Control of Ion Energy Distributions
on Plasma Electrodes
P. Diomede, D. J. Economou and V. M. Donnelly
Plasma Processing Laboratory, University of Houston
DOE Plasma Science Center Teleseminar, February 8, 2013
1
Outline
• Introduction/Motivation
• 3 Methods to control IEDs on plasma electrodes
• PIC-MCC simulations and comparisons with
experiments
• Model for rapid calculation of IED and comparisons
with experiments
• Conclusions
2
Introduction / Motivation
• Control of the energy of ions bombarding a substrate is
important for both plasma etching and PECVD.
• The ion energy must be high enough to drive anisotropic
etching, but not too high to induce substrate damage and/or
loss of selectivity.
• As device dimensions keep shrinking, requirements on
selectivity and substrate damage become ever more
stringent.
• In addition, the ion bombardment energy is critical for
controlling film microstructure and properties in PECVD.
• Such requirements impose strict limits not only on the mean
ion energy but also on the ion energy distribution (IED).
3
IED on an electrode biased with sinusoidal RF voltage
 i 3s M 1 / 2

(
)
 rf
2 2eVs
i/rf <<1  wide (bimodal) IED
i/rf >>1  narrow (single peaked) IED
i = ion transit time through sheath
rf = period of the rf sheath E-field =2/
4
IED for Sinusoidal Sheath Voltage
IEDs on the grounded electrode of a
13.56 MHz Ar CCP at 75 mTorr. Peak
separation is reduced for heavier ions.
Single peak is centered at the DC sheath
voltage. Impurity ions are used to avoid
charge transfer collisions.1
IEDs on the grounded electrode
of an Ar CCP at 50 mTorr. A single
peak is obtained at high enough
frequencies.2
1. J. Coburn and E. Kay, J. Appl. Phys., 43, 4965 (1972).
2. K. Kohler et al., J. Appl. Phys., 58, 3350 (1985).
5
Three principal ways to control IEDs
1. Plasma is generated by independent source power. Apply judicious bias
voltage waveform on the substrate electrode immersed in the plasma.
The substrate bias has minor effects
on the plasma chemistry.
The energy of ions is determined by
the substrate voltage.
The voltage appearing on the face of the
substrate is at a constant negative value
(Vfront), except for small excursions to
positive values to neutralize the charge.
M. A. Wank, R. A. C. M. M. van Swaaij, P. Kudlacek, M.
C. M. van de Sanden, and M. Zeman, J. Appl. Phys.
108, 103304 (2010)
6
Effect of non-sinusoidal bias waveforms on IEDs
Computational investigation by Agarwal
and Kushner using an ICP reactor scale
model.
This voltage waveform on the
substrate is positive during a=10%
of the cycle.
15 mTorr Ar/c-C4F8=75/25 gas mixture.
500 MHz TVW frequency
A. Agarwal and M. J. Kushner, J. Vac. Sci. Technol. A 23, 1440 (2005)
7
Three principal ways to control IEDs
2. Produce the plasma with customized voltage waveforms.
The Electrical Asymmetry Effect
• The Electrical Asymmetry Effect (EAE) provides a new method to control the ion
energy distribution (IED) on plasma electrodes. Importantly, the ion flux can also
be controlled, independently of the ion energy.
• A voltage of the form V (t )  U1 cos(2f1t  q1 )  U 2 cos(2f 2t )
is applied to an electrode of a capacitively-coupled plasma (CCP) reactor, with
f2=2f1. The DC bias (thus the ion energy) can be varied simply by changing the
phase q1.
• Adding higher harmonics enhances the EAE, but implementation becomes
cumbersome.
• A DC bias can be imposed even on a geometrically symmetric system (equal
electrode areas).
8
Control of ion energy distributions using the electrical
asymmetry effect
Measured ion energy distribution functions in a geometrically and electrically
asymmetric discharge at the powered (left) and grounded (right) electrode (Argon, 1
Pa, d = 4 cm, U1 = U2 = 100 V, f1 = 13.56 MHz, f2 = 27.12 MHz).
V (t )  U1 cos(2f1t  q1 )  U 2 cos(2f 2t )
U. Czarnetzki, J. Schulze, E. Schüngel and Z. Donkó, PSST, 20, 024010 (2011)
9
Independent Control of Ion Flux and Ion Energy
V (t )  U1 cos(2f1t  q1 )  U 2 cos(2f 2t )
Mean ion energy and ion flux as a function of q1 in an argon CCP
discharge. 7.5 mTorr, U1=U2=100 V, f1=13.56, f2= 2f1.
As the phase shift q1 is varied, ion energy varies but ion flux
remains almost constant.
U. Czarnetzki, J. Schulze, E. Schüngel and Z. Donkó, PSST, 20, 024010 (2011)
10
Gaussian Voltage Pulses
Gaussian voltage pulses (repetition
frequency of 13.56 MHz) of the form
V( t )  V0 exp[ a( t  t0 )2 ]
D  2 ln 2 / a
V0 = voltage amplitude
t0 = time of pulse max, D = FWHM
IED depends on
FWHM (D) of
applied voltage
T. Lafleur and J. P. Booth, J. Phys. D: Appl. Phys., 45, 395203 (2012)
11
Three principal ways to control IEDs
3. Apply synchronous bias on boundary electrode during
afterglow of pulsed plasma
Boundary Electrode
Boundary Voltage
Bias ON
Plasma
Power
Plasma
ON
OFF
For a grounded conductive substrate, the sheath
voltage is equal to the plasma potential.
Substrate
12
Te and Vp during a pulse
Time-resolved Langmuir probe measurements
ON
4.0
16
OFF
14
3.5
12
10
2.5
Vp(V)
Te(eV)
3.0
2.0
1.5
8
6
1.0
4
0.5
2
0.0
0
10 20 30 40 50 60 70 80 90 100
time (s)
0
0
10
20
30
40
50
60
70
80
90 100
time (s)
• Te is hardly affected by the application of the DC bias, while Vp is raised.
• The spread in the energy of ions entering the sheath scales with Te.1
1. K.-U. Riemann, Phys. Fluids 24 2163 (1981)
13
13
Time-Averaged Ion Energy Distribution
IEDs in pulsed Ar ICP with synchronous DC bias
voltage applied to the boundary electrode
0.05
Separation of the
peaks can be tuned
by DC bias value
and pressure.
0.04
Narrow IED can be
achieved in the
afterglow.
0.03
0.02
Full width at half
maximum (FWHM)
of the IED ranges
from 1.7 to 2.4 eV.
Ar press. (mTorr):
7
0.01
14
50 28
0.00
0
4
8
12
16
20
24
28
32
Energy (eV)
H. Shin, W. Zhu, L. Xu, D. J. Economou and V. M. Donnelly, PSST, 20 055001 (2011).
14
IEDs in pulsed Ar ICP with different synchronous DC bias
voltages applied to the boundary electrode
• DC Bias applied continuously on the BE.
• Peak at high energy is shifted by the energy
of the applied dc bias for positive biases.
• Low energy peak not detected by the
measurements which discriminate lowenergy ions having a broad angular
distribution.
M. D. Logue, H. Shin, W. Zhu, L. Xu, V. M. Donnelly, D. J. Economou and M. J. Kushner, PSST, 21 065009 (2012)
15
PIC-MCC Simulations
• Simulation of pulsed plasma with
synchronous boundary voltage.
• Comparison with experimental data.
16
Simulation of Pulsed CCP Reactor with DC Bias in Afterglow
• Pulsed plasma is sustained in capacitively coupled plasma (CCP) reactor.
• 50 V DC bias is applied on the upper (boundary) electrode in the afterglow to
modify the IED on the lower (substrate) electrode.
17
Application of DC Bias in the Afterglow of a Pulsed
Plasma
• After plasma power turn off (afterglow), Te and Vp decay rapidly.
• Apply synchronously tailored positive bias voltage Vdc during specified
time window in the afterglow.
• Bias raises plasma potential, modifying the IED on the wafer.
18
PIC simulation of Ar CCP: IED without Bias
Ar plasma, VRF = 300 V, nRF = 13.56 MHz, p = 10 mTorr, d = 6 cm
10 kHz pulse frequency 50% duty ratio
IED for continuous wave (cw)
plasma w/o bias
1.2
1.0
Normalized IED
1.0
Normalized IED
IED for pulsed plasma
(10 kHz, 50% duty cycle) w/o bias
1.2
0.8
0.6
0.4
0.8
0.6
0.4
0.2
0.2
0.0
0.0
0
50
100
150
200
Ion energy (eV)
• Bimodal distribution centered around 1/2 VRF.
• Tail to the left of the main peak due to ionneutral collisions.
• Multiple secondary peaks given by ions
created by CE collisions.
0
50
100
150
200
Ion energy (eV)
• Bimodal IED is retained, originating from
the power ON fraction of the cycle
• New peak appears at very low energies due
to ions bombarding the substrate during the
afterglow.
19
IEDs with Staircase DC Bias Applied in Afterglow
• Afterglow starts at time t = 50 s.
• Additional peaks appear in the IED.
• Peak location can be controlled by the value of the applied bias voltage.
20
IEDs with Staircase DC Bias Applied in Afterglow (2)
Peak strength can be controlled by the duration of the respective DC bias voltage.
The relative strength of the other two peaks can be controlled by the duty ratio.
P. Diomede, V. M. Donnelly and D. J. Economou, J. Appl. Phys., 109, 083302 (2011)
21
EEPF and Electron Density Evolution
2
15
-3
ne (10 m )
3
1
0
0
10
20
30
40
50
60
70
80
90 100
Time (s)
• In the afterglow of pulsed CCP, apply 50 V DC during t = 70-85 s, followed by 300 V DC
during t = 85-100 s.
• EEPF is temporarily heated when the bias is applied but the electron density evolution is
hardly affected.
22
Comparison of PIC Simulation with Experimental Data
11
11
4.0x10
11
Dt = 38 s
3.6x10
simulation
11
3.2x10
Ion flux (a.u.)
IEDF
0.03
4.4x10
Dt = 48 s
50-98s
60-98s
70-98s
80-98s
Dt = 28 s
0.02
Dt = 18 s
0.01
11
2.8x10
11
2.4x10
11
2.0x10
11
1.6x10
11
1.2x10
10
8.0x10
10
4.0x10
0.0
0.00
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Energy (eV)
Energy (eV)
IEDs predicted by the PIC simulation of the afterglow (right) compared to data# (left). The low
energy peak of the data is due to the active glow (not simulated by PIC).
3.0
2.5
Electron temperature in the
afterglow predicted by PIC (line),
compared to data# (points).
Te (eV)
2.0
1.5
1.0
0.5
0.0
30
40
50
60
70
Time (s)
80
90
100
Pulsed Ar plasma, 10 KHz
modulation, 20% duty, 14
mTorr, 120 W average
power, 24.4 V DC bias
applied in afterglow during
time windows shown
above.
# H.
Shin, W. Zhu, L. Xu, D. J. Economou and V. M.
Donnelly, PSST, 20 055001 (2011).
23
Simulation of Pulsed H2 CCP Reactor with DC Bias in Afterglow
The Bari hybrid model for H2 CCPs
Neutral species: fluid model for H atoms and H2(v = 0,…14).
Plasma kinetics: PIC/MCC applied to electrons and four ionic
species (H3+, H2+, H+, H-).
24
Application of DC Bias in the Afterglow of a Pulsed
Plasma
• After plasma power turn off (afterglow), Te and Vp decay rapidly.
• Apply synchronously tailored positive bias voltage Vdc during specified
time window in the afterglow.
• Bias raises plasma potential, modifying the IED on the wafer.
25
Number densities and electron KE Evolution
15
+
H3
mid-plane of the discharge (x = 3 cm)
15
1.0x10
e
14
• Plasma ON (t=0 s): increase approaching
quasi-steady-state values ~ 20 s.
• Plasma OFF (t=50 s): decay throughout
the afterglow .
• H2+ ions disappear after 5 s into the
afterglow.
-
8.0x10
-
H
14
6.0x10
14
4.0x10
+
H2
14
2.0x10
+
H
0.0
0
10 20 30 40 50 60 70 80 90 100
6
time (s)
5
Electron KE (eV)
-3
number density (m )
1.2x10
• Plasma ON (t=0 s): rapidly rise to a peak
early, quasi-steady-state ~ 10 s.
• Plasma OFF (t=50 s): plummet during the
first few s and decay at a much slower rate
later in the afterglow.
• DC bias ON (t=70 s): temporary heating.
4
3
2
1
0
0
10 20 30 40 50 60 70 80 90 100
time (s)
RF ON
RF OFF DC ON
Hydrogen plasma
VRF = 300 V, nRF = 13.56 MHz, p = 50 mTorr
d = 6 cm, 10 kHz pulse, 50% duty ratio
26
IEDs for continuous wave (cw) plasma w/o bias (1)
1.0
simulation
Normalized IED
0.8
Normalized IED
1.0
+
H3
0.6
0.4
0.2
H+
simulation
0.8
0.6
0.4
0.2
0.0
0.0
0
50
100
150
0
Ion energy (eV)
experiment
50
100
150
Ion energy (eV)
H3
+
• Bimodal structure and tail towards lower energies
due to ion-neutral collisions.
• The H+ IED bimodal structure has a wider energy
spread, due to the lower mass of H+.
• Predicted bimodal distribution, with a more
intense peak at lower energy, is close to the
experimental IED for H3+.
H2, VRF = 300 V, nRF = 13.56 MHz, 50 mTorr, 6 cm
Experiments: D. O’Connell et al. Phys. Plasmas 14, 103510 (2007)
27
IEDs for continuous wave (cw) plasma w/o bias (2)
1.0
• H2 IED exhibits multiple peaks,
explained by symmetric charge
exchange collisions during the
sheath collapse.
• Ions thus created experience only
a fraction of amplitude of the
oscillating sheath voltage.
• Computed H2+ IED is in good
agreement with experimental
results.
• The energy dependence of the
acceptance angle of the ion optics
contributes to an artificial
distortion of the IED in the low
energy region.
simulation
+
H2+
Normalized IED
0.8
0.6
0.4
0.2
0.0
0
50
100
150
Ion energy (eV)
experiment
H2+
H2, VRF = 300 V, nRF = 13.56 MHz, 50 mTorr, 6 cm
Experiments: D. O’Connell et al. Phys. Plasmas 14, 103510 (2007)
28
Computed IEDs for pulsed plasma with 50 V DC bias in the
afterglow
+
0.8
0.6
0.4
0.2
+
H2
0.8
0.6
0.4
0.2
0.0
0.0
0
50
100
150
1.0
H
+
0.8
0.6
0.4
0.2
0.0
0
50
100
Ion energy (eV)
0
50
100
150
Ion energy (eV)
Ion energy (eV)
Normalized IED
1.0
H3
Normalized IED
Normalized IED
1.0
150
• Additional peaks appear in the H3+
and H+ IEDs.
• Peak location can be controlled by
the value of the applied bias voltage.
• H2+ disappear in the afterglow due
to the rapid decay of Te.
H2, VRF = 300 V, nRF = 13.56 MHz, 50 mTorr, 6 cm
10 kHz pulse, 50% duty ratio
29
Model for Rapid Calculation of IED
on Electrode in Contact with Plasma
Bulk Plasma (n0, Te)
Sheath
Electrode (Target)
Blocking capacitor, Cb
Applied rf, Vrf
Assumptions: Bulk n0 and Te are not influenced by rf bias.
Sheath is collisionless.
Ion flux at sheath edge is time-independent.
30
Semi-analytic Model
Schematic of the sheath region
Electrode
Sheath
Pre-sheath
Plasma
(bulk)
Id
x
1. Electrode immersed in semi-infinite plasma of
given electron (ion) density and electron
temperature.
2. Electron, ion and displacement currents flow
through the sheath.
3. Non-linear sheath capacitance Cs is calculated
from the electric field at the electrode, E.
n0, Te
Ie
Cs   0 A
Ii
V=VS
V=V1
V=0
E
2n1kTe
0
[exp(
E
Vs
e(Vs  V1 ) Vs
)   2 ]1 / 2
kTe
V1
A. Metze, D. W. Ernie, H. J. Oskam, J. Appl. Phys., 60, 3081 (1986).
P. Miller and M. Riley, J. Appl. Phys., 82, 3689 (1997).
T. Panagopoulos and D. Economou, J. Appl. Phys., 85, 3435 (1999).
31
Equivalent Circuit Model
Vrf
Cb
Subscripts T and G refer to “target” and
“ground” electrodes, respectively.
VT
d
(Vrf  VT )  CT
dt
d
CT (VP  VT )  CG
dt
Cb
CT
IT
VP
IG
CG
Vd  (VT  V p )
dVd

dt
i
d
(VP  VT )  IT  0
dt
d
VP  IT  I G  0
dt
Ions respond to
a “damped” potential Vd
Voltage Vrf is applied through blocking capacitor, Cb.
Given n0, Te, Vrf and Cb, calculate VT , Vp, and Vd.
A. Metze et al., J. Appl. Phys., 60, 3081 (1986).
32
Ion Energy Distribution
Support (y,y+dy)
Vd(t)
t
0
0
2

y+dy
y
dy
1
f ( y) 
2

# of points in 0<t  2
such that
Vd (t )  y
1
dVd
d (t )
f ( y )  IED
Vd  Vd (t )  " damped " sheath voltage
y = ion energy
Sample damped sheath
potential waveform
y  Vd (t )  t  V ( y)
1
d
1
f ( y) 
2

# of points in 0< t  2
such that Vd (t )  y
dVd 1 ( y)
dy
P. Diomede, M. Nikolaou, D. J. Economou, Plasma Sources Sci. Technol., 20, 045011 (2011).
E. Kawamura, V. Vahedi, M.A. Lieberman, C.K. Birdsall, Plasma Sources Sci. Technol., 8, R45 (1999).
33
Comparison of Semi-analytic Model with Experimental Data (1):
Pulsed Argon Plasma with DC bias in the afterglow
1.2
1.2
experiment
model
1.0
0.8
Normalized IED
Normalized IED
1.0
0.6
0.4
0.8
0.6
0.4
0.2
0.2
0.0
0.0
0
5
10
15
20
25
30
0
5
10
15
20
25
30
Ion energy (eV)
Ion energy (eV)
IEDs predicted by the semi-analytic model (right) compared to data# (left).
20
Plasma potential w/o DC bias
predicted by the semi-analytic
model (line), compared to data#
(points).
Vp (V)
15
10
Pulsed Ar plasma, 10 KHz
modulation, 20% duty, 14 mTorr,
120 W average power, 24.4 V DC
bias applied in afterglow during
∆tb = 45-95 µs.
5
# H.
0
0
20
40
60
Time (s)
80
100
Shin, W. Zhu, L. Xu, D. J. Economou and V. M.
Donnelly, PSST, 20 055001 (2011).
34
Comparison of Semi-analytic Model with Experimental Data (2):
Helicon plasma with bias voltage waveform on the substrate
Experimental Target voltage, 500 kHz, ne = 2.6×1016 m-3,
Te = 3eV
X. V. Qin, Y.-H. Ting, and A. E. Wendt, PSST 19 065014
(2010).
Target voltage in the semi-analytic model
(a)
0
-100
-200
-300
(b)
0
Voltage (V)
-100
-200
-300
(c)
0
-100
-200
-300
(d)
0
-100
-200
-300
0
1
2
3
4
5
Time (s)
The simulated voltage waveforms are quite representative of the measured
waveforms except for the “ringing”.
35
Comparison of Semi-analytic Model with Experimental Data (2):
Helicon plasma with bias voltage waveform on the substrate
Experimental Ar+ IEDs
X. V. Qin, Y.-H. Ting, and A. E. Wendt, PSST 19 065014
(2010).
IEDs from the semi-analytic model
1.0
0.8
(a)
0.6
0.4
0.2
Normalized IED
0.0
1.0
(b)
0.8
0.6
0.4
0.2
0.0
1.0
(c)
0.8
0.6
0.4
0.2
0.0
1.0
(d)
0.8
0.6
0.4
0.2
0.0
0
100
200
300
400
Ion energy (eV)
• Predicted peak locations and heights of the IED are in agreement with the measurements.
• The FWHM of the experimental peaks is larger, because of the ringing of the applied voltage
waveforms.
36
Comparison of Semi-analytic Model with Experimental Data (3):
ETP with bias voltage waveform on a dielectric substrate
The substrate bias has minor effects
on the plasma chemistry.
The energy of ions is determined by
the substrate voltage.
The voltage appearing on the face of the
substrate is at a constant negative value
(Vfront), except for small excursions to
positive values to neutralize the charge.
M. A. Wank, R. A. C. M. M. van Swaaij, P. Kudlacek, M.
C. M. van de Sanden, and M. Zeman, J. Appl. Phys.
108, 103304 (2010)
37
Comparison of Semi-analytic Model with Experimental Data (3):
ETP with bias voltage waveform on a dielectric substrate
• Electrode downstream of
expanding thermal hydrogen
plasma (H3+).
• Biased through blocking
capacitor, Cb = 166 pF.
• Vp~0.2 V, Te = 0.15 eV, p =
18 Pa, ne = 2 x 1010 cm-3
Voltage applied
to blocking cap.
Voltage of substrate electrode.
Top figs.: Kudlacek et al.#
Bottom figs.: Semi-analytic
model prediction.
CB = 1.66 nF, AG/AT =25
• The energy peaks location
and the voltage waveform
on substrate electrode are
predicted.
#P. Kudlacek, R. F. Rumphorst and M.C.M. van de Sanden, J. Appl. Phys., 106, 073303 (2009).
38
Comparison of Semi-analytic Model with Experimental Data (4):
Control of IEDs using the electrical asymmetry effect
Measured ion energy distribution functions in a geometrically and electrically
asymmetric dual frequency discharge at the powered (left) and grounded (right)
electrode (Argon, 1 Pa, d = 4 cm, U1 = U2 = 100 V, f1 = 13.56 MHz, f2 = 27.12 MHz).
V (t )  U1 cos(2f1t  q1 )  U 2 cos(2f 2t )
U. Czarnetzki, J. Schulze, E. Schüngel and Z. Donkó, PSST 20, 024010 (2011)
39
Electrical Asymmetry Effect: Semi-Analytic Model Prediction
powered electrode
grounded electrode
0.20
0.08
0.04
0
20
40
60 80 100 120 140 160
Ion energy (eV)
re
eg
(d
q
1
q
(d
eg
re
es
)
0
15
30
45
60
75
90
)
0.00
0.00
0
15
30
45
60
75
90
IED (a.u.)
0.08
es
0.02
0.12
0
10
20
30
Ion energy (eV)
40
1
0.04
IED (a.u.)
0.16
0.06
50
Cb = 0.7 pF, AG = 2 AT , Te = 3 eV, n0 = 2 x 1015 m-3, M = 40 amu (Ar+), f1 = 13.56
MHz, f2 = 27.12 MHz, U1 = U2 = 100 V, instrumental broadening 2 eV.
40
Concluding Remarks
 Several methodologies can be implemented to tailor the ion




energy distribution on plasma electrodes.
PIC-MCC and hybrid simulations of a pulsed plasma with
synchronous DC bias applied in the afterglow, showed that it is
possible to tailor IEDs to have distinct energy peaks with
controlled energies and fraction of ions under each peak.
Simulations were in good agreement with measurements.
Although PIC simulation provides detailed information (e.g., IAD
in addition to IED), fast execution of semi-analytic model is
advantageous for initial screening of tailored voltage waveforms.
Models/simulations in synergy with experiments are critical to
understand and predict the behavior of plasmas and to unravel
new strategies for tailoring IEDs.
41
Acknowledgements
Prof. M. Nikolaou, University of Houston
Dr. H. Shin, University of Houston, currently at Lam Research Corp.
W. Zhu, University of Houston
Prof. S. Longo, University of Bari and CNR/IMIP, Italy
Prof. M. Capitelli, University of Bari and CNR/IMIP, Italy
Financial Support:
DoE Plasma Science Center
NSF
42