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Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F1
45th International Symposium of the American Vacuum SocietyBaltimore, MarylandNovember 2-6, 1998.
MULTI-FREQUENCY OPERATION OF RIE AND ICP SOURCES*
Shahid Rauf and Mark J. KushnerDepartment of Electrical & Computer Engineering
University of Illinois, Urbana-Champaign
*Work supported by AFOSR/DARPA, SRC and NSF.
AGENDA
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F2
• Introduction
• Computational Model
• Asymmetric Capacitively Coupled Discharge
• Electrode Currents and Voltages
• Effect of Frequency, Voltage Waveform and Source Interaction
• Inductively Coupled Plasma
• Electrode Currents and Voltages
• Effect of Frequency and Source Interaction
• Conclusions
INTRODUCTION
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F3
• Source frequency has a strong influence on plasma characteristics in radio frequency (rf) discharges.
• Multiple sources at different frequencies are often simultaneously used to separately optimize the magnitude and energy of ion fluxes to the substrate.
• The sources can, however, nonlinearly interact if the frequencies are sufficiently close, and resulting plasma and electrical characteristics can be different than due to individual sources.
• A plasma equipment model has been used to investigate the interaction of multiple frequency sources in both capacitively and inductively coupled discharges.
• In this talk, we discuss the effect of frequency on plasma and electrical characteristics, and describe the consequences of source interactions.
THE COMPUTATIONAL MODEL
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F4
The Hybrid PlasmaEquipment Model
s(r,z), I (coils), J(r,z,φ)N(r,z) Es(r,z,φ)
S(r,z),Te(r,z),
µ(r,z)
Eθ(r,z,φ)
B(r,z,φ)ELECTRO-MAGNETICS
MODULE
CIRCUITMODULE
I,V (coils) Eθ
ELECTRONMONTECARLO
SIMULATION
ELECTRONENERGY
EQN./BOLTZMANN
MODULE
NON-COLLISIONAL
HEATING
FLUID-KINETICS
SIMULATION
HYDRO-DYNAMICSMODULE
CIRCUITMODEL
Vrf, Vdc
• Our computational platform consists of the coupled Hybrid Plasma Equipment Model (HPEM) and a circuit model.
• The circuit model uses intermediate results from the HPEM to compute voltages (dc, fundamental and harmonics) at electrodes.
ne, Te,
vi
SHEATH-CIRCUIT MODEL
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F4a
• The reactor and circuitry are replaced by the following equivalent circuit.
Sheath 1 Sheath 2 Sheath N
RC1
CC1
LC1
RB1
CB1
VS1
LB1
RA1
CA1
LA1
RB2
CB2
VS2
LB2
RA2
CA2
LA2
RBN
CBN
VSN
LBN
RAN
CAN
LANRCN-1
CCN-1
LCN-1
Reactor
GEC REFERENCE CELL
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F5
• We first explore the effects of frequency and source interactions in the capacitively coupled GEC reference cell with Ar at 100 mTorr.
• Sources and blocking capacitors have been connected to both electrodes.
Radius (cm)0.0 10.2
0.0
10.9[e] (Max = 1.18 × 1010 cm-3)
107 4
Electrode 1
Electrode 2
Pump Port
Showerhead
1
Dark SpaceShield
E1
E2
G
C2V2
C1V1
• Ar, 100 mTorr, V1 = 100 V, V2 = 0 V.
SHEATH VOLTAGES AND CURRENTS
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F6
• A negative dc voltage appears across the capacitor C1 (dc bias) to balance
currents through the powered and grounded surfaces.
• The sheath currents are fairly nonlinear with large higher harmonics.
58.84 59.00Time (µs)
0
-150
50
VE1+VC1
VG
VE1
VC1
-50
-100
-20058.84 59.00Time (µs)
-0.15
0.15
0.0
IE1
IE2IG
• Ar, 100 mTorr, V1 = 100 V, V2 = 0 V, 13.56 MHz.
EFFECT OF SOURCE FREQUENCY
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F7
• Total current through electrodes and walls increases with frequency because of enhancement of displacement current.
• Larger current leads to more electron heating and larger electron densities.
10 20 30Frequency (MHz)
0.10.20.30.40.50.60.7
0.0
IE1
IE2
IG
10
5
0
Center×0.1
Above E1
-50
-60
-70
-80
Bias (C1)Sheath (E1)
10 20 30Frequency (MHz)
• Electron temperature decreases with frequency, resulting in better electron confinement between electrodes and smaller dc biases.
• Ar, 100 mTorr, V1 = 100 V, V2 = 0 V.
INTERACTION OF MULTIPLE FREQUENCY SOURCES - I
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F8
• In these results, a 13.56 MHz source (V1=100 V) is connected to E1 while a
27.12 MHz source is connected to E2.
• Electron density increases with V2 (27.12 MHz) due to the enhancement of
displacement currents.
10
5
0
Center×0.1
Above E1
0 10020 806040V2(27.12 MHz) (V)
10
-10
-30
-50
-70Electrode E2
Bias (C2)
Sheath
-40
-50
-80
-60
-70
Electrode E1
Bias (C1)
Sheath
0 10020 806040V2(27.12 MHz) (V)
• The dc bias magnitude on E1 decreases with increasing V2 (27.12
MHz) due to source interactions.
• Ar, 100 mTorr, V1 (13.56 MHz) = 100 V.
INTERACTION OF MULTIPLE FREQUENCY SOURCES - II
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F9
• In these results, we show the sheath voltages and currents for only the 13.56 MHz source, 27.12 MHz source and their combination.
• Sheath voltages at E1 and E2 are primarily governed by the sources connected to them.
• The sheath voltage at the grounded wall is, however, in the linear regime and the two sources interact increasing the sheath voltage drop.
• DC bias at E1, which is the difference between the dc sheath voltage at E1 and wall, therefore decreases in magnitude.
2
0
-2
1.2
0
-1.2
0
-200
-100
0
-1600
-60
13.56
Both
13.56
Both
(a)
(c)
27.12
Both (b)
13.56
27.12
Both
(e)
27.12
Both (d)
-30
-80
79.0 80.0Time (1/13.56 µs)
79.5
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F17
ARBITRARY VOLTAGE WAVEFORMS
0
100
-100
0
100
-100
0
100
-100
0
100
-100
(a)
(b)
(c)
(d)
0 2πωt (rad)
0 2πωt (rad)
π 0 2πωt (rad)
π
-90
0
-180
-90
0
-180
-80
0
-160
-75
0
-150
0.00
0.25
-0.25
0.00
0.70
-0.70
0.00
0.25
-0.25
0.00
1.70
-1.70
! By varying the rf bias voltage waveform, one can control the dc bias, sheathvoltage, plasma characteristics and the ion energy distribution at the substrate.
EFFECT OF WAVEFORM ON PLASMA PARAMETERS
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F18
• Waveforms which have higher first harmonic lead to larger dc biases.• Higher first harmonics also lead to enhanced power deposition in the plasma and higher electron densities.
10.9
0.00.0 10.2 0.0 10.2 0.0 10.2
Radius (cm) Radius (cm) Radius (cm)
0.0
0.9
0.6
0.3
0.0
1.2
0.8
0.4
1.5
0.0
0.5
1.0
Triangular Wave Sinosoidal Wave Square Wave
[e] (1010 cm-3) [e] (1010 cm-3) [e] (1010 cm-3)
• Since displacement current increases with frequency, waveforms with larger amplitudes at higher harmonics result in larger plasma densities.
INDUCTIVELY COUPLED PLASMA (ICP) SOURCE
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F10
• We next consider the effects of rf bias frequency and rf source interaction in an ICP reactor.
• For circuit simulation, the dielectric window is replaced by effective capacitors.
Radius (cm)0.0 17.0
0.0
15.0
[e] (Max = 5.4 × 1011 cm-3)
107 4
PumpPort
Coils Showerhead
Electrode (S1)S3S2
1
C1V1
1
2
3
4 5
CW4 CW5
• Ar, 20 mTorr, 500 W, V1 (13.56 MHz) = 100 V.
TYPICAL SHEATH VOLTAGES AND CURRENTS
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F11
• Most of the rf current flows out through the grounded surfaces.
0 2π 4πωt (radians)
0
-20
-40
-60
-80
-100
-120
-140
1.5
0.0
-1.5
I5I4
6
4
2
0
-2
-4
-6
-8
0 2π 4πωt (radians)
• Sheath voltage is larger near the grounded walls at 10 MHz because of low plasma density (i.e., high impedance) adjacent to them.
• Ar, 20 mTorr, 500 W, V1 (10 MHz) = 100 V.
V1
V2,3
V4 V5
10 MHz
I1
I3
I2
10 MHz
EFFECT OF RF BIAS SOURCE FREQUENCY
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F12
• Since plasma is generated by the inductive source, rf bias frequency does not significantly affect the electron density.
• Displacement current through the sheaths increases with bias frequency, enhancing the total sheath current.
10 20 30Frequency (MHz)
30
0
-60
0
5
10
-30 Sheath
Bias (C1)
8
6
4
2
010 20 30
Frequency (MHz)
• Ar, 20 mTorr, 500 W, V1 = 100 V.
WHY DOES RF BIAS FREQUENCY STRONGLY EFFECT DC BIAS?
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F13
• Most of the current through the substrate is conduction while that at grounded surfaces is displacement.
• An increase in rf bias frequency, therefore, decreases the sheath impedance more strongly at grounded surfaces than at the substrate.
• The resulting disproportionate change in sheath voltage at different surfaces modifies the dc bias at the substrate.
0 4πωt (radians)
2π
0
-20
-40
-60
-80
-100
-120
-140
10
5
0
-5
-10
-15
-200 4π
ωt (radians)2π
• Ar, 20 mTorr, 500 W, V1 (30 MHz) = 100 V.
V1
V2,3
30 MHzI1
I3
I2
30 MHz
DEPENDENCE OF DC BIAS ON INDUCTIVE POWER DEPOSITION
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F14
• Dc bias was positive at low frequencies (in the previous results) because electron density is much larger near the powered electrode than the grounded surfaces.
• By powering only the outer two coils, electron density profile can be shifted towards the grounded wall (S3).
• This changes the dc bias at the powered substrate (S1) from 10.8 V
to -21.9 V.
• Ar, 20 mTorr, 500 W, V1 (13.56 MHz) = 100 V.
Radius (cm)0.0 17.0
0.0
15.0
[e] (Max = 3.2 × 1011 cm-3)
10 74
1S1
S3
RF SOURCE INTERACTION IN ICP REACTOR
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F15
• In these results, a 13.56 MHz source (V1 = 100 V) is connected to S1 while a
27.12 MHz source is connected to S3.
30 11050 9070VS3(27.12 MHz) (V)
45
25
15
12
8
4
0
-4
35
Electrode S1
Bias (C1)
-VSheath
6.0
5.8
5.6
5.4
5.2
5.030 11050 9070
VS3(27.12 MHz) (V)
• Sheath voltage at S1 is mainly
governed by the rf bias source.
• The two rf sources, however, interact at the grounded surface S2 and
change the sheath voltage there.
• Dc bias at S1 is therefore modified.
• Ar, 20 mTorr, 500 W, V1 (13.56 MHz) = 100 V.
CONCLUSIONS
Optical & Discharge PhysicsUniversity of Illinois
AVS98_P1_F16
• The effect of rf bias source frequency and source interactions have been discussed in both capacitively and inductively coupled sources.
• In the capacitively coupled GEC reference cell, frequency had a significant effect on currents and electron density, but not dc bias.
• On the other hand, rf bias source frequency appreciably modified the dc bias in the inductively coupled plasma reactor, but not plasma density.
• Multiple rf sources at different frequencies were found to interact with each other in both inductively and capacitively coupled reactors.
• This interaction was strong near surfaces where sources were not attached and very weak in sheaths connected to the sources.
• Due to this inhomogeneous and nonlinear response of different sheaths to multiple sources, the electrical characteristics of the discharge were significantly modified.