p. diomede, d. j. economou and v. m. donnellydoeplasma.eecs.umich.edu/files/psc_economou1.pdfsources...
TRANSCRIPT
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P. Diomede, D. J. Economou and V. M. DonnellyPlasma Processing Laboratory, University of Houston
Acknowledgements: DoE Plasma Science Center, NSF
Presented at the 57th AVS Conference, Albuquerque, NM 2010
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Introduction / Motivation
• Control of the energy of ions bombarding a substrate i n contact with plasma is critical for plasma processing.
• The ion energy must be high enough to drive anisotro pic etching, but not too high to induce substrate damag e and/or loss of selectivity.
• As device dimensions continue to shrink, precise con trol of the ion energy distribution (IED) becomes increasingly important.
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Goal and Approach
Goal : Develop methodologies to achieve “tailored” ion energy distribution functions (IEDFs).
Approach:� Use combination of modeling/simulation and
experiments.� Modeling is semi-analytic.� Simulation is PIC using XPDP1
(V. Vahedi, G. DiPeso, C. K. Birdsall, M. A. Lieberman, and T. D. Rognlien, Plasma Sources Sci. Technol. , 2, 261 (1993); Verboncoeur, Alves, Vahedi, Birdsall, J. Comp. Phys., 104, 321 (1993)).
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Electrode Immersed in a Plasma
Plasma density and electron temperature are not aff ected by the applied potential
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Blocking capacitor, C b
Applied rf, V rf
Bulk Plasma (n 0, Te)
Electrode (Target)
Sheath
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Semi-analytic Model (1)Schematic of the sheath region
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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.
1 21 1
0 1
22 /e s s
e
n kT e(V V ) VE [exp( ) ]
kT Vε−= − + −
0ss
EC A
Vε ∂= −
∂
A. Metze et al., J. Appl. Phys., 60, 3081 (1986).P. Miller and M. Riley, J. Appl. Phys., 82, 3689 (1997).T. Panagopoulos and D. Economou, JAP, 85, 3435
(1999).
V=VS V=V1 V=0
Id
Ie
Ii
Electrode Sheath Pre-sheath Plasma (bulk)
xn0, Te
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Semi-analytic Model (2)
� Equivalent circuit model, A. Metze et al., J. Appl. Phys., 60, 3081 (1986).
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0
0
b rf T T P T T
T P T G P T G
d dC (V V ) C (V V ) I
dt dtd d
C (V V ) C V I Idt dt
− + − + =
− + + + =
Desired voltage Vrf is applied through blocking capacitor, Cb. Given n 0, Te, Vrf and Cb, calculate V d, VT and Vp.
Ions respond toa “damped” potential Vd
IG
IT
VP
CG
CT
VT
Cb
VrfSubscripts T and G refer to “target” and “ground” electrodes, respectively.
i
pTddVVV
dt
dV
τ)( −−
−=
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Semi-analytic Model (3)
� Having determined Vd, find ion energy distribution P(E).
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2d
d
E eV
dVP( E )
d( t )π ω
−
=
=
A. Metze et al., J. Appl. Phys., 60, 3081 (1986).E. Kawamura et al., Plasma Sources Science & Technology, 8, R45 (1999).
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Target voltage and Ar + IEDF, 500 kHzF. L. Buzzi et al. PSST, 18 (2009) 025009
PIC simulation : ne = 4×1016 m-3, Te = 2eV
Tailored voltage waveforms: Spikes (1)
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Semi-analytical model : ne = 4×1016 m-3, Te = 2 eV, CB = 5 µF, AS/AT = 5
Tailored voltage waveforms: Spikes (2)
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Tailored voltage waveforms: Spikes (3)
PIC simulation : ne = 4×1016 m-3, Te = 2eV, f = 10MHz
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Semi-analytical model : ne = 4×1016 m-3, Te = 2 eV, CB = 5 µF, AS/AT =1
Tailored voltage waveforms: Spikes (4)
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Tailored voltage waveforms: Staircase (1)
Target voltage and Ar + IEDF, 500 kHzF. L. Buzzi et al. PSST, 18 (2009) 025009
PIC simulation :ne = 4×1016 m-3, Te = 2eV
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Semi-analytical model : ne = 4×1016 m-3, Te = 2 eV, CB = 5 µF, AS/AT =5
Tailored voltage waveforms: Staircase (2)
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Tailored voltage waveforms: Square Wave (1)Experiments (dashed line) : H3+ ions, 195 kHz P.Kudlacek et al. JAP 106 (2009) 073303
PIC simulation : ne = 2×1016 m-3, Te = 0.15 eV
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Semi-analytical model : ne = 2×1016 m-3, Te = 0.15 eV, CB = 5 µF, AS/AT =5
Tailored voltage waveforms: Square Wave (2)
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Tailored voltage waveforms: Square Wave (3)
PIC simulation : ne = 2×1016 m-3, Te = 0.15 eV, f = 13.56 MHz
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Semi-analytical model : ne = 2×1016 m-3, Te = 0.15 eV, CB = 5 µF, AS/AT =1
Tailored voltage waveforms: Square Wave (4)
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Experiments (dashed line) : H3+ ions, CB = 166 pF, 27.7 kHz P.Kudlacek et al. JAP 106 (2009) 073303
Tailored voltage waveformsSquare Wave with blocking capacitor (1)
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Tailored voltage waveforms: Square Wave with blocking capacitor (2)
Semi-analytical modelne = 2×1016 m-3, Te = 0.15 eV, CB = 500 pF, AS/AT =1
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Tailored voltage waveforms: Square Wave + slope with blocking capacitor (1)
Experiments (solid line) : H3+ ions, CB = 166 pF, 33.3 kHz P.Kudlacek et al. JAP 106 (2009) 073303
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Semi-analytical modelne = 2×1016 m-3, Te = 0.15 eV, CB = 1.66 nF, AS/AT =1
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Tailored voltage waveforms: Square Wave + slope with blocking capacitor (2)
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Summary
� The energy distribution of ions bombarding the substrate can be tailored by applying voltage waveforms with special shapes (e.g., spikes, staircase, square wave).
� Semi-analytic model can rapidly identify voltage waveforms that result in tailored IEDFs.
� PIC simulation is useful for verifying and fine tuning such waveforms.
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