Simulation of Magnetically Confined Plasma for Etch Applications

Computational Optimization of
Magnetically Enhanced CCP Plasma
Uniformity for Disk Etch Applications

Vladimir Kudriavtsev, Wenli Collison
Huong Nguyen, Pat Ward, Michael Barnes,
Mark Kushner

62nd Annual Gaseous Electronics Plasma Conference
GEC 09 - American Physical Society
October, 2009
Think Lean – Create Value

Summary


Magnetic Field Line Uniformity Analogy

-improve magnetic line angle
uniformity and desired cross-section
and you will improve
plasma uniformity
-best way to do it to increase magnet to
substrate distance, however that
weakens corresponding magnetic field


Two Configurations

Initial Optimized – Rev1

HM H

HM H

HM=62.5…125 mm, H=50 mm HM=125 mm, H=113 mm
Magnet moves up/down Plasma gap increases, ground
to electrode area increased


CF4 Chemistry Model (HPEM)


K Pole Magscans

Close Distance 62.5 mm away

View from bottom

Magnetic steel enclosure

Magnets


Magnetized CCP

• 2-dimensional HPEM Hybrid Model of Ar Plasma

• Electron energy equation for bulk electrons
• Continuity, Momentum and Energy (temperature) equations
for all neutral and ion species.
• Poisson equation for electrostatic potential

•Gas phase reactions:
•Surface reactions:
AR + E > AR* + E
AR + E > AR* + E Ar* > Ar
AR + E > AR^ + E + E Ar^ > Ar
AR* + E > AR^ + E + E
AR* + AR* > AR^ + AR + E
AR* + E > AR + E
AR^ + AR > AR + AR^
Ar^-ion


ELECTRON ENERGY TRANSPORT

3  5 
∂ ne kTe  / ∂t = S (Te ) − L(Te ) − ∇ ⋅  Φ kTe − κ (Te ) ⋅ ∇Te  + S EB
2  2 
Φ = qne µ e ⋅ E − D ⋅ ∇ne B field affected
transport
S(Te) = Power deposition from electric fields
L(Te) = Electron power loss due to collisions
Φ = Electron flux
κ(Te) = Electron thermal conductivity tensor
SEB = Power source source from beam electrons
• All transport coefficients are tensors:
 α 2 + Br2 αBz + Br Bθ − αBθ + Br Bz 
mν m 1  
A = Ao r 2   − αBz + Br Bθ
qα  α 2 + B  
α 2 + Bθ2 αBr + Bθ Bz 

   − αBθ + Br Bz − αBr + Bθ Bz α 2 + Bz2  
α=
(iω +ν m ) , Ao = isotropic
q/m

PLASMA CHEMISTRY, TRANSPORT AND ELECTROSTATICS

• Continuity, momentum and energy equations are solved for each species
(with jump conditions at boundaries)
∂ Ni r
= −∇ ⋅ ( N i vi ) + Si + S EB
∂t
r
∂ ( N i vi ) 1 rr qi N i r r r
∂t
= ∇(kN iTi ) − ∇ ⋅ (N i vi vi ) +
mi mi
( )
E + vi × B − ∇ ⋅ µ i
mj r r
−∑ N i N j (vi − v j ) ij
ν
j mi + m j
∂ ( N iε i ) Nqν 2
+ ∇ ⋅ Q i + Pi ∇ ⋅ U i + ∇ ⋅ ( N i U iε i ) = i i i
2 2
E2
∂t mi (ν + ω )
i
2
N i qi 2 mij
+ Es + ∑ 3 N i N j Rij k B (T j − Ti ) ± ∑ 3 N i N j Rij k BT j
miν i j mi + m j j

• Implicit solution of Poisson’s equation
 r 
(
∇ ⋅ ε ∇Φ(t + ∆t ) = - ρ s + ∑ qi N i - ∆t ⋅ ∑ q i∇ ⋅ φi  )
 i i 

Initial Configuration
CF4 gas 50sccm, 100mTorr, 100W CCP power.
Magnet direction: Horizontal right. 125mm distance from substrate to magnet.
Electron density.

-10

E
-5 2.6E+10
1cm above the substrate 2.3E+10
2.0E+10
1.7E+10
1.4E+10
Z (cm) 0 1.1E+10
8.0E+09
4E+10
5.0E+09
2.0E+09
3.5E+10 E

3E+10 5

2.5E+10
E

2E+10

10
1.5E+10

-10 -5 0 5 10
1E+10
1.5 2 2.5
R (cm)
3 R (cm)


F radical density.

-10

F
1.1E+13
1E+13
-5 9E+12
8E+12
7E+12
6E+12
5E+12
Z (cm)

4E+12
0 3E+12
2E+12
1E+12

5

10

-10 -5 0 5 10
R (cm)


Plasma potential.

-10

P-POT
-5 60
46
31
17
3
Z (cm)

-11
0 -26
-40

5

10

-10 -5 0 5 10
R (cm)


Optimal Rev1
Magnet: Horizontal right. 125mm from substrate to magnet, 113mm gap in plasma zone.
Electron Density.

0
E
5.5E+10
5.0E+10
4.5E+10
5 4.0E+10

Z (cm)
3.5E+10
6E+10 3.0E+10
2.5E+10
5.5E+10 2.0E+10
E
1.5E+10
10
5E+10 1.0E+10
5.0E+09
4.5E+10
E

4E+10
15
3.5E+10

3E+10

-10 -5 0 5 10
2.5E+10
R (cm)
2E+10
1.5 2 2.5 3
R (cm)
1cm below the substrate


Optimal Rev1
CF and CF2 densities.

0 0
CF2
CF
2.4E+13
2.0E+13
2.2E+13
1.8E+13
2.0E+13
1.6E+13 5 1.8E+13
5

Z (cm)
1.4E+13 1.6E+13
Z (cm)

1.2E+13 1.4E+13
1.0E+13 1.2E+13
8.0E+12 1.0E+13
6.0E+12 8.0E+12
4.0E+12 10
10 6.0E+12
2.0E+12 4.0E+12
2.0E+12

15
15

-10 -5 0 5 10
-10 -5 0 5 10 R (cm)
R (cm)


Optimal Rev1
F radical density and plasma potential.

0 0
F P-POT
9.0E+12 20
8.0E+12 10
7.0E+12 0
5 6.0E+12 5
Z (cm)

-10
5.0E+12

Z (cm)
-20
4.0E+12
-30
3.0E+12
2.0E+12 -40
1.0E+12 -50
10 -60
10 -70

15
15

-10 -5 0 5 10
R (cm) -10 -5 0 5 10
R (cm)


Comparison – Plasma Density Ne
Decreasing the distance from magnet to substrate, while keep 113mm gap in plasma zone.
Rev.1 Config

E
0 5.50E+10
E
5.08E+10
5.5E+10 0 4.67E+10
0 4.7E+10
E
4.25E+10
3.8E+10 3.83E+10
3.0E+10 5.5E+10 3.42E+10
2.2E+10 5.0E+10 5 3.00E+10
1.3E+10 4.5E+10 2.58E+10

Z (cm)
5.0E+09
5 4.0E+10 2.17E+10

Z (cm)
5 3.5E+10 1.75E+10
Z (cm)

3.0E+10 1.33E+10
2.5E+10 9.17E+09
2.0E+10 5.00E+09
1.5E+10
10
10
1.0E+10
10 5.0E+09

15 15

15
-10 -5 0 5 10
-10 -5 0 5 10 R (cm)
-10 -5 0 5 10 R (cm)
R (cm)

136mm 125mm 113mm
0
0
0 E E
E 5.50E+10 4.5E+10
5.05E+10 4E+10
5.50E+10
4.59E+10
5.00E+10 3.5E+10
4.14E+10
4.50E+10 5 3E+10
4.00E+10
3.68E+10 5
3.23E+10 2.5E+10
5 3.50E+10 2E+10
2.77E+10
3.00E+10
1.5E+10
Z (cm)

2.32E+10
2.50E+10

Z (cm)
1.86E+10 1E+10
2.00E+10
Z (cm)

1.41E+10 5E+09
1.50E+10
9.55E+09
1.00E+10
5.00E+09
10 5.00E+09

10 10

15
15
15
-10 -5 0 5 10
-10 -5 0 5 10 R (cm)
R (cm) -10 -5 0 5 10
R (cm)

92.5mm 74mm No magnet, 92.5mm


Comparison – F radical number density
Rev.1 Config
F
1.20E+13
0 F
0 1.10E+13 0
1.00E+13 1.1E+13
9.00E+12 F 1E+13
8.00E+12 9E+12
9.0E+12 8E+12
7.00E+12
8.0E+12 7E+12
6.00E+12 7.0E+12
5 6E+12
5 5.00E+12 5
Z (cm)

6.0E+12 5E+12

Z (cm)
4.00E+12

Z (cm)
5.0E+12 4E+12
3.00E+12 4.0E+12 3E+12
2.00E+12 3.0E+12 2E+12
1.00E+12 2.0E+12 10 1E+12
1.0E+12
10 10

15
15
15

-10 -5 0 5 10 -10 -5 0 5 10
-10 -5 0 5 10 R (cm) R (cm)
R (cm)

136mm 125mm 113mm
0
0
0
F F
F
1.1E+13 1.5E+13
1E+13 1E+13
9E+12 1.4E+13
9E+12
8E+12 5 1.3E+13
8E+12
7E+12 5 1.2E+13
7E+12
6E+12 1.1E+13
5 6E+12
5E+12 1E+13
5E+12
4E+12 4E+12 9E+12

Z (cm)
8E+12
Z (cm)

3E+12 3E+12
Z (cm)

2E+12 10 2E+12 7E+12
1E+12 1E+12 6E+12
5E+12
10 4E+12
10 3E+12
2E+12
15 1E+12

15
15
20

-10 -5 0 5 10 -10 -5 0 5 10
-10 -5 0 5 10 R (cm) R (cm)
R (cm)



Comparison – CF2 polymer number density
Rev.1 Config
CF2
0 CF2
2.40E+13
0 2.20E+13 2.4E+13
2.00E+13 2.2E+13
1.80E+13 2E+13
1.60E+13 1.8E+13
1.40E+13 1.6E+13
0 5 1.4E+13
1.20E+13
5 1.00E+13 1.2E+13
Z (cm)

CF2

Z (cm)
8.00E+12 1E+13
6.00E+12 2.4E+13 8E+12
4.00E+12 2.2E+13 6E+12
2.00E+12 2.0E+13 10 4E+12
5 1.8E+13 2E+12

Z (cm)
10 1.6E+13
1.4E+13
1.2E+13
1.0E+13
8.0E+12 15
10
6.0E+12
15 4.0E+12
2.0E+12

-10 -5 0 5 10 -10 -5 0 5 10
R (cm) 15 R (cm)

-10 -5 0 5 10

136mm 125mmR (cm)
113mm

0
0 0
CF2
CF2
2.4E+13 CF2
2.6E+13
2.2E+13 2.6E+13
2.4E+13 2.4E+13
2E+13
2.2E+13 2.2E+13
1.8E+13 5 2E+13 5 2E+13
5 1.6E+13 1.8E+13
1.8E+13
1.4E+13 1.6E+13
1.6E+13 1.4E+13
1.2E+13

Z (cm)
1.4E+13 1.2E+13
1E+13
Z (cm)

1.2E+13 1E+13
8E+12
Z (cm)

8E+12
1E+13
6E+12 10 6E+12
8E+12 10 4E+12
4E+12
6E+12 2E+12
2E+12
10 4E+12
2E+12

15 15

-10 -5 0 5 10
15 R (cm)

20
-10 -5 0 5 10
R (cm) -10 -5 0 5 10
R (cm)



Comparison- Radial Profiles
Decreasing the distance from magnet to substrate while keep 113mm gap in plasma zone.
Electron density at 1cm below the substrate. R is from inner radius of substrate to outer
radius of substrate.
distance from magnet to substrate
136mm 125mm 113mm 92.5mm 74mm

5E+10
5E+10 5E+10 5E+10 5E+10

4.5E+10 E
E E 4.5E+10 E 4.5E+10 E
4.5E+10 4.5E+10

4E+10
4E+10 4E+10 4E+10
4E+10

3.5E+10

E
3.5E+10

E
3.5E+10 3.5E+10 3.5E+10
E
E
E

3E+10
3E+10 3E+10
3E+10 3E+10

2.5E+10
2.5E+10 2.5E+10
2.5E+10 2.5E+10

2E+10
2E+10 2E+10 1.5 2 2.5 3
2E+10 2E+10 1.5 2 2.5 3 1.5 2 2.5 3 R (cm)
1.5 2 2.5 3 1.5 2 2.5 3 R (cm) R (cm)
R (cm) R (cm)

136mm 125mm 113mm 92.5mm 74mm
3E+11 3E+11
3E+11
3E+11 3E+11

2.5E+11 E 2.5E+11 E
2.5E+11 E
2.5E+11 E 2.5E+11 E

2E+11 2E+11
2E+11
2E+11 2E+11

1.5E+11
E
1.5E+11

E
1.5E+11
E

1.5E+11
E

1.5E+11
E

1E+11 1E+11
1E+11
1E+11 1E+11

5E+10 5E+10
5E+10
5E+10 5E+10

0 0
0 0 1 2 3 4 0 0.5 1 1.5 2 2.5 3 3.5 4
0 0 0 1 2 3 4 R (cm)
0 0.5 1 1.5 2 2.5 3 3.5 4 0 1 2 3 4 R (cm)
R (cm) R (cm) R (cm)


Uniformity Initial Configuration
R range: from inner edge of the substrate to the outer edge of the substrate.
Uniformity% Uniformity%
Min Ne Max Ne Mean Ne (Stdev/Mean) (Max-Min)/2/Mean
Kpole_CF4 with magnet, 62.5mm distance,
50mm gap, 50sccm, 100mTorr, 100W, 300G 1.59E+10 2.37E+10 2.02E+10 13.6 19.3 Initial

Kpole_CF4 with magnet, 125mm distance, Distance to magnet increased, uniformity gets worse
50mm gap, 50sccm, 100mTorr, 100W, 35G 1.44E+10 3.64E+10 2.65E+10 26.1 41.5

Kpole_CF4 with magnet, 92.5mm distance, If gap is increased, uniformity gets better
80mm gap, 50sccm, 100mTorr, 100W, 90G . 3.24E+10 4.71E+10 3.90E+10 12.2 18.8

Kpole_CF4 with magnet, 125mm distance, If gap is increased & distance, uniformity gets better
113mm gap, 50sccm, 100mTorr, 100W, 35G . 3.65E+10 4.58E+10 4.13E+10 6.96 11.3 R.1Opt

Kpole_Ar with magnet, 62.5mm distance, AR
50mm gap, 30sccm, 5mTorr, 200W, 300G 8.63E+10 9.76E+10 9.32E+10 4.16 6.02

Kpole_Ar with magnet, 125mm distance,
50mm gap, 30sccm, 5mTorr, 200W, 35G
AR
9.61E+10 1.11E+11 1.06E+11 4.68 7.00

Kpole_Ar with magnet, 125mm distance,
113mm gap, 30sccm, 5mTorr, 200W, 35G 7.74E+10 1.008E+11 9.071E+10 8.28 12.89 AR


Uniformity Initial Configuration
50sccm, 100mTorr, 100W CCP power.


Kpole_CF4, no magent, 125mm from magnet No Mag
to substrate, 50mm gap in plasma zone. 1.70E+10 2.41E+10 2.05E+10 10.4 17.3

Kpole_CF4 with magnet, 125mm from magnet Initial

Kpole_CF4 with magnet, 125mm from magnet

Kpole_CF4 with magnet, 62.5mm from magnet

Kpole_Ar with magnet, 125mm from magnet to
substrate, 50mm gap in plasma zone.
AR
1.35E+11 1.61E+11 1.54E+11 5.4 8.4


Uniformity – Rev 1 (CF4)

Kpole_CF4 with magnet, 136mm
distance, 113mm gap, 50sccm,
100mTorr, 100W, 26G . 3.45E+10 3.76E+10 3.66E+10 2.73 4.3
distance, 113mm gap, 50sccm, Rev.1 Opt
100mTorr, 100W, 35G . 3.65E+10 4.58E+10 4.13E+10 6.96 11.3

100mTorr, 100W, 50G 3.44E+10 4.54E+10 4.02E+10 8.13 13.7

Kpole_CF4 with magnet, 92.5mm
100mTorr, 100W, 90G 3.18E+10 4.23E+10 3.60E+10 9.17 14.6

100mTorr, 100W, 190G 2.62E+10 4.04E+10 3.24E+10 13.6 21.9
Kpole_CF4 without magnet,
92.5mm distance, 113mm gap, No Magnet
50sccm, 100mTorr, 100W 4.47E+10 4.89E+10 4.74E+10 2.94 4.5


Uniformity Rev 1 (CF4)
R range: from 0 to the outer edge of the powered electrode.

Uniformity% Uniformity% Voltage
Min Ne Max Ne Mean Ne (Stdev/Mean) (Max-Min)/2/Mean drop(V)*
100mTorr, 100W, 26G . 2.97E+10 3.91E+10 3.63E+10 6.84 12.9 73.50

100mTorr, 100W, 35G . 3.25E+10 5.69E+10 4.37E+10 16.3 27.9 81.82

100mTorr, 100W, 50G 2.84E+10 6.39E+10 4.31E+10 21.5 41.2 81.3

Kpole_CF4 with magnet, 92.5mm
100mTorr, 100W, 90G 2.74E+10 2.09E+11 5.05E+10 82.6 179.88 83.4

100mTorr, 100W, 190G 2.20E+10 2.56E+11 4.89E+10 98.7 238.77 96.4
Kpole_CF4 without magnet,
92.5mm distance, 113mm gap,
No Mag
50sccm, 100mTorr, 100W 4.08E+10 4.90E+10 4.69E+10 5.22 8.65 61.8


Summary

Plasma uniformity improves with increase in plasma gap
(chamber height) while keeping substrate to magnet
distance constant
Plasma uniformity improves as magnet is moved away from
the substrate (for fixed chamber dimensions)
Plasma uniformity without magnetic field enhancement is
higher
Simultaneous increase in plasma chamber height (plasma
volume, ground area) with increase in substrate to magnet
distance produces sharp improvement in plasma uniformity


Phase II Optimization work
Widen Kpole magnetic steel zone => expand source width

Remove magnetic steel enclosure, expand magnetic field wider

Remove powered electrode area in the center, to match disk geometry

ceramic

Electrode (disk with the hole)


Further K-Pole Optimization
R is from inner radius of substrate to outer radius of substrate.

100mTorr, 100W, 35G . 3.65E+10 4.58E+10 4.13E+10 6.96 11.3

100mTorr, 100W, 50G . Larger
magnetic steel. 3.09E+10 4.84E+10 3.94E+10 13.4 22.2

100mTorr, 100W, 30G . No ++
Magnetic steel. 3.30E+10 3.85E+10 3.60E+10 4.57 7.7

100mTorr, 100W, 50G 3.44E+10 4.54E+10 4.02E+10 8.13 13.7

100mTorr, 100W, 42G, no +
magnetic steel. 3.50E+10 4.27E+10 3.95E+10 5.75 9.8


Further Source Optimization
R is from inner radius of substrate to outer radius of substrate.

100mTorr, 100W, 35G . 3.65E+10 4.58E+10 4.13E+10 6.96 11.3 Rev.1 Opt

distance, 113mm gap, 50sccm, +
100mTorr, 100W, 16G. Weaker B
field. 2.84E+10 3.40E+10 3.18E+10 6.18 8.9

distance, 113mm gap, 50sccm, +++
100mTorr, 100W, 35G. No
powered electrode at the center. 4.59E+10 5.03E+10 4.86E+10 2.46 4.5

Rev.2 Optimized


Magnet Inclination Influence (different source)

current
Angled
magnets

Uniformity (Stdev/Mean)
Uniformity (measure 1cm below substrate from R=0 to R=5cm)
80.00%
70.00%
60.00%
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%
0 20 40 60 80 100 120 140 160 180
incline B angle

New results for Hybrid ICP/CCP plasma source show significant effect of magnet
inclination on plasma uniformity.
Explore effects of adjustable magnet inclination in Kpole source configuration
with objective to tune uniformity without sacrificing plasma density

Conclusions

Computational optimization of magnetically enhanced CCP plasma
source was conducted, leading to progressive improvement of the
source design, with plasma uniformity reduced from 26% down to 2.5%
Two conceptual source chamber layouts were considered, with second
being clearly more beneficial. This layout has increased plasma gap and
ratio of ground area to electrode area and considerably weaker
magnetic field near substrate.
Further promise is shown due to electrode modification (removing
electrode material in the center) and in adaptive adjustment of Kpole
magnet angles (currently angle is zero).


Supplemental Materials

Ar Plasma Results


Experimental & Computational
Superposition (Ar plasma)

B field
Think Lean – Create species
AR* Value

50 mm top to substrate
distance
5 mtorr
Zone of plasma light collapses
towards the electrode (sheath)
as P increased

Think Lean – Create Value 100 mtorr

Simulation of Magnetically Confined Plasma for Etch Applications

Simulation of Magnetically Confined Plasma for Etch Applications

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