P. Diomede, D. J. Economou and V. M. Donnellydoeplasma.eecs.umich.edu/files/PSC_Economou1.pdfSources Sci. Technol . , 2, 261 (1993); Verboncoeur, Alves, Vahedi, Birdsall, J. Comp.

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.

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

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

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)( −−

−=

Semi-analytic Model (3)

� Having determined Vd, find ion energy distribution P(E).

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11

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


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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


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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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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


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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

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)

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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P. Diomede, D. J. Economou and V. M. Donnellydoeplasma.eecs.umich.edu/files/PSC_Economou1.pdfSources Sci. Technol . , 2, 261 (1993); Verboncoeur, Alves, Vahedi, Birdsall, J. Comp.

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