PHYSICS OF PLASMAS 18, 053503 (2011)
Temporally resolved ion velocity distribution measurements
in a radio-frequency plasma sheath
B. Jacobs,1,a) W. Gekelman,1 P. Pribyl,1 and M. Barnes2
1
University of California, Los Angeles, California 90095, USA
MS Barnes Engineering, San Ramon, California 94583, USA
2
(Received 7 December 2010; accepted 22 March 2011; published online 23 May 2011)
The ion velocity distribution function (IVDF) above and within a radio-frequency (RF) biased
plasma sheath is studied experimentally with a pulsed laser-induced fluorescence diagnostic in an
industrial plasma etch tool. Temporally resolved measurements taken at eight different phases of
the 2.2 MHz bias waveform show that the ion dynamics vary dramatically throughout the RF cycle
(the ratio of the average ion transit time through the sheath to the RF period is sion=sRF ¼ 0.3). The
position of the presheath=sheath edge is constant throughout the RF cycle and the time-averaged
ion flux is conserved within the sheath region. The characteristic bimodal structure of the
time-averaged ion distributions found in previous experiments is observed to arise from the
time-dependent ion dynamics, in accord with existing theory. The large temporal variation of
C 2011 American Institute
the IVDF has implications for the plasma chemistry and etching quality. V
of Physics. [doi:10.1063/1.3577575]
I. INTRODUCTION
The study of sheaths (the transition layer surrounding any
physical surface exposed to a plasma discharge) is one of the
oldest and most enduring topics in plasma physics. Much work
has been done to investigate plasma sheaths since the introduction of the term by Langmuir in 1923.1 The directed flux of
ions resulting from sheath electric fields is used extensively in
materials processing for a wide variety of applications including deposition of thin films, reactive ion etching (RIE), and ion
implantation (doping).2 The application of a bias voltage to an
object (substrate) immersed in a plasma expands the sheath
region and increases the energy of ions incident upon the substrate. For industrial plasma processing of poorly conducting
substrates (such as the ubiquitous silicon wafer), steady-state
dc biases cannot be maintained; therefore, radio-frequency
(RF) biases which result in zero net electrical current to the
substrate are utilized. It is also understood that the plasma
sheaths play a role in the operation of Ion Cyclotron Resonance Frequency (ICRF) antennas in fusion plasmas.3,4
The key parameter determining the dynamics of ions
within an RF sheath is the ratio of the average ion transit time
through the sheath to the RF period: sion=sRF.2 At very low
values of sion=sRF, the sheath potential changes very slowly
compared to the ion motion and ions respond to the instantaneous sheath fields; theories treating the sheath as an ensemble of dc sheaths accurately describe the ion dynamics and
the sheath impedance is mainly resistive.2 At very high values
of this ratio, the sheath potential changes rapidly and the ions
respond to the average sheath fields; the sheath is primarily
capacitive.2 The intermediate regime, where sion=sRF 1, is
the most complicated case. The interplay between the changing sheath potential and the finite ion transit time affects the
ion dynamics, and the sheath impedance has significant resistive and capacitive components. In this regime, the ion flux to
a)
Present address: Applied Materials, Santa Clara, California 95050, USA.
1070-664X/2011/18(5)/053503/11/$30.00
the substrate is predicted to vary dramatically throughout the
RF cycle.5–8 Additionally, for low to moderate values of
sion=sRF, the ion bombardment energy at the object (substrate)
surface has been predicted to be strongly dependent on the
RF phase, giving rise to broad, bimodal time-averaged ion
energy distributions (IEDs).2,5,9–14
Some authors use the ratio of the RF frequency to the ion
plasma frequency (xRF=xpi) instead of sion=sRF to classify RF
sheaths; however, Kawamura et al. have shown that these ratios
are nearly equal for typical laboratory plasma conditions.2
Laser-induced fluorescence (LIF) is a noninvasive optical
technique for measuring the ion velocity distribution function
(IVDF), f(v), in a plasma15 with good spatial16 and temporal17
resolution, and has been used to probe the sheath18,19 and presheath20–22 regions. Other optical techniques such as LIF-dip23
and Fabry–Perot interferometry24 have also been used to
investigate ion dynamics in RF plasmas.
The LIF technique employed in this work utilized a
common three level scheme, where metastable Arþ* is
excited by laser radiation at 611.492 nm and decays with the
emission of a 460.957 nm fluorescence photon (wavelengths
given in vacuum).18 Argon ions in the metastable 3D0 2G9=2
(state 0: lifetime s0 > 10 ls18) are excited with a laser tuned
near k0 ¼ 611.492 nm to excite to 4P0 2F7=2 (state 1) which
then decays to 4S0 2D5=2 (state 2) with the emission of a fluorescence photon at 460.957 nm (s12 ¼ 8.5 ns).25 Ions moving
along the direction of laser propagation will have their
absorption resonance wavelengths Doppler-shifted from k0
as given by the formula,
Dk ¼ k0 kL ¼ vjj k0 =c;
(1)
where kL is the laser wavelength, vjj is the ion velocity parallel to the laser wavevector, and c is the speed of light. The
LIF distribution is obtained by scanning the laser frequency
across the ion resonance and by recording the resulting fluorescence signal. In practice, the experimentally observed
18, 053503-1
C 2011 American Institute of Physics
V
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053503-2
Jacobs et al.
total LIF signal (integrated over all kL) is proportional to the
ion density, but also depends on numerous other factors,
such as laser intensity,25 electron temperature (and, therefore, the population of ions in metastable state 0),26 and
detection optics. The effect of these other factors makes it
very difficult to get an absolute measurement of density calculated from first principles. Instead, LIF is effectively a
diagnostic of the Doppler line shape, and can be used to
determine the relative ion distribution function. When
the density is calibrated by an independent measurement,
*
fi( fi ðx; vjj ; tÞ, vjj,t) can then be determined in absolute units.
With the knowledge of the IVDF, a number of fundamental
plasma parameters can be calculated, including ion flow
velocity, momentum flux, and heat flux.27
Early work using LIF to investigate dc sheaths in low
density plasma above a biased conducting electrode was conducted by Goeckner et al.18 The very low density (108 cm3)
of their plasma produced a large sheath (2 cm thick) with a
relatively low applied bias voltage of 100 V, and yielded
many spatially resolved points of measurement. 1D22,28 and
2D planar29 and tomographic30 measurements of the IVDF
have been made in the presheath region (presheaths are transition regions which develop in order to satisfy the Bohm criterion:1 ions enter the sheath region with velocities equal to
the sound speed). Gulick et al.31 have compared LIF presheath measurements to Mach probe data; they used a deconvolution technique to account for the bandwidth of their
laser. Time-averaged measurements have been obtained in
an RF sheath as a function of height above an electrode in a
capacitively coupled nitrogen discharge by Woodcock
et al.;19 the plasma density was also evaluated.
Another optical diagnostic known as LIF-dip spectroscopy has also been used to investigate dc and RF sheaths. In
contrast to Doppler LIF, LIF-dip is a two-laser diagnostic
that measures the Stark splitting of Rydberg states to obtain
the electric field experienced by an ion, rather than the complete IVDF.23 Phase-resolved measurements of electric fields
within collisional RF sheaths have been conducted by Barnat
et al.32,33 Takizawa et al. have used LIF-dip to measure electric fields within dc high voltage sheaths.34,35
In this paper, we report time-resolved measurements of
the IVDF within an RF sheath and presheath obtained by
LIF at eight different phases of a 2.2 MHz RF bias waveform. Complications of the LIF diagnostic technique due to
mechanisms that can broaden the measured distribution are
discussed in Sec. II, as well as the deconvolution method
used to mitigate their effects. Experimental details of the
plasma device and the LIF diagnostic are presented in
Sec. III; in Sec. IV the measured IVDFs are presented and
profiles of the computed moments of the ion distributions
above the substrate are shown (density, flux, flow velocity,
and heat flux). The observed ion behavior is compared to
theory and implications of this work are discussed in Sec. V.
II. LIF BROADENING MECHANISMS AND
DECONVOLUTION
Various mechanisms can broaden the shape of the measured LIF distribution relative to the true ion velocity distribu-
Phys. Plasmas 18, 053503 (2011)
tion.31,36,37 The measured distribution function fLIF(kL), is the
convolution of all broadening effects with the IVDF. Assuming a Gaussian lineshape for all broadening effects, the full
width at half maximum (FWHM) linewidths Dkxxx add to the
IVDF Doppler linewidth Dki in quadrature to equal the measured LIF linewidth DkLIF as described by Eq. (2),
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(2)
DkLIF ¼ Dk2i þ Dk2x þ Dk2xx þ Dk2xxx þ ::: :
Often, broadening mechanisms
arepnegligible
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficompared
to the Doppler linewidth Dki ¼ k0 =c 2ln2Ti =Mi of typical plasmas. For example, possible effects on the measured
LIF distribution such as Stark (pressure) broadening, and
broadening due to Zeeman splitting do not apply to this
work: the plasma investigated was low pressure with no
applied magnetic field.37 Other broadening effects can be
accounted for by means of deconvolution methods.
•
•
•
Natural linewidth broadening
The natural linewidth has been calculated37 to be
Dknat ¼ 2.33 105 nm, much less than the Doppler linewidth for even very cold 0.001 eV ions with
Dki ¼ 2.36 104 nm. This broadening effect is negligible
even for low-temperature plasmas.
Laser bandwidth broadening
A laser tuned to a frequency kL is actually composed of a
spectrum of frequencies centered about kL. Although the
precise details of the laser spectrum depend on various
conditions within the laser cavity, a Gaussian frequency
distribution (FWHM is DkL) is an excellent approximation.
The bandwidth of the dye laser used in this work is
DkL ¼ 1.36 103 nm, as measured by a Fabry–Perot interferometer. For ion temperatures measured in these
experiments, Ti > 0.20 eV, the contribution due to the laser
bandwidth was not negligible, but was less than the effect
of saturation broadening.
Saturation broadening
The high powers of pulsed lasers can easily distort the
shape of the measured LIF distribution by an effect called
saturation broadening, or power broadening.36 At low laser
powers, the relatively small amount of laser radiation outside the laser’s FWHM bandwidth will excite negligible
number of ions, and fLIF is approximately proportional to
the IVDF fi. As the laser power is increased, at some point
the transition will begin to saturate: higher laser powers
will not result in the excitation of more ions within the
laser’s bandwidth. However, the small amount of ions
excited outside the laser bandwidth will continue to
increase until at very high laser power, the fluorescence
signal from these ions will be comparable to that from the
ions within the nominal velocity window. This will effectively increase the laser’s bandwidth and broaden the
measured distribution.
Using the technique outlined by Goeckner and Goree,
optimum laser pulse energy was found which avoided saturation broadening.36 However, for the current experiment,
the LIF signal-to-noise ratio was such that the ions in the
sheath could not be resolved at this laser energy due to the
much lower ion density in that region. Therefore, it was
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053503-3
•
Temporally resolved ion velocity distribution measurements
necessary to increase the laser energy into the saturation
broadening regime. Saturation-broadened distributions in
the bulk plasma had a measured DkLIF ¼ 1.52 102 nm,
increasing the measured temperature of a true
Dki ¼ 3.34 102 nm, Ti ¼ 0.2 eV distribution to an artificially high TLIF ¼ 4.2 eV. In the sheath we study ions of
hundreds of electron volts, much larger than even the erroneously high TLIF. Additionally, this effect is mitigated by
using a deconvolution technique to recover fi from fLIF.
Deconvolution
The mathematical problem of the convolution of two distribution functions is well-defined38 and describes a variety
of physical processes, including the Doppler-shifted LIF
diagnostic used in this work, as well as various broadening
mechanisms of the LIF distribution as discussed. The
object o(t) and source s(t) (sometimes called the “kernel”
or “spread function”) distribution functions are convolved
together to form the image function i(t).
Although the convolution operation is commutative, o is
usually assumed to be the “stationary” distribution while s is
“scanned” across it. Mathematically, the convolution operation is defined as
iðtÞ ¼ ðs oÞðtÞ ð þ1
sðt sÞoðsÞds:
(3)
1
Relating the convolution operation to the act of measurement of a distribution with an instrument, i(t) is the
measured distribution (the LIF distribution in this work), o(t)
is the true distribution under investigation (ion the IVDF),
and s(t) is the instrument response to a “point-source” or
delta-function distribution (primarily due to the laser spectrum and saturation broadening in this case).
The operation of deconvolution, solving for o(t) when i(t)
and s(t) are known (as is often the case experimentally), is not
a well-defined problem and can have a wide variety of mathematically correct solutions for o(t).38 This can complicate the
recovery of a true physical distribution o(t) function from the
measured distribution i(t). Despite this defect, deconvolution
techniques have been used in various LIF studies. Gulick
et al.31 have deconvolved the IVDFs from LIF measurements
of presheath ion flows; Smith et al.39 have used deconvolution
with LIF measurements of Hall Thrusters.
A considerable amount of work has been performed
developing and comparing various numerical deconvolution
techniques.40,41 A particular useful method known as maximum-entropy deconvolution has been described in detail38
and an implementation of this technique is readily available.42 This deconvolution technique tends to conserve the
area under a peak;38 this has the effect that the calculated
density of a broadened (uncorrected) LIF distribution fLIF(k)
will have the same calculated density as the deconvolved distribution fi(k).
Figure 1 shows an example of a deconvolution operation
in the presheath region. The spread function width was determined empirically by comparing deconvolved data far from
the substrate with raw data at the same location that was
taken at much lower laser intensities (and, therefore, avoided
Phys. Plasmas 18, 053503 (2011)
FIG. 1. LIF deconvolution example. The uncorrected LIF measured distribution is i (data were taken at 42 mm above the substrate, in the presheath
region), the spread function due to saturation broadening is s and the deconvolved IVDF is o.
the power saturation effect), possible because the ion density
is much higher here than in the sheath region.
III. EXPERIMENT
This diagnostic used a pulsed dye laser (Sirah CobraStretch) that was pumped by a frequency-doubled Nd:YAG
laser (spulse ¼ 3 ns, k ¼ 532 nm, Spectra Physics QuantaRay). The experiment was run at 10 Hz (the laser pulse repetition rate). Figure 2 shows the optics setup within the Laser
Room. The dye laser spectrum was measured with a Fabry–
Perot interferometer to be approximately Gaussian with a
FWHM bandwidth of DkL ¼ 0.0013 nm (corresponding to
a laser temperature of TL ¼ 0.033 eV); however, there is a
broadband (as wide as the laser’s dye curve: 598–636 nm),
unpolarized component of the radiation output due to a phenomenon called amplified spontaneous emission (ASE).43
Although ASE can be minimized through the proper alignment of the dye laser resonance cavity, it cannot be completely eliminated. In this case, the estimated fraction of ASE
is less than 1% of the total radiation output, but it is desirable
to reduce it as much as possible as it causes a constant background LIF signal at all laser wavelength tunings. The dye
laser output energy was also very high (typically 90
mJ=pulse), much higher than the damage threshold for the
optical fiber (approximately 1 mJ=pulse). To address both of
these issues, two high power Glan-Thompson polarizing
beam splitters (BS1 and BS2) were employed in series. BS1
is aligned such that its polarization axis was parallel to the
FIG. 2. (Color online) Schematic diagram of the Laser Room optics showing the lasers, iodine calibration system, and beam shaping optics. The
abbreviations are BD for beam dump, BS for beam splitter, L for lens, M for
mirror, ND for neutral density filter, and PMT for photomultiplier tube. The
upper optical system conditions the beam profile and couples the beam into
the optical fiber. As discussed in the text, the iodine vapor system provides
an absolute wavelength calibration of the dye laser.
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053503-4
Jacobs et al.
dye laser’s polarization. Half of the unpolarized ASE radiation was thus split off from the main beam, and sent to a
beam dump. The other half of the ASE radiation was subsequently polarized along the same axis as the laser radiation
and unavoidably transmitted through the optical system. The
axis of BS2 was adjustable; rotating it 90 would pass anywhere from 100% to 0% of the incident polarized light (as
the axis of BS2 was rotated from parallel to perpendicular to
the axis of BS1), and this was used to reduce the laser energy
so as to not damage the optical fiber. Excess radiation was
sent to another beam dump. The adjustable beam splitter was
also used to adjust the energy of the output beam to a desired
level. The dye laser operation was most stable with the YAG
laser set to its maximum energy level. High energy laser
pulses (60 lJ) were needed to probe the low density plasma
sheaths, while low energy laser pulses (3 lJ) were sufficient
elsewhere and were used to avoid power saturation effects.
A beam sampler (BS3) split off approximately 2% of the
beam for wavelength calibration using an iodine vapor cell,
described below. The remaining beam was prepared for the
optical fiber by a spatial filter consisting of L1, A1, and L2.
L1 was a spherical, focal length ¼ 50 mm lens, which focused
the beam onto A1, a 250 lm diameter ceramic aperture. This
small aperture acted as an effective point source of light,
which was collimated by lens L2 (spherical, f.l. ¼ 75 mm),
resulting in a Gaussian spatial energy distribution of the laser
beam. The beam was coupled into the fiber by lens L3 (a
microscope objective with effective f.l. ¼ 24.5 mm,
FIG. 3. (Color online) Chamber schematic: The laser beam is incident from
the top of the machine such that the vertical IVDF can be measured. The silicon substrate was supported by a ceramic chuck with an embedded RF electrode referenced to the grounded chamber walls. The laser radiation
transmitted from the Laser Room by the optical fiber is collimated into a 1
cm diameter beam by lens L1. Beam splitter BS1 splits a portion of the
beam into a laser energy meter. The beam passes through a quartz vacuum
window on the top of the chamber and strikes the wafer at normal incidence
to measure the vertical (z component) of the IVDF. The CCD camera is
carefully aligned such that its line of sight grazes the surface of the wafer,
allowing LIF measurement down to 1 mm above the wafer surface. The fluorescence light passes through another quartz window on the side of the
chamber, and is focused onto the CCD detector by a standard F=1.4 camera
lens L2. F1 is a narrow (1 nm bandwidth) interference filter centered on the
fluorescence wavelength of 461 nm to block background plasma light and
scattered laser radiation.
Phys. Plasmas 18, 053503 (2011)
NA ¼ 0.10). The 30 m long (200 lm core diameter) multimode optical fiber transmitted the laser radiation to the etch
tool (located in the Plasma Processing Lab, down the hall
from the Laser Room). A Gaussian intensity profile is ideal
for uniformly filling a multimode optical fiber: this was necessary when operating near the damage threshold of the fiber.
The Intevac Corporation donated a state of the art
plasma etch tool for processing industry-standard 30 cm diameter silicon wafer substrates for use in this experiment.
The chamber (see Fig. 3) was approximately cylindrical,
with a maximum inside diameter of 55 cm and a height of 40
cm. The experimental bulk plasma was produced by a low
frequency (600 kHz, 425 W) inductively coupled plasma
(ICP) discharge. A higher frequency (2.2 MHz, 1.6 kW)
capacitively coupled RF bias was applied simultaneously
through a metal electrode inside a ceramic support structure
holding the substrate; the vacuum chamber walls served as
the path for currents to return to ground.
The RF bias voltage was measured at the base of the
electrode assembly; the peak-to-peak amplitude was 1282 V.
As there are measured stray impedances in the RF bias feedthrough and electrode assembly (see Fig. 4), a deembedding
procedure44 was performed to extract the actual voltage at
the substrate surface; this yielded a sheath voltage peak-topeak amplitude of 1152 V.
Argon (80%) and oxygen (20%) were fed into the chamber, with a fill pressure of 0.5 mTorr. Oxygen was added to
the argon discharge to prevent the deposition of opaque films
on the vacuum windows. The LIF signal was reduced by less
than 22% by the presence of oxygen, and its presence was
neglected in the Bohm velocity calculations.
The collimated laser beam (1 cm diameter) passed
through the top window, striking the substrate at normal
FIG. 4. Circuit diagram of the RF bias circuit and hardware connections. A
2.2 MHz low impedance RF supply45 transmits power through a resonant
tank circuit. The RF voltage VRF and current IRF are monitored after the tank
circuit. The connections leading up to the capacitive plasma applicator have
an effective inductance LHW. The series capacitances of the RF electrode
embedded in the ceramic chuck and the wafer itself were calculated from
first principles. The complex plasma impedance was treated as a variable parameter in the circuit analysis.
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053503-5
Temporally resolved ion velocity distribution measurements
Phys. Plasmas 18, 053503 (2011)
FIG. 5. Timing and triggering diagram
showing the equipment and connections
used to phase lock the laser pulse to the
RF waveform, as well as to synchronize
the CCD camera exposure gate to the
laser (and thus the LIF signal).
incidence, 7.5 cm from its center. Fluorescence light from
the illuminated plasma passed through a narrow (Dk ¼ 1 nm)
band-pass interference filter to a fast (sexposure 3ns) 14 bit
CCD camera (Cooke Corporation DiCam-Pro). Each pixel in
the 320 640 camera images corresponded to an area of 354
lm 88.5 lm within the imaged plane, as verified by photographing a target probe of known dimensions. The laser
pulse was phase-locked to the RF bias waveform with a timing jitter of about 9% of the period (tjitter 40 ns) and LIF
data were taken at eight different phases. A transverse spatial
average across the fluorescing region (horizontal extent
dx 1cm) was taken at each position above the substrate
and 1000 CCD images were taken at each laser wavelength
to improve the signal-to-noise ratio of the diagnostic. The
laser step size was 0.001 nm, and scan range was from 611.3
to 611.6 nm (300 steps).
The YAG laser operates at a 10 Hz pulse repetition rate,
and requires its flash lamps to fire approximately 210 ls
before the Q-Switch opens and fires the 3 ns laser pulse. The
timing jitter in the actual firing of the laser pulse with respect
to the Q-switch input trigger is about 40 ns and is limited by
the internal laser electronics. Figure 5 shows a diagram of
the timing=triggering setup for phase locking the laser pulse
to the bias waveform.
The experiment’s 10 Hz signal is generated by the internal clock of the PG1 Pulse=Delay generator. One channel
sends a pulse to fire the YAG flash lamps with no delay, and
210 ls later, a second channel sends a pulse to the gate of a
custom-built RF phase lock module. A calibrated transformer on the output terminal of the RF bias source acts as a
bias current monitor, and provides the 2.2 MHz RF signal to
the phase lock module. The phase lock module produces a
voltage pulse on the first rising zero-crossing of the RF
waveform after the gate signal arrives. This phase-locked
output pulse triggers another Pulse=Delay Generator PG2.
PG2 triggers both the YAG Q-Switch and the CCD camera. In order to have as short an exposure as possible and
exclude unnecessary background plasma light, the camera
exposure and the arrival of the LIF laser pulse need to be
synchronized within just a few nanoseconds. The path delays
of the Q-Switch trigger cable and optical fiber (about 30 m
each) combined with the internal electronic delays of the
YAG laser and the CCD camera complicated this synchronization. In order to verify timing, a ceramic tipped probe was
inserted into the chamber, with the tip in the camera’s field
of view and intersecting the laser beam to scatter the laser
light. The unfiltered camera was set to a 3 ns exposure and
the relative delay between the Q-switch trigger and CCD
camera trigger was adjusted on PG2 until scattered laser light
was observed by the camera (the camera’s gain and numerical aperture were set very low to avoid image sensor damage). In this manner, an ideal Q-Switch=CCD camera delay
of 60 ns was found. With this delay fixed, the timing of the
laser=camera was adjusted to scan the RF waveform. The
triggering setup is illustrated in Fig. 6.
Timing was monitored on a digital oscilloscope. The RF
bias monitor signal was acquired on one channel, with the
CCD gate (exposure) signal on another. Finally, the laser
pulse was monitored by a fast, unbiased photodiode (risetime
1 ns) looking at scattered laser light. The oscilloscope was
set to “Analog Persist” mode, and triggered by the CCD gate
signal. The laser pulse was found to lie reliably within a 40
ns time window 60 ns after the camera gate signal. The phasing of the RF signal was also found to be stable at each delay
setting of PG2 (Fig. 7).
In order to have high confidence in the dye laser wavelength tuning, it was necessary to perform an absolute wavelength calibration with an iodine vapor cell during each of
the LIF scans. Molecular iodine vapor is an excellent calibration medium, due to its dense spectrum of strong absorbance
lines in the visible range;26 several lines occur over the
standard LIF scan wavelength range.
A LABVIEW program was created to coordinate the LIF
data acquisition with by the CCD camera, the dye laser
wavelength tuning, and the iodine calibration system.
Langmuir probes were inserted into the bulk plasma to
measure an electron temperature Te ¼ 1.6 eV, a plasma potential Vp ¼ 5.4 V, and a bulk plasma density n0 ¼ 6.9 1010
cm3. The calculated Bohm velocity46 or sound speed of the
system was uB ¼ cs ¼ 1.93 km=s (the Bohm criterion states
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053503-6
Jacobs et al.
Phys. Plasmas 18, 053503 (2011)
FIG. 8. Bulk plasma electron temperature Te vs time t afer ICP power
turn-off (solid curve). Data were taken with a swept (ssweep ¼ 2 ls). Langmuir probe at several times in the plasma discharge after-glow. The dashed
cuve is an exponential fit to the decaying electron temperature. Extrapolation of the fit to t ¼ 0, gives the electron temperature during an ICP pulse
to be Te 1.6 eV.
FIG. 6. Timing and triggering graph illustrating how the 10 Hz YAG laser
output and camera exposure gate are phase-locked to the 2.2 MHz bias
waveform. PG1 is internally triggered at 10 Hz, acting as the clock for the
experiment. PG1 outputs a trigger to the YAG flash lamps, and then a 100
ls long gate signal to the phase lock unit. The phase lock unit gets a continuous RF bias signal from the bias current monitor. Upon receiving the gate
signal, the phase lock unit will output a trigger pulse upon the next rising
zero-crossing of the RF waveform. This output pulse triggers PG2, phaselocking it to the RF waveform. PG2 can be adjusted to select the RF phase
at which the LIF envelope occurs.
that the average ion velocity reaches this value at the sheath
edge, independent of the RF bias phase6,47). Typical bulk ion
temperatures measured by LIF (at low laser power) were
Ti ¼ 0.21 eV.
A Langmuir probe was used to characterize the plasma
discharge. During the operation of the ICP power supply, RF
radiation at 600 kHz and various harmonics was picked up
by the Langmuir probe circuitry, interfering with measurement of Te. The ICP source was observed to modulate the
plasma potential Vp as well. These effects interfered with the
measurement of the bulk, time-averaged plasma parameters
with swept Langmuir probes. RF-compensation48 of Langmuir probes is typically employed to avoid these problems,
but for this work we used a different technique. The ICP RF
and Bias RF were modulated off and measurements taken
during the plasma decay period (often called the plasma af-
FIG. 7. (Color online) Oscilloscope traces showing RF phase locking of
laser pulses, horizontal divisions are 100 ns for a total displayed time of 1
ls. The oscilloscope was operated in analog persist mode: over 1000 overlapping data acquisitions are shown. The three different channels are the RF
bias current monitor, the photodiode signal (laser pulses), and the camera
gate signal. The actual CCD exposure (and, therefore, laser pulse envelope)
is delayed 60 ns from the gate signal. Laser pulses arrive within a time envelope 40 ns wide, in a well-defined phase interval of the 2.2 MHz RF
waveform.
ter-glow). Measured temperature and density were then extrapolated back to the plasma pulse. Figure 8 shows a graph
of the electron temperature after the turn-off of the 600 kHz
ICP power supply with no RF bias power. The electron temperature was calculated from the I-V characteristic curve of
each sweep at various times in the after-glow. For this measurement, the probe tip (3.18 mm diameter tantalum disk)
location was 14 cm above the center of the substrate, in the
bulk plasma.
Extrapolation of an exponential fit of Te to t ¼ 0, the
time of the ICP power supply turn-off, indicates that the
electron temperature during the ICP plasma discharge (and,
therefore, during the LIF measurements described later in
this chapter) was Te 1:6 eV. Due to the rapidly falling
electron temperature after the ICP turn-off, there is an uncertainty in this estimate for electron temperature of 60.2 eV.
Using this value for Te, the calculated ion transit time (from
the formula given by Barnes et al.13) is ion sion 130 ns,
giving sion =sRF 0:3.
Ion saturation current was collected with another Langmuir probe at various locations in the plasma to measure
bulk and presheath plasma density n ni ne . The ion saturation probe collection tip consisted of a single-sided tantalum disk 4.75 mm in diameter. The tip was always oriented
such that the disk was parallel to the substrate; the “bottom”
side of the disk was insulated from the plasma by vacuum
epoxy. The probe tip was mounted to a thin (3 mm diameter)
ceramic shaft that penetrated the plasma, which was in turn
mounted to a long stainless steel shaft. The stainless steel
shaft entered the chamber wall through an o-ring sealed vacuum feedthrough. The tantalum disk was connected in series
with a 100 kX resistor and a dc bias source (Vprobe ¼ 45 V
with respect to chamber ground). Ion saturation current was
measured by monitoring the voltage across the resistor.
Figure 9 shows density measured by ion saturation current in a vertical scan above the substrate (radial position
r ¼ 7 cm from center of substrate). Figure 10 shows density
measurements taken in a radial scan across the substrate surface at vertical position z ¼ 3 cm above the substrate. Data
were acquired at our normal plasma operating conditions
with an RF bias during the plasma discharge. The
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053503-7
Temporally resolved ion velocity distribution measurements
Phys. Plasmas 18, 053503 (2011)
FIG. 9. Ion density ni as a function of height z above the substrate as measured by a Langmuir probe biased to collect ion saturation current
(Vbias ¼ 45 V). Data were taken at a radial position r ¼ 7 cm from the center of the 30 cm diameter substrate.
measurement was averaged over several thousands of ICP
periods. The ion saturation measurements were considerably
less sensitive to the RF interference than the swept probe
measurements. Similar density profiles (not shown) were
measured without an RF bias. The densities measured in Fig.
9 were used to provide an absolute density calibration for the
LIF diagnostic.
FIG. 11. Camera images with laser wavelength tuned (a) far from resonance
k0 and (b) on resonance k0. Background images are subtracted from each
frame (a) is dark, indicating the low noise level within the wings of the LIF
distribution and the very small ion population with v ¼ 60 km=s; (b) shows a
large fluorescence signal from ions with v ¼ 0 km=s.
All LIF data collected for this work were obtained with
the laser beam oriented along the z-axis (vertically); and
therefore, all velocities v are the z-components of the 3D velocity ~
v.
With the laser tuned far from the rest ion resonance frequency k0, no fluorescence signal was detected (the ion population is vanishingly small for v > 60 km=s), but a constant
background of 461 nm radiation from the plasma was
detected. Averaging 50 camera images with no LIF signal
gave a “background image” of the plasma which was subtracted from every camera image of the scan. Figure 11
shows camera images with this background image subtracted; two frames are shown: the first is with the laser
wavelength kL far from k0, and the second with the laser
tuned to the rest ion resonance, kL ¼ k0.
LIF data were taken at eight different phases of the 2.2
MHz RF waveform (RF period 455 ns). Each phase-
resolved measurement had a time resolution of 40 ns, or
less than one-eighth of the total RF period. The definition of
each phase interval is shown in Fig. 12; phase 0 is taken to
be the phase at which the sheath voltage is most negative.
Two sample ion velocity distributions obtained by LIF
are shown in Fig. 13. Both IVDFs were taken at the same
phase (p=2 as defined by Fig. 12): high above the substrate,
at z ¼ 42 mm, the IVDF is Gaussian and centered about
v ¼ 0. In contrast, at z ¼ 1.06 mm in the sheath, large ion
drifts are present and the distribution is very nonGaussian.
Transforming the ion distribution function from velocity
space to energy space gives the ion energy distribution.
Although the current LIF data are phase-resolved, many theories and other experiments present time-averaged IEDs.
Time-averaged, bimodal IEDs with sharp edges (small tails)
have been reported from experiments9–12,49 and from theoretical models.2,5,9,10,12–14,50 For comparison, the time-averaged IED obtained by LIF is shown in Fig. 14 for the lowest
point of observation, z ¼ 1.06 mm. The bimodal distribution
FIG. 10. Ion density ni as a function of radial position r across the 30 cm diameter substrate as measured by a Langmuir probe biased to collect ion saturation current (Vbias ¼ 45 V). Data were taken at a vertical position z ¼ 3
cm above the 30 cm diameter substrate. Fill pressure was 0.5 mTorr.
FIG. 12. Phase reference diagram. One cycle of the RF sheath voltage
waveform is shown. Ions experience a maximum attractive force toward the
substrate at the time when the voltage is most negative (phase 0).
IV. LIF DATA
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053503-8
Jacobs et al.
Phys. Plasmas 18, 053503 (2011)
FIG. 15. Collection of vertical IVDFs measured by LIF at z ¼ 42 mm.
FIG. 13. Time-resolved normalized IVDFs at phase p=2 (see Fig. 12)
acquired by LIF at two different heights above the substrate surface:
z ¼ 1.06 mm (dashed curve) and z ¼ 42 mm (solid curve).
is fairly sharp on the low-energy side, but has a long, gentle
tail on the high energy side. A sharp peak on the high energy
side, if present, may be located closer than 1 mm to the substrate; this is in a region where the fast ion detection by LIF
is problematic for two reasons. First, the ion density is
reduced due to conservation of their time-averaged flux: as
they accelerate, their number density is depleted to below
the threshold of measurement in this experiment. Second,
finite LIF transition time effects make observation of the
fastest ions even less likely due to the fact that their residence time in the final millimeters of the sheath is so short.
Figure 15 shows a family of vertical IVDFs taken in the
bulk plasma, at z ¼ 42 mm above the substrate. All eight
phases of LIF data are shown. The IVDFs are independent of
the RF phase as the bias voltages do not penetrate far into
the presheath region.47
Figure 16 shows a family of IVDFs taken at z ¼ 1.06
mm above the substrate. The shape of the IVDFs depend
strongly on the RF phase; the observation of very high
energy ions (p=4 and p=2) is delayed by about a quarter of
the RF period from the phase of maximum ion acceleration
(the most negative sheath potential). This has been predicted
by Bose et al.5 to be due to the ion inertia.
Figure 17 shows four 3D surface contours of IVDF’s;
each contour shows the data taken at a different phase of the
RF bias.
Figure 17(a) shows LIF data acquired at phase 0, when
the RF sheath voltage magnitude is maximum. Here, large
ion velocities in excess of 33 km=s (227 eV) are observed
and there is a significant ion density at the lowest point of
measurement, z 1 mm above the substrate. This indicates
that there is a large ion flux to the substrate at this time.
Figure 17(b) shows LIF data acquired at phase p=2
when the RF sheath voltage magnitude is decreasing from its
greatest value. At this phase, ion velocities in excess of 45
km=s (or 423 eV) are observed, and the ion density is still
large near the substrate. This results in a large ion flux at this
phase.
Figure 17(c) shows LIF data acquired at phase p, when
the RF sheath voltage is near zero (see Fig. 12). Here, ions
reach only moderate velocites (less than 23 km=s or 110
eV). Additionally, the ion density is quite low near the substrate, resulting in a small ion flux at this phase.
Figure 17(d) shows LIF data acquired at phase 3p=2,
when the RF sheath voltage magnitude is increasing from
near zero; however, ions still reach only moderate velocities
(less than 20 km=s or 84 eV) at the lowest point of observation, z 1 mm above the substrate surface and the ion density is still low near the substrate.
A great deal of plasma information may be extractedfrom the IVDF fi(v, z). The ion flux is defined as
ð
(4)
Ci ¼ vfi ðvÞdv:
Several authors5–8 have predicted that the applied RF
bias will modulate the ion flux to the substrate, a behavior
FIG. 14. Time-averaged vertical ion energy distribution measured by LIF at
z ¼ 1.06 mm. The energy spltting of the two peaks is DEi ¼ 380 eV at this
location. The expected DEi at z ¼ 0, the substrate surface is 1100 V.
FIG. 16. Collection of IVDFs measured by LIF at z ¼ 1.06 mm.
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Temporally resolved ion velocity distribution measurements
Phys. Plasmas 18, 053503 (2011)
this is in accord with the assumption that the sheath is collisionless.2 The phase lag between maximum ion acceleration
(most negative sheath voltage drop) and the observation of
the highest energy ions (corresponding to observation of
large flow velocities and heat fluxes) is consistent with the
lag expected from theories accounting for transit time
effects. Bose et al.5 calculated the phase lag between the
maximum ion flux to the wafer and the most negative RF
bias voltage (phase 0). The important parameters in their
model are sion=sRF and eVs0 =kTe (Vs0 is the time-averaged
sheath voltage drop); the model gives a phase shift of 0.3p
radians for this experiment. The largest ion flow velocity
was observed at phase p=4; the largest ion flux at the lowest
measurement position (1 mm above substrate) occurs
between phases p=4 and p=2. Bose et al. suggested modification of Miller and Riley’s unified sheath model51 to account
for the modulation of ion flux throughout the sheath during
an RF cycle.
The ion flow velocity (average ion velocity) may also be
calculated from the IVDF,
Ð
Ð
vfi ðvÞdv
vfi ðvÞdv
:
(5)
ui ¼ Ð
¼
ni
fi ðvÞdv
FIG. 17. (Color) 3D surface plots of IVDF as a function of height above the
substrate taken at four phases (see Fig. 12). The white line at z ¼ s ¼ 3.6 mm
shows the location of the sheath boundary.
that was clearly observed in this experiment. Figure 18
shows ion flux profiles above the substrate calculated from
LIF data. In the lower 1 mm of the sheath (not observed with
LIF), we expect differences between the fluxes at various
phases to increase, resulting in an approximately sinusoidally
modulated ion current at the substrate surface. The calculated Bohm flux at the sheath edge, CB ¼ nsuB where ns is the
ion density, was 3:7 1013 m2 s1 , in agreement with the
time-averaged ion flux in the sheath measured by LIF,
Ci ¼ 4:3 6 0:8 1013 m2 s1 . Additionally, the time-averaged ion flux is approximately constant in the sheath region;
FIG. 18. Vertical ion flux (Ci) vs height (z) above the substrate. (a) The flux
at various times in the first half of an RF period and (b) the second. Flux profiles for all eight phases and the time-averaged flux profile (bold curve) is
shown in both panels. The time-averaged flux profile is approximately flat
throughout the sheath region (z < 3.6 mm), as expected from ion continuity
in a collisionless sheath. The broken horizontal line indicates the value of
the calculated Bohm flux CB ¼ ns uB ¼ 3:7 1013 m2 s1 . The observed
position of the sheath edge z ¼ s 3.6 mm is shown.
In this manner, the ion flow velocity was calculated
from the LIF data as a function of position for each of the
eight phases, as shown in Fig. 19. At phases 0 – 3p=4, Fig.
19(a), all flow velocites are large within the sheath, but there
is significant variation in the flow profiles throughout this RF
half-cycle. In contrast, at phases p – 7p=4, the flow profiles
are very similar, even within the lower region of the sheath
[Fig. 19(b)]. The horizontal line shows the Bohm velocity
uB ¼ 1.93 km=s, which intersects the time-averaged flow velocity at z 3.6 mm (60.09 mm, the pixel size); this is taken
to be the location of the presheath=sheath edge.1,47
The total heat flux as a function of height above the wafer may also be calculated from the IVDF (electrons contribute negilibly to the heat flux due to their low mass):
ð
(6)
Q ¼ Mi v3 fi ðvÞdv:
Profiles of heat flux (directed toward the substrate) are
shown in Fig. 20. The time-average heat flux is approximately linear with height in the lower sheath region. Extrapolating the time-averaged heat flux profile to the substrate
surface at z ¼ 0, the value is 16.8 kW=m2. Assuming a
FIG. 19. Vertical ion flow velocity ui vs height z above the substrate. Profiles at all eight phases are shown as well as the time-average (bold curve).
A horizontal line indicates the Bohm speed uB ¼ 1.93 km=s. The position of
the observed sheath edge z ¼ s 3.6 mm is shown.
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053503-10
Jacobs et al.
Phys. Plasmas 18, 053503 (2011)
FIG. 20. Vertical heat flux Q vs height z above the substrate. Profiles at all
eight phases are shown as well as the time-average (bold curve). The position of the observed sheath edge z ¼ s 3.6 mm is shown.
constant flux across the 300 mm diameter substrate, the total
heat flux to the substrate is Q ¼ 1.2 kW compared to the total
input bias power of 1.6 kW. Note that, because of these
power levels, the semiconductor plasma processing industry
uses sophisticated substrate cooling techniques to maintain
desired substrate temperatures.
V. DISCUSSION
In this work, large changes in the structure of the IVDF
within the sheath were observed as a function of time during
the 2.2 MHz RF cycle. The finite time period required (8.5
ns) for LIF excitation and decay25 of the argon ions resulted
in skewed IVDFs close the substrate surface. This would
have the effect of reducing the measured high-energy (highvelocity) portion of the ion distribution compared to the true
ion distribution. An approximate limit on the maximum ion
velocity, vmax, which can be observed with an LIF diagnostic
having a fluorescence decay time of s12 at a distance d above
a substrate is
vmax d
:
s12
(7)
Note that this is not a strict equality as the population of ions
in excited state 1 decay exponentially to state 2 after excitation with a time constant of s12.
The most energetic ions were observed shortly after the
time of maximum ion acceleration (the time when the RF
sheath potential was most negative), highlighting the importance of ion transit time effects. This phase lag was found to
be consistent with theory.5 The ion flux to the substrate was
observed to peak between p=4 and p=2 radians after the
phase of maximum ion acceleration, in agreement with the
predicted value of 0.3p radians. The time-averaged ion flux
Ci ¼ 4:3 6 0:8 1013 m2 s1 was near the value of the
calculated Bohm flux CB ¼ 3:7 1013 m2 s1 and approximately constant in the sheath region; this is in accord with
the assumption that the sheath is collisionless at this
pressure.2
The observed sheath width of s ¼ 3.6 mm was in accord
with theory presented in Ref. 51, which predicts s ¼ 3.1 mm.
Additionally, the position of the sheath edge was found to be
invariant with the RF phase, as predicted by Riemann47 as
well as Xiang and Waelbroeck6 in this frequency regime.
Characteristic double-peaked (bimodal) time-averaged
ion energy distributions were observed in the sheath in this
experiment, consistent with previous work.2,5,9–14,49,50 The
LIF diagnostic was unable to measure within the lowest 1
mm of the sheath (z < 1 mm); however, the maximum energy
splitting of the two peaks of the IED, DEi ¼ 380 eV, was
observed at the lowest point of measurement, z ¼ 1.06 mm.
This value for the splitting was considerably lower than
some estimates of expected energy splitting at the substrate
surface of DEi ¼ 1100 eV.15 The sheath electric field is greatest near the substrate;52 therefore, it is not unreasonable for
the bulk of the energy spread (60%) to develop in the lowest 30% of the sheath. The low-energy portion of the timeaveraged IED was primarily due to ions at phases when the
RF voltage magnitude was low (phases p – 7p=4): these ions
will gain only a modest amount of additional energy in the
remaining 1 mm of the sheath. The high-energy portion of
the IED was primarily due to ions at phases when the RF
voltage was very negative; these ions will gain a significant
amount of energy as they traverse the last 1 mm of the
sheath.
Plasma etch processes depend crictically on the power
absorbed by the substrate and the substrate temperature;53
the extreme modulation of the heat flux by the RF bias suggests that etching and other plasma enhanced chemical processes are similarly modulated.
ACKNOWLEDGMENTS
This research was supported by the State of California
and Intevac Corporation under the California MICRO program, grant no. 05-080 and is currently supported by the
NSF. The work was performed at the UCLA Basic Plasma
Science Facility, which is funded by the Department of
Energy and the National Science Foundation under a cooperative agreement. We would like to thank the Intevac Corporation for the donation of the plasma etch tool as well as
technical support. We also acknowledge the expert technical
assistance of Zoltan Lucky, Marvin Drandell, and Mio
Nakamoto; and would like to thank Mark Kushner for helpful discussions relating to this work.
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