Ion energy distribution function measurements by laser-induced
fluorescence in a dual radio frequency sheath
Nathaniel B. Moore,a) Walter Gekelman, and Patrick Pribyl
Basic Plasma Science Facility, University of California, Los Angeles, 1000 Veteran Ave., Los Angeles,
California 90095
(Received 13 October 2015; accepted 21 December 2015; published 5 February 2016)
Ion dynamics are investigated in a dual frequency radio frequency sheath as a function of radius
above a 30 cm diameter biased silicon wafer in an industrial inductively coupled (440 kHz, 500 W)
plasma etch tool. Ion velocity distribution (IVD) function measurements in the argon plasma are
taken using laser induced fluorescence. Planar sheets of laser light enter the chamber both parallel
and perpendicular to the surface of the wafer in order to measure both parallel and perpendicular
IVDs at thousands of spatial positions. A fast (30 ns exposure) charge coupled device camera
measures the resulting fluorescence with a spatial resolution of 0.4 mm. The dual-frequency bias on
the wafer is comprised of a 2 MHz low frequency (LF) bias and a 19 MHz high frequency bias. The
laser is phase locked to the LF bias and IVD measurements are taken at several different LF phases.
Ion energy distribution (IED) function measurements and calculated moments are compared for
several cases. IEDs were measured at two disparate phases of the phase-locked LF bias. IEDs were
found to be multipeaked and were well-approximated by a sum of Maxwellian distributions. The
calculated fluxes in the dual frequency case were found to be substantially more radially uniform
than the single frequency bias case. For industrial applications, this radially uniform ion flux is eviC 2016 American
dently a trade off with the undesirable multipeaked structure in the IEDs. V
Vacuum Society. [http://dx.doi.org/10.1116/1.4941069]
I. INTRODUCTION
Plasmas are used extensively in several of the processes
in the fabrication of microelectronic devices. One such process, ion etching, typically utilizes radio frequency (rf) biasing of the substrate in order to accelerate ions in the plasma
to bombard the substrate at high energies. The region of the
plasma where these ions experience the largest acceleration
is a narrow (millimeter to submillimeter) region above the
surface of the wafer called the sheath. The acceleration in
this region will largely determine the ion energies, flux, and
angle of impact at the surface of the substrate.1 These parameters are critical in determining etch selectivity, etch rates,
and etch anisotropy. The control of these parameters is thus
important in achieving high quality etching. Unfortunately,
ions in the sheath are difficult to study directly using traditional probe diagnostic techniques due to the size of the
sheath and its transient nature caused by the rf biasing.
Furthermore, analytic studies prove extremely difficult due
to the highly nonlinear physics of the sheath.
Several experimental and computational studies have
investigated ion properties in plasmas with single frequency
rf sheaths.2–25 Ion energy distribution functions (IED) have
been found to be extremely dependent on the ratio of the
bias frequency to the ion transit frequency, xrf =xion . The
time-averaged IEDs are found to be bimodal, with the separation between the peaks, DEi , dependent on bias frequency
regime.1 For low frequency (LF) biases ðxrf =xion 1Þ, the
ions traverse the sheath more rapidly than the sheath potential changes. This results in a broad IED. The sheath is
a)
Electronic mail: moore@physics.ucla.edu
021303-1 J. Vac. Sci. Technol. A 34(2), Mar/Apr 2016
essentially an ensemble of dc sheaths and can be modeled
using the Child-Langmuir law.1 Conversely, for high frequency biases (xrf =xion 1Þ, ions respond to the timeaveraged potential and the peaks in the IED converge
(DEi ! 0), resulting in a monoenergetic distribution.
With a single frequency rf bias, however, it is difficult
to achieve independent control of the ion energies and
flux.1 Many novel bias configurations have been investigated in order to solve this issue and achieve greater control of the ion energy and angular distribution functions.
For example, one such technique is to use nonsinusoidal
waveforms to bias the substrate.12 Studies into these bias
configurations have included slow voltage ramps,26 pulsed
dc bursts,27 tailored waveforms calculated using computation techniques.9 Pulsed plasmas have also been investigated as a method of controlling ion energy distribution
functions.2,28
One of the most widely used methods to attempt to control the ion energy distribution function in the sheath is to
use a dual frequency bias.1,12 By using both a LF and high
frequency bias together, it can be possible to achieve independent control of the ion energy and flux.29–31 In such a
configuration, the goal is that the LF power controls the ion
energy while the high frequency (HF) controls the ion density, and hence the ion flux bombarding the surface of the
wafer or substrate.1 Several experiments performed till date,
however, have shown some degree of coupling between high
and LF biases and hence some coupling between the ion
energies and flux.32–35
Most investigations into dual frequency sheaths have
been computational.30,31,36,37 Kim et al.30 developed an analytic model for dual frequency sheaths using an effective
0734-2101/2016/34(2)/021303/9/$30.00
C 2016 American Vacuum Society
V
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021303-2 Moore, Gekelman, and Pribyl: IED function measurements
frequency and compared the results to particle-in-cell (PIC)
simulations. Using the approximation of an effective frequency, the authors obtained several other effective plasma
parameters, such as plasma density, plasma potential, and
particle currents. The authors also found that the reduction in
the size of the bulk plasma due to expansion of the sheath
can be significant and needs to be taken into consideration.
Boyle et al.31 used a PIC simulation to show that is possible
to achieve independent control of the ion energy and flux in
a capacitively coupled plasma (CCP) reactor by using two
frequencies that are sufficiently different. However, for their
simulations, in order for this independent control to be
achieved, the sheath size must be comparable to the size of
the bulk plasma. These conditions are not typical for etch
tools. Kim and Lee38 confirmed this assertion as they found
that with a larger bulk plasma size (20 times larger than
the sheath), the plasma density increases with LF power
rather than decreasing.
Investigations of the ion energy distribution in a dual frequency sheath have also been performed using computational techniques.7,37 Lee et al.7 performed PIC simulations
to calculate IEDs, plasma potential, self-bias, and densities
in a CCP reactor. The authors found the IED to be multipeaked. With increasing LF voltage, the shape of the IEDs
changed such that the peaks in the distribution smoothed out.
The sheath width, plasma potential, and self-bias also
increased with increased LF voltage while the plasma density decreased. Zhang et al.37 used a hybrid model to calculate ion energy and angular distributions in a CCP reactor.
The authors found the IEDs to be bimodal and multipeaked
in between. The relative heights of the bimodal peaks, and
hence the ion flux, could be controlled by changing the input
high frequency power. The authors also investigated effects
from changing the relative phases between the low and high
frequency powers. They found that by alternating between
disparate phases in the high frequency power, the smaller
peaks between the broad bimodal peaks were smoothed out.
Several experimental investigations into dual frequency
sheaths have also been performed.32,33,35,39,40 Booth et al.32
measured electron density and ion flux in a 50 mTorr Ar/O2
CCP using a hairpin resonator probe and ion flux probe,
respectively. Measurements were taken in the bulk plasma at
several combinations of 2 and 27 MHz bias powers. The
investigators found that both electron density and ion flux
increased with both increasing low and high frequency
power and the ratio of the two to be relatively constant. This
demonstrated that the plasma density and flux can still be
strongly coupled to the LF bias in a dual frequency bias configuration. The authors also speculated that the effect from
the LF power could be caused by enhanced ionization caused
by secondary electron emission from the oxidized silicon
wafer. As there is oxygen present in the plasma, the surface
of the silicon wafer will oxidize to SiO2, which has a much
larger (16 times) secondary electron yield than Si.41
Electron density measurements have been performed in
the plasma bulk in dual frequency CCP reactors by using rf
compensated Langmuir probes.33,34 Yuan et al.34 found in a
plasma driven with 60/13.56 MHz biases, at lower pressures
021303-2
(10 mTorr), the electron density did not change appreciably
with varying LF power, suggesting that independent control
of the ion energy and flux can be achieved in these conditions. At higher pressures (30–100 mTorr), this was not the
case as increasing the LF power also increased the plasma
density. Measurements performed by Ahn and Chang33 in a
2/27.12 MHz dual frequency capacitive discharge were consistent with these results, because at higher pressures (50 and
300 mTorr), increasing the 2 MHz power simultaneously
increased the electron density.
Liu et al.35 measured argon and oxygen ion energy distribution functions on a grounded electrode in a dual frequency CCP using an energy resolved mass spectrometer.
The authors investigated the dependence of the bimodal
shape of the IED on a LF bias frequency and power. The
measurements showed a strong dependence of the high
energy peak on frequency and power. As the frequency of
the LF bias increased, the separation between the two
peaks of the distribution decreased as the high energy
peak approached the lower energy peak. The low energy
peak remained at relatively the same energy, corresponding to approximately the floating potential, at all frequencies. The size of the peak increased with frequency,
suggesting that the sheath remains collapsed for a longer
time. The opposite dependence was observed with increasing bias power.
In the work described in this article, direct measurements
of ion velocity distributions (IVDs) in a dual frequency (2.2
and 19 MHz) rf sheath are described. The measurements are
taken using planar laser-induced-fluorescence (LIF) in a commercial inductively coupled plasma (ICP) sustained in an Ar/
O2 gas mixtures of a few mTorr pressure with the dual frequency rf bias on the substrate. IVDs are measured from the
bulk plasma, into the presheath and through the sheath. The
biases used in this experiment place this experiment in the intermediate regime, x2 MHz =xion ¼ 0:5, x2 MHz =xion ¼ 0:76,
and x19 MHz =xion ¼ 5:5. The results are compared to measurements taken previously25 above a single frequency biased
wafer in the same etch tool.
II. EXPERIMENT
A. LIF diagnostic
Laser-induced fluorescence is a noninvasive plasma
diagnostic that has been used to measure various ion and
plasma properties, such as densities, drift velocities, and
energy distribution functions.42–44 By using cylindrical
optics, a planar sheet of laser light can be produced to measure these quantities at multiple spatial positions simultaneously. Of interest to the fabrication of microelectronic
devices, LIF has been used to measure ion properties within
dc and rf sheaths.22,45–54 LIF-dip, a two-step LIF process,
has also been used to measure the electric field within an rf
sheath.55,56
The particular scheme used in this experiment uses the
3d0 2G9/2–4p0 7F7/2 transition in argon, shown in Fig. 1. In
this scheme, a metastable ion state (state 1, 3d0 2G9/2)
absorbs a 611.492 nm (2 eV) photon to transition to an
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021303-3 Moore, Gekelman, and Pribyl: IED function measurements
021303-3
FIG. 1. (Color online) Groatian diagram of the LIF scheme used for this
experiment. Argon ions in the metastable state 3d0 2G9/2 are pumped to an
excited state 4p0 2F7/2 by using a tunable dye laser. The excited state will either radiatively relax to the original state or to a new state, 4s0 2D5/2. This
relaxation will result in a fluorescing photon which can be detected by, for
example, a CCD camera.
excited state (state 2, 4p0 7F7/2). State 2 is extremely short
lived (on the order of nanosecond) and will radiatively relax
to the original state 1 or to a new state 3 (4s0 2D5/2). In this
process, a photon corresponding to the energy transition will
be emitted. The 461 nm photon emitted from the state 1 to
state 3 transition is the desired LIF signal. This signal can be
measured by using an imaging device, such as a CCD camera, with an appropriate narrow band-pass 461 nm filter to
mask out the laser pump beam and any light from background radiation. The measured signal will be proportional
to the metastable ion (state 1) density, which well represents
the ground state density.57
By probing the metastable state with a range of laser frequencies (such as with a tunable dye laser), it is possible to
measure the ion velocity distribution function. From the
frame of reference of the ion, the incident laser light will be
Doppler shifted by amount dependent on the ion of the velocity. By using the Doppler equation 2pD ¼ 2pðL 0 Þ
¼~
v ~
k ¼ k k, where L is the laser frequency, 0 is the excitation frequency, ~
v is the ion velocity, and ~
k is the laser
wavevector, one can solve for the ion velocity component
parallel to the incident laser light. By scanning over a range
of laser frequencies, one can thus obtain the ion velocity distribution function.
B. Experimental setup
The plasma source (Fig. 2) used in this experiment is a
modified commercial ICP reactor donated by the Intevac
Corp. The chamber is approximately cylindrical with a diameter of 50 cm and a height of 40 cm. Windows and ports
have been added to chamber sides for the purpose of diagnostics. The ICP coils are situated on top of the chamber and
secured onto a ceramic in a “top hat” configuration. The
coils are driven at 440 kHz at 500 W continuous wave. Gas
is fed in through the top of the chamber via gas inlets in an
FIG. 2. Schematic of the inductively coupled plasma chamber. A dual frequency (2 and 19 MHz) bias was applied to the wafer at the bottom of the
chamber via an electrostatic chuck.
aluminum top. An Ar/O2 gas (80% Ar, 20% O2) is used at a
0.6 mTorr fill pressure. Oxygen is added to the argon gas primarily as an in situ cleaning method. The sputtering of silicon was found to quickly coat the chamber windows and
interfere with optical measurements. The added oxygen
reacts with the sputtered silicon forming quartz allowing the
quartz windows to remain transparent for the CCD camera
measurements. In addition, the added oxygen better emulates
the electronegative gasses typically used in processing plasmas. The fill pressure is artificially lower than what is typically used in industry (10–100 mTorr) as higher pressures
would result in neutral quenching of the metastable ions and
hinder LIF data acquisition. The bulk plasma parameters
were measured using a Langmuir probe. For these measurements the plasma was pulsed and measurements taken in the
afterglow 50 ls after shutoff. This was determined to be a
short enough time that plasma parameters did not change
appreciably. For this study, Te 2 eV (dTe/Te 0.3) and
ni 2 1010 cm3 (dn/n 0.35).
A 30 cm diameter silicon wafer was electrostatically
clamped to the chuck located at the bottom of the chamber.
The wafer was surrounded by a dielectric focus ring. LIF
measurements were taken over a volume of the outer 4 cm of
the wafer and from the surface to 3 cm above the surface.
Measurements focused on the outer edge of the wafer in
order to observe any potential radial variation in the energy
distribution functions and calculated moments.
The wafer bias was powered by a 2.2 MHz and a tunable
10–20 MHz source. In order to reduce the wafer etch rate,
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021303-4 Moore, Gekelman, and Pribyl: IED function measurements
the bias was operated at a 10% (10 ms on) duty cycle.
Measurements were taken during the last 1 ms of the bias.
This was sufficiently long enough for the bias waveform to
stabilize. A function generator output sinusoidal voltage
waveforms at 10 ms pulse duration (10% of the experiment
repetition rate) to the tunable high frequency source. This
output was amplified to the kilowatt level, and in this setup,
maximum power transfer to the pedestal was found to occur
at 19 MHz driving frequency. Peak to peak voltage at maximum power (1930 W) was measured to be 600 V at the base
of the pedestal. The 2.2 MHz source was fixed and output a
peak power of 1960 W at 2500 V peak to peak. A separate
tank circuit was constructed for each bias individually. The
rf power was delivered to the chuck via a low inductance
(10 nH) copper tube.
For the LIF scheme outlined previously, a tunable Sirah
Cobra-Stretch dye laser was used to probe wavelengths
around the 611.492 nm excitation. The laser was pumped by a
Spectra Physics Quanta-Ray Nd:YAG laser frequency
doubled to 532 nm. The laser repetition rate was 10 Hz with
each pulse lasting 10 ns with an energy of 450 mJ. The dye
used was a mixture of Rhodamine B and Rhodamine 101,
resulting in a pulse energy of 80 mJ per pulse. The dye laser
bandwidth, measured by a Fabry-Perot interferometer, was
Dk ¼ 1.36 103 nm.48 Glan-Thompson polarizers were
used to reduce the laser power to 200 lJ per pulse so as to
not damage the fiber optic cable that delivered the laser beam
to the processing chamber. The laser power (104 kW/m2
entering the reactor per laser pulse) was measured at the
reactor-side of the fiber optic cable. This laser intensity is
large enough that power broadening, which has been shown
to occur at intensities of <103 kW/m2 for low temperature
ions, will greatly affect the width of the observed spectra.53
The implications of this broadening are addressed in the
experimental results. For each data run, the laser wavelength
was stepped form 611.250 to 611.750 nm using 1 pm increments. The laser wavelength was monitored continuously
using a high precision High Finesse wavelength meter
accurate to within 0.5 pm (or in units of ion velocity, to within
3 102 m/s).
The beam exiting the fiber on the reactor side was collimated onto a planoconvex lens by aspherical lens. Two cylindrical lenses were then used in order to create a planar
sheet of laser light that allowed fluorescence to be measured
at thousands of spatial positions simultaneously. The laser
sheet entered the chamber through a rectangular window
located at the top of the machine. The beam was oriented
perpendicular to the surface of the wafer in order to measure
the perpendicular velocity component of the ions traversing
the sheath. Laser light reflected from the surface of the wafer
will also contribute to the observed LIF signal corresponding
to ions directed away from the sheath and toward the plasma
bulk. These data were not considered, and only results from
the ions moving toward the wafer are presented.
The LIF measurements were taken using a fast (30 ns exposure), 12 bit DiCam-Pro Intensified CCD camera, which
recorded images 1280 pixels wide by 1056 pixels tall. The
camera was centered vertically along the top edge of the
021303-4
wafer and was positioned to capture the fluorescence above
the outer 10 cm of the wafer. Images were averaged over
1000 shots and 2 2 pixel bins twice, once by the acquisition software and again before the final analysis resulting in
a final resolution of 320 256 pixels. The absolute spatial
calibration was performed by imaging an aluminum plate
with gridded with 1 1 cm squares, which was placed in the
laser path inside the plasma chamber. The resulting spatial
resolution for each pixel was 0.4 0.4 mm.
The repetition rate of the experiment was 10 Hz. Timings
are shown in Fig. 3. Both the 2 and 19 MHz sources are triggered simultaneously (at t ¼ 0) and are on for 10 ms. The
laser flash lamps and a phase lock are triggered at t ¼ 9 ms.
The phase lock receives a signal from the 2 MHz bias and
outputs a trigger once the voltage waveform undergoes a
zero-crossing. This allows the laser Q-switch to be phase
locked to the LF bias. The Q-switch timing is variable,
depending on the desired LF bias phase for LIF measurements. The camera is triggered 500 ns after the Q-switch
fires.
A photodiode was used to observe the laser light immediately before the laser sheet entered the plasma chamber. The
phase calibration was performed by comparing the photodiode signal with the measured waveform. The phase could
be adjusted by changing the delay between the phase lock
and the laser Q-switch.
III. EXPERIMENTAL RESULTS
A. IED measurements
The voltage delivered to the wafer was measured at the
base of the copper pedestal using a resistive voltage divider.
A network analyzer was used to measure the frequency
response of the voltage divider to ensure voltage measurements in the desired 2–19 MHz frequency range were correct. These results showed the response to be comparable to
a dc signal, as desired. During a separate single frequency
operation, the calibrated peak-to-peak voltage measurements
of the 2 MHz bias were measured to be 2500 V and the
19 MHz to be 900 V. During dual frequency operation, the
high frequency voltage remained at 900 V while the 2 MHz
component of the measured voltage dropped to 1900 V.
FIG. 3. Timing diagram for the experiment. Shown are rf ON gate pulses and
the laser and camera timings.
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021303-5 Moore, Gekelman, and Pribyl: IED function measurements
The 2 MHz bias was phase-locked to the laser Q-switch.
Phase-locking the experiment to the 2 MHz bias resulted in a
time-averaged 19 MHz voltage added to the LF bias, the
upper and lower bounds of which are shown along with the
filtered 2 MHz. LIF measurements were taken at two disparate phases of the LF rf cycle, denoted by ULF ¼ p and
ULF ¼ 0, corresponding to the most negative (ULF ¼ p) and
least negative (ULF ¼ 0) phases. Due to the highly asymmetric geometry of the capacitive discharge and the blocking capacitor, the dc self-bias across the sheath is approximately
half of the applied peak-to-peak voltage. In other words, the
maximum potential drop across the sheath would be approximately 2800 V with a dc bias of 1400 V.
Using the Child sheath approximation,58 the calculated
sheath widths of the low and high frequency sheath separately are sLF ¼ 7.8 mm and sHF ¼ 4.5 mm, where sLF is the
LF sheath width and sHF is the high frequency sheath width.
The sheath width is thus controlled primarily by the LF bias.
As the LF bias is phase-locked in this experiment, the sheath
front during data acquisition can be thought of as slowly
moving LF sheath with oscillations due to the high frequency time-averaged sheath.
The ion transit parameters for the two biases are
x2MHz =xion ¼ 0:76 for the LF bias and x19MHz =xion ¼
5:5.12 This places the lower frequency sheath in the intermediate frequency (xrf =xion 1) regime, meaning the sheath
will change substantially as the ion traverses the region. The
19 MHz sheath is closer to the high frequency approximation
(xrf =xion 1), but still low enough that the phase at which
the ion enters the sheath is important to the evolution of the
ion energies through the sheath.
For previous experiments in this plasma chamber,22,25 a
deconvolution algorithm was used to obtain the IVD from
the broadened LIF measurements. For this experiment, however, a deconvolution was not performed. Measurements of
cold ions in the plasma bulk show power broadening of
20 eV. The observed distributions in this experiment had
peak widths ranging from 150 to 400 eV, corresponding to
uncertainties in the peak widths of 13% and 5%, respectively. Furthermore, peaks less than 20 eV in width and
spaced by less than this amount thus cannot be resolved.
This broadening is acceptable for this study as the location
of the peak centers in the IEDs is of much more interest than
the width of the peaks. The LIF signal corresponding to the
high energy ions was sufficiently small such that the deconvolution algorithm would suppress the high energy peaks
and leave only the central peak corresponding to the cold
ions. The decrease in LIF signal for this experiment can be
explained by a lower bulk plasma density (26% lower than
in previous experiments) and lower densities of high energy
ions within the sheath due to the substantially larger bias voltages. From flux conservation, larger ion velocities will
result in a corresponding drop in the ion density. This lower
density will in turn result in a lower LIF signal at higher
velocities.
Ion energy distribution functions at a height of 0.8 mm
for the phase ULF ¼ p are shown in Fig. 4(a). Measurements
are shown only up to 2000 eV as the LIF signal was
021303-5
FIG. 4. (Color online) Comparison of distribution functions (normalized to
the distribution maxima) at a height of 0.8 mm for two different radial positions for the (a) ULF ¼ p phase and (b) ULF ¼ 0 phase. The peak corresponding to the cold ions (a relative height of 2 and peaked near 10 eV) was
fit to a Maxwellian and subtracted out to emphasize the remaining fast ions.
unreliable above this point due to the aforementioned
decrease in ion densities. The energy distribution functions
shown are normalized to the maximum of each distribution.
A large low energy peak at 20 eV was well observed in the
ion energy distributions into the sheath. This peak was
removed to further emphasize the high energy ions responsible for etching. The large low energy peak could result from
ionization or charge exchange within the sheath. While the
mean free path for collisions exceeds the sheath width, a
small number of charge exchange collisions are still possible. At a distance of r ¼ 13 cm, the density 4 mm above the
wafer was observed to about 6% of the plasma bulk. Using
the measured sheath width and the ion charge exchange
mean free path kce ¼ 6:7 cm, we estimate the proportion of
collided ion flux to be 5.7%.1 This is consistent with the
observed density. Booth et al. have also observed enhanced
ionization near a silicon wafer in a 50 mTorr Ar/O2 plasma,
possibly due to SiO2 secondary electron emission from oxygen ions bombarding the wafer.32 Secondary emission is not
likely to be significant in this experiment, however, as the
fill pressure is much lower. As such, the electron ionization
mean free path is 1 m. Contributions from charge exchange
are on the order of ten times larger than the contributions
from second electron ionization collisions. Toward the edge
of the sheath, the distribution function is comparatively flat
and higher energy peaks emerge as the ions approach the wafer surface. The observed peaks are rather broad, which can
partially be attributed to the aforementioned broadening of
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021303-6 Moore, Gekelman, and Pribyl: IED function measurements
the LIF measurement. Notably, the ion energy distribution
functions close to the surface of the wafer are multipeaked.
If there is ionization within the sheath, these peaks would
arise due to the rf modulation of the high frequency bias, as
described in Wild and Koidl.23 The number of high frequency periods that an ion would experience as it traverses
the sheath is given by the ratio of the ion transit time across
the expanded LF sheath to the period of the high frequency
bias. This ratio is 6.6, meaning that we would expect to see
up to six peaks in the distribution function. As measurements in this experiment were not reliable up to the
expected maximum energy of 2950 eV, it is not certain if
the observed results agree completely with the theoretical
prediction. Additional peaks above 2000 eV could be
present.
A comparison of the IEDs in Fig. 4(a) at two different radial positions (r ¼ 12.1 and r ¼ 14.6 cm) show differences
between the IED peaks in the two cases. Similar peaks such
as those seen closer to the midwafer are observed in the distribution function at the wafer edge, including the multipeaked structure. The location of the peaks is similar to
those observed at the smaller radial position.
Distribution function measurements for the collapsed
sheath phase (ULF ¼ 0) for two different radii are shown at
the same height of 0.8 mm in Fig. 4(b). For this less negatively biased phase, fewer high energy ions are observed as
compared to the ULF ¼ p phase. The multipeak structure
observed in the expanded sheath case is also not present for
this case. If the peaks are caused by rf modulation from the
higher frequency source, fewer peaks would be expected in
this phase. A smaller sheath width would result in a shorter
ion transit time across the sheath and thus an ion would experience fewer cycles of the high frequency bias. This would
result in few peaks in the energy distribution function. The
cold peak was once again removed.
For a purely high frequency sheath, one would expect to
see a single peak in the distribution function corresponding
to the time-averaged potential drop across the sheath. In this
experiment, that would correspond to an energy peak around
450 eV. Closer to the intermediate frequency regime, a bimodal structure would be expected. Broadening of the LIF
signal, however, might prevent resolution of the peak separation. As LF bias is also present, the value of the peak
energy will change depending on the sheath potential for
this particular phase. It is difficult to determine the exact
effect from the LF bias in this experiment, however, as
the sheath is changing substantially as the ion traverses
the sheath. Single peaks are observed in the distribution
function at 450 eV at the wafer edge and approximately
600 eV more toward midwafer. These values agree with
the expectation of a peak near the time-averaged value of
the 19 MHz bias. The larger energy toward the midwafer
suggests a more significant contribution from the changing sheath width and potential as compared to larger radial positions.
After removal of the cold central peak, the remaining
peaks in the distribution functions are very well approximated by the sum of several Maxwellian distributions
021303-6
centered around different velocities. The ion velocity distribution functions for both the midwafer and wafer edge case
presented in Fig. 4(a) were each fit to a sum of four
Maxwellian distribution functions. The resulting ion energy
distributions are shown in Figs. 5 and 6. In Figs. 5(a) and
6(a), the sum of the Maxwellian fits are shown to compare
favorably with the measured data. The IEDs corresponding
to the four separate ion energies are shown in Figs. 5(b) and
6(b) along with the overall sum. For the midwafer case (Fig.
5), the four peaks were centered at 110, 370, 780, and
1600 eV. Energies at the wafer edge were larger (Fig. 6),
with peaks centered at 130, 610, 1030, and 1800 eV. It is difficult to say whether any individual peak is due solely to any
specific bias as opposed to the combination of the two. A
single peak might be expected near 2350 eV corresponding
to the 1900 V peak-to-peak 2 MHz bias in addition to the
450 V time-averaged 19 MHz. Measurements did not extend
to this energy range, however.
B. Calculated ion density and flux
Integrating the ion distribution functions over all measured velocities yields
the spatial dependence of the ion denÐ
sity (nðr; z; tÞ ¼ f ðr; z; vz ; tÞdvz ), as shown in Fig. 7. For
these calculations, data corresponding to ions moving away
from the wafer surface were once again ignored as it was not
possible to distinguish between an ion moving upwards and
fluorescence resulting from reflected light off the surface of
the wafer. The data presented are normalized to maximum
density of the three separate cases (ULF ¼ p, ULF ¼ 0, and
FIG. 5. (Color online) (a) Comparison of the measured IED (normalized to
the distribution maximum) at height of 0.8 mm at midwafer to a fit comprised of the sum of four Maxwellian distributions at 110, 370, 780, and
1600 eV and (b) the individual Maxwellian fits.
J. Vac. Sci. Technol. A, Vol. 34, No. 2, Mar/Apr 2016
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021303-7 Moore, Gekelman, and Pribyl: IED function measurements
021303-7
FIG. 6. (Color online) (a) Comparison of the measured IED (normalized to
the distribution maximum) at height of 0.8 mm at the wafer edge to a fit
comprised of the sum of four Maxwellian distributions at 130, 610, 1030,
and 1800 eV and (b) the individual Maxwellian fits.
unbiased), approximately 2 1010 cm3. The bulk plasma
density was the same for each case. For the dual frequency
ULF ¼ p (expanded sheath) phase shown in Fig. 7(a), the
density is shown to be highly radially nonuniform. At the
wafer edge, densities are a factor of two lower than those
seen toward the middle of the wafer. This trend continues
even several centimeters above the wafer, well outside the
sheath region. Densities for the dual frequency ULF ¼ 0 (collapsed sheath) case are shown in Fig. 7(b) and compared
with measurements from a case with a single frequency bias
[Fig. 7(c)] and an unbiased case [Fig. 7(d)]. The densities for
the latter three cases are essentially the same and are much
more radially uniform than the dual frequency expanded
sheath (ULF ¼ p) case. This discrepancy in radial uniformity
could possibly be due to effects from ponderomotive forces.
By approximating the amplitude of the electric field from the
sheath potential drop, the ponderomotive potential from the
1900 V 2 MHz bias was approximately 180 V. Using this
potential, the ratio of the energy stored in the ponderomotive
electric field to the thermal energy of the ions, E2 =nkT, is
approximately 5. This suggests that one would expect this
electric field to move the density outward. The effects from
the ponderomotive potential due to the 2 MHz bias are substantially larger than the effects from the high frequency bias
(a ponderomotive potential of a few volts). The ponderomotive potential in the dual frequency case is also approximately twice as large as the potential from the single
FIG. 7. (Color) Calculated densities for the (a) ULF ¼ p, (b) ULF ¼ 0, (c) single frequency (2 MHz only) U2 MHz ¼ p, and (d) unbiased cases (linear
scale). In Figs. 6(a) and 6(b), both biases are present. The densities in the
expanded sheath case (ULF ¼ p) of dual frequency operation were found to
be comparatively more radially nonuniform than the other cases with lower
densities observed toward the wafer edge.
frequency case where a 650 V bias was used. The gradient
of the electric field would also be most pronounced near the
edge of the wafer, which is consistent with the shape of the
density profile. Zhang et al.37 have reported similar measured and computed density radial profiles in a capacitively
coupled device. Densities were radially uniform with a single high frequency (60 MHz) bias, but the addition of a LF
bias resulted in a decreased plasma density toward the wafer
edge.
Ð
Calculated fluxes (Ci ðr; z; tÞ ¼ vz f ðr; z; vz ; tÞdvz ) are
shown for the two phases ULF ¼ p and ULF ¼ 0 in Fig. 8 as
a function of radial position and height above the wafer. The
calculated ion flux from measurements taken at the time of
the most negative phase of a single frequency bias experiment is also shown for comparison. In the dual frequency
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021303-8 Moore, Gekelman, and Pribyl: IED function measurements
FIG. 8. (Color) Spatial variation of the ion flux directed to the surface of the
wafer for the (a) dual frequency expanded sheath (ULF ¼ p), (b) dual frequency collapsed sheath (ULF ¼ 0), and (c) single frequency (2 MHz only)
U2 MHz ¼ p cases. The observed ion flux during dual frequency operation
was substantially more radially uniform than in the single frequency case.
expanded sheath case, the flux increases as the ions move
from the plasma bulk toward the presheath. As the ions
approach the sheath, the flux reaches a maximum and
remains relatively constant through the sheath and to the surface of the wafer. Fluxes observed in the dual frequency collapsed sheath case are much lower, as expected. The flux in
this case is relatively constant in the presheath and decreases
as the ion traverse the sheath toward the wafer, in contrast to
the dual frequency expanded sheath ULF ¼ p phase. In both
cases, the flux was seen to be relatively radially uniform,
which would be desired for processing plasmas. This is in
stark contrast to observations made during a single frequency operation. The ion fluxes observed under these conditions were extremely nonradially uniform, as shown in
Fig. 8(c).
IV. SUMMARY AND CONCLUSIONS
Planar laser-induced fluorescence has been used to measure the ion velocity distribution functions above a dual rf biased silicon wafer in an industrial plasma etch tool.
Measurements were phase locked to the 2 MHz LF bias
while the 19 MHz high frequency bias was time-averaged.
Multipeaked IEDs were observed in the sheath for the most
strongly biased phase. While the exact locations of the peaks
021303-8
varied with radius across the surface of the wafer, the overall
structure was similar. These results and the number of peaks
are consistent with other experiments and simulations.23,37
For a disparate collapsed sheath phase of the 2 MHz bias, the
measured IEDs exhibited few peaks. One peak roughly corresponded to the time-average of the high frequency bias
with the exact position again depending on the radial
position.
Densities, velocities, and ion fluxes were calculated from
the measured IVDs. The radial dependence of the ion density
differed substantially between the two phases investigated.
For the strongly biased LF case, the density was highly dependent on the radial position with densities decreasing substantially toward the wafer edge. This decrease in ion
density was not observed in the disparate low bias phase
where the density was relatively radially uniform and similar
to the density profile above an unbiased wafer. These trends
are consistent with other experiments and simulations.37
Velocity profiles exhibited less radial variation, though mean
velocities at the edge of the wafer were observed to be
slightly larger. A comparison of the maximum velocity
measured in the two phases is consistent with the expectations, given the peak-to-peak voltage of the applied biases.
Ion fluxes showed no strong radial dependence, a characteristic which would be desired in an industrial setting. This is
in stark contrast to the single frequency case where measured
fluxes were extremely radially nonuniform. Uniformity in
the flux would provide a more uniform etch radially across
the wafer. It appears that for this dual frequency case, the
desired uniformity in the flux is a trade off with the potentially undesirable multipeaked structure observed in the ion
energy distribution functions.
The results from this study have provided insight into the
ion dynamics within both a single and dual rf sheath in an
industrial etch tool. Such results are important to both the
improvement of existing processing techniques and the validation of simulations and models. A comparison of the experimental results with results from computer simulations
can help to improve the underlying models, which can then
in turn be used to help guide further progress in processing
techniques.
ACKNOWLEDGMENTS
This work was performed at the UCLA Basic Plasma
Science Facility and was supported by the National Science
Foundation PHY-1004203. The authors would like to thank
Mark Kushner for his advice and guidance, Zoltan Lucky,
Marvin Drandell, and Tai Ly for their technical assistance,
and the Intevac Corporation for donation of the plasma etch
tool.
1
M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Discharges
and Materials Processing (Wiley, Hoboken, NJ, 2005).
2
D. J. Economou, J. Vac. Sci. Technol., A 31, 050823 (2013).
3
A. Metze, D. W. Ernie, and H. J. Oskam, J. Appl. Phys. 60, 3081 (1986).
4
M. S. Barnes, J. C. Forster, and J. H. Keller, IEEE Trans. Plasma Sci. 19,
240 (1991).
5
D. B. Graves and M. J. Kushner, J. Vac. Sci. Technol., A 21, S152 (2003).
J. Vac. Sci. Technol. A, Vol. 34, No. 2, Mar/Apr 2016
Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. IP: 128.97.43.39 On: Fri, 05 Feb 2016 18:38:29
021303-9 Moore, Gekelman, and Pribyl: IED function measurements
6
V. Georgieva, A. Bogaerts, and R. Gijbels, Phys. Rev. E 69, 026406
(2004).
7
J. K. Lee, O. V. Manuilenko, N. Y. Babaeva, H. C. Kim, and J. W. Shon,
Plasma Sources Sci. Technol. 14, 89 (2005).
8
Z. Q. Guan, Z. L. Dai, and Y. N. Wang, Phys. Plasmas 12, 123502
(2005).
9
A. Agarwal and M. J. Kushner, J. Vac. Sci. Technol., A 23, 1440 (2005).
10
A. Agarwal, P. J. Stout, S. Banna, S. Rauf, K. Tokashiki, J.-Y. Lee, and K.
Collins, J. Appl. Phys. 106, 103305 (2009).
11
P. Benoit-Cattin and L.-C. Bernard, J. Appl. Phys. 39, 5723 (1968).
12
E. Kawamura, V. Vahedi, M. A. Lieberman, and C. K. Birdsall, Plasma
Sources Sci. Technol. 8, R45 (1999).
13
T. Panagopoulos and D. J. Economou, J. Appl. Phys. 85, 3435 (1999).
14
J. W. Coburn and E. Kay, J. Appl. Phys. 43, 4965 (1972).
15
K. Kohler, D. E. Horne, and J. W. Coburn, J Appl. Phys. 58, 3350 (1985).
16
A. D. Kuypers and H. J. Hopman, J. Appl. Phys. 67, 1229 (1990).
17
A. Manenschijn, G. C. A. M. Jannssen, E. van der Drift, and S. Radelaar,
J. Appl. Phys. 69, 1253 (1991).
18
M. A. Sobelewski, J. K. Olthoff, and Y. Wang, J Appl. Phys. 85, 3966
(1999).
19
M. A. Sobelewski, J. Appl. Phys. 95, 4593 (2004).
20
J. R. Woodworth, M. E. Riley, P. A. Miller, G. A. Hebner, and T. W.
Hamilton, J. Appl. Phys. 81, 5950 (1997).
21
J. R. Woodworth, I. C. Abraham, M. E. Riley, P. A. Miller, T. W.
Hamilton, B. P. Aragon, R. J. Shul, and C. G. Wilson, J. Vac. Sci.
Technol., A 20, 873 (2002).
22
B. Jacobs, W. Gekelman, P. Pribyl, and M. Barnes, Phys. Rev. Lett. 105,
075001 (2010).
23
C. Wild and P. Koidl, J. Appl. Phys. 69, 2909 (1991).
24
E. A. Edelberg and E. S. Aydil, J. Appl. Phys. 86, 4799 (1999).
25
N. B. Moore, W. Gekelman, P. Pribyl, Y. Zhang, and M. J. Kushner, Phys.
Plasmas 20, 083506 (2013).
26
S.-B. Wang and A. E. Wendt, J. Appl. Phys. 88, 643 (2000).
27
E. V. Barnat and T.-M. Lu, J. Appl. Phys. 92, 2984 (2002).
28
L. Xu, D. J. Economou, V. M. Donnelly, and P. Ruchhoeft, Appl. Phys.
Lett. 87, 041502 (2005).
29
M. A. Lieberman, J. Kim, J. P. Booth, P. Chabert, J. M. Rax, and M. M.
Turner, SEMI Technology Symposium, SEMICON Korea, Seoul, Korea,
22 January 2003 (2003), pp. 31–37.
30
H. C. Kim, J. K. Lee, and J. W. Shon, Phys. Plasmas 10, 4545 (2003).
31
P. C. Boyle, A. R. Ellingboe, and M. M. Turner, J. Phys. D: Appl. Phys.
37, 697 (2004).
32
J. P. Booth, G. Curley, D. Marić, and P. Chabert, Plasma Sources Sci.
Technol. 19, 015005 (2010).
021303-9
33
S. K. Ahn and H. Y. Chang, Appl. Phys. Lett. 95, 111502 (2009).
Q. H. Yuan, Y. Xin, G. Q. Yin, X. J. Huang, K. Sun, and Z. Y. Ning,
J. Phys. D: Appl. Phys. 41, 205209 (2008).
35
J. Liu, Q.-Z. Zhang, Y.-X. Liu, F. Gao, and Y.-N. Wang, J. Phys. D: Appl.
Phys. 46 235202 (2013).
36
E. Kawamura, M. A. Lieberman, and A. J. Lichtenberg, Phys. Plasmas 13,
053506 (2006).
37
Y. Zhang, M. J. Kushner, S. Sriraman, A. Marakhtanov, J. Holland, and A.
Paterson, J. Vac. Sci. Technol., A 33, 031302 (2015).
38
H. C. Kim and J. K. Lee, Phys. Rev. Lett. 93, 085003 (2004).
39
T. Gans, J. Schulze, D. O’Connell, U. Czarnetzki, R. Faulkner, A. R.
Ellingboe, and M. M. Turner, Appl. Phys. Lett. 89, 261502 (2006).
40
A. Ushakov, V. Volynets, S. Jeong, D. Sung, Y. Ihm, J. Woo, and M. Han,
J. Vac. Sci. Technol., A 26, 1198 (2008).
41
K. Wittmaack, Surf. Sci. 419, 249 (1999).
42
R. A. Stern and J. A. Johnson, Phys. Rev. Lett. 34, 1548 (1975).
43
D. D. Burgess and C. H. Skinner, J. Phys. B 7, L297 (1974).
44
D. N. Hill, S. Fornaca, and M. G. Wickham, Rev. Sci. Instrum. 54, 309
(1983).
45
N. Sadeghi, M. van de Griff, D. Vander, G. M. W. Kroesen, and F. J. de
Hoog, Appl. Phys. Lett. 70, 835 (1997).
46
L. Oksuz, M. Atta Khedr, and N. Hershkowitz, Phys. Plasmas 8, 1729
(2001).
47
N. Claire, G. Bachet, U. Stroth, and F. Doveil, Phys. Plasmas 13, 062103
(2006).
48
B. Jacobs, W. Gekelman, P. Pribyl, M. Barnes, and M. Kilgore, Appl.
Phys. Lett. 91, 161505 (2007).
49
D. C. Zimmerman, R. McWilliams, and D. A. Edrich, Plasma Sources Sci.
Technol. 14, 581 (2005).
50
D. Lee, H. Hershkowitz, and G. Severn, Phys. Plasmas 15, 083503 (2008).
51
R. McWilliams, J. P. Booth, E. A. Hudson, J. Thomas, and D.
Zimmerman, Thin Solid Films 515, 4860 (2007).
52
M. J. Goeckner, J. Goree, and T. E. Sheridan, Phys. Fluids B 4, 1663
(1992).
53
M. J. Goeckner and J. Goree, J. Vac. Sci. Technol., A 7, 977 (1989).
54
S. Jun, H. Y. Chang, and R. McWilliams, Phys. Plasmas 13, 052512
(2006).
55
E. V. Barnat and G. A. Hebner, Appl. Phys. Lett. 85, 3393 (2004).
56
E. V. Barnat, P. A. Miller, G. A. Hebner, A. M. Paterson, T.
Panagopoulos, E. Hammond, and J. Holland, Plasma Sources Sci.
Technol. 16, 330 (2007).
57
M. J. Goeckner, J. Goree, and T. E. Sheridan, Phys. Fluids B 3, 2913
(1991).
58
C. D. Child, Phys. Rev. (Ser. I) 32, 492 (1911).
34
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Redistribution subject to AVS license or copyright; see http://scitation.aip.org/termsconditions. IP: 128.97.43.39 On: Fri, 05 Feb 2016 18:38:29