undergraduate thesis slide

1. ION ENERGY DISTRIBUTION OF MULTI-FREQUENCY
CAPACITIVELY COUPLED PLASMA
Submitted by
Tahmid Syed Abtahi

2. OUTLINE
• Introduction
• Theory
o Basic Plasma Properties
o Plasma Sheath
o Plasma Reactors
o DC Breakdown and Discharge

3. OUTLINE
• Ion Energy Distribution For A Triple Frequency Collisional Sheath
• Conclusion
• Future Plan

4. Degree of Ionization, η
η= ni/(ni + na)
DEFINITION OF PLASMA

5. DEBYE SHIELDING
The free charges in a
plasma will move in
response to any electric
field in such a way to
decrease
the Effect of the
field,Quasi-Neutrality.

6. PLASMA OSCILLATIONS
The time required for an electron to move a Debye
length
Plasma Frequency

7. SHEATH: NON-CONDUCTING SURFACE
•The electron flux to the wall will be
greater initially.
•Causing plasma become more
positive and developing an electric
field.
• Potential falls off from the wall into
the plasma over Debye length

8. SHEATH: CONDUCTING ELECTRODE
The potential on the electrode is negative
And large, attract ions and repel e-.
Ions crosses the sheath, strike the electrode
At x=Sm.
Current density J = eniui
Potential V(x) is given by the equation

9. PLASMA COUPLING
INDUCTIVELY COUPLED
PLASMA
CAPACITIVELY COUPLED
PLASMA

10. Planar Reactor
Inductively Coupled Reactor
Capacitive Barrel Reactor
Downstream Reactor
PLASMA REACTORS

11. DC BREAKDOWN

12. • The cathode region
• Secondary electron generation
• Ionization of the cathode sheath
• Ion charge exchange in the
cathode sheath Ar+ + Ar = Ar +
Ar+
• The anode region , Vdrop= 3KT/e
• The negative glow region
• Beyond the negative glow
• The positive column
DC GLOW DISCHARGE

13. DC Glow Discharge
The negative glow region along with
the cathode and associated dark space
Comprise a SELF-SUSTAINING discharge
Configuration [24]
[24] S. M. Rossnagel , Jerome J. Cuomo , William D. Westwood Bell ,Handbook of plasma processing technology Fundamentals,
Etchin Deposition and Surface Interactions;Noyes Publications, Park Ridge, New Jersey, U.S.A. ,1990.

14. WHY CCP,IED ?
• CCP widely used in etching, thin film deposition and surface
treatment
• Better control over etch rates

15. MULTIPLE FREQUENCY OPERATION
Goto et al demonstrated
Independent control of the ion density and the ion bombardment energy by selecting
appropriate excitation frequencies in a dual RF excitation system
H. H. Goto, H.-D. Lowe, and T. Ohmi, J. Vac. Sci. Technol. A, vol.10, p. 3048, 1992.

16. ION ENERGY DISTRIBUTION FOR
TRIPLE FREQUENCY COLLISIONAL
MODEL

17. BASIC ASSUMPTION

18. TRIPLE FREQUENCY CAPACITIVE DISCHARGE
Current density across the sheath [21] ,
𝐽𝑟𝑓= 𝐽1cos(ω1 𝑡)+ 𝐽2cos(ω2 𝑡)+ 𝐽3cos(ω3 𝑡)
Instantaneous electron sheath edge expressed as a step like electron density
profile
Ion motiontime independent and collision less
Sheath in triple frequency capacitive discharge [21],
𝑠(𝑡) = 𝑠 − 𝑠1 sin ω1 𝑡 − 𝑠2 sin ω2 𝑡 − 𝑠3 sin ω3 𝑡
[21] S H Lee, Pawan K Tiwari, JK Lee. Plasma Sources Sci. Technol.18 (2009) 025024 (9pp)

19. IED
For single frequency, sheath potential[45]
𝑉𝑠 𝑥, 𝑡 = 𝑉𝑠 [1 + λ sin(ω𝑡)]
𝑥
𝑑
4
3
For triple frequency RF discharge similar equation
𝑉𝑠 𝑥, 𝑡 = 𝑉𝑠[1 + λ1 sin(ω1 𝑡)][1 + λ2 sin(ω2 𝑡)][1 + λ3 sin(ω3 𝑡)]
𝑥
𝑑
4
3
Electric field in the sheath region
𝐸𝑠 𝑥 = −
4𝑒 𝑉𝑠
3𝑑
[1 + λ1 sin(ω1 𝑡)][1 + λ2 sin(ω2 𝑡)][1 + λ3 sin(ω3 𝑡)]
𝑥
𝑑
4
3
[45] W J Goedheer, Plasma Sources Sci. Technol.9 (2000) 507–516

20. Applying law of momentum and other conditions energy becomes
𝐸 = 𝑒 𝑉𝑠 1 −
2
3𝑑
2𝑒 𝑉𝑠
𝑀
λ1
ω1
𝑐𝑜𝑠 ω1 𝑡 +
λ2
ω2
𝑐𝑜𝑠 ω2 𝑡 +
λ3
ω3
𝑐𝑜𝑠 ω3 𝑡
2
Spread over energy width ∆𝐸
Δ𝐸 = 𝐸 𝑐𝑜𝑠ω𝑖 𝑡 = −1 − 𝐸 𝑐𝑜𝑠ω𝑖 𝑡 = +1
Δ𝐸 =
8𝑒 𝑉𝑠
3𝑑
2𝑒 𝑉𝑠
𝑀
λ1
ω1
+
λ2
ω2
+
λ3
ω3
IED

21. As ω3 is the highest frequency,
λ1
ω1
≫
λ2
ω2
≫
λ3
ω3
ΔE results in,
Δ𝐸 =
8𝑒 𝑉𝑠
3𝑑
2𝑒 𝑉𝑠
𝑀
λ1
ω1
Binomial expansion of E gives,
𝐸 ≈ 𝑒 𝑉𝑠 1 −
4
3𝑑
2𝑒 𝑉𝑠
𝑀
λ1
ω1
𝑐𝑜𝑠 ω1 𝑡 +
λ2
ω2
𝑐𝑜𝑠 ω2 𝑡 +
λ3
ω3
𝑐𝑜𝑠 ω3 𝑡
IED

22. After differentiating and neglecting phase angles near 180 and 0
degree we get the distribution
𝑓 𝐸 =
𝑑𝑛
𝑑𝐸
=
𝑑𝑛
𝑑𝑡1
𝑑𝑡1
𝑑𝐸
=
Г
𝑑𝐸
𝑑𝑡1
=
Г
4𝑒 𝑉𝑠
3𝑑
2𝑒 𝑉𝑠
𝑀
λ2sin(ω2 𝑡)
=
2Г
ωΔ𝐸
1
1 − 𝑐𝑜𝑠2 ω2 𝑡 1/2
So ion energy distribution of triple frequency CCP is,
𝑓 𝐸 =
2Г
ωΔ𝐸
1 −
2
Δ𝐸
2
𝐸 − 𝑒 𝑉𝑠
2
IED
1
1

23. EFFECTIVE VOLTAGE METHOD
Sheath voltage
𝑉𝑠(𝑡)
𝑉𝑠(𝑓) 𝑉𝑖(𝑓)
𝑉𝑖(𝑡) IED
Fourier Transform
Filter
Inverse Fourier Transform
𝒅𝑽𝒊
𝒅𝒕
−𝟏
Filter transfer function, ∝ 𝒇 =
𝟏
((𝒄𝒇𝝉 𝒊) 𝒑+𝟏) 𝟏/𝒑
[16] M.A. Lieberman, Nano electronics And Plasma Processing-The Next 15 Years And Beyond

24. MODEL CONSIDERATION
IED Model:
•Analytical model proposed by S H Lee, Pawan K Tiwari, JKLee [21]
•Semi Analytical model proposed by Alan C. F. Wu, M. A. Lieberman, J.
P. Verboncoeur [16]
Plasma Sheath Model:
•Collisional Triple Frequency capacitively coupled plasma sheath
modeled by M. T. Rahman, M. N. A. Dewan, M. R. H. Chowdhury [3]
REF: [21] S H Lee, Pawan K Tiwari, JK Lee. Plasma Sources Sci. Technol.18 (2009) 025024 (9pp)
[16] Alan C. F. Wu, M. A. Lieberman, and J. P. Verboncoeur. In: J. Appl. Phys. 101 (2007),p. 056105.
[65] Rahman, M.T, Dewan, M.N.A.,Plasma Science, IEEE Transactions on (Volume:42, Issue: 3 ),p 729

25. SIMULATION RESULT
LF= 1MHz
α= 15
β= 50
Jlf = 10 Am-2
n0=2x1016 m-3
P=100mTorr
Normalized IED from JK LEE model
Normalized IED from Lieberman model
0 100 200 300 400 500 600 700 800 900 1000
0
0.5
1
1.5
2
2.5
x 10
-7
Energy in eV
NormalizedIED(1/eV)
20 25 30 35 40 45 50 55 60 65
0
0.5
1
1.5
2
2.5
3
3.5
Energy in eV
NormalizedIED(1/eV)

26. EFFECT OF PRESSURE ON IED
IED distribution for triple frequency driven CCP
0 50 100 150 200 250 300 350
0
0.5
1
1.5
2
2.5
3
3.5
Energy in eV
NormalizedIED(1/eV)
p=3mtorr
p=10mtorr
p=100mtorr
LF= 1MHz
α= 15
β= 50
Jlf = 10 Am-2
n0=2x1016 m-3

27. EFFECT OF PRESSURE ON IED
Mid Position of
Energy Band
(in eV)
Width of Energy
Band
(in eV)
1 mTorr 436.8617 127.8113
10 mTorr 138.1478 71.8736
20 mTorr 97.6852 60.4382
30 mTorr 79.7597 54.6121
40 mTorr 69.0739 50.8223
50 mTorr 61.7816 48.0648
100 mTorr 43.6862 40.4175
Parameters: LF= 1MHz, α= 15, β= 50, Jlf = 10 Am-2,
n0=2x1016 m-3

28. EFFECT OF ION DENSITY ON IED
LF= 1MHz
α= 15
β= 50
Jlf = 10 Am-2
n0=nx1016 m-3
P=10mTorr
IED distribution for triple frequency driven CCP
0 50 100 150 200 250 300 350 400
0
0.5
1
1.5
2
2.5
3
Energy in eV
NormalizedIED(1/eV)
n=1
n=2
n=5

29. EFFECT OF ION DENSITY ON IED
Mid Position of
Energy Band
(in eV)
Width of Energy
Band
(in eV)
2x1016 m-3 43.6862 40.4175
20x1016 m-3 4.3686 1.2781
40x1016 m-3 2.1843 0.4519
60x1016 m-3 1.4562 0.2460
80x1016 m-3 1.0922 0.1598
100x1016 m-3 0.8737 0.1143
200x1016 m-3 0.4369 0.0404
Parameters: LF= 1MHz, α= 15, β= 50, Jlf = 10 Am-2,
p=100 mTorr

30. EFFECT OF CURRENT DENSITY ON IED
LF= 1MHz
α= 15
β= 50
n0=2x1016 m-3
P=10mTorr
IED distribution for triple frequency driven CCP
0 100 200 300 400 500 600
0
1
2
3
4
5
6
7
Energy in eV
NormalizedIED(1/eV)
J=5
J=10
J=15

31. EFFECT OF CURRENT DENSITY ON IED
Mid Position of
Energy Band
(in eV)
Width of Energy
Band
(in eV)
0.1Am-2 4.3686e-04 1.2781e-05
1 Am-2 0.1381 0.0227
10 Am-2 43.6862 40.4175
20 Am-2 247.1263 384.5181
30 Am-2 680.9999 1.4362e+03
Parameters: LF= 1MHz, α= 15, β= 50, n0=2x1016, m-3,
pressure= 100 mTorr

32. EFFECT OF LOW FREQUENCY ON IED
LF= fxMHz
α= 15
β= 50
Jlf = 10 Am-2
n0=2x1016 m-3
P=10mTorr
IED distribution for triple frequency driven CCP
20 40 60 80 100 120 140 160 180
0
5
10
15
20
25
30
35
Energy in eV
NormalizedIED(1/eV)
f=1
f=2

33. EFFECT OF LOW FREQUENCY ON IED
Mid Position of
Energy Band
(in eV)
Width of Energy
Band
(in eV)
1 MHz 43.6862 40.4175
1.5 MHz 15.8532 7.2141
2 MHz 7.7227 2.1242
3 MHz 2.8025 0.3791
4 MHz 1.3652 0.1116
Parameters: α= 15, β= 50, n0=2x1016, m-3, n0=2x1016m-3,
pressure= 100 mTorr

34. CONCLUSION
• Ion Energy Distribution (IED) in multi-frequency RF source driven
capacitively coupled plasma are determined.
•Effects of various input parameters (pressure, ion density, frequency, frequency
ratios , ion density ratio) on IED have been investigated.

35. CONCLUSION
• Position and width of IED can be adjusted with the choice of fundamental
frequency, pressure and ion density

36. Thank you