with pure N2O for different pressures and
flow rates, in the absence of discharge. This calibration is
incorporated also into the model in order to estimate the
residence time, τ(t), because it influences the removal of the
stable species by pumping, especially at low flow rates. In the
present model, which takes into account the two different
volumes, these pumping terms have been considered twice for
each stable species: once in the differential equation corre-
sponding to the volume VP and the other one in that corre-
sponding to VA, each one of them with a weight proportional
to the respective volume. In the case of atoms and excited
molecules, pumping effects can be considered negligible since
these species disappear very quickly, and have not been included
in the model. The gas flow input of fresh N2O has been taken
also into account separately into two parts, flowing simulta-
neously to both volumes, each one of them in a quantity
proportional to the VP and VA values.
Differential Equations. As shown in Table 2, the present
kinetic model is based on the resolution of two sets of
interdependent coupled differential equations, obtained from the
reactions included in Table 1. One of these sets accounts for
the reactions and processes occurring in the plasma volume,
VP, initiated by the dissociation and electron impact excitation
of the N2O molecules in this volume, which are renewed partly
due to gas flow input and partly by diffusion from the rest of
the reactor. It is just in this plasma volume where the transient
species are assumed to be confined and where the stable
products are generated. The other set of differential equations
explains what happens in the remaining volume of the reactor,
VA, where diffusion from the plasma volume is the only source
of the stable products N2, O2, NO and NO2, where the precursor
N2O is continuously renewed mostly by the gas flow input, and
where a portion of fresh N2O is lost, transferred to the plasma
volume by diffusion.
4. Results and Discussion
Diffusion processes involving the stable species, which are
considered to be the only mechanisms of interchange of matter
between the two volumes VP and VA, are taken into account by
means of the corresponding terms included in the differential
equations. These terms are formulated by considering a finite
difference of the concentrations of each stable species between
VP and VA at every moment and by estimating the diffusion
Figure 3a shows the temporal variations in the N2O ground
state population produced by the hollow cathode discharge, as
derived from the absorbance spectra experimentally observed
along the optical path-length of the IR beam across the cell.
These results were obtained in a 2 mbar, 80 mA, 45 Hz
modulated N2O discharge, at two different gas flow rates, 3

N2O-Modulated Hollow Cathode Discharge
J. Phys. Chem. A, Vol. 104, No. 35, 2000 8189
TABLE 2: Set of Coupled Differential Equations Obtained from the Reactions Included in Table 1a
d[N2O]
V
N OVR
VP
P ) Φ
P - (kD1 + kD2 + kD3 + kE1 + kE2)[N2O]P[e-]VP + kQ1[N2O]P[N2O(001)]VP -
2
dt
VP
(kG1 + kG2)[N2O]P[O(1D)]VP + kQ2[N2O]P[N2O(100)]VP + kW5[N2O(001)]VP + kW6[N2O(100)]VP + [N2O(001)]
+
τ1
V
V
A
[N2O(100)] P - [N2O] P - D
{[N2O]P - [N2O]A}
P τ N OL
2
τ2
d[NO]P
VP
) kD3[e-]VP{[N2O]P + [N2O(001)] + [N2O(100)]} + 2kG1[O(1D)]VP{[N2O]P + [N2O(001)] + [N2O(100)]} -
kG7[NO]P[N]VP - kG4[NO]P[O(3P)][M]VP - kD4[NO]P[e-]VP + kD5[NO2]P[e-]VP + kG6[NO2]P[O(3P)]VP -
dt
V
A
kW7[NO]P[O(S)]VCSC - kG8[NO]P[O(1D)]VP + kG5[NO2]P[O(1D)]VP - P[NO]P - D
{[NO]P - [NO]A}
τ
NOL
d[N ]
VP 2 P ) (kD1 + kD2)[e-]VP{[N2O]P + [N2O(001)] + [N2O(100)]} + kG2[O(1D)]VP{[N2O]P + [N2O(001)] +
dt
V
[N2O(100)]} + kG7[NO]P[N]VP + kW4[N]VP - P[N2]P - DN {[N2]P - [N2]A}
1
2
A
L
2
τ
d[O2]P
VP
VP
VP
) kG2[O(1D)]VP{[N2O]P + [N2O(001)] + [N2O(100)]} + kW3[O(3P)][O(S)]VP + kG5[O(1D)][NO2]VP +
dt
V
2 P τ
A
L
kG6[O(3P)][NO2]VP - (kD6 + kD7)[O2][e-]VP + kG8[O(1D)][NO]VPSC - [O ] P - DO {[O2]P - [O2]A}
2
d[NO2]P
) -kD5[NO2]P[e-]VP + kG3[O(1D)][N2O(001)]VP + kG4[NO]P[O(3P)][M]VP - kG5[O(1D)][NO2]PVP -
dt
V
2 P τ
A
L
kG6[O(3P)][NO2]PVP + kW7[NO]P[O(S)]VCSC - [NO ] P - DNO {[NO2]P - [NO2]A}
2
d[O(1D)]
) kD2{[N2O]P + [N2O(001)] + [N2O(100)]}[e-]VP + kD7[e-][O2]PVP - kQ3[N2]P[O(1D)]VP - (kQ4
+
dt
kG8)[NO]P[O(1D)]VP - (kG1 + kG2)[O(1D)]{[N2O]P + [N2O(001)] + [N2O(100)]}VP - kG3[N2O(001)][O(1D)]VP -
kG5[NO2]P[O(1D)]VP - kW1[O(1D)]VP
d[O(3P)]
VP
) kD1{[N2O] + [N2O(001)] + [N2O(100)]}[e-]VP + kD4[NO]P[e-]VP + kD5[NO2]P[e-]VP + (2kD6
+
dt
kD7)[O2]P[e-]VP + kQ3[O(1D)][N2]VP + kQ4[O(1D)][NO]PVP - kG4[O(3P)][NO]P[M]VP - kG6[O(3P)][NO2]PVP -
kG7[NO]P[N]VP + kW1[O(1D)]VP - kW2[O(3P)]VP - kW3[O(3P)][O(S)]VPSC
d[N2O(001)]
VP
VP
VP
) -(kD1 + kD2 + kD3)[N2O(001)][e-]VP + kE1[N2O]P[e-]VP - (kG1 + kG2 + kG3)[N2O(001)][O(1D)]VP -
kQ1[N2O(001)][N2O]PVP - kW5[N2O(001)]VP - [N2O(001)]
dt
VP
τ1
d[N2O(100)]
) -(kD1 + kD2 + kD3)[N2O(100)][e-]VP + kE2[N2O]P[e-]VP - kQ2[N2O(100)][N2O]PVP -
(kG1 + kG2)[N2O(100)][O(1D)]VP - kW6[N2O(100)]VP - [N2O(100)]
dt
VP
τ1
[N]
dt
) kD3{[N2O]P + [N2O(001)] + [N2O(100)]}[e-]VP + kD4[NO]P[e-]VP + kG3[N2O(001)][O(1D)]VP - kG7[NO]P[N]VP +
kG8[NO]P[O(1D)]VP - kW4[N]VP
[O(S)]
dt
SC
) kW2[O(3P)]VP - kW3[O(3P)][O(S)]VPSC - kW7[NO]P[O(S)]VCSC
d[N2O]
V
N OVR
V
A
VA
A ) Φ
A - [N2O]A A - D
{[N2O]A - [N2O]P}
N OL
2
2
dt
τ

8190 J. Phys. Chem. A, Vol. 104, No. 35, 2000
de los Arcos et al.
TABLE 2 (Continued)
d[NO]
V
A
VA
VA
VA
VA
A ) - A[NO]A - D
{[NO]A - [NO]P}
dt
τ
NOL
d[N ]
V
2 A ) - A[N2]A - DN {[N2]A - [N2]P}
A
L
2
dt
τ
d[O ]
V
2 A ) - A[O2]A - DO {[O2]A - [O2]P}
A
L
2
dt
τ
d[NO ]
V
2 A ) - A[NO2]A - DNO {[NO2]A - [NO2]P}
A
2
dt
τ
L
a φN O is the flow rate of N2O into the reactor in molecules s-1, VR is the reactor volume (cm3), VP is the plasma volume (cm3), VA is the volume
2
of the whole reactor minus the plasma volume (cm3), SC is the cathode surface (cm2), VC is the cathode volume (cm3), and τ is the reactor residence
time (s). DX are the diffusion coefficients for the different species. A is the transversal area where the diffusion takes place (cm2) and L is the
diffusion length. The first 10 equations account for the evolution of the concentrations of the different species inside de plasma volume. The 11th
one accounts for atomic oxygen adsorbed in the cathode wall, and the last five indicate those of the different species in the volume VA without
plasma.
and 108 sccm. In the simple geometrical assumption of the
present work, it may be considered that the N2O population is
observed through the VP and VA volumes, weighted with their
respective optical path lengths, as displayed in Figure 1.
In Figure 3a, the theoretical results of the present model are
given too. To compare, the results obtained by applying the
former model, in which the stable species are assumed to be
homogeneously distributed, are also shown. The large differ-
ences between the predictions of the two models are worth
noting, both in the amplitude of modulation and in the time
evolution of the calculated signals. The present model, which
introduces just two different concentration distributions and
incorporates diffusion terms connecting them, leads to an
amplitude of oscillation larger by an order of magnitude than
that of the former one, hence approaching much better the
experimental results as shown in Figure 3a. However, the new
amplitudes of oscillation are still smaller than the measured
values by a factor between two and five, depending on the flow.
The improvement achieved in the prediction of the shape of
the modulated signals is apparent in Figure 3b where the time
profiles corresponding to the present and to the previous model
have been scaled to the measurements. The neglect in the model
A/L ) 10 cm has been selected. This value is consistent with a
diffusion length about L ∼ 1-2 cm and a diffusion area of
approximately A ∼ 10-20 cm2, which are compatible with the
geometry of the plasma volume. The value of L is of the same
order as the distance that the stable species involved in the
kinetics of the N2O discharge travel by diffusion during a time
interval of ∼1-2 ms (i.e., during the temporal range of the
duration of the transients observed in the present work), and
the value of A is intermediate between that of the cathode
circular ends (5 cm2) and that of the plasma surface (35 cm2),
but closer to the first one. Concerning this diffusion area, the
logic option at first sight would be to consider a value equal to
that limiting the plasma volume; nevertheless, one should take
into account that diffusion through the curved surface of the
plasma cylinder should be significantly limited by the proximity
of the cathode wall, which avoids largely the renewal of fresh
N2O in this direction. Consequently, a diffusion area closer to
that of the cathode ends seems more appropriate.
In the preceding papers,12,13 the plasma volume was thought
to be located inside the cathode and to be limited by a cylinder
with a radius of 5 mm and a length coincident with that of the
cathode, 90 mm, in agreement with the measurements of charge
density obtained in ref 12 by a double Langmuir probe;
nevertheless, the precise geometrical distribution of the plasma
region in those cases was really irrelevant and only its total
volume had to be taken into account because, for the unstable
species, only the plasma size, and not its shape, was considered
in the model and, with regard to the concentrations of the stable
species, they were supposed homogeneous throughout the whole
cell volume. In the present model, the plasma volume (VP ) 7
cm3) has been maintained, but a slightly different geometry has
been assumed in order to explain better the experimental data.
Figure 4 shows the predicted changes in the ground-state
populations of N2O as well as the behavior of the other species,
estimated separately for each of the two volumes VP and VA
considered in the model. The results portrayed in this Figure
correspond to the slowest and fastest flow studied. It can be
seen clearly that the modulation of the N2O population in the
ground state is only noticeable inside the plasma volume, where
all the kinetic processes take place, and is negligible elsewhere
in the cell; therefore, it is easy to see that a better agreement
with the large modulation amplitude of the experimental results
would be obtained if a longer optical path length of the IR beam
could be assumed through the plasma region, VP, and a
correspondingly shorter one could be assumed through VA. So,
of N2O excitation processes (i.e., the assumption kE1 ) kE2
)
0) leads to a practical disappearance of the modulation of the
N2O ground state concentration nearly as effective as that
obtained by disregarding diffusion effects (i.e., by using the
former model),15 thus indicating that both kinds of processes
are essential in order to explain the observed effects in the
modulated discharge.
Concerning the diffusion terms of the form ([X] - [X′])-
DXA/L, different values of the ratio A/L between 0.3 and 30 cm
have been tried. It has been observed that too small A/L values
(too small diffusion area or too large diffusion length) lead to
a temporal behavior of the modulated N2O absorption signal
with rise and fall time constants markedly slower than those of
the experimental data, and to a slightly higher value of the mean
concentration of N2O in the pseudo-stationary state; whereas
too high A/L values (too large diffusion area or too short
diffusion length) lead to modulation signals with rise and fall
time constants too fast in comparison with the experimental
results, as well as to a somewhat lower mean value of the N2O
concentration. In contrast with the very sensitive dependence
of the signal time profile on the selected A/L value, it has been
observed that the amplitude of modulation is hardly dependent
on this parameter, except for its highest values. Finally, a ratio

N2O-Modulated Hollow Cathode Discharge
J. Phys. Chem. A, Vol. 104, No. 35, 2000 8191
Figure 5. Mass spectrometer outputs in mV of N2O (44 amu), N2 (28
amu) and O2 (32 amu) sampled at one edge of the discharge cell, drawn
at modulation frequencies of 1 Hz (left-bottom panel) and 20 Hz (right-
bottom panel) for a 1 mbar, 36 sccm, 100 mA discharge and compared
with the absolute concentration values predicted in VA by the present
theoretical model. In the upper panels, the theoretical predictions of
the behavior of N2O, N2 and O2 inside the plasma volume, VP, are shown
too.
Figure 4. Theoretical predictions of the time dependent concentrations
of the major products of the discharge N2O, N2 and O2 in the two
volumes VP and VA considered in the present model, with the hollow
cathode discharge cell operating at 45 Hz and 2 mbar, for the two gas
flow rates, 3 and 108 sccm. The behavior of the (001) vibrational excited
level of N2O in the plasma volume is shown too.
is assumed to be confined; the concentration of NO and NO2
in both volumes and of the unstable species in VP are too small
to be shown in a linear scale in Figure 4. As can be seen in the
lower panels of this figure, the concentrations of the precursor
and of the stable species N2 and O2 outside the plasma volume
do not undergo any appreciable modulation following the
modulation of the discharge at this frequency. This fact justifies
the lack of detection of modulated N2O, N2 and O2 signals at
45 Hz when studied by mass spectrometry. On the contrary
(upper panels of Figure 4), a modulation is seen in the simulation
inside the plasma volume for all of these species, although with
time constants much slower than those corresponding to
excitation and de-excitation of N2O. This is in agreement with
the slower nature of the dissociation and recombination pro-
cesses in the N2O discharge. For the (001) vibrational mode of
N2O, a modulated behavior similar to the ground state of the
precursor but with a phase difference of 180° can be noticed.
The slower processes just mentioned begin to be relevant with
decreasing discharge frequencies. Modulation of the N2O, N2
and O2 concentrations outside the plasma volume, which begins
to be noticeable below ∼20 Hz and increases in amplitude at
lower frequencies, can be detected by mass spectrometric
measurements. These results are shown in Figure 5, where the
mass spectrometer outputs in mV of N2O (44 amu), N2 (28 amu)
and O2 (32 amu) sampled at one end of the discharge cell are
drawn at modulation frequencies of 1 Hz (left-bottom panel)
and 20 Hz (right-bottom panel) for a 1 mbar, 36 sccm, 100 mA
discharge and are compared with the absolute concentration
values predicted in the VA volume by the present theoretical
model. The good global agreement between experiment and
theory is worth noting. In the upper panels of Figure 5, the
theoretical predictions of the time evolution of these major
an increase of the length of the plasma cylinder was assumed,
by extending it to the position of the anodes (140 mm), while
accordingly decreasing the value of its radius to 4 mm, to
maintain the same value of VP. This geometric distribution of
the plasma volume is shown schematically in Figure 1. In any
case, the differences between the former and the present VP
dimensions are within the instrumental spatial resolution of the
double Langmuir probe, which is limited by its finite dimen-
sions, 1 mm in the transversal direction, defined by the distance
between the two wires, and 10 mm in the longitudinal direction,
equivalent to their lengths. On the other hand, more recent and
sensitive measurements made with the Langmuir probe showed
that a small charge density (∼10%) extends also outside the
cathode. Actually, the calculated values of Figure 3 correspond
to the effective plasma distribution given above (a cylinder 140
mm long and with a radius of 4 mm) and displayed in Figure
1. A further lengthening of the plasma region preserving its
volume would increase even further the amplitude of modulation
of the signal corresponding to the ground-state population of
N2O, and would improve the agreement between the predicted
values and the experimental data.
Besides the ground-state population of the precursor, Figure
4 shows the concentrations of the stable products of the
discharge N2 and O2 inside and outside the plasma volume (VP
and VA), within two periods of the 45 Hz modulated discharge,
for the two gas flow rates, 3 and 108 sccm. Their concentrations
are remarkably smaller than that of the precursor for the highest
flow rate (108 sccm) but increase above the N2O concentration
for 3 sccm. The population of the (001) vibrational level of
N2O is displayed too, but only in the plasma volume where it

8192 J. Phys. Chem. A, Vol. 104, No. 35, 2000
de los Arcos et al.
5. Summary and Conclusions
In this work the time evolution of the ground-state N2O
concentration associated with fast transients of a 45 Hz, square
wave modulated, hollow cathode discharge of nitrous oxide has
been studied, once the slow transients corresponding to the
ignition of the modulated discharge have finished. To achieve
the needed time resolution in the order of a millisecond, the
former experimental scheme had to be improved and a step-
scan mode of detection for absorption measurements was
implemented in the FTIR spectrometer. This is a nontrivial
modification and, as far as we know, very few time-resolved
absorption measurements with a step-scan FTIR instrument have
been reported previously.
In contrast to the behavior observed in the N2O infrared data,
which correspond to the whole length of the discharge cell, mass
spectrometric measurements, performed at the end of the cell
(i.e., outside the plasma volume) have revealed that in order to
observe a significant modulation in the concentration of the
major species (N2O, N2, and O2), the modulation frequencies
have to go well below 20 Hz.
To justify the experimental results, an improved kinetic model
based on previous works has been used. Within this model, the
fast transient behavior of the N2O ground state population is
attributed to the excitation of the vibrational symmetric and
asymmetric stretching modes of this molecule, combined with
the assumption of a nonuniform distribution of concentrations
along the whole cell and with the occurrence of diffusion effects.
On the other hand, the modulation of concentration of the major
products observed at one end of the cell confirms the inhomo-
geneous distribution of species and the diffusion effects,
independently of vibrational excitation processes. In an attempt
to keep the model uncomplicated, the new data have been treated
in the simplest way compatible with the observations, namely
by dividing the cell volume into two (one for the plasma and
the other one for the rest) interconnected by diffusion. These
assumptions had not been included in previous studies of
N2O plasmas performed on the stationary state of MW, RF
and DC discharges7,8,12 but they are necessary to explain the
present experimental data. With this modifications of the
model, the agreement with the continuous and the slow transient
results of previous works12,13 is maintained. The present results,
as well as those obtained in ref 13 show the advantages of
modulated discharges as compared with continuous ones. The
use of different modulation frequencies can provide different
time scales, which can be of great help to elucidate the
elementary physicochemical processes happening inside the
plasma.
Figure 6. Simulation of the ignition and the extinction of the
continuous N2O discharge with the present model until the attainment
of the respective stationary states and comparison with the theoretical
predictions obtained without including diffusion effects.13
species inside the plasma volume VP are shown too; their
behaviors display larger and more sudden concentration varia-
tions than those predicted and observed experimentally in VA.
Consequently, this fact confirms once more the existence of
diffusion effects, which are not noticeable either in DC
discharges, or in typical high frequency (e.g., microwave or radio
frequency) discharges, but can be evinced by a suitable choice
of the range of discharge modulation frequencies.
To demonstrate further the validity of the present kinetic
model, Figure 6 shows the simulation of the ignition and the
extinction of the continuous N2O discharge, which was studied
in an earlier work,13 until the attainment of the respective
stationary states, and its comparison with the theoretical
predictions of the former model. Only the concentrations of the
stable species are shown in this figure for a gas flow rate of 3
sccm with the A/L value of 10 cm previously used, and a very
encouraging agreement can be observed to exist between both
models. The agreement reached for the unstable species (not
shown for clarity of display) is as good as that for the stable
ones. When the ratio A/L is very large, the diffusion processes
become instantaneous; then the concurrence between the nu-
merical predictions of both models is complete, since conceptu-
ally they become the same. If the A/L ratio were diminished
markedly under the value used in the present work, slight
discrepancies would appear with the experimental results as well
as with the predictions of the former model. In that case, fresh
N2O would be renewed much more slowly inside the plasma
region and a smaller decrease in N2O dissociation would be
obtained; consequently, lower concentration of the major
products N2 and O2 would be achieved too, and the fast transient
behavior of NO and NO2 at the ignition of the discharge would
be slower.
Further improvements intended to account for larger varia-
tions in the population of the N2O ground state and that could
fit better the experimental amplitude of modulation obtained in
this work would have to include most surely additional N2O
excitation channels and a more precise knowledge of the
geometrical distribution of the various species within the plasma,
as well as a refined position dependent treatment of the diffusion
effects.
Acknowledgment. The technical advice and support of J.
M. Castillo, M. A. Moreno and J. Rodr´ıguez have been most
valuable for the achievement of the present experiments. The
SEUID of Spain (Projects PB98-0762-C03-02 and PB96-0881)
and the Consejer´ıa de Educacio´n y Cultura of Madrid, C.A.M.
(Project 07N/0024/1999) are gratefully acknowledged for
financial support.

N2O-Modulated Hollow Cathode Discharge
J. Phys. Chem. A, Vol. 104, No. 35, 2000 8193
Volman, D., Hammond, G. S., Neckers, D. C., Eds.; John Wiley and Sons:
New York, 1993.
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