Chapter 4 – FPI Results and Discussion
Chapter 4 – FPI Results and Discussion
4.1 Introduction
Chapter 4 deals with the experimental results and discussion for the high resolution
spectroscopic study of Cl and Ga lines using Fabry Perot Interferometry (FPI). The section is in
three parts. Firstly, the kinetic energies and trends observed for these species will be presented.
It is then shown that the emission linewidths are truly due to Doppler broadening, and not some
other effect. Finally models will .be developed to explain some of the observed results.
4.2 Fabry Perot Fringes
A typical FP spectrum is given in fig.4.1. This shows the raw data (obtained in real time) on
top, with the smoothed and processed data below. With the FSR (peak separation) known
accurately from prior calibration (see section 2.10.5.4), the FWHM of the peaks is easily
calculated. This process was performed for one Ga and three Cl emission lines (see section
2.10.7) using Cl2, CF2Cl2 and CFCl3 gas plasmas. The emission linewidth of these lines was
measured while varying certain plasma conditions, namely power, flow, frequency and pressure.
Chapter 4 – FPI Results and Discussion
Fig.4.1. Output interference fringes obtained from the FP.
(A) Raw data. (B) Smoothed data.
4.3 Reproducibility
The FP spectrum was monitored for several interference orders to obtain accurate values of the
FWHM measurements for each emission line. Also, each set of plasma conditions was repeated
at least once to ensure that measurements were consistent. Reproducibility for all the Cl
emission lines was extremely good: within a spectrum, all the peaks would have the same
FWHM to within 5% of each other. Run-to-run reproducibility was also very good: a
measurement of the FWHM could be repeated for identical plasma conditions separated by a
time delay of a few days and the values obtained would be within 5% of each other.
The Ga emission lines however, exhibited unpredictable behaviour. The observed intensities
and linewidths of the FPI spectrum were very erratic. These features seemed to depend upon
Chapter 4 – FPI Results and Discussion
several uncontrollable factors. In particular, they seemed to be very sensitive to (a) the
pumpdown time and base pressure of the etcher, (b) whether a new or previously-etched GaAs
wafer was used, and (c) the position of the GaAs wafer on the lower electrode.
Various experiments were performed to try and find the reason for this unpredictability, but
no definitive answer was obtained. Temperature variations in the laboratory during the run were
ruled out by recording a HeNe spectrum under identical conditions to the plasma runs. No
erratic behaviour was seen in this HeNe spectrum. This result effectively ruled out mechanical
vibrations and other external causes. The conclusion was that the unpredictable behaviour of the
Ga line was a real effect occurring within the plasma.
Day-to-day reproducibility for Ga line emission was therefore very difficult to obtain. A
measurement of the FWHM linewidth on one day for a set of plasma conditions, would often be
completely different if measured the next day, under supposedly identical conditions. This
difference could be as much as a factor of 2. However, it was found that measurements taken
with very short delays between plasma runs gave readings that were within 10% of each other.
Consequently all trend graphs (e.g. variation of linewidth with power), were accomplished
within the same plasma run in a period of less than 30 minutes. All measurements for the
different plasma conditions were made without turning the plasma off. The FP spectrum would
be taken for a particular parameter setting (e.g. power = 100 V), stored onto tape, and then the
parameter would be adjusted to the next setting (e.g. 200 W) as quickly as possible and another
reading taken. The ‘fast scan’ option (see section 2.10.3) of the PC system was used to obtain
data as rapidly as possible. Acceptable trend graphs for the Ga* line were obtained in this way.
If these trend experiments were repeated on a different day, the trend would be qualitatively
similar, but the absolute magnitude of the linewidths observed would be different.
4.4 The Magnitude of Atomic Kinetic Energies
Measurements of the FWHM linewidths of the 3 Cl and 1 Ga emission lines were made and
processing of the raw data (deconvolution of the instrumental, isotope and hyperfine effects) was
performed. The kinetic temperatures, T, of the emitting species were then calculated using
Equation (1.4.12). This equation is valid since all the observed lineshapes closely fitted a
Gaussian profile. The fact that Lorentzian lineshapes were not observed indicates that Doppler
broadening is the dominant effect in these linewidth measurements. More discussion of this can
be found in section 4.7. The kinetic energy, E, in eV corresponding to this temperature can then
be calculated from
E = (3/2) kT / e
(4.1)
where k is Boltzmann’s constant and e is the electronic charge.
The magnitude of the kinetic energy observed using the standard plasma conditions (see
section 2.7) for the 3 process gases and 4 emission lines is given in table 4.1. The error values
are based upon estimates of the accuracy of the FP measurements.
The values in table 4.1 show that all the kinetic energies are large, with all the excited atoms
exhibiting temperatures significantly above the ambient gas temperature of about 300 K
(~0.04 eV). In particular, the Ga atom kinetic energy is remarkably high.
Chapter 4 – FPI Results and Discussion
Line
FWHM / Å
T/K
E / eV
Error / eV
Cl 4526 Å
0.0197
1318
0.17
0.03
CF2Cl2
Cl 4601 Å
0.0230
1745
0.22
0.03
Cl 7256 Å
0.0618
5032
0.65
0.03
Ga 4172 Å
0.0417
13601
1.76
0.10
Cl 4526 Å
0.0197
1318
0.17
0.03
CFCl3
Cl 4601 Å
0.0200
1330
0.18
0.03
Cl 7256 Å
0.0546
3928
0.51
0.03
Cl2
Cl 4526 Å
0.0202
1384
0.18
0.03
Cl 7256 Å
0.0358
1683
0.22
0.04
Table 4.1. Temperatures and energies from the observed emission linewidths.
Gas
Comparing the energies calculated from the 3 Cl emission lines for the CF2Cl2 plasma, it is
seen that the energy is divided into two sets. The 4526 Å and 4601 Å lines (henceforth called the
blue lines) both exhibit energies of about 0.2 eV, whereas the 7256 Å line (the red line) shows a
significantly higher energy of 0.65 eV. For CFCl3 this pattern is repeated, with the blue lines
having a smaller value then the red line. However for Cl2 plasmas, both the red and the blue
lines show approximately the same energy of about 0.2 eV.
Comparing the energy values from the same emission line for different process gases, an
interesting trend is seen. The 4526 Å blue Cl line shows virtually the same energy for all 3
processes gases. However, the 7256 Å red Cl line shows a different energy value for every
process gas. For CF2Cl2 and CFCl3 plasmas, this value is large (0.65 and 0.51 eV, respectively),
but for the Cl2 plasma the line shows a similar energy to the blue lines (0.22 eV). This may
indicate that the red line is monitoring two different process, one in Cl2 plasmas and another in
the two Freon plasmas. This will be discussed in section 4.7.7.
4.5
Variation of Atom Kinetic Energies and Emission Line Intensities with Plasma
Parameters
More information about the emitting species can be obtained by studying the trends of
linewidth and absolute intensity with the various plasma conditions, such as power, pressure,
flow rate and frequency. Each of these parameters will be discussed in turn in the following
sections.
4.5.1 RF Power
There was a significant increase in the FWHM linewidth with increasing RF power for every
emission line studied, and for every process gas employed. An example is illustrated in fig.4.2
for CF2Cl2 plasmas. Typically, the linewidth increased linearly by about 60% as the power
increased from 50 W to 400 W. This indicates that the average kinetic energy of the excited
species increases with applied RF power.
The intensity of all the emission lines (Cl and Ga) was linearly dependent upon RF power.
Chapter 4 – FPI Results and Discussion
This trend was repeated for all 3 process gases. An example of this is given in fig.4.3 for the
4526 Å Cl line from a CFCl3 plasma.
Fig.4.2. FWHM linewidth versus RF power for the observed emission lines in
a CF2Cl2 plasma, under standard process conditions.
Fig.4.3. Intensity of the 4526 Å Cl emission line versus
RF power from a CFCl3 plasma.
Chapter 4 – FPI Results and Discussion
4.5.2 RF Frequency
Fig.4.4 shows the variation of emission linewidths with RF frequency. For all the gases
studied there was no discernible change in linewidth in any of the emission lines with frequency.
This is not surprising, since the range over which frequency could be varied (4-20 MHz) was
limited.
Fig.4.4. FWHM linewidth versus RF power for a CF2Cl2 plasma,
Using the standard process conditions.
However, the intensity of the two types of Cl line exhibited different trends with frequency.
The blue lines (4526 Å and 4601 Å) showed no dependence of intensity upon frequency for any
of the gases (see fig.4.5). But the red (7256 Å) line exhibited a linear increase in intensity with
increasing frequency (see fig.4.6) for all 3 process gases. The Ga emission line intensity also
appeared to be independent of frequency.
Chapter 4 – FPI Results and Discussion
Fig.4.5. Intensity of the 4526 Å Cl emission line versus
RF frequency in a CF2Cl2 standard process plasma.
Fig.4.6. Intensity (I) of the 7256 Å Cl emission line versus
RF frequency in a standard CF2Cl2 plasma.
Chapter 4 – FPI Results and Discussion
4.5.3 Gas Flow Rate
The variation of linewidth with flow rate is shown in fig.4.7. As for the RF frequency
graphs, for all gases used there was no significant change in linewidth of any of the emission
lines with flow.
Fig.4.7. FWHM linewidth versus gas flow rate for a CF2Cl2 standard plasma.
For all gases, the intensity of all the emission lines gradually decreased with increasing gas
flow. This was only a small effect as can be seen in fig.4.8.
Fig.4.8. Intensity of the 4526 Å Cl emission line versus
Gas flow rate in a CFCl3 standard plasma.
Chapter 4 – FPI Results and Discussion
4.5.4 Gas Pressure
This provided a surprising result. As the pressure was increased from 30 to 220 mTorr, the
linewidths of all 3 Cl emission lines for all 3 process gases increased linearly (see fig.4.9).
Fig.4.9. FWHM linewidth versus process pressure for a standard CF2Cl2 plasma.
The Ga emission line showed different behaviour from the Cl lines. It exhibited no
dependence of linewidth upon pressure, and its linewidth remained constant over the entire
pressure range studied.
The intensity of all of the emission lines initially increased with pressure (see fig.4.10). The
intensity reached a maximum at about 75 mTorr and then slowly decreased as the pressure was
raised still further. This trend held for all gases. The Ga line also exhibited this behaviour and
the intensity of Ga emission was observed to be directly proportional to GaAs etch rate (see
fig.1.7).
Chapter 4 – FPI Results and Discussion
Fig.4.10. Intensity of the 7256 Å Cl emission line versus
pressure in a standard CF2Cl2 plasma.
Chapter 4 – FPI Results and Discussion
4.6 XPS Study of GaAs Etched Wafers
An XPS study of the etched wafer surface was undertaken to investigate the processes
occurring on the surface of an etching GaAs wafer that might produce fast excited Ga* atoms.
The main results confirmed the conclusions drawn by Wade [43] in a similar study. A typical
wide-range XPS plot is shown in fig.4.11. Peaks corresponding to Ga and As can be seen, along
with C, F and Cl peaks. These indicate that the etched surface is covered in a thin
chlorofluorocarbon polymer layer. Depth profiling showed that the thickness of this polymer
coating was less than 0.1 µm.
Fig.4.11. XPS spectrum of a GaAs wafer etched in the standard process
conditions for a CF2Cl2 plasma.
Peaks due to O2 can also be seen due to re-oxidation of the etched GaAs surface when the
wafer was removed from the etcher. The presence of Al peaks on the wafer surface shows that
Al from the lower electrode or the chamber walls has been etched or sputtered off and
redeposited onto the wafer. This is a well-known phenomenon in high power etch processes
[48]. A more detailed XPS study of GaAs etching using the same standard process conditions
that we used for the FPI studies can be found in Wade [43].
Chapter 4 – FPI Results and Discussion
4.7
Explanation of the Observed Results
There are a number of curious effects that have been observed that require an explanation.
Firstly, the magnitude of the atomic kinetic energies is much greater than those expected for
thermal equilibrium at room temperature. Also, we need to explain the kinetic energy variations
observed with varying plasma parameters, particularly pressure.
Before attempting to explain these observed trends, we need to ensure that the linewidths
measured were true Doppler widths, and not an artifact of the apparatus or attributable to some
other effect (see section 1.4.6.3).
4.7.1 Calculation of Quenching Rates
When an excited species undergoes a collision with another molecule or surface, reaction
apart, two outcomes are possible. First, the collision may cause relaxation of the excited species
in a way that does not cause fluorescence. This process is known as collisional quenching. The
result of quenching is seen as a decrease in emission intensity with increasing pressure. The
second collision process is emission linewidth broadening, the so-called pressure broadening
effects. These will be dealt with in section 4.7.2.
Fig. 4.10 shows a decrease in intensity of Cl* emission with increasing pressure. However,
this is not necessarily due to quenching since other effects may be occurring in the plasma to
reduce the intensity, for example the electron density may change. Therefore, we now calculate
approximate values for the quenching rates in our plasma system to determine whether
quenching is significant. We assume that the quenching species is the undissociated process gas,
in this case CF2Cl2, which will be the most abundant species in the plasma having a density at
60 mTorr of about [CF2Cl2] = 2×1015 cm-3.
The Stern Volmer equation [165] states that the ratio of the fluorescence intensity with no
quenching, If0, to the intensity, If, observed in the presence of a quenching species, Q, of
concentration, [Q], is given by
If0 / If = 1 + kQ[Q] / kf
(4.2)
where kf is the fluorescence rate, equal to the Einstein A coefficient [164] for the transition,
kf = A
(4.3)
and kQ is the first order quenching rate constant. For the Cl emission lines observed in the
present work, kf ~ 108 s-1. For gas phase reactions, the largest possible value of kQ that could be
obtained in our system is ~109 cm-3 s-1. Using Equation (4.2) we have that at a pressure of
60 mTorr
Chapter 4 – FPI Results and Discussion
Intensity ratio = 1 + 10-9 [2×1015] / 108
= 1.02
and at a pressure of 200 mTorr
=
1.07.
Thus, on increasing the pressure from 60 to 200 mTorr we expect a maximum decrease in
emission intensity due to quenching of less than 5%. Since fig.4.10 shows a 70% drop in
intensity over this pressure range, we can say that quenching is not the cause of this loss of
intensity. Other factors are required to explain this effect, such as a decrease in electron density
as the pressure increases.
4.7.2 Pressure Broadening Effects
We showed in the previous section that quenching by collisions is insignificant in our plasma
system. This leaves line broadening as the other outcome for collisional processes. Therefore,
we now examine whether collisional effects are capable of broadening emission lines to the
extent observed experimentally. We do so by calculating the collision diameter, d, of the
colliding species that would be required to cause observable line broadening in our plasmas.
Using data from fig.4.9, the linewidth of the 7256 Å emission line was observed to increase
from 0.051 Å to 0.0721 Å over a pressure range of 38-206 mTorr, corresponding to a density
change of l.33×1015-7.21×1015 cm-3. In other words, a broadening of 0.04 cm-1 (or a frequency
change of 1.2×109 Hz) was observed in a density increase, ∆N, of 6×l015 cm-3. If this increase in
emission frequency were entirely due to pressure broadening effects, it would have to be the
approximate first order rate constant for collisions, i.e. k1 = 1.2×109 s-1.
The second order rate constant for collisions can then be calculated from
k2 = k1 / ∆N
(4.4)
Thus, k2 = 2×10-7 cm3 s-1. This rate constant is related to the velocity, v, and effective diameter,
d, of the colliding species by
k2 = πd 2 ν
(4.5)
For a thermal temperature of about 300 K, ν ~ 400 m s-1 for Cl atoms, thus the diameter of the
effective collision sphere for the Cl atom is about 126 Å. This is obviously between 1 and 2
orders of magnitude too large for the collision diameter of a Cl atom, or even of a Freon
molecule. Therefore, collisions between neutral species cannot be responsible for the observed
linewidth broadening in these plasmas. This conclusion corroborates the observation that all
lineshapes were Gaussian and not Lorentzian.
However, longer range interactions between charged particles and atomic Cl might be able to
Chapter 4 – FPI Results and Discussion
cause sufficient perturbation of the excited Cl atomic energy levels to show up as broadening
effects. The two main effects would be electron-atom and ion-atom interactions. Therefore, a
calculation of the concentration of electrons and/or ions needed to produce the observed
broadening is required.
First an estimate of the charged particle density, N, necessary to cause this broadening gives
the result that N~1016 cm-3, which is about 5 orders of magnitude larger than typical electron and
ion densities in RIE plasmas. This immediately makes this hypothesis unlikely. Furthermore,
we can calculate the interaction distance, r, over which this perturbation should occur. The
formulae for ion-induced dipole interactions
V(r) = -α (Ze)2 / ( 2r4 (4πε0)2 )
(4.6)
where α is the atom polarisability, Z is the number of charges on the ion, e is the electronic
charge and ε0 is the permittivity of free space. V is the interaction energy, which we require to be
about the same as the energy increase shown by the linewidth broadening. For the 7256 Å
emission line, using Z = 1 and α = 2.426×1040 J-1 C2 m2 [160], and V(r) = 7.55×10-25 J for a
0.02 Å linewidth broadening, we obtain r~40 Å, corresponding to a collision cross section, α, of
about 5000 Å2. This value of α is much larger than experimental values which are typically
between 1 and 5 Å2 (e.g. from ref.[49], σ(e-Ar)~4 Å2 and σ(e-CF2Cl2) ~ 1 Å2). Therefore, these
longer range interactions also cannot be responsible for the observed linewidth broadening.
Another possible candidate for a pressure broadening collision partner is a Rydberg atom.
These are atoms which have an electron excited into a higher principal quantum number than in
the ground state. These Rydberg atoms can have very large cross-sections, since the excited
electron is much further from the nucleus. We shall therefore calculate whether Rydberg atoms
could produce the observed linewidth broadening.
Berkowitz [167] gives an expression for calculating the approximate radius of a Rydberg
atom. In order to obtain the radius value of about 126 Å (calculated earlier) that is necessary to
explain the observed broadening, the electron in a Rydberg atom would have to have a principal
quantum number of n = 14, which for a Cl atom is prohibitively large. Also we need to assume
that the concentration of these n = 14 Rydberg atoms in the RIE plasma is about 1016 cm-3, which
is clearly unrealistic. Therefore Rydberg atoms, too, cannot cause significant linewidth
broadening in our plasmas.
The conclusions from all the previous calculations are that collisional effects by neutrals,
ions, electrons or Rydberg atoms cannot explain the broad linewidths observed in the
experimental RIE plasma.
Chapter 4 – FPI Results and Discussion
4.7.3
Self-Absorption and Self-Reversal
Another effect that could contribute to linewidth broadening in the plasma is self-absorption. It
could be the case that the optical depth of the plasma was so great in the relevant emission line,
that any photons emitted from the discharge were reabsorbed by other atoms on their journey to
the plasma window. These photons may be lost to the detector, since they could decay by a
different route. Such self-absorption causes a flattening of a spectral line, thus altering its
lineshape and giving a seemingly broader FWHM linewidth.
For the Cl emission lines, a photon emitted from the centre of the discharge will obey the
Beer-Lambert law:
I = I0 exp(- α N l)
(4.7)
where I is the observed intensity at the plasma window, I0 the original intensity at the discharge
centre (which is the position in the plasma sampled by the lens and FP optics), l the optical path
length (about 10 cm), N the number density of Cl atoms in the correct state for reabsorption and
a the absorption coefficient. The latter parameter, α, is a function of frequency and can be
estimated from the expression [110]
α( ν) = A c2 / (8π ν2)
(4.8)
where A is the Einstein A coefficient for a transition of frequency ν and c is the speed of light.
Thus for the 4601 Å Cl line, A = 0.039×108 s-1 and so α = 3.28×10-8 m2.
We also need to estimate N, the relevant concentration of Cl atoms. This is not the
concentration of ground state Cl atoms, since the lower level of the emission lines was not the
ground state. There were generally three states involved. For example, for the 4601 Å
transition, the three states are [164] the upper excited state (3) which is 2P0½, the lower excited
state (2) 2P½ and the ground state (1) 2P03/2 (see fig.4.12).
Fig.4.12. The energy states involved in the 4601 Å spectral line [164].
In order for self-absorption to affect the lineshape of the 4601 Å line, there must be a
Chapter 4 – FPI Results and Discussion
significant population in state (2) at any one time. One mechanism for this would be if state (2)
was a metastable level, so that the population in this state could build up. However, since the
lifetime of this state is only 5.7 ns [177], any population would rapidly decay to the ground state
(1). Another mechanism for producing a large population in state (2) is reabsorption of photons
from the ground state, a pumping mechanism (see later).
In order to investigate self-absorption, a computer program was written to calculate a selfabsorbed line profile using the expressions [110]
I = f1(ν - ν0) exp{-(α N l f2(ν - ν0))}
(4.9)
f1(ν - ν0) = {1 / (∆ν D √π)} exp( -4 ln 2(ν - ν0)2 / ∆ νD2 }
(4.10)
f2(ν - ν0) = √π ∆ ν D f1(ν - ν0)
(4.11)
with ∆ νD being the Doppler frequency width of a transition of frequency ν0, α being the
absorption coefficient at the frequency of ν0, l the optical path length in metres, N the number
density of Cl atoms and I the frequency dependent intensity of the line.
For different input values of N, the program calculated and plotted out the expected peak
shape. An example is shown in fig.4.13. As N is increased, the peak shape does not change
noticeably for N < 1017 m-3. A significant measurable change in intensity and linewidth is only
seen for N > 1018 m-3 (fig.4.13e), while for N > 5×1019 m-3 (fig.4.l3h) self-reversal occurs.
Fig.4.13. Output of the self-absorption simulation program
using different values for the population density, N, in state (2).
(a) 108, (b) 1011 (c) 1015 (d) 1017 (e) 1018 (f) 2.5×1018, (g) 5×1018, and (h) 1019 m-3.
Using this simulation, we can now compare the experimentally observed lineshapes to those
predicted by the program. The value for the observed linewidth for the Cl lines is such that if it
was due to a thermal (300 K) line being broadened by self-absorption, a number density would
be required which would make self-reversal very apparent, and the line would appear as a
doublet. Since the observed lines were definitely not self-reversed and fit a Gaussian exactly
within experimental error, this mechanism is therefore very unlikely.
We can emphasis this point further by a few calculations. We shall calculate the pumping
intensity required to populate state (2) to the density of 1018 m-3 that is required for noticeable
Chapter 4 – FPI Results and Discussion
linewidth broadening. At steady state, the number of particles in state (2), N2, is constant.
Therefore,
dN2/dt = pump up rate - (pump down rate + fluorescence rate)
=B12 I N1 - (B21 I N2 + A21N2 ) = 0
where I is the intensity of the emission line, N1 is the number of atoms in state (1), A21 is the
Einstein A coefficient for spontaneous emission from state (2) to state (1), and B12 and B21 are the
Einstein B coefficients for stimulated pumping and emission, respectively. Rearranging this
expression, we obtain
N2 / N1 = B12 I / (B21 I + A12)
(4.12)
Using [110] the expression
B = A λ3 / 8π hc
and the fact that A12 = 1.74×108 s-1 [164], we obtain that B12 ~ B21 = 8.3×1010 J-1 m2 s-1. In order
to see significant lineshape changes in the 4601 Å line, we require N2 = 1018 m-3 which
corresponds roughly to 1 in 2000 of the total Cl atom population in the plasma. Using therefore,
N2/N1 = 1/2000 and solving Equation (4.12) for I, we obtain I = 1.05×106 W m-2 Hz-1 pumping
ground state (1) atoms to state (2). This intensity is incident across the whole lineshape of
Doppler width
∆vD = 2 ν0 (2kT ln2 / mc2)½
where ν0 is the central frequency, T is the kinetic temperature (about 300 K), and m is the mass
of the atom. Thus ∆νD = 4.71×109 Hz. Therefore, the intensity, I0, required in the entire
emission line will be
I0 = I ∆νD ~ 5000 W m-2
If we estimate that the glow region of the plasma is a sphere of radius about 5 cm, then the
surface area of the plasma is about 0.03 m2. Therefore, the power in this one emission line
would need to be 5000×0.03 = 157 W in order to obtain a population in state (2) of 1018 m-3.
Since the RF generator is supplying a power input to the whole plasma of only 100 W, this value
of power in the 1335 Å line is clearly impossible. Hence, we can say that state (2) is not
populated sufficiently to cause self-absorption of the 4601 Å line.
Similar analysis of all the other Cl emission lines studied confirms this result.
The same arguments apply to Ga* emission. First, the observed Ga* lineshapes were all
Gaussian, and no evidence of self-absorption or reversal was seen. Secondly the concentration
of atomic Ga in the plasma is expected to be small, since most Ga is removed from the GaAs
Chapter 4 – FPI Results and Discussion
surface combined within compounds such as GaCl and GaCl2 [43]. Some Ga atoms are also
deposited elsewhere, such as on the walls of the reactor, further reducing the concentration of Ga
atoms in the gas phase. Furthermore, calculations based upon the arguments outlined above for
the rate of pumping and fluorescence to and from state (2) (in this case the 2P03/2 state of Ga, see
fig.4.20) show that self-absorption in Ga can be ignored also.
The conclusions from these calculations for both Cl and Ga, are that self-absorption is not
responsible for any significant linewidth broadening in any of the emission lines studied in the
experimental RIE system.
4.7.4
Lifetime Broadening
The natural broadening expected as a result of the Heisenberg Uncertainty Principle can be
calculated for the 4 emission lines (see section 1.4.6.3.1). These are:
4526 Å expected broadening < 1×10-5 Å
4601 Å expected broadening < 1×10-5 Å
7256 Å expected broadening = 5.6×l0-5 Å
4172 Å expected broadening = l.4×10-5 Å
These values confirm that, as expected, lifetime broadening is negligible.
4.7.5
Electron Resonance Broadening
The linewidth broadening, δλ, expected from electron resonance effects (see section
1.4.6.3.7) is given by [118]
δλ = ( λ / c)2 3kTe / me
(4.13)
where λ is the transition wavelength, kTe is the average electron energy and me is the mass of an
electron. Hence, for the 7256 Å transition, δλ = 6×10-8 Å, which is negligible. Calculations for
the other transitions agree with this conclusion. Consequently, we can ignore electron resonance
effects as a cause of linewidth broadening.
4.7.6 Stark Broadening
In order to consider the Stark effect as a possible cause for linewidth broadening, we need to
calculate the electric field, E, associated with charged particles in the plasma. From von Engel
[118], the Debye radius, Λ, of a plasma is given by
Λ = 7×103 (kTe / N )½
(4.14)
Chapter 4 – FPI Results and Discussion
where kTe is the average electron energy in eV and N is the electron density. For kTe ~ 5 eV and
N ~ 2×1017 m-3, we obtain that Λ = 0.035 mm. The average electric field, √(E2) is given by [118]
√(E2) = (kTe / Λ3)½ (2 / ε0) ½
(4.15)
giving √(E2) ~ 2000 V m-1. For an electric field of this size, we should expect [119] a linewidth
broadening of <10-4 Å, which proves that for RIE plasmas Stark broadening is negligible.
4.7.7
Mechanism for Producing Hot Cl Atoms
It has been shown that the observed linewidths and their increase with power and pressure is
not a result of experimental procedures or phenomena other than Doppler broadening.
Therefore, the observation of ‘hot’ Cl and Ga atoms and their power and pressure dependences
represent real velocities. In the next few sections, a model will be outlined which attempts to
explain some of these observations.
Chapter 4 – FPI Results and Discussion
Fig.4.14. The energy levels in atomic Cl from which observations of emission were studied.
Also shown are the transitions from the lower levels to the ground state.
4.7.7.1 Cl2 Plasmas
First, let us examine the results from Cl2 plasmas. An energy level diagram showing the
excited states of Cl* relevant to the present study is given in fig.4.14. Cl2 plasmas are relatively
simple, since excited Cl atoms can only be formed by a few processes. The most important are
(A) Electron Impact Excitation of Ground State Cl Atoms
e + Cl → e + Cl*
(B) Electron Impact Dissociation of Cl2 Molecules
e + Cl2 → Cl– + Cl*
(C) Charge Exchange
Cl– + Cl+ → Cl* +Cl
The main point to note is that since only the most intense Cl emission lines were observed, the
mechanism for producing Cl* must be a majority process. There are a number of other, more
exotic reaction schemes which could produce excited Cl atoms, but these would only form an
insignificant fraction of the Cl emission compared with processes (A) and (B). Some of these
minority processes will be discussed in section 4.7.7.1.1. Process (C), although fast [168], is also
negligible, since the concentrations of the two species involved is too small. The number of Cl+
and Cl– ions in the plasma is very small compared to the number of neutral Cl2 molecules or Cl
atoms. Process (C) therefore, will not be a majority process and can be neglected.
Reactions (A) and (B) can be distinguished by the kinetic energy possessed by the Cl* atoms.
Since electrons have a low mass, they can impart excitation energy to Cl atoms, but not
momentum. Reaction (A) would therefore produce excited atoms moving only at the
equilibrium gas temperature. These ‘cold’ excited Cl atoms would have on average only about
0.04 eV of kinetic energy.
Reaction (B) however, involves the breaking of the Cl-Cl bond. The electron strikes the
molecule and forms an excited Cl2– transition state, which has an energy excess and is unstable.
This dissociates as the ion vibrates, with all its available energy being distributed into the two
products. Hence the Cl– ion and Cl* atom both receive this energy in the form of electronic
excitation and kinetic energy. Since both dissociation products have equally large masses, they
can fly apart in opposite directions with equally large velocities and still conserve momentum.
The magnitude of the kinetic energy given to the Cl* will be a complicated function of the energy
distribution function and the initial electron energy and angle of approach to the Cl2 molecule.
However, the energy will in general be greater than thermal, and the atoms will appear ‘hot’.
Emission lines from excited hot atoms will show a broadened linewidth as a result.
Chapter 4 – FPI Results and Discussion
Therefore, we suggest that reaction (B) is the main mechanism responsible for producing Cl*
in these studies. More evidence for this hypothesis can be found by examining the results of
other workers’ studies of the mechanisms of Cl2 dissociation reactions.
Fig.4.15. Approximate potential energy curves for the ground state of Cl2 and the four states
of Cl2- correlating the dissociation limit of Cl(2P) and Cl-(1S), after Tam and Wong [171].
Various workers have studied electron attachment and dissociation of Cl2 [169-173]. Tam
and Wong [171] have studied attachment to Cl2 for electrons with energies up to 8 eV. They
conclude that the dissociation of Cl2 proceeds via the 2Σu+, 2Πg and 2Πu resonant states of Cl2–
and produces Cl atoms in the 2P3/2, ground state or 2P1/2 spin orbit state (see fig.4.15). They also
found that Cl2 exhibits maxima in its electron attachment cross section at 0 and 2.5 eV. Kurepa
and Belic [170] also report another maximum at 5.75 eV. This total cross-section curve is given
in fig.4.16. Electrons with ≤ 5.75 eV might be able to dissociate Cl2, but since the lowest excited
state from which emission can be observed is 10.63 eV above the ground state, these low energy
electrons would only be able form hot Cl atoms in the ground state. In order to produce hot,
excited Cl*, we need electrons with an energy Ee where Ee is given by [170]
Ee = 2KE(Cl*) - EA(Cl) + DE(Cl2) + Eex(Cl)
where KE is the kinetic energy of the excited species, EA is the electron affinity of Cl to form
Cl-, DE is the dissociation energy for the Cl-Cl bond and Eex is the energy necessary to excite an
electron from the ground state to the state of interest. Using the appropriate values of these for
Chapter 4 – FPI Results and Discussion
Cl and Cl2 [160], we get Ee ≥ 9.9 eV. This represents the minimum energy required to produce
one of the hot Cl* atoms seen experimentally.
Fig.4.16. Total electron attachment cross-section of the Cl2 molecule in the energy region
between 0 and 12 eV, after Kurepa and Belic [170].
Kurepa and Belic [170] report that using electrons with only slightly higher energy than this,
11 eV, a highly excited 2Σg+ state of Cl2- is formed, with a large amount of energy available for
distribution into excited Cl atom products. They also experimentally measured the kinetic
energies of Cl- and Cl* atoms formed by electron attachment to Cl2 with low energy (< 8 eV)
electrons. Their results are shown in fig.4.17. Since the energy of the incident electrons is too
low to produce excitation of the Cl atom, these atoms are only formed in the ground state, and so
the excess energy is transferred entirely to kinetic energy. Therefore, kinetic energies of several
eV are seen. A linear dependence of kinetic energy on electron energy is also observed. If
electrons with energy greater than the first major excited state (8.92 eV) are used, it is likely that
some of the energy will be transferred into excitation of the Cl atoms, with the small remainder
appearing as translational energy. This translational energy should still exhibit a linear
dependence upon initial electron energy.
Chapter 4 – FPI Results and Discussion
Fig.4.17. Experimentally obtained total kinetic energies of the Cl* and Cl– pair against
incident electron energy. Ground state Cl is the full line, excited (2P, 0.11 eV) Cl is the dashed
line (after ref.[170]).
A complication is that at very high electron energies, ion-pair formation can occur,
producing Cl+ and Cl-. The total cross-section for negative ion formation processes in Cl2 at
higher electron energies is given in fig.4.18. The curve shows a peak between 11 and ~30 eV
corresponding to electron attachment reactions, and then a broad hump at E > 50 eV due to ionpair formation. In most RIE systems very few electrons have energies of 50 eV or more (except
secondary electrons, see section 7.3). Therefore, ion-pair production will not be a major
mechanism and will not be discussed further.
Chapter 4 – FPI Results and Discussion
Fig.4.18. Total cross-section curve for negative ion formation processes in Cl2 at electron
energies between 11 and 100 eV, after ref.[170].
Gottscho and Donnelly [109] studied F* , Ar* and Cl* emission from CF4/O2/Ar and Ar/Cl2
discharges by FPI and high resolution OES. Their conclusions were that since Ar* and F* both
exhibited cold (360 K) translational energy distributions, they were both formed by electron
impact excitation of the ground state atom (reaction (A)). The 8376 Å Cl* emission line on the
other hand, showed substantial broadening during the cathodic portions of the RF cycle,
suggesting that other excitation mechanisms such as dissociation reactions were important for
this species. This is further evidence for reaction (B) being the main formation route for the
observed Cl* states.
Before we settle on this reaction as the only mechanism worth considering, we shall look
briefly at some other mechanisms which might account for the observed linewidth broadening.
4.7.7.1.1 Other Mechanisms for Hot Excited Atom Production
There are other, more exotic mechanisms apart from reactions (A)-(C), which might be
responsible for the production of hot excited atoms within an RIE plasma. Cl– ions formed by
attachment reactions of electrons to Cl atoms within the sheath region (stabilised by collision or
emission), could be accelerated out of the sheath into the plasma. The fast Cl– ion could then
undergo a collision with a gas molecule or electron, causing electron loss, and leaving the now
neutral atom in an excited state. Cl– ions would be preferentially formed in a region of the
sheath where electrons are slow moving. Simulations of electron trajectories (see section 7.2.6)
show that electrons enter the sheath, slow down, then turn around and are accelerated back into
the plasma. The position at which these electrons are relatively slow-moving is about 2-5% of
the distance into the sheath. When simulations are performed for Cl– ions which are formed in
this region and then accelerated out, values of their kinetic energy were calculated to be about
0.2 eV. This value is close to the energies observed experimentally for the hot Cl* atoms of 0.2
Chapter 4 – FPI Results and Discussion
to 0.65 eV.
However, it is unlikely that Cl– ions would be able to reach the centre of the discharge (from
where the observations were taken) before losing their energy in collisions. Also, it is unlikely
that this rather exotic mechanism would produce Cl* in sufficient quantities to compete with
emission from those produced via reaction (B).
Another possible mechanism is fast atom production in the sheath from scattering by high
energy positive ions. These atoms undergo many further collisions and some will leave the
sheath region and re-enter the plasma bulk (i.e. backscatter). Computer simulations of this
phenomenon for Ar gas (see section 6.15.2) show typically that the average energy of excited
atoms re-entering the plasma is 0-0.5 eV, again close to the energy observed for Cl*. The
simulated energy values also increased with increasing power as observed experimentally, but
unfortunately decreased with pressure, in direct contrast to the experimental results. Also, again,
this could not be a majority process, and so is unlikely to compete with dissociation reactions.
A third mechanism is due to reflections of fast atoms from the electrode or substrate surface.
Fast atoms produced by ion-impact collisions in the sheath can have energies up to several
hundred eV (see section 6.12). These atoms might strike the electrode surface and backscatter
through the sheath still at very high energies. Some of these will be in an excited state.
Collisions with gas molecules will eventually slow these fast atoms down to the thermal
equilibrium energy. Atoms adsorbed onto the electrode surface could also be sputtered off in a
similar way, or Cl+ ions could be neutralised on striking the surface and be backscattered as fast
neutrals. However, as was shown in section 4.7.1, electronic transitions generally occur much
faster than collisional processes. Consequently, if atoms were reflected from the surface in an
excited state most would radiate before they suffered even one collision. Since these atoms
would be travelling with high velocity, measurement of the average kinetic energy of the excited
atoms would yield a much higher value than observed experimentally. Therefore, this
mechanism is also discounted.
The main conclusion to be drawn from the preceding sections is that the most probable
mechanism responsible for producing the observed hot Cl* emission lines is electron impact
dissociation (reaction (B)) of Cl2, by electrons having energies between 11 and 40 eV. Electrons
with energy lower than 11 eV will not produce Cl* in the required excited states, whereas those
with energy greater than about 40 eV produce ion-pairs.
Since Cl2 is an EN plasma, the mean electron temperature will be high (see section 1.3.4.4.6),
having values up to 5-10 eV [81,82]. Assuming a Maxwellian distribution with mean 5 eV, the
probability of finding electrons with energy E, where 11 < E < 30 eV is ~25% [47]. Therefore,
there are plenty of electrons with sufficient energy to produce the observed results. The exact
number of these electrons will depend strongly upon the electron energy distribution, and any
factor which changes the mean electron temperature will strongly affect the number of electrons
available to cause these reactions. We shall return to this point in section 4.7.7.3.
4.7.7.2
CF2Cl2 and CFCl3 Plasmas
We shall now examine the results from the more complex Freon process gases, and compare
these results to those seen with Cl2.
Chapter 4 – FPI Results and Discussion
Compared to CF2Cl2 or CFCl3, Cl2 is a simple process gas, and there is only one parent
molecule (namely Cl2) from which to produce Cl*. Consequently, all observed emission lines
exhibit an average kinetic temperature which is approximately the same, in this case ~0.2 eV.
More complex process gases however can have a variety of different parent species from which
to form Cl*. For example, in a CF2Cl2 plasma we have processes such as
e + CF2Cl2
e + CF2Cl2
e + CF2Cl
e + CFCl
→
→
→
→
CF2Cl– + Cl
CF2 + 2C1 + e
CF2 + Cl + e
CF + Cl + e
∆H = +3.4 eV [160]
∆H = +5.6 eV [174]
amongst many others. The ∆H values quoted above are for the production of ground state Cl. In
order to produce excited Cl*, the electron impact energy would need to be significantly higher,
and the ∆H value larger also. Of the main processes detailed above, only the first two will be
majority processes, since the concentration of the undissociated parent gas, CF2Cl2, will be much
greater than that of any dissociation products. Since the intermediate ion (CF2Cl2–) that is
formed by electron impact can distribute its excess energy in a different way to that of Cl2–, the
Cl* produced when it dissociates will have a different kinetic energy to that produced from
dissociation of Cl2.
When a parent molecule dissociates, the kinetic energy of the products will be inversely
proportional to their relative masses. For example, when CF2C12 dissociates into the relatively
massive CF2Cl– and light Cl*, conservation of momentum dictates that CF2Cl– should have a low
velocity whilst Cl* will recoil with a far higher velocity. This is a crude approximation, since
energy disposal into internal excitations have not been considered. However, generally
speaking, we should expect that observed Cl* velocity for dissociation of massive parent
molecules would be higher than that from Cl2 dissociation. Values of Cl* velocities seen from
dissociation of CFCl3 would be different to that seen from CF2Cl2, since the molecule has a
different mass and a different transition state is involved in the dissociation. This is what is
observed. Cl emission (7256 Å) showed an averaged kinetic energy of 0.65 eV from CF2Cl2
plasmas, and 0.51 eV from CFCl3 plasmas.
e + CF2Cl2 → CF2Cl– + Cl* (0.65 eV)
e + CFCl3 → CFCl2– + Cl* (0.51 eV)
The interesting result is that even though the 7256 Å line shows this result, the two blue Cl* lines
(4526 and 4601 Å) showed the same kinetic energy in all process gases. This is an indication
that these blue lines are monitoring a Cl* formation process that is common to all three process
gases. This common process must be a majority process (for the same reasons as before), and
one that is likely to produce lower energy Cl* atoms. The most likely candidate for this process
is a decomposition of Cl2 molecules.
In Freon plasmas, Cl2 is formed by recombination of Cl atoms, either at surfaces, S, such as
the chamber walls or electrodes, or in the bulk plasma via an intermediary third body, M, to
remove excess energy.
Chapter 4 – FPI Results and Discussion
Cl + Cl (+ S) → Cl2
Cl + Cl (+ M) → Cl2
or via a reaction such as
e + CF2Cl2 → CF2 + Cl2 + e
This is followed by the same Cl* -formation process that we have suggested for Cl2 plasmas.
e + Cl2 → Cl– + Cl* (0.2 eV)
It is not known at present why the blue emission lines monitor only the Cl2 dissociation
mechanism and not the dissociation of the parent gas, whilst the red line behaves in the opposite
fashion. The following hypothesis is presented as a possible explanation.
In Cl2 plasmas, Cl2 is present mainly as unreacted process gas. This gas will be at the ambient
temperature, in thermal equilibrium with the plasma. Electron attachment reactions then occur,
which form an activated complex (or transition state), Cl2–‡, which then dissociates to form Cl–
and Cl*. The Cl can be formed in many different states, and so we observe emission in both the
red and blue regions of the spectrum.
For Freon plasmas, e.g. CF2Cl2, electron attachment reactions produce an activated complex,
CF2Cl2–‡. When this decays into CF2Cl– and Cl* it is possible that the internal energy
rearrangement is such that only the red emission line is produced. Hence, when monitoring the
red Cl* emission line we obtain an energy value indicative of the dissociation of the parent gas.
The fact that blue lines are observed at all in Freon plasmas suggests that these are due to
dissociation of Cl2, which was formed by recombination of Cl atoms at the surfaces of the
reactor. However, the problem arises that if we observe blue emission lines from Cl* due to Cl2
dissociation, we should also observe red emission lines from the same process, as was seen
previously in Cl2 plasmas. The fact that the red lines showed no component with energy 0.2 eV
indicates that in Freon plasmas, Cl2 may dissociate by a different mechanism than in Cl2
plasmas.
The explanation could be that in Freon plasmas, Cl2 is created in the plasma, rather than
piped in from a cylinder. Therefore it is possible that Cl2 produced by a chemical reaction in the
plasma may not be at thermal equilibrium with the other gases. These Cl2 molecules may have
some degree of internal energy above that of the other gas phase species, in the form of
rovibrational excitation or simply translational velocity. In fact optical emission from Cl2* has
been observed for CF2Cl2 plasmas using the present system [43].
If this energetic Cl2 molecule is now struck by an electron, it may form a different activated
complex, Cl2–‡‡ than that obtained in Cl2 plasmas. Consequently, it is possible that Cl2–‡‡ may
dissociate in such a way that only blue lines are produced.
This hypothesis may be summarised as follows;
Chapter 4 – FPI Results and Discussion
Cl2 plasmas
CF2Cl2 plasmas
CFCl3 plasmas
where † indicates Cl2 in a state with extra internal energy and ‡ and ‡‡ indicate activated
complexes. Hence, when studying Cl2 plasmas, we see red and blue emission lines both with
energy 0.2 eV corresponding to Cl2 dissociation. When studying Freon plasmas, we see red
emission lines corresponding to dissociation of the Freon, and blue lines from the dissociation of
Cl2†.
Various workers have studied some of the processes occurring within Freon plasmas, and the
mechanisms of electron impact reactions in such gases. Detailed calculations of the collision
Chapter 4 – FPI Results and Discussion
cross sections for these processes [176], studies of electron impact induced light emission [175],
or analysis of the Boltzmann equation[147] for these parent gases yield no extra clues as to the
mechanisms involved or provide evidence for or against the proposed hypothesis.
4.7.7.3 The Observed Trends with Plasma Conditions
More information on the mechanism of Cl* production can be derived by examination of the
trends of Cl* kinetic energy and intensity observed with the various plasma conditions (see
figs.4.2-4.10). All Cl emission lines followed generally the same trends with each plasma
parameter, and we shall examine each of these in turn.
(a) RF Power: As the power increases, all the observed Cl* emission lines showed a linear
increase in kinetic energy (see fig.4.2). Also, the intensity of all Cl* lines increased linearly with
power. This result is expected, since increasing the power supplied to the plasma at constant
pressure (i) increases the average energy per species in the gas phase, (ii) increases the ion and
electron temperatures, and (iii) increases the rates of any chemical reactions. By increasing the
RF power, the extra energy given to the electrons is distributed into internal excitation and
kinetic energy of the dissociation fragments. Moreover, since the Maxwell-Boltzmann
distribution for electron energies will be shifted to higher values as the average electron
temperature increases, an increase in the number of electrons in the high-energy tail of the
distribution causes more excitation and dissociation reactions within the plasma, making the
emission lines more intense (see fig.4.3).
(b) Gas Flow Rate: This parameter does not generally affect the electron temperature of a
plasma, and is important only in controlling the residence time of a reactive gas species (see
section 1.3.4.4.4). For the range of flows used in these experiments, the residence time may be
calculated [43] to be between 1 and 8 s, which is very long compared to the characteristic times
associated with collisions or emission. Hence it is not surprising that a variation of flow over this
limited range had very little effect upon Cl* translational energies or emission intensities (see
figs.4.7 and 4.8).
(c) Frequency: None of the observed Cl* emission lines showed any dependence of kinetic
energy upon applied RF frequency (see fig.4.4). The reason for this is probably the limited range
of frequencies available with the present apparatus. Between 4 and 20 MHz the nature of the
plasma, i.e. ion energy distributions (see section 5.3.6), reactions in the bulk, etc., do not change
significantly (see section 1.3.4.4.2). Only at frequencies below about 1 MHz does the plasma
behaviour become significantly modified.
However, frequencies below 4 MHz were
unobtainable due to the limitations of the matching network.
The emission intensities of the Cl lines were also generally independent of frequency
(fig.4.5), with the sole exception of the red 7256 Å line, which showed a linear dependence of
intensity upon frequency for all process gases (fig.4.6). This cannot be explained at present.
(d) Pressure: The surprising result is that the kinetic energy of the Cl* atoms increases with
increasing pressure (fig.4.9). This is contrary to the intuitive idea that if there are more particles
Chapter 4 – FPI Results and Discussion
present, then for the same input power, each particle (such as an electron), on average, should
have less energy. The present model of Cl* formation by 11-30 eV electron impact dissociation
of a parent molecule would therefore require that in order to obtain a larger Cl* kinetic energy,
the incident electron must also have greater energy. This apparent anomaly is difficult to
resolve.
It is known that the electron temperature, kTe, of highly EN plasmas (such as Cl2, CF2Cl2,
and CFCl3) is much greater than that for EP plasmas (5-10 eV as compared to 1-2 eV for Ar
[81,82], see section 1.3.4.4.6). The reason for this is twofold. First the low energy electrons are
removed from the plasma by electron attachment reactions to form negative ions. This leaves the
high energy tail of the electron energy distribution; hence the average kTe increases (and the
distribution will now be distorted from the Maxwell-Boltzmann profile). Secondly, with far
fewer electrons present in the plasma with which to receive energy from the applied electric
fields, those remaining electrons will obtain even more energy than they would have been able to
in an EP plasma.
Therefore the suggestion is, that as the pressure of an EN plasma increases, this has the effect
of reducing the total number of free electrons and increasing the average energy of those
remaining electrons. This will lead to a distribution where there are very few low energy
electrons, and proportionately more high energy ones, as is illustrated in fig.4.19.
Fig.4.19. The electron energy distribution in a plasma. (a) The near Maxwellian distribution
characteristic of an EP or low pressure EN plasma. (b) An exaggerated illustration showing the
expected change to the distribution as the pressure of an EN plasma increases. Curve (b) is no
longer Maxwellian; the low energy electrons are depleted leaving only higher energy electrons.
Thus, the average energy of the electrons shifts to higher energy, but the absolute number of
electrons decreases.
The reason why the electron density should decrease with increasing gas pressure is still
unclear, but a possible explanation is as follows [186]. The number of electrons in a plasma is
determined by the rate constants for production and loss mechanisms for electrons. In the case
of EN plasmas, most electrons will be trapped in the form of negative ions such as Cl–. Cl– ions
can be neutralised by collision with electrons
(D)
e + C1 → Cl + e + e
or by collisions with surfaces or other species in the plasma, represented by S and M,
Chapter 4 – FPI Results and Discussion
respectively.
(E)
(F)
M + Cl– → M + Cl + e
S + Cl– → S + Cl + e
The efficiency of reactions (D), (E) and (F) will depend upon the concentrations of the species
involved and the energy of the collision.
At low pressures, the collision energy is likely to be high, since all species within the plasma,
including electrons and Cl–, will have high velocities. Therefore we expect that Cl– ions will be
neutralised rapidly, and the electron density will remain high.
At higher pressures, however, the same RF input power is distributed to many more species.
Consequently, each species will obtain, on average, less energy. In other words, the
temperatures of the bulk plasma species, M and Cl– will decrease. Therefore, reactions (E) and
(F) will occur to a lesser extent and so fewer electrons will be liberated. If less electrons are
present, reaction (D) also will be inhibited.
The result will be a positive feedback scenario, whereby as the pressure rises, fewer Cl– ions
are neutralised, leading to a decreased electron density. This in turn leads to an increase in
temperature of those electrons that remain free. These high energy electrons are the ones that
cause dissociation reactions, and hence produce hot excited Cl*. If the proportion of these
electrons (compared to the lower energy ones) increases, it is expected that the resulting Cl* will
also possess increased energies.
Also, although the proportion of high energy electrons increases (i.e. the curve skews to
higher energies), the absolute number of all electrons will be greatly reduced due to negative ion
formation reactions. Therefore we expect to see a decrease in intensity of these emission lines as
the pressure is increased, which agrees with experiment (fig. 4.10).
It must be pointed out however, that the above is only a hypothesis, and very little evidence
exists for or against it. The only known measurements of kTe in very EN RIE plasmas (CCl4 and
SF6) were by a Langmuir probe technique [81,82]. As the pressure was increased, the results
indicated that kTe stayed constant or even decreased slightly. However, owing to the difficulties
in interpreting Langmuir probe data (especially those applying a compensating RF signal, see
section 1.4.5), coupled with the experimental problems of the probe tips etching away, and
reproducibility problems, this finding is treated with skepticism.
4.7.7.4 Final Points about Cl* Emission Processes
The two types of Cl* emission lines showed different behaviour under different plasma
conditions. It has not been possible to explain all of these observations, however a detailed
analysis of the transitions involved in excited Cl* [164,177] yields the following information,
which might shed some light on our results when more FPI data are collected.
(i) The upper energy levels of the blue lines (2P03/2 for the 4526 Å and for the 4601 Å line) are
both very high in energy (11.94 eV and 11.97 eV, respectively), and close to the ionisation
limit of Cl (13.01 eV). There are very few energy levels above these from which they can
Chapter 4 – FPI Results and Discussion
be populated by electronic transitions. In fact, there have been no transitions observed from
higher states to the 11.94 eV state [164]. Therefore, it is likely that the only majority
mechanism for populating these two states (and hence giving rise to the two blue emission
lines) is either a direct single-step electronic excitation, or via a dissociation of the parent
gas, as suggested here. Multi-step excitation is not possible due to the relative rates of
emission and collision (see sections 4.7.1 and 4.7.2).
By way of contrast, the upper level of the red 7256 Å line (4S03/2) has a lower energy
(10.63 eV), and consequently, it is populated by both direct excitation and dissociation
processes, and by many electronic transitions from the numerous higher-lying states.
(ii) The blue emission lines are 2P0J → 2PJ transitions, whereas the red line is a 4S0J → 4PJ+1
transition.
(iii) The red emission line has a much shorter lifetime (0.05 / µs) than the 4526 Å (0.24 µs) and
4601 Å (0.26 µs) lines.
(iv) The lower level of the red line (2P5/2) is the lowest energy excited state of Cl* (except for the
0.11 eV 2P01/2 state) at an energy of 8.92 eV.
(v) The relative rates of emission from the 3 lower states to the ground state also reveal
differences. The 4P5/2 state decays by only one route (1389 Å UV line) to the ground state.
Transitions to the 0.11 eV (2P01/2) state are forbidden by the selection rules. The lifetime of
the allowed transition is 4 µs, making the state almost metastable. In contrast, the blue line
lower states can decay by two routes, either to the ground state (2P03/2) or the 0.11 eV state.
The lifetimes, τ, of these UV transitions are very short:
4526 Å
4526 Å
4601 Å
4601 Å
(9.32 eV, 2P03/2)
(9.32 eV, 2P3/2)
(9.28 eV, 2P1/2)
(9.28 eV, 2P112)
→
→
→
→
2 0
P 3/2
P 1/2
2 0
P 3/2
2 0
P 1/2
2 0
(1347 Å, τ = 2.4 ns)
(1363 Å, τ = 13 ns)
(1335 Å, τ = 5.8 ns)
(1351 A, τ = 3.1 ns)
With insufficient data to be able to build a more detailed model of the exact processes
occurring within our reactor, a conclusive explanation of the observed results is not possible at
this time. Further work to study the emission from other excited Cl states is encouraged to solve
these problems.
4.7.8 The Mechanism for Producing Hot Ga* Atoms
In section 4.7.7 a model has been outlined that qualitatively explains the observed energies,
intensities and behaviour of excited Cl* atom emission with changing plasma conditions. This
model now has to be extended to include the observed results for the Ga (4172 Å 2S1/2 → 2P03/2)
transition.
Any model for Ga* production must also be consistent with the Cl model outlined earlier.
Consequently, the main arguments of that model must also apply to the Ga model. These are (i)
the process must be a majority one, (ii) hot atoms result mainly from dissociation reactions, and
(iii) the average electron temperature of EN gases increases with applied RF power and pressure,
but stays constant with flow and frequency (for the ranges of these parameters studied).
Chapter 4 – FPI Results and Discussion
The magnitude of the Ga* kinetic energy was typically 1.8 eV, corresponding to an
equilibrium temperature of 13600 K, although the observed energy could vary between 1 and
3 eV from day-to-day (see section 4.3). Wade [43] developed a model for the etching of GaAs in
CF2Cl2 plasmas which concluded that the main Ga etch product from a GaAs surface is GaCl.
Hence, a dissociation reaction such as
e + GaCl → Ga* + Cl–
can be envisaged, which will produce hot excited Ga*. GaCl is observed in bulk fluorescent
emission from GaAs etching in CF2Cl2 [43] and electron impact excitation reactions such as
GaCl (1Σ+) + e → GaCl (3P0)
∆H = +3.66 eV
are thought to occur readily. With higher energy electrons, dissociation reactions become
increasingly more likely [178].
The energy level diagram for the observed Ga emission is shown in fig.4.20. The important
point to note is that the excited states from which the observed Ga* emission arises have very
low energy (3.08 eV, compared to 10-11 eV for the Cl emission lines). Consequently, the energy
of electrons needed to dissociate GaCl and produce excited dissociation products is much lower
than that for the Cl lines. Dissociation of GaCl to form 2S1/2 Ga* atoms and Cl– only requires
electrons with 1.37 eV [43], hence virtually all the electrons present in an EN plasma will have
sufficient energy to initiate this reaction. In fact, this energy is so low, it is highly likely that the
majority of the Ga* 2S1/2 level is populated by electronic transitions from higher levels, rather
than directly from the dissociation reaction.
Chapter 4 – FPI Results and Discussion
Fig.4.20. Energy level diagram of atomic Ga emission, after Wade [43].
According to our model, changing the flow or frequency does not affect the average electron
temperature, so Ga* atom kinetic energy is unaffected (see figs. 4.4 and 4.7).
If the model for kTe variation with pressure outlined in section 4.7.7.3 is correct, increasing
the pressure should not alter the Ga* kinetic energy either (as seen in fig.4.9). Even at relatively
high pressures there are still plenty of electrons with energy greater than 3 eV. Hence, excited
Chapter 4 – FPI Results and Discussion
Ga* atoms will still be produced that will decay rapidly to the 2S1/2 level from which we then
observe the 4172 Å emission line.
Increasing the power however, will still increase the electron temperature, and so directly
affect the observed Ga* kinetic energy (see fig.4.2). The intensity of Ga* emission is observed to
be directly proportional to the GaAs etch rate (see fig.1.7), i.e. the density of Ga atoms in the
plasma is the crucial factor in the intensity of Ga* emission rather than the effect of electron
temperature. Hence, we cannot use the variation of Ga* emission intensity as a monitor of the
electron temperature as readily as was done for the reactant gases.
4.7.8.1 Alternative Mechanisms for Hot Ga* Production
Ga* emission exhibited a number of strange results and apparently anomalous effects that
suggest that the GaCl dissociation mechanism outlined in section 4.7.8 may not be the complete
story. First, the magnitude of the observed Ga* kinetic energy was much higher than seen for
Cl*. One explanation might be that since Ga requires much less energy to excite it than Cl, a
high energy electron will have enough energy to produce excited Ga* and dissociation products
with high velocities. A second difference is the lack of dependence of Ga* energy upon pressure,
which is unlike Cl*. Thirdly, as was noted in section 4.3, Ga* emission intensities and linewidths
were very unpredictable and erratic, with extremely poor day-to-day reproducibility. There was
an apparent sensitivity to wafer conditions and chamber history effects.
Combining these discrepancies suggests that surface reactions may play an important role in
*
Ga formation. It might be possible that the extremely hot Ga* that is observed is, in fact,
directly sputtered from the GaAs wafer surface. Wade [43] concludes that sputtering does play a
part and may contribute significantly to the emission at 4172 Å.
In order to test this sputtering hypothesis, the ion energy distribution (IED) for positive ions
striking the cathode was crudely estimated using the IED simulation program described in
Chapter 5. Values for the required input parameters were mi = 35 (Cl+), V0 = 400 V, lmax = 2 mm,
Ae = 0.4, kTe = 5 eV, kTi = 0.05 eV and frequency = 13.56 MHz (see section 5.3 for details on the
importance of these parameters). These values were based upon experimental data taken from
the Minstrel etch processes. This IED was used as an input for the ion-surface interaction
program, TRIM, (see Chapter 8) to calculate the expected sputter yield and energy of ejected
particles from a 50:50 amorphous Ga:As surface, using a value for the density of GaAs of
5.3174 g cm-3 and surface binding energy of 5.11 eV [43].
These input data were used to calculate the energy at which Ga and As atoms are sputtered
from the GaAs surface. The energy distribution of sputtered particles resembles a Maxwellian
curve, with an average energy of about 17.5 eV and a tail extending to energies up to 100 eV.
An example of a similar sputtered atom energy distribution (for Ar+ ion bombardment of Si) is
given in fig.8.3 in Chapter 8.
We need therefore to calculate how far Ga atoms sputtered from the surface with energies of
17.5 eV will travel, on average, before being reduced to the observed energy of about 1 eV. The
Ga-Ga bond length is 2.422 Å [160], which is a rough approximation to the diameter of a Ga
atom. A CF2Cl2 molecule will have a diameter of about 6 Å as a first approximation,
consequently the collision cross section for Ga/CF2Cl2 is, therefore, about 55 Å2. The mean free
path for a typical Ga atom in a 60 mTorr CF2Cl2 plasma will therefore be about 0.6 mm. If we
Chapter 4 – FPI Results and Discussion
make the further crude assumption that at every collision the Ga loses half its kinetic energy, we
will need about 4 collisions to reduce 17 eV to 1 eV. Hence, the Ga atoms will travel a
maximum distance of 2.4 mm before being reduced to this energy. Since this can be
approximated by a 3-dimensional random walk of 4 steps, each of size 0.6 mm, the average
vertical distance from the GaAs surface that a Ga atom will travel before being reduced to an
energy of 1 eV will be about 0.95 mm. This distance is still inside the sheath. Since emission
was only observed from the centre of the discharge at a distance of about 30 mm from the
electrode, sputtering seems to make an unlikely contribution to the observed emission.
Furthermore, the sputter yield of 0.073 atoms per ion calculated using TRIM for these plasma
conditions allows a rough estimate of the etch rate of GaAs due to purely physical means to be
calculated. This value is about 0.4 Å min-1, which is at least three orders of magnitude smaller
than the observed experimental etch rates of between 1000 and 10000 Å min-1. In other words,
there are far too few fast sputtered Ga atoms to account for the experimental observations. Most
of the Ga must be etched by a predominantly chemical mechanism, which would produce ‘cold’
molecules, such as GaCl, rather than hot atoms.
The main conclusions of these calculations are that the sputtering model is invalid, and that
failing a better model, the GaCl dissociation model proposed in section 4.7.8 remains the most
likely explanation for the experimental observations.
4.8 Summary of FPI Results
The overall conclusions from this brief study of atomic kinetic energies in RF systems is that:
(a) Excited atoms are produced with high kinetic energies, 0.2-0.65 eV for Cl*, and 1-3 eV
for Ga*.
(b) This implies an electron impact dissociation mechanism from a parent species is
involved, such as Cl2, CF2Cl2 or CFCl3 for Cl* emission, and GaCl for Ga* emission.
(c) The red (7256 Å) Cl* line appears to monitor the dissociation of the parent molecule,
whereas the two blue Cl* lines (4526 and 4601 Å) appear to only monitor dissociation of
Cl2 that has been formed by recombination reactions.
(d) An increase in Cl* kinetic energy with applied RF power and pressure suggests a direct
dependence of electron temperature upon these parameters.
(e) The observation that different Cl* emission lines monitor apparently different reactions
suggests that the Cl2 molecules formed by recombination reactions are created with some
degree of internal energy. This extra energy (rovibrational or translational) differentiates
these Cl2 molecules from Cl2 process gas which will be in equilibrium with the other
species in the plasma.
(f) Sputtering is not an important mechanism for Ga production.
The models proposed here do not explain all the observed results. For example, it is unknown
why the 7256 Å Cl* line should exhibit a different dependence of intensity upon frequency to the
two blue lines. The absolute magnitudes of the observed kinetic energies are also difficult to
explain; why should the Cl* atoms have an average energy of 0.2 eV, not 2 eV or 20 eV?
Finally, the observed erratic behaviour of the Ga* emission line is also puzzling, as is the
Chapter 4 – FPI Results and Discussion
extremely large kinetic energy it exhibits.
It is hoped that future FPI work will examine Cl-containing plasmas in greater detail than was
possible here, so leading to a more accurate model of the mechanisms producing excited hot Cl*
and Ga* species.