Two-dimensional Simulation of RF CF 4 Discharge Using the - - PowerPoint PPT Presentation

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Two-dimensional Simulation of RF CF 4 Discharge Using the - - PowerPoint PPT Presentation

Jul 06, 2023 379 likes •518 views

Two-dimensional Simulation of RF CF 4 Discharge Using the Particle-in-Cell/Monte Carlo Method Kazuki DENPOH Central Research Laboratory, Tokyo Electron Ltd. Kenichi NANBU Institute of Fluid Science, Tohoku Univ. GEC-51 & ICRP-4 K. Denpoh

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SLIDE 1
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

Two-dimensional Simulation of RF CF4 Discharge Using the Particle-in-Cell/Monte Carlo Method

Kazuki DENPOH

Central Research Laboratory, Tokyo Electron Ltd.

Kenichi NANBU

Institute of Fluid Science, Tohoku Univ.

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SLIDE 2
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

OUTLINE

  • Introduction
  • Modeling of rf CF4 plasma

– Plasma reactor model – Species and collisions – Particle-in-Cell/Monte Carlo method

  • Results

– Discharge structure – Energy/Angular distribution functions

  • Summary
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SLIDE 3
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

Introduction

  • Fluorocarbon gases(CF4, C2F6, C4F8, ...) are widely used in

plasma-assisted etching processes.

  • In previous work, we were successful in 1-D simulation of rf

CF4 plasma using PIC/MC method.

– 1-D discharge structure (density, temperature, reaction rate, etc...) – sustaining mechanism – effects of secondary electron emission and electrode spacing

  • In this work, the 1-D PIC/MC code is extended to

axisymmetric plasma.

– 2-D discharge structure – Energy/Angular distribution functions

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SLIDE 4
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

Modeling of RF CF4 Plasma

  • Species

– CF4 – electron – CF3

+, CF2 +, CF+, C+, F+

– F-, CF3

  • Collision

– electron-CF4 – ion-CF4 – positive-negative ion recombination

k = 5.5×10-13 (m-3s-1)

– electron-CF3

+ recombination

k = 3.95×10-9 Te

  • 0.5Ti
  • 1

(m-3s-1) z r

CF4 200 mTorr

～

D=25.4 mm Rd=60 mm Rc=75 mm Vd=Vrfsin2πft+Vdc Vrf=200 V γ=0 V=Vasin2πft Cb

10

  • 2

10

  • 1

10 10

1

10

2

10

3

Electron Energy (eV)

10-3 10

  • 2

10

  • 1

10 101 102

Cross-Section (10-16 cm2)

Qm Qv4 Qv3 Qv2×3 Qdn Qi(CF3

+)

Qi(CF2

+)

Qi(CF+) Qi(C+) Qi(F+) Qa(F-) Qa(CF3

  • )
slide-5
SLIDE 5
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

Ion-CF4 Collision Model

  • The RRK theory is adopted to describe unimolecular decomposition of

activated complex.

  • Elastic collision and 183 endothermic reactions (dissociation, electron

detachment).

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SLIDE 6
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

Particle-in-Cell / Monte Carlo Method

  • Poisson equation: ADI with multi-grid method
  • Equation of motion: Leap-frog scheme
  • Collisions: Monte Carlo

Motion & Collisions ( F → X,C ) ( C → C’ ) Charge Density ( X →ρ) Force ( E → F ) Electric Field ( ρ→ E ) Δt

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SLIDE 7
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

Electric Field (2π f t = π)

  • 6
  • 4
  • 2

2 4 5 10 15 20 25 15 30 45 60 75

Ez (10

4 V/m)

z (mm) r (mm)

  • 2

2 4 5 10 15 20 25 15 30 45 60 75

Er ( 1

4 V/m)

z ( m m ) r ( m m )

  • Double-layer can be observed in both Ez and Er.
  • Electric field is strengthened around the edge of powered electrode.
slide-8
SLIDE 8
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

Electron and Ion Densities

  • CF3

+, F-, and CF3

  • are dominant

ions in the discharge.

  • Negative ion density is about 30

times greater than electron density.

  • Densities have maxima around the

edge of powered electrode.

5 10 15 20 25

z (mm)

1 2 3

Density (10

16 m

  • 3)

Electron (×10) CF3

+

F

  • CF3
  • Electron

CF3

+

F- CF3

slide-9
SLIDE 9
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

Electron and Ion Temperatures

Electron CF3

+

F- CF3

  • Bulk electron temperature is about

1.7 eV.

  • High temperature region

– Electron: around the edge of powered electrode – CF3

+: on the powered electrode

– F- and CF3

  • : in the middle of sheath

near the powered electrode

slide-10
SLIDE 10
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

Reaction Rates

  • Discharge is sustained by electrons

produced in ionization.

  • Major loss process of negative ions

is ion-ion recombination.

  • CF3

+-CF4 reactions are remarkable

in the sheath.

5 10 15 20 25

z (mm)

2 4 6 8

Rate (×10

20 m

  • 3s
  • 1)

Ionization Electron Attachment Electron Detachment (×10) Ion-ion Recombination Electron-CF3

+ Recombination (×10)

CF3

+-CF4 Reaction

Ionization Electron Attachment Ion-ion Recombination CF3

+-CF4 reactions

slide-11
SLIDE 11
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

  • 200
  • 100

100 200 5 10 15 20 25 15 30 45 60 75

V ( V ) z (mm) r (mm)

EEDF, IEDF and Time-Averaged Potential

  • Negative-ion flux onto powered electrode is 0.
  • The ion energy at maximum IEDF agrees with potential fall from Vp to Vdc.

(Plasma potential Vp is 61 V. Self-bias Vdc is -62 V.)

25 50 75 100 125 150

Energy (eV)

0.00 0.05 0.10 0.15 0.20

EDF

Electron Positive Ion

slide-12
SLIDE 12
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

EADF and IADF

  • IADF is directional as expected.
  • EADF can be described as Cosine Law.

30 60 90

Angle (deg.)

0.0 0.2 0.4 0.6 0.8 1.0

EADF

r = 4.7 mm r = 30.4 mm r = 55.1 mm Cosine Law Electron 30 60 90

Angle (deg.)

2 4 6 8 10 12

IADF

r = 4.7 mm r = 30.4 mm r = 55.1 mm Cosine Law Positive Ion

slide-13
SLIDE 13
  • K. Denpoh and K. Nanbu

GEC-51 & ICRP-4

Summary

  • Axisymmetric PIC/MC code for rf CF4 discharge has been

developed.

  • Discharge structure is characterized by an enhanced electric

field around the edge of powered electrode.

  • Double-layer appears also in radial component of electric field

near cylindrical reactor wall.

  • We also investigate the energy/angular distribution functions
  • f charged species arriving at the powered electrode.