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 and K. Nanbu
OUTLINE • Introduction • Modeling of rf CF 4 plasma – Plasma reactor model – Species and collisions – Particle-in-Cell/Monte Carlo method • Results – Discharge structure – Energy/Angular distribution functions • Summary GEC-51 & ICRP-4 K. Denpoh and K. Nanbu
Introduction • Fluorocarbon gases(CF 4 , C 2 F 6 , C 4 F 8 , ...) are widely used in plasma-assisted etching processes. • In previous work, we were successful in 1-D simulation of rf CF 4 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 GEC-51 & ICRP-4 K. Denpoh and K. Nanbu
Modeling of RF CF 4 Plasma z • Species D =25.4 mm – CF 4 – electron CF 4 200 mTorr γ =0 r + , CF 2 + , CF + , C + , F + – CF 3 R c =75 mm – F - , CF 3 - V d = V rf sin2 π ft + V dc C b V rf =200 V R d =60 mm ～ • Collision V = V a sin2 π ft – electron-CF 4 10 2 – ion-CF 4 Q m Cross-Section (10 -16 cm 2 ) Q v3 10 1 + ) Q i (CF 3 – positive-negative ion Q v4 Q dn recombination 0 10 Q i (C + ) Q v2 × 3 k = 5.5 × 10 -13 (m -3 s -1 ) Q i (F + ) -1 10 + recombination + ) – electron-CF 3 Q i (CF 2 Q i (CF + ) k = 3.95 × 10 -9 T e -2 Q a (F - ) -0.5 T i -1 (m -3 s -1 ) 10 - ) Q a (CF 3 10 -3 -2 -1 0 1 2 3 10 10 10 10 10 10 Electron Energy (eV) GEC-51 & ICRP-4 K. Denpoh and K. Nanbu
Ion-CF 4 Collision Model The RRK theory is adopted to describe unimolecular decomposition of • activated complex. Elastic collision and 183 endothermic reactions (dissociation, electron • detachment). GEC-51 & ICRP-4 K. Denpoh and K. Nanbu
Particle-in-Cell / Monte Carlo Method Poisson equation: ADI with multi-grid method • Equation of motion: Leap-frog scheme • Collisions: Monte Carlo • Motion & Collisions Charge Density ( F → X , C ) ( C → C ’ ) ( X → ρ ) Δ t Force Electric Field ( E → F ) ( ρ → E ) GEC-51 & ICRP-4 K. Denpoh and K. Nanbu
Electric Field (2 π f t = π ) Double-layer can be observed in both E z and E r . • Electric field is strengthened around the edge of powered electrode. • 4 4 2 4 V/m) 2 4 V/m) 0 0 0 1 ( E z (10 E r -2 -2 -4 25 25 20 20 z (mm) z 15 15 -6 75 ( m 15 60 10 m 10 30 45 ) 45 30 5 5 60 15 0 0 75 0 r (mm) ) m m ( r GEC-51 & ICRP-4 K. Denpoh and K. Nanbu
Electron and Ion Densities - are dominant + , F - , and CF 3 CF 3 • Electron ions in the discharge. Negative ion density is about 30 • times greater than electron density. Densities have maxima around the CF 3 + • edge of powered electrode. 3 + -3 ) CF 3 F - 16 m 2 Density (10 - F - CF 3 1 CF 3 - Electron ( × 10) 0 0 5 10 15 20 25 z (mm) GEC-51 & ICRP-4 K. Denpoh and K. Nanbu
Electron and Ion Temperatures Bulk electron temperature is about • Electron 1.7 eV. High temperature region • – Electron: around the edge of powered electrode CF 3 + – CF 3 + : on the powered electrode – F - and CF 3 - : in the middle of sheath near the powered electrode F - CF 3 - GEC-51 & ICRP-4 K. Denpoh and K. Nanbu
Reaction Rates Discharge is sustained by electrons • Ionization produced in ionization. Major loss process of negative ions • is ion-ion recombination. + -CF 4 reactions are remarkable CF 3 Electron Attachment • in the sheath. 8 Ionization Electron Attachment Electron Detachment ( × 10) -1 ) Ion-ion Recombination 6 Ion-ion Recombination -3 s + Recombination ( × 10) Electron-CF 3 20 m + -CF 4 Reaction CF 3 Rate ( × 10 4 + -CF 4 reactions CF 3 2 0 0 5 10 15 20 25 z (mm) GEC-51 & ICRP-4 K. Denpoh and K. Nanbu
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 V p to V dc . • (Plasma potential V p is 61 V. Self-bias V dc is -62 V.) 0.20 200 0.15 100 EDF ) Electron V 0.10 ( 0 V 0.05 -100 Positive Ion 25 20 z (mm) 15 -200 0.00 15 10 30 0 25 50 75 100 125 150 45 5 Energy (eV) 60 0 75 r (mm) GEC-51 & ICRP-4 K. Denpoh and K. Nanbu
EADF and IADF IADF is directional as expected. • EADF can be described as Cosine Law. • 1.0 12 Positive Ion Electron 10 0.8 r = 4.7 mm r = 4.7 mm r = 30.4 mm r = 30.4 mm 8 EADF IADF r = 55.1 mm r = 55.1 mm 0.6 Cosine Law Cosine Law 6 0.4 4 0.2 2 0 0.0 0 30 60 90 0 30 60 90 Angle (deg.) Angle (deg.) GEC-51 & ICRP-4 K. Denpoh and K. Nanbu
Summary • Axisymmetric PIC/MC code for rf CF 4 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 of charged species arriving at the powered electrode. GEC-51 & ICRP-4 K. Denpoh and K. Nanbu
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