Breakdown, steady-state, and decay regimes in pulsed oxygen

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					Breakdown, steady-state,                        and decay regimes                      in pulsed oxygen             helicon
diffusion plasmas
         C. Charlesa) and FL W. Boswell
         Plasma Research Laboratory, Research School of Physical Sciences and Engineering, Australian National
         University, ACT 0200, Australia
         (Received 24 October 1994; accepted for publication 24 March 1995)
         Continuous and pulsed oxygen plasmas have been created in a helicon diffusion reactor used for the
         deposition of silicon dioxide films. An energy selective mass spectrometer and a Langmuir probe
         attached to the wall of the silica-covered aluminum diffusion chamber below the source have been
         used to characterize the plasma [ion energy distribution function (IEDF), plasma potential, floating
         potential, plasma density]. The ion flux can be significantly modified by pulsing the discharge. In the
         continuous case, the IEDF of the 0; ions escaping from the plasma to the sidewalls of the chamber’
         consists of a single peak at an energy corresponding to the plasma potential in the chamber (~32 V).
         In the pulsed case, the IEDF exhibits two additional peaks at high (~60 eV) and low (-15 eV)
         energy as a result of different states of the plasma during the -pulse period: three regimes
         corresponding to the plasma breakdown, steady state, and decay have been observed and
         characterized. The time decay of the fundamental mode of diffusion in the post-discharge was
         measured and calculated (about 1 ms). The breakdown regime is highly dependent on the state of
         the plasma at the end of the post-discharge. 0 1995 American Institute of Physics.

I. INTRODUCTION                                                           consists of a 15-cm-diam, 30-cm-long glass tube (the source)
     The use of the helicon radio-frequency (rf) source for               surrounded by a helicon antenna8 and two solenoids, which
plasma processing has been widely demonstrated over the                   are contiguous with a 35-cm-diam, 30-cm-long aluminum
past decade.lm3 Silicon dioxide deposition from oxygen/                   diffusion chamber surrounded by two solenoids. The cham-
silane plasmas has been recently carried out.4*5As there is no            ber walls, covered with silica on the inside from previous
driven electrode, the substrate, which is placed at the bottom            operation cycles with silane/oxygen plasmas, are water
of the diffusion chamber attached to the helicon source, can              cooled and maintained at a temperature of about 15 “C. The
be either independently biased or allowed to float. It has b&en           reactor (source and chamber attached) is pumped down to a
shown that the ion flux impinging onto the substrate during               base pressure of a few 10v5 Torr (1 Ton-= 133 Pa) by using a
the deposition process is an important parameter.5’ It can be
                                                     6                    turbomolecular pump placed on top of the source. The gas
controlled by increasing the source rf power to increase the              inlets are situated on top of the chamber and gas flows of
ion current or increasing the rf bias on the substrate to in-              lo-100 seem lead to pressures of a few millitorr, measured
crease the ion energy. Another way of decoupling the roles of             by a baratron gauge mounted at the back of the chamber.
the neutral species and of the ions is by pulsing the plasma,             Only oxygen is used in the experiments presented here.
as the neutral species generally have longer lifetimes com-               When operating in its resonant regime, this type of reactor
pared to that of ions? Another motivation for pulsing the                 produces high plasma densities:3Z9 the matching network
plasma is simply to reduce the heat load on the reactor walls             configuration used for the experiments presented in this pa-
and substrate.                                                            per consists of a high impedance (two loops in series) silver-
     We present here initial results obtained in the simplified           plated cbpper antenna connected to variable vacuum capaci-
case of an oxygen plasma excited in the helicon deposition                tors to form an L resonant circuit; operating conditions are a
reactor. Similar results were obtained for high oxygenlstiane             radio-frequency (13.56 MHz) power of 800 W, an oxygen
ratios (O-JSi&=lO).     The plasma is characterized (ion en-              gas flow of 30 seem inducing a pressure of 2 mTorr, and a
ergy distribution function, floating potential) in the silica-            magnetic field configuration inducing a B, component of the
covered diffusion chamber attached to the helicon source for              field of about 80 G in the source and 70 G in the middle of
continuous and pulsed excitation (frequency ranging from 20               the diffusion chamber. In pulsed operation, the rf generator/
Hz to 5 kHz and duty cycle ranging from 10% to 80%).                      matchbox system has rise and fall times of about 80 and 60
Analysis of the breakdown, steady-state, and decay regimes                p, respectively.
is made.
II. PLASMA DEPOSITION REACTOR                                              III. DIAGNOSTICS
     The reactor has been described in previous publi-                          In order to investigate the plasma equilibrium, two types
cations;‘ 5 its schematic is shown in Fig. l(a). Briefly, it
        *4’                                                                of diagnostics were mounted in turn on the chamber via the
                                                                           side port situated 12 cm from the bottom of the chamber
“Permanent address:Laboratoire des Plasmaset Couches Minces, Institut      [Fig. l(a)]: an energy selective mass spectrometer (Hiden
 des Makiaux de Nantes-CNRSUMR 110.2 rue de la Houssinike, 44 072          Analytical Limited Plasma Monitor type HAL EQP for
 Names, France; Electronic mail:                    masses I-300 amu) and a Langmuir Probe (LP) of area 0.1

766       J. Appl. Phys. 78 (2), 15 July IQ95              0021-8979/95/78(2)ff66/8/$6.00              Q 1995 American Institute of Physics

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                                                                               FIG. 2. IEDF of the 0: ions escapingradially from the diffusion chamberto
                                                                               the walls obtainedwith the spectrometerfor a 13.56 MHz continuousoxy-
     Load lock and                                                             gen plasma at 800 W and 2 mTorr power and pressureconditions, respec-
       oartridge                                                               tively (the internal chamber radius is 17.2 cm and the spectrometerion
  transfer                                                                     extractor plate is situated at a radial position of 19 cm).

                                                                               Though the corresponding increase in the thickness of the
                         lenses                                                silica covering the reactor walls is small compared to the
                                                                               initial thickness resulting from months of deposition, small
                                                                               changes in the wall state are likely to be an additional pa-
                                                                               rameter. In pulsed operation, the dwell time of the spectrom-
                                                                               eter was chosen so as to average the ion collection over
                                                                               many pulses and the signal collected by the Langmuir probe
                                                                               was monitored on a high input impedance (1 Ms1) oscillo-
             (ionizer)        electrostatic t
                              energy       to pump
                              analyzer                                    b)
 FIG. 1. (a) Schematicof the helicon depositionreactor showing major com-
 ponents.(b) Schematicof the energy selectivemass spectrometermounted          IV. EXPERIMENTAL RESULTS
 on the chambersideport shown in (a).
                                                                               A. Continuous           excitation-Discharge                              steady state
                                                                                    Characterization of an oxygen plasma in the silica-
 cm’ The spectrometer, which was differentially pumped to a
     .                                                                         covered diffusion chamber has been previously performed
 pressure of 2.10F7 Torr, was mounted directly on the cham-                    for continuous excitation. *O The positive and negative ions
 ber wall so as to provide the closest extraction possible. The                extracted from the plasma by using the mass spectrometer
 spectrometer can be used either to analyze the ions (positive                 placed on the chamber sidewall are Ol, O+, and O- ions,
 or negative) or the neutrals escaping radially from the plasma                respectively. The ion energy distribution function (IEDF) of
 [Fig. l(b)]. In th e ex p eriments presented here, only the ions              the 0: ions is shown in Fig. 2. Similar results are obtained
 extracted directly from the plasma are analyzed. The spec-                    for the 0’ ions. The IEDF exhibits a single peak at an en-
 trometer consists of an ion extractor with a 300~pm-diam                      ergy corresponding to the height of the sheath in front of the
 aperture followed by an electrostatic energy analyzer                         earthed analyzer which we take to be the local plasma po-
 matched to a quadrupole mass filter and a channeltron detec-                  tential (~32 V with respect to ground). A similar value for
 tor. The internal radius of the chamber and the thickness of                  the plasma potential (-35 V) was obtained by positioning
 the chamber wall are 17.2 and 1.5 cm, respectively, and the                   the Langmuir probe close to the wall (x= 16.5 cm). This
 ion extractor was positioned at a radius of 19.2 cm (X axis)                  high value of the plasma potential compared to previous
 from the main vertical axis (z axis) of the reactor. The Lang-                experiments * in helicon systems with conducting chamber
 muir probe was directly mounted on the chamber on the                         walls”*” is a result of the charging effect of the silica-covered
 same port and could be moved along the chamber radius (r).                    insulating walls at the initiation of the discharge. A floating
 Each of the two diagnostics available was used continuously                   potential of 25-30 V with respect to ground has been mea-
 but many depositions of SiOZ were done in the reactor be-                     sured with the LP situated very close to the wall, suggesting
 tween the series of measurements obtained with the Hiden                      a positive wall potential of a few tens of volts in steady state.
 spectrometer and the following series of measurements ob-                     A plasma density of about 3.10” cmm3 was measured with
 tained with the Langmuir probe in the pure O2 plasma.                         the LP in the center of the diffusion chamber.

 J. Appl. Phys., Vol. 78, No. 2, 15 July 1995                                                    C. Charles and I?. W. Boswell        767
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          IO     r7I-l.j-i                          a         I         r   i    b   1             12
                                                                                                                                                      I   ’ I   ’ I    ’

                                                                                             +-  10
                                                                                             ‘;j  8
                                                                                             b                       Low
                                                                                             5       6           :                   ,
                                                                                                          r .*

           oi,----L--’                                  “\I                  ”       1
                10           20   30    40      50            60            70       80                  10          20    30   40    50  60               70    80        90
                                       Energy    (eV)                                                                            Energy (eV)

 FIG. 3, IEDF of the 0,’ ions escapingradially from the diffusion chamberto
 the walls obtainedwith the spectrometer a pulsed (square-wave
 lation at 5 kHz) oxygen plasma at 800 W and 2 mTon power and pressure
                                          for                        modu-
                                                                                                                -r1-rv-7-‘ b)
                                                                                             7       8                                                                     -I
  B. High pulsing frequency-Discharge                              initiation                 ij
                                                                                             “0      6
       The breakdown mechanisms have been previously ana-
  lyzed by Boswell and Vender in a similar system.l’ They                                    5
  have shown that the breakdown regime corresponds to a ca-
  pacitive coupling with most of the energy stored in the

                                                                                                     2       ; \J!
  sheath. An experiment was carried out by forcing the plasma
  into such a capacitive mode: a square-wave modulation of
  high frequency (5 kHz) was used to pulse the plasma and this                                       0   1fk!TEc!ddL,
                                                                                                         10          20    30   40    50  60               70    80

  resulted in a triangle signal on the rf antenna, due to the rise                                                               Energy (eV)
  and fall times of the rf generator. In that configuration the rf
  could not achieve any steady state and there was no post-                               FIG. 4. EDF of the 0: ions escaping radially from the diffusion chamberto
  discharge as the decay time of the rf generator is about 60                                                                    for
                                                                                          the walls obtainedwith the spectrometer a pulsedoxygen plasma(a) 250
  ,YS.The corresponding 0: IEDF is shown in Fig. 3. It shows                              ys-on/2 ms-off and (b) 250 ~-on/125 ,M-off at 800 W and 2 mTorr power
  a single peak at about 60 eV. The higher ion energy com-                                and pressure conditions,respectively.
  pared to that of the continuous case suggests a higher plasma
  potential, hence a higher electron temperature.‘ Hence, by                              4(a) and 4(b). It can be seen that there is always a dominant
  pulsing the plasma, we can double the plasma potential and                              peak at 30-40 eV and a higher- and lower-energy peak, the
  this has a significant interest in ion energy-dependent surface                         energy and amplitude of which depend on the pulsing con-
  processes.                                                                              ditions.
       Analysis of intermediate pulsing frequencies was then                                   The medium energy peak (30-40 eV) can be associated
  made to further investigate the continuous and breakdown                                with the single peak of the IEDF observed in the contin-
  regimes and to have some insight into the post-discharge                                uous case (Fig. 2), while the high- and low-energy peaks
  regime.                                                                                 cIearly result from pulsing the plasma. The high-energy peak
                                                                                          (50-80 eV) is likely related to the breakdown regime
  C. Medium pulsing frequency                                                             (Fig. 3), i.e., to the start of the pulse. Boswell and Porteous
                                                                                          have shown a rapid decay of the plasma potential in the
        As accurate time-resolved measurements of plasma po-
                                                                                          post-dischargeI and this suggests that the low-energy peak
  tential are difficult to perform, a first approach consists of
                                                                                          (lo-20 eV) corresponds to ions extracted to the earthed ana-
  performing real-time measurements of the floating potential
                                                                                          lyzer in the post-discharge.
  by using the LP and time-integrated measurements of the
  IEDF by using the spectrometer. To allow a comparison be-
  tween the two diagnostics, the LP was maintained very close                             2. Floating potential
  to the wall, i.e., close to where the extractor plate of the mass                           Time-resolved measurements of the floating potential
  spectrometer would be. Moreover, we concentrate on the                                  were performed for pulsing conditions which allowed mea-
  floating potential as it should give an idea of the wall poten-                         surements of three distinct peaks in the 0: IEDF. Figure 5
  tial.                                                                                   shows two typical results for a time-on of 250 pus and two
                                                                                          values for the time-off (500 ps and 2 ms). It cansbe seen that
  1. Ion energy distribution             functions (IEDFs)                                a plasma exists in the post-discharge as the tloating potential
      The ion energy spectrum was investigated for a variety                              is not equal to zero. As the time-off is decreased, the begin-
  of pulse conditions. Two typical features are shown in Figs.                            ning of the time-on moves into the post-discharge of the

  768          J. Appl. Phys., Vol. 78, No. 2, 15 July 1995                                                                                      C. Charles and R. W. Boswell
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                                                                                               80 ,-Y                      a a,,,,,   a s , .ra,,,     ~-rm-mm,,

                                                                                                                            A     I                    High
                                                                                                                       A    .

                                                                                                                  cl   a@ B      a    o                Medium
                                                                                                                                 .        ..m.

               0         500         1000      1500   2000          2500       3000               10'.         102           IO3                 104            lo5
                                            Time (ps)                                                                  Time-off  (.us)

FIG. 5. Time evolution of the floating potential obtainedwith the Langmuir            FIG. 7. Energy at maximum intensity of the low [(O) first series, (0)
probe positioned near the wall (x=16.5 cm) for pulsed excitation with a               secondseries], medium [(II!) tirst series, (II) secondseries], and high [(A)
constanttime-on (250 +) and two time-off durations[( +) 500 ,us and (0)               first series, (A) secondseries] peaks as a function of the time-off for two
2 ms]; same power and pressureconditions as in Fig. 2.                                seriesof pulsedoxygen plasmasoperatingat 800 W and 2 mTorr power and
                                                                                      pressureconditions, respectively: the first series correspondsto a constant
                                                                                      time-on of 250 ps and a time-off varying from 50 ps to 2 ms; the second
preceding pulse and sees a floating potential which is higher.                                            to
                                                                                      seriescorresponds a square-wave      modulation (t,,=t,n=T/2) of variable
                                                                                      frequency (from 20 Hz to 2 kHz).
The floating potential at the end of the 250 ,USpulse is con-
stant and independent of the time-off.
     A more detailed analysis of the floating potential decay
                                                                                      rent on the probe. An agreement within a few volts was
in the post-discharge was performed by applying signifi-
                                                                                      observed between both methods. It can be seen that the de-
cantly different pulsing conditions (2 ms-on/8 ms-off and
                                                                                      cay curve is universally independent of the pulsing condi-
250 ,us-on/2 ms-off) and by using two methods for the mea-
surement of Vf. The results are shown in Fig. 6. The first
“static” method consisted of connecting the LP directly to a
high impedance (1 Ma) oscilloscope. The 2 ms-on/8 ms-off                              3. IEDFs peak energies
case allowed the plasma to be well stabilized by the end of
                                                                                            a. High-energy peak. A wider range of pulsing condi-
the pulse, and to be completely extinguished at the end of the
                                                                                      tions was applied to look at. the energy of the three peaks
off-period. We note that very few differences in the decay
                                                                                      observed in the IEDF [Figs. 4(a) and 4(b)]. The correspond-
time are observed between the 2 ms-on/8 ms-off and the 250                            ing evolution of the energy at maximum intensity ofthe three
~-on92 ms-off cases.                                                                  peaks is plotted in Fig. 7 as a function of the time-off. Two
     A second “dynamic” method was used for the 2 ms-on/8
                                                                                      consecutive series of measurements were made: the first se-
ms-off case, which consisted of adjusting the bias on the LP                          ries (shown by open triangles, squares and circles) consists
for different times in the post-discharge to obtain a zero cur-                       of a constant time-on (250 ,us) and a variable time-off (from
                                                                                       125 w to 2 ms) and the second series (shown by solid tri-
                                                                                      angles, squares, and circles) corresponds to a longer time
          35 rtt--m-l?--rrmni--r-r-l                                                  scale where the plasma is pulsed with a square wave of vari-
          30         d   B)$b                                                         able frequency f, i.e., variable period T (from f = 2 kHz, i.e.,
          25                          %                                               t,=t,,=Tl2=250         ,us tof=20   Hz, i.e., t,,=t,,=Tl2=25

                                            g++%-++                                   ms).
                                                                                            The energy of the high peak is highly dependent on the
                                             % &A                                     time-off. This effect indicates the importance of the time
                                                 O&b                                  when the discharge is off, on the plasma breakdown at the
                                                  %                                   beginning of the pulse. Measurements of the floating poten-
                                                                                      tial in the post-discharge have shown (Figs. 5 and 6) that the
                                                                                      plasma is not completely extinguished a few ms after the rf
          -5 t,-.*            1.11
                                 I     I , ,11.?.1   # 11 ltrr* I     L--.Li          has been turned off. Hence, when the time-off is reduced, the
               IO0        *    10’            lo2             IO3               IO4   plasma density when a subsequent rf pulse is applied, is
                                        Time-off  (ps)                                greater and less ionization is required to reach equilibrium.
                                                                                      When the time-off is reduced to 50 ,us, the effect of the
FIG. 6. Tie evolution of the floating potential in the post-discharge  mea-           capacitive mode decreases and the energy of the high peak
sured with the LP (time-off referencedat the end of the pulse, LP positioned          decreases strongly to values close to that of the continuous
at x- 16.5 cm, 800 W and 2 mTorr power and pressureconditions,respec-                 case (Fig. 7). The energy of the peak saturates at about 70 eV
tivelyj for various pulsing conditions and methods of measurements:      (0)
static method, 250 ,us-on/2 ms-off; (+) static method, 2 ms-on/8 ms-off;              when boffreaches l-2 ms. At that time in the post-discharge,
(,A) dynamic method; 2 ms-on/8 ms-off.                                                the floating potential has decreased to just a few volts (Fig.

J. Appl. Phys., Vol. 78, No. 2, 15 July 1995                                                    C. Charles and R. W. Boswell        769
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  6) and the residual ion density in the chamber is much
  smaller (<lo%) than the ion density at the end of the pulse
  (see Sec. IV D 1).
       b. Medium energy peak. The energy of the medium peak              s
                                                                              10”                                                        10'

  does not vary significantly with the time-off. When the time-                                                                                 Z
  off is minimized to 50 p, the medium peak energy of ~35                 2     0
                                                                              10’                                                        100 i
  eV is very similar to that of the continuous case (~32 eV) as          4                                                 0

  the rf signal on the helicon antenna is never turned off com-                                                            f                  4
  pletely due to the 60 p.s decay time of the rf generator.              g    109                                                        10-i I$
  Hence, the medium peak likely corresponds to the latter part           0.                                                          l        G
  of the 250 ,us pulse, where the plasma is in its most stabi-                108 L-&d            I   I    > t    I         I   ,A       10-2
  lized phase. Its energy corresponds to the plasma potential in                 0           1       2        3            4         5
  that part of the pulse.                                                                         Time-off (~10~ ~8)
        A small difference in energy (from 35 to 40 eV) is ob-
  served when the time-off is increased from 50 ,!G to 2 ms             FIG. 8. Tie evolution of the (+) plasmadensity and (0) floating potential
  while maintaining a constant time-on of 250 ,US (open                                                               measuredwith the LP po-
                                                                        (samevalues as in Fig. 6) in the post-discharge
  squares in Fig. 7) which could be due to a shift in the wall          sitioned at x= 16.5 cm for a 2 ms-on/g ms-off puIsed excitation (same
                                                                        power and pressureconditions as in Fig. 2).
  potential over time’ or to small changes in the plasma equi-
  librium during the latter part of the pulse as a result of
  changes in the wall state during the post-discharge.
        The second series of measurements (solid squares in Fig.
  7) shows that the steady state reached on a large pulsing time        the loss of fast electrons with a small decrease in nP as the
  scale (t,,S2 ms) corresponds to a plasma potential equal to           positive ions stream to the wails with a velocity dependent
  that obtained for the continuous plasma (-32 V).                      on their ambipolar speed during the discharge.
        c. Low-energy peak. The energy of the low peak (lo-20                 (ii) Following the rapid cooling of the electrons, attach-
  ev) as a function of the time-off suggests that the corre-            ment will occur and the diffusion will begin to be dominated
  sponding ions are collected directly from a particular state of       by the movement of cool ions (positive and negative) in a
  the plasma during the post-discharge. The decay time of the           plasma with a plasma potential decreasing as a result of the
  rf generator is about 60 ps and the decay time of the electron        electron density decrease (attachment) in order to maintain
  temperature, estimated by the decay of the oxygen atomic              sheath equilibrium. As shown by Boswell and Vender,14 the
  emission lines, is of the order of 10 ~CLS less. The decay of         ion velocity is about twice the thermal velocity in the post-
  the electron temperature in the post-discharge is faster than         discharge of a parallel plate Particle In Cell computer simu-
  that of the plasma densityI and the plasma potential would
                                                                        lation, and the decay rate of this diffusion mode, which pro-
  rapidly approach the floating potential in the post-discharge.
                                                                        ceeds for a few hundreds of ,us, would be about 400 J.JS
  Hence, the results in Fig. 6 suggest that a plasma potential
                                                                        which can be seen in Fig. 8. The authors above have also
  (relative to earth, not to the chamber wall) of lo-20 V still
                                                                        shown that the positive-ion velocity in the post-discharge of
  exist in the post-discharge which could be responsible for the
  presence of the low-energy peak. The results in Fig. 7 show           an electronegative plasma depends on the energy distribution
  that the variation of the low-energy peak when the time-off is        function of the negatively charged particlest5 and the latter is
  changed is smaller than that .observed for the medium and             likely a changing parameter when varying the operating con-
  high-energy peaks.                                                    ditions.
                                                                              (iii) Moreover, the walls are still charged and the de-
   D. Post-discharge                                                    crease in Vf as a function of time shows that, during this
                                                                        variation, more negative ions are lost from the plasma than
   1. Floafing potential    and plasma densify                          positive ions. An electric field must be created in the plasma
        A more detailed analysis of the plasma density in the           to drive this diffusion which will proceed more rapidly than
   post-discharge was made: the decay rate of the positive              the fundamental mode, corresponding to a simple diffusion
   charge current on the LP biased at - 100 V was analyzed for          of ions in a cavity filled with the thermal O2 neutral gas, but
   the 2 ms-on/8 ms-off case and the corresponding plasma               less rapidly than the ambipolar driven diffusion existing dur-
   density (pt,) is plotted versus the time-off on a semilogarith-      ing the discharge.
   mic scale in Fig. 8. The corresponding values of Vf (Fig. 6)               (iv) Following the enhanced loss of negative ions and
   are also shown in Fig. 8. After approximately 0.5-l ms, the          the collapse of the plasma potential during this higher mode
   floating potential has decreased to a few volts and the plasma       of diffusion, the cold plasma of positive and negative ions
   density has decreased by a factor of 5. Subsequently, both           diffuses with a time constant of about 1 ms. Equality of
   decrease with a time constant of 1 ms.                               positive and negative fluxes exists at the wall and no electric
        During the first few hundred microseconds of the post-           field is present in the discharge. This second mode of diffu-
   discharge, a number of phenomena are occurring:                       sion is equivalent to the fundamental mode of the cavity and
       (i) The initial rapid changes in V, in the first few tens of     its decay rate can be calculated by assuming diffusion in a
   microseconds (after the rf is completely turned off) reflect         cylindrical chamber.‘ 7 6,‘

   770      J. Appl. Phys., Vol. 78, No. 2, 15 July 1995                                                         C. Charles and R. W. Boswell
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2, Fundamental        mode of diffusion                                                time-on
     The decay rate of the charged particle density in a cylin-         pulsing
drical cavity after the ionization has been turned off can be           signal
estimated by the following:
(i)                                                 )
           Assuming a simple diffusion of the 0,‘ Of, and O-
           ions in an O2 gas at a pressure p of 2 mTorr and a           rf signal
           temperature T of 300 K equal to the positive (T+)                 0”
           and negative (T-) ion temperatures (T= T- = T+) .
(ii)       Neglecting the effect of the static magnetic field on
           first order: the Larmor radius of a 0; ion of thermal
           velocity about 4.10’ m s-i is about 2 cm and the total       high
           cross section for a 0: ion in a 0, gas is about 5. lo-l5     peak
           cm” inducing a mean-free path of a few centimeters at
           a pressure of 2 mTorr.
(iii)      Assuming no reflection at the wall and a constant av-
           erage diffusion coefficient D’ for the positive ions        energy
           and a decay of the positive particle density as e-*lr.      peak

        The decay rate of the fundamental mode is then given by

                                                                (1)    IOW
where A is the diffusion length of the cavity and D+ the
diffusion coefficient of the positive ions.
     The diffusion length of a cylindrical cavity is defined by       FIG. 9. Schematicof the pulsing conditions and correspondingion current
                                                                      contributions for each peak (seeFig. 4j for t,,=ZSO ,us.
        $( ?J+( y,                                              0)
where r and H are the radius and height of the cavity, re-            sion coefficient of about 25.103 cm2 s-’ (pD+=pD,/2)         in
spectively.                                                           oxygen at a pressure of 2 mTorr (1 mmHg=l Torr). The
    In the fundamental mode where T+ = T- = T, the diffu-             diffusion length of the 17-cm-radius, 30-cm-long chamber is
sion coefficient of the positive ions is given by                     about 5.7 cm, leading to a decay rate of about 1 ms [Eq. (l)].
                                                                      This calculated decay rate is in good agreement with the
                                                                      experimental decay rate. This rather long decay time com-
                                                               (3)    pared to electropositive plasmas likely results from the elec-
                                                                      tronegativity of our oxygen plasma.14
where D, is the ambipolar diffusion coefficient.
    For ions in thermal equilibrium with the gas at tempera-
ture T, the relationship between the coefficient of diffusion         3. IEDFs peak intensities
D and the mobility fi is
                                                                           The previous approach on the plasma diffusion in the
        D    kT                                                       post-discharge allows a more detailed analysis of the ion
        P     e                                                       energy spectra obtained with the spectrometer. Though the
where k is the Boltzmann constant and e the electron charge.          absolute number of ions related to each peak corresponds to
     The pressure-ambipolar diffusion coefficient pD, can be          the peak area, analysis of the results will simply be made
estimated for oxygen ions in oxygen using the data reported           using the peak intensity. Moreover, only a global analysis of
in the literature for helium:t6.i7                                    the results will be made as the spectrometer measurements
                                                                      correspond to timeintegrated measurements over many
                                                                      pulses and the time evolution of the plasma potential during
        i%ioQ=k$9He~                                           (5)    a pulse is an unknown parameter. As schematically shown in
            L                                                                                          the
                                                                      Fig. 9 for t,, equal to 250 ,!,bs, high-, medium-, and low-
where & is the zero-field mobility of the ions in the corre-          energy peaks are associated with the breakdown, steady-
sponding gas and p is the gas pressure.                               state, and decay regimes induced by pulsing the plasma, re-
     4 pressure-ambipolar diffusion coefficient (pD,) of 460          spectively. The duty cycle DC is defined by to,J(ton+toF),
cm’ mmHg s-i and a zero-field mobility (Elgf) of 10.6 cm’             and the effective duty cycle DC, for a particular peak i
V-’ s-i have been reported for helium. Zero-field mobilities          (i=high, medium, or low) at energy eVj is Atil(t,n+to~j,
of 0: and O+ ions in oxygen are in the 2.1-2.5 cm2 V-’ s ‘  -’        where At, is the time during which the plasma potential is
range. By assuming an average mobility of 2.3, Eq. (5) leads          Vi. The intensity measured by the spectrometer corresponds
to a pressure-ambipolar diffusion coetficient (p 0,) of about         to the time integration over Ati of the ion intensity signal
100 cm’ mmE-Ig s-i for oxygen. Equation (3) gives a diffu-            I(t) divided by the period (ton+toR):

J. Appl. Phys., Vol. 78, No. 2, 15 July 1995                                                   C. Charles and R. W. Boswell         771
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             10s                                       I,    --
      %I            I’        \
                          * s 11111’              x
                                          ’ I ’ b1’               -7a)

                                                                                       sa IO6                     Q ’ 4            ; 0
                                                                                                                                   + @
                                                                                       1                                               f

                                                                                              IO3                       I     I1 *1*1
                                                                                                                                    I   , I 1 I I,,, I   I >
                                   IO2                 IO3                                          10’         lo*               IO3              104         10s
                                     Time-off    (p)                                                                        Time-off (~8)

                                                                                FIG. 11. Intensity of the low peak of the 0: IEDF as a function of the

       -T,,,,, ------Go
   Frlo’ I, sx’
   Y F-
                                                                                time-off for pulsed oxygen plasmasoperatingat 800 W and 2 mTon power
                                                                                and pressureconditions,respectively[(0) &,a=250p (first seriesin Fig. 7);
                                                                                (Nj f,,,=foff (second series in Fig. 7); (+) calculated intensity using the
   g 1.s
                                                                                diffusion model and a LP spectrometercalibration at ton=1 ms; multiple
                                                                                crossesfor particular valuesof the time-off correspondto various valuesof
                                                                                the duty cycle].
       u)                    0’
      .g 10s
       8                                                                        decreases by a factor of about 3 while the floating potential
       Q                                   d \                                  decreases from 25 to 15 V. This last point will probably alter
      5                                                                         the plasma potential time evolution during the pulse hence
      p                                                                         modifying At,,, .
      I      105                                                                     The variation of the medium energy peak intensity is
                                   lo*               IO3
                                      Time-off   (ps)
                                                                                similar to that of the high peak, i.e., as 1ltoFf. An increase of
                                                                                the time-off by a factor of 10 (from 50 to 500 psj results in
FIG. 10. (a) linen&y of the high peak of the 0: IEDF as a function of the
                                                                                an equivalent decrease of the peak intensity (from ~2.10~ to
time-off for pulsedoxygen plasmasoperatingat 800 W and 2 mTon power             2.10’ cts s-l) and the discussion on Atmedium      should be simi-
and pressure conditions,respectively[(A) ton=250 p-s (first seriesin Fig. 7);   lar to that of A thigh. When the time-off is minimized to 50
dashedline shows a variation proportional to l/for]. (b) Intensity of the       ,xs, the intensity (~2.10~ cts s-l) of the peak is very close to
medium peak of the 0; IEDF as a function of the time-off for pulsed
oxygen 800 W and 2 mTorr power and pressurecon-             that of the continuous case (~3.10~ cts s-t) as the rf signal
ditions, respectively[(Cl) to,=250 /JS (first series in Fig. 7); dashedline     on the helicon antenna is never turned off completely due to
shows a variation proportional to l/f,,].                                       the 60 ,LS decay time of the rf generator.
                                                                                     The low-energy peak intensity is plotted as a function of
                                                                                the time-off in Fig. 11. The variation of the peak intensity as
                    1                                                           a function of the time-off is significantly different from that
          [p-----            l(t)dt.
               OII+ ‘
                    off                                                         observed for the medium- and high-energy peaks. Figure 6
                                                                                showed that the decay curve of the floating potential is uni-
      For the medium- and high-energy peaks, only a quaiita-                    versally independent of the pulsing conditions and the sim-
tive description can be made as the plasma potential evolu-                     plest analytical model of the low-energy peak intensity
tion during the pulse is not known. The evolution of the peak                   versus the time-off can be made with the following assump-
intensity versus the time-off is shown in Figs. 10(a) and                       tions:
 10(b), respectively.
      The high-energy peak intensity varies as llt,n: an in-                    !ij           The plasma potential at the wall is assumed to be
crease of the time-off by a factor of 10 (from 50 to 500 p)                                   constant in the post-discharge and equal to the energy
results in an equivalent decrease in the high peak intensity                                  V,,, of the low peak.
(from ~5.10~ to ‘    5.104 cts s-t). However, when toff is in-                  (ii)          The .variation of the plasma density in the post-
creased from 50 to 500 ps, the duty cycle decreases by a                                      discharge results from two modes of diffusion, a high
factor of 2.5 (from 83% to 33%). Hence, the decrease of the                                   mode and a low mode, the latter corresponding to the
factor of 10 in the peak intensity shows that the time inte-                                  fundamental diffusion mode of the cylindrical cavity.
gration of I(t) over At,,, is about four times higher for the                       The time evolution of the ion density corresponding to
50 ,us-off case than that of the 500 w-off case. This is not                    the high mode of diffusion can be described by
inconsistent with the results of Fig. 8, which shows that the
initial plasma conditions at the beginning of the pulse
strongly differ in both cases: when t,n is increased from 50                                I1=Zol exp-S              for OGt,&l           ms,                       (7)
to 500 ps, the density of positive ions escaping the plasma                                                71

772             J. Appl. Phys., Vol. 78, No. 2, 15 July 1995                                                                        C. Charles and R. W. Boswell

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   where I,, is the ion density at the end of the pulse (t,,n=O)             The results in Fig. 8 show that
   and Q-,is the decay rate of the high diffusion mode (7-t-400                     I 01
   I-.)*                                                                     I o2=7.                                                          (9)
         The ion density corresponding to the fundamental mode
   of diffusion is                                                           For post-discharge durations smaller than 1 ms, the ion
                                                                         density corresponding to the low-energy peak measured by
                                                                         the spectrometer can be estimated as follows:
                        (toff- f2)                                                         toff             -r,,7l[exp-!t,ffl71)-11
       11=Io2   exp-                 for to+1   ms,                                              Z,(t)dt=                              3
                            r.2.                                                                                                            (10)
                                                                                       I0                            ton + 4Jff
                                                                         where T is the period.
   where I,, 1s the Ion density at tog--t2= 1 ms and r2 is the               For post-discharge durations higher than 1 ms, the ion
   decay rate of the fundamental mode of diffusion (~~‘ ms).             density is

                                                                                 Lm+       bff


        The calibration between the two diagnostics (LP and              ACKNOWLEDGMENTS
   spectrometer) was made at ton= 1 ms and the results obtained
   from the model are shown in Fig. 11. A good agreement                     This research has been partially funded by and carried
   between the calculated and measured intensity of the low-             out on behalf of the Harry Tribugoff AM Research Syndi-
   energy peak is obtained. This simple model does not take              cate. The authors would like to thank Dr. Nader Sadeghi for
   into account the plasma potential variation in the post-              very helpful discussions.
   discharge, which would be necessary for a more accurate
   modelling of the EDF’ low peak. Still, it shows that the
   low-energy peak observed in pulsed EDFs can be associated
   to the decay of the plasma in the post-discharge.
                                                                          ‘ J. Perry and R. W. Boswell, Appl. Phys. Lett. 55, 148 (1989).
   V. CONCLUSION                                                           A.
                                                                          ‘ J. Perry, D. Vender,and R. W. Boswell, J. Vat. Sci. Technol. B 9, 310
       Analysis of the continuous discharge has shown that a              3R. W. Boswell. A. J. Perry, and M. Emami, J. Vat. Sci. Technol.A 7,3345
  higher plasma potential (about 30 V) is obtained in our depo-             (1989).
                                                                          4C. Charles, G. Giroult-Math&cow&i, R. W. Boswell. A. Goullet, G. Tur-
  sition system compared to previous measurements in a sys-                ban, and C. Cardinaud,J. Vat. Sci. Technol.A 11, 2954 (1993).
  tem with conductive chamber walls, as a result of the charge            5G. Giroult-Matlakowski, C. Charles,A. Durandet,R W. Boswell, S. Ar-
  effect of the wall towards positive voltages at the initiation of        mand, H. M. Persing,A. 5. Perry, P. D. Lloyd, S. R. Hyde, and D. Bogsa-
  the discharge. Moreover, the plasma potential can be doubled              nyi, J. Vat. Sci. Technol. A 12, 2754 (1994).
                                                                          ‘ Joubert, R Burke, L. Vallier, C. Martinet, and R. A. B. Devme, Appl.
  (about 60 V) by pulsing the discharge at high frequency (5               Phys. Lett. 62, 228 (1993).
  kHz) so that no post-discharge-and no steady-state regimes              ‘ W. Boswell and R. K. Porteous,J. Appl. Phys. 62, 3123 (1987).
  exist and the coupling is maintained capacitive. Changes in             sR. W. Boswell, Phys. Lett. 33A, 457 (1970).
  the ion energy distribution function have also been observed             R.
                                                                          ‘ W. Boswell, PlasmaPhys. Controll. Fusion 26, 1147 (1984).
                                                                         “C Charles and R. W. Boswell, I. Vat. Sci. Technol.A (to be published).
  in pulsed operations using medium range frequencies (from              ” C’Charles R. W. Boswell, and R. K. Porteous,J. Vat. Sci. Technol.A 10,
  20 Hz to 2 kHz). Analysis of these changes has lead to some              398 (1992;.
  insight into the plasma breakdown, steady-state, and post-              *R.
                                                                         ‘ W. Boswell and D. Vender,Plasma Source Sci. Technol. (to be pub-
  discharge regimes. The time decay of the fundamental mode                lished).
                                                                         “R W. Boswell and R. K. Porteous,Appl. Phys. Lett. 50, 1130 (1987).
  of diffusion in the post-discharge is about 1 ms and the               t4R: W. Boswell and D. Vender.IEEE Trans. Plasma Sci. 19, 141 (1991).
  breakdown mechanism highly depends on the plasma re-                   “R W. Boswell A. J. Lichtenberg,and D. Vender,IEEE Trans. PlasmaSci.
  maining at the end of the post-discharge. Still, further experi-         20, 141 (19923.
  ments need to be carried out for a more detailed understand-           16EarlW. McDaniel, Collision Phenomena in Ionized Gases (Wiley, New
                                                                            York, London, Sydney, 1964), Chap. 9, pp. 478-480 and Chap. 10, pp.
  ing of the time-dependent plasma parameters, as it should be             488-521.
  of great interest when analyzing the plasma-surface interac-           “J. L. Delcroix and A. Bers, Physique des Plasmas (Intereditionset CNRS
  tion during deposition.                                                  Editions, Paris, 1994), Chap. 5, pp. 201-243.

  J. Appl. Phys., Vol. 78, No. 2, 15 July 1995                                                    C. Charles and R. W. Boswell         773
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