Surface processes in low-pressure capacitively coupled plasmas

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Surface processes in low-pressure capacitively coupled plasmas

PT19 - Cottbus, 17-19 June 2019.

Aranka Derzsi^1,2, Benedek Horváth¹, Zoltán Donko¹, Julian Schulze^2,3

1Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest, Hungary

2West Virginia University, Morgantown, USA

3Institute of Electrical Engineering and Plasma Technology, Ruhr-University Bochum, Germany

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Contents Outline

Study of the effects of surface processes on the discharge characteristics and control of particle flux- energy distribution functions in low-pressure capacitively coupled plasmas (CCPs)

• Method: Particle-in-Cell/Monte Carlo Collisions (PIC/MCC) simulations

–

simple / realistic description of the surface processes

• Electron – surface interactions

–

realistic model, including electron induced secondary electron emission (SEE)

–

the role of electron-induced SEs in low-pressure CCPs

• Heavy-particle (ions, fast neutrals) – surface interactions

• Heavy-particle induced SEE

–

the influence of the energy-dependence of the SE yield on the plasma parameters

–

the effect of surface conditions on the control of ion properties by VWT

• Heavy-particle induced sputtering

–

control of the sputter flux by VWT

• Conclusions

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PIC/MCC simulations of CCPs

The interactions of plasma particles with the boundary surfaces affect the discharge by particle absorption, emission and reflection. In the simulations, these interactions are described by using surface coefficients.

 The implementation of realistic surface coefficients in the discharge models is important!

Monte Carlo:

collisions, add/remove particles

Assign charges to grid points

Check for boundaries: particle absorption, electron

emission, etc.

Move particles:

new positions and velocities

Calculate electric field at grid points

Calculate forces at particle positions

C. K. Birdsall, IEEE Trans. Plasma Sci. 19 (1991)

Particle-In-Cell & Monte Carlo Collisions (PIC/MCC) method

• particle reflection

• absorption

• secondary electron emission (SEE)

…..

Surface coefficients – constant (simple approach)

– functions (realistic approach)

Plasma particle - surface interactions

Particle based simulations are widely used to study various phenomena in low-pressure CCPs. The calculated discharge characteristics can be largely influenced by the surface coefficients used in the simulations.

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In PIC/MCC simulations of capacitively coupled RF discharges the electron-surface interaction is generally described by a simple model.

 a constant probability for the elastic reflection of the electrons is used

(the elastic electron reflection coefficient is typically set to 0.2, irrespectively of the discharge conditions)

 the other electron-surface processes (e.g. SEE by electron impact) are completely neglected

 the effects of the electrode material and surface conditions on these processes are not accounted for

Electron–surface interaction – description in PIC/MCC

simulations

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Secondary electrons induced by electrons

Yu et al., J. Vac. Sci. Technol. 20 950 (2002)

- total SEE coefficient

If a surface is bombarded with primary electrons (PE), secondary electrons (SE) are released.

- elastic reflection

- inelastic backscattering - emission of true SEs ( δ-

electrons )

D. Ruzic et al., J. Vac. Sci. Technol. 20 1313 (1981)

true

Schematic energy distribution of electron induced SEs

H. Seiler, J. Appl. Phys. 54 R1-18 (1983)



σ

depends on the PE’s energy and angle of incidence



σ

varies for different materials and depends on the surface properties

σ

SiO2 / Si

5, 7, 10, 20, 60 min oxidation

Isenpov Z et al, Nucl. Instr. Meth.. 268 3315 (2010)

A realistic model for the electron-surface interaction can be implemented in PIC/MCC simulations of CCPs.

σ = η

_e

+ η

_i

+ δ

η

_e

η

_i

δ

flux

PE Total

flux SE Total

 

(6)

Model for electron induced SEE

k w V

 

_max

[ we

⁽¹^ ⁾

]



0 max

0

) ) (

,

(   



 

 

  w



 

 

 _max,₀ ²

max( ) 1 2 

 



 k^s



 

 

 _max,₀ ²

max( ) 1 2 

 



 ^k^s







 

1 if 25 . 0

1 if 56 . 0

w k w

h

_e

 r

_e



_V

 h

_e_,max

w

₁

e

^(1w¹⁾

if 

_e,0

   

_e_,max

h

_e_,max

[ 1 w

₂

] ^e

^w²

^if ^ ^> ^

e,max

  ï

ï

0 , max ,

0 , 1( )

e e

w e



 



 

e

w

e



 

^,^max

2

( )  



h

_i

 r

_i



_V

  h

_e

 h

_i

 d

d  (1 r

_e

 r

_i

) 

_V

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Model for electron induced SEE

Param. Description Value Ref.

1 ε0 the threshold energy for electron induced

SEE 15 eV

2 ε_max,0 the energy of PE at the maximum

emission for normal incidence 400 eV [1]

3 σmax,0 the maximum emission at normal

incidence 2.5 [1]

4 k_s smoothness factor of the surface 1 [2-4]

5 ε_e,0 the threshold energy for elastic reflection 0 eV

6 ε_e,max the energy of PE at the maximum elastic

reflection 5 eV [5]

7 γ_e,max the maximum of the elastic reflection 0.5 [5]

8 Δ_e control parameter for the decay of η_e 5 [6]

9 re portion of the elastically reflected

electrons 0.03 [7]

10 r_i portion of the inelastically reflected

electrons 0.07 [7]

Model parameters for SiO₂ surfaces

Coefficients for the electron-induced SEE as the function of the incident electron’s energy for normal incidence,

for SiO₂ surfaces

[1] H. Seiler, J. Appl. Phys. 54 R1-18 (1983).

[2] J. R. M. Vaughan, IEEE Transactions on Electron Devices 36 1963 (1989).

[3] J. R. M. Vaughan, IEEE Transactions on Electron Devices 40 830 (1993).

[4] J. P. Verboncoeur, Plasma Phys. Control. Fusion 47 A231–A260 (2005).

[5] S. Barral, K. Makowski, Z. Peradzynsky, Phys.. Plasmas 10 4137 (2003).

[6] D. Sydorenko, PhD thesis (2006).

[7] V. P. Gopinath, J. P. Verboncoeur, C. K. Birdsall, Phys.. Plasmas 5 1535 (1998).

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Electron induced SEE in single-frequency Ar discharges

- only elastic electron reflection is taken into account

- the electron-induced SEE is neglected

- constant electron reflection coefficient: 0.2

- elastic reflection η_e - inelastic backscattering η_i - electron induced SEE δ

η_e, η_i, δ – depend on the PE’s energy and angle of incidence

• Argon + SiO₂ electrodes

• 6.7 cm electrode gap

• Driving voltage waveform:

• Frequency: 13.56 MHz

• Voltage amplitude range: 100 V – 2000 V

• Pressure: 0.5 Pa

• Gas temperature: 400 K

• Ion-induced SEEC: γ = 0.4 Discharge

conditions

Electron induced SEECs for SiO2

Model A

with simple description of the electron-surface interaction

Model B

with realistic description of the electron-surface interaction

PIC/MCC simulations are performed by using different approaches to describe the electron-surface

interactions:

) 2 cos(

)

(t V₀ ft

V  

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Plasma density

The central ion density obtained from model A and model B, n^A_iand n^B_i (left scale), and the density ratio n^B_i /n^A_i (right scale) as a function of the driving voltage

amplitude, V₀.

At high voltage amplitudes a significant difference is found between n^A_iand n^B_i .

Higher plasma density is obtained from the model which takes into account the electron-surface interaction in a realistic way.

6.7 cm, 0.5 Pa, 13.56 MHz, γ = 0.4

B Horváth, M Daksha, I Korolov, A Derzsi, J Schulze, Plasma. Sources Sci. Technol. 26 124001 (2017)

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Spatio-temporal distribution of discharge characteristics

• Model A: α-mode discharge operation

• Significantly different ionization dynamics in model B: two beams of energetic electrons are

generated at both electrodes during a RF period

(I) Strong ionization at the expanding sheath edge (II) Additional ionization

during sheath collapse

• Electric field reversal during sheath collapse in model B

Spatio-temporal maps of some selected discharge characteristics from models A and B

6.7 cm, 0.5 Pa, 13.56 MHz, 1000 V, γ

= 0.4

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Ionization rate

Contributions of different plasma particles to the total ionization obtained from model B.

δ-electrons (SEs induced by electrons) play an important role in the ionization dynamics.

The most significant portion of the ionization is directly generated by δ-electrons.

6.7 cm, 0.5 Pa, 13.56 MHz, 1000 V, γ = 0.4

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Electron induced SEE

• Formation of different groups of energetic SEs that hit the powered (grounded) electrode at different times around its sheath collapse and induce emission of δ-

electrons.

• γ-electrons generated at one electrode can hit the opposite electrode at high energies during the local sheath collapse and cause the emission of a high number

of δ-electrons.

• These δ-electrons cause significant ionization in the bulk and induce emission of SEs.

t/T_RF

6.7 cm, 0.5 Pa, 13.56 MHz, 1000 V, γ = 0.4

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Heavy-particle induced SEE – description in PIC/MCC simulations

A. V. Phelps and Z. Lj. Petrovic, Plasma Sources. Sci. Technol. 8 R21 (1999)

The SE yield depends on the incident particle energy and on the surface

conditions.

• electrons and ions are traced; other plasma species (e.g. fast neutrals) are not included in the model

• only the ion-induced SEE is taken into account

• a constant value for the (ion-induced)

secondary electron emission coefficient (SEEC), γ, is assumed

• γ = 0.1 in most studies, independently of the discharge conditions, the electrode material and the surface conditions

A. V. Phelps and Z. Lj. Petrovic PSST 8 R21 (1999)

A. V. Phelps, L. C. Pitchford, C Pédoussat, Z. Donko, PSST 8 B1-B2 (1999)

Z. Donko Phys. Rev. E 64 026401 (2001)

Formulas for energy-dependent SE yields for ions and atoms for

“clean” and “dirty” metal electrodes in Argon

Heavy-particle induced SEE

Simple description

Realistic description

• fast neutrals are also included in the model; SEs are induced by fast neutrals as well

• an effective SE yield, γ*, is calculated self- consistently

• γ* depends on the discharge conditions and surface properties

i N k

a a N

k

i i

N

a

i



 





¹ ¹

*

) ( )

(   



 ^

ⁱ

⁽ ^

ⁱ

^), ^

^a

⁽ ^

^a

⁾

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Heavy-particle induced SEE in multi-frequency Ar discharges Contents

• Amplitudes of the harmonics:

• The identical phases of the even harmonics (θ₂= θ₄ = θ) are varied from 0^o to 180^o.

• The phases of the odd harmonics are set to 0^o (θ₁ = θ₃ = 0^o) → peaks-type waveforms

• Driving voltage waveform

• Argon, 3 cm electrode gap

• Pressure: 3 Pa

• Gas temperature: 400 K

• Fundamental frequency: 13.56 MHz

• Number of harmonics: N = 1…4

• Voltage amplitude: = 800 V

What is the effect of using different models for the SEE

on the control of ion properties?









^N

k

kft

t

1

) 2

cos(

)

(   

 



^N

k k tot

1



N k N

k

1

0



  

 1

2

0

 

N



tot



tot

 f

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PIC/MCC models

Model Heavy particles – surface

interaction Electron–surface

interaction Particle species

A

simple description γ constant γ = 0.0, 0.2, 0.3

simple description

η_e= 0.2 e^-, Ar⁺

B

realistic description γ = γ*_d dirty surfaces γ = γ*_c clean surfaces

simple description

η_e= 0.2 e^-, Ar⁺, Ar^f

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Control of ion properties – model A (γ = 0.2)

Control of ion properties – model A (γ = 0.0, 0.2, 0.3)

0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0 0

5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0

0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0

0 5 1 0 1 5 2 0 2 5 3 0 3 5

0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0 0

5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0

0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0

0 5 1 0 1 5 2 0 2 5 3 0 3 5 ( a )

M e a n i o n e n e r g y

<E i > [ eV ]

( b )

Grounded electrode

I o n f l u x

N = 1 N = 2 N = 4

 = 0 . 0

 = 0 . 2

 = 0 . 3

G i [ 1014 m-2 s-1 ]

( c )

Powered electrode <E i > [ eV ]

 [ d e g ]

( d )

G i [ 1014 m-2 s-1 ]

 [ d e g ]

For certain constant values of γ, the mean ion energy can be controlled at constant ion flux by adjusting θ.

At low / high values of γ, <E_i> cannot be controlled separately from Г_i by adjusting θ.

A. Derzsi, B. Horváth, I. Korolov, Z. Donko, and J. Schulze, J. Appl. Phys. submitted

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Ionization dynamics – model A (γ = 0.0, 0.2, 0.3)

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

I o n i z a t i o n r a t e [ 1 0^{2 1} m^{- 3}s^{- 1} ]

x /L

0 . 1 0 . 2 0 . 4 0 . 8 1 . 6 3 . 2 6 . 3 1 0 . 0

( a ) N = 4 ,  = 0^o,  = 0 . 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8

1 . 0 ( b ) N = 4 ,  = 9 0^o,  = 0 . 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8

1 . 0 ( c ) N = 4 ,  = 1 8 0^o,  = 0 . 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8

1 . 0 ( d ) N = 4 ,  = 0^o,  = 0 . 2

x /L

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8

1 . 0 ( e ) N = 4 ,  = 9 0^o,  = 0 . 2

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8

1 . 0 ( f ) N = 4 ,  = 1 8 0^o,  = 0 . 2

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8

1 . 0 ( g ) N = 4 ,  = 0^o,  = 0 . 3

x /L

t /T_{R F}

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8

1 . 0 ( h ) N = 4 ,  = 9 0^o,  = 0 . 3

t /T_{R F}

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8

1 . 0 ( i) N = 4 ,  = 1 8 0^o,  = 0 . 3

t /T_{R F}

γ = 0.0

γ = 0.2

γ = 0.3

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Control of ion properties – model B ( γ*

_d

/ γ*

_c

)

By using realistic SEECs for heavy particles, Г_i doesn’t remain constant as a function of θ for high values of N.

0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0

0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0

5 1 0 1 5 2 0

0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0

0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0

5 1 0 1 5 2 0 ( a )

M e a n i o n e n e r g y

<Ei > [ eV ]

( b )

Grounded electrode

I o n f l u x

*_d *_c N = 1

N = 2 N = 4

Gi [ 1014 m-2 s-1 ]

( c )

Powered electrode <Ei > [ eV ]

 [ d e g ]

( d )

Gi [ 1014 m-2 s-1 ]

 [ d e g ]

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Self-consistently calculated SEEC – model B model B ( γ*

_d

/ γ*

_c

)

γ* changes as a function of θ for all N due to the change of the heavy particle energies at the electrodes.

0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0 0 . 0 0

0 . 0 5 0 . 1 0 0 . 1 5 0 . 2 0



d

*



[ d e g ]

N = 1 N = 2 N = 4

P o w .

G r .



_c

*

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Discharge conditions

Heavy-particle induced sputtering in multi-frequency Ar discharges

f = 13.56 MHz N = 1… 4

~ 1000 V

Sputtering yield

N. Matsunami et al., At. Data Nucl. Data Tables 31 1 (1984)

• Clean surfaces

• Sputtering (Cu)



_tot









^N

k

kft

t

1

) 2

cos(

)

(   







^N

k k tot

1



N k N

k

1

0



  



1 2

0

 

N



tot



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Control of heavy-particle properties – model B (γ*

_c

)

Tuning the control parameter for the particle energies (θ) leads to changes of the sputter yields due to heavy particles at both electrodes –

control of the flux of sputtered atoms at the electrodes.

6.7 cm, 0.5 Pa, f = 13.56 MHz, N ≤ 4, Φ_tot = 1000 V, γ*_c= 0.07

Sputtered Cu flux [1014 cm-2 s-1 ]

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Conclusions

 The various surface processes can have a strong influence on the discharge characteristics and the quality of the control of the particle properties at the electrodes

 The simulation results are largely influenced by the assumptions made on the surface coefficients

 It is important to use realistic surface coefficients in the simulations - assuming e.g. constant heavy-particle induced SEE coefficients in PIC/MCC simulations of CCPs or neglecting the electron induced SEE is not realistic under many discharge conditions

 Need for systematic experimental benchmark of particle based simulation tools

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Conclusions

 The various surface processes can have a strong influence on the discharge characteristics and the quality of the control of the particle properties at the electrodes

 The simulation results are largely influenced by the assumptions made on the surface coefficients

 It is important to use realistic surface coefficients in the simulations - assuming e.g. constant heavy-particle induced SEE coefficients in PIC/MCC simulations of CCPs or neglecting the electron induced SEE is not realistic under many discharge conditions

 Need for systematic experimental benchmark of particle based simulation tools

Acknowledgements US NSF grant no. 1601080

National Research, Development and Innovation Office: K – 119357 and PD-121033 grants German Research Foundation (DFG) within the frame of the collaborative research centre SFB-TR 87

Thank you for your attention.

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Plasma density under various discharge conditions

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The role of δ- electrons in the ionization dynamics

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Control of heavy-particle properties – model B (γ*

_c

)

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Control of the flux of sputtered atoms– model B (γ*

_c

)

6.7 cm, 0.5 Pa, f = 13.56 MHz, N ≤ 4, Φ_tot = 1000 V, e- refl. 20 %, γ*_c= 0.07

[1014 cm-2 s- 1 ]

Surface processes in low-pressure capacitively coupled plasmas