Design specific variation in pattern transfer by via/contact etch ...

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Flux Boundary Condition Surface Across-die distribution of radical concentration c Γ = 8π surface Radical Flux at Top of the Feature λ π λ ∫ ϕ ∫ ( ϕ ) 2 r d 1 N r1 , 1 r1dr 1 3 0 0 2 r r 2 r r 2 ( h + r + r1 ) Γ Y C dS2 r Γi = 2 πh Pattern-dependent Flux Consumption ( r) ∫ δδ Ω = sin Θ Θδδ Θ Θδϕ δϕ φ 1 r 2 2 Ni ( r) ci h = 4 π R r χ r r r r ∫∫ 1 πR dS 1 ( r+ r) ρ( r, φ ) 1 0 0 Θ r r 2 r r 12 r r r r = r − r Surface “2” dS 2 i i r1dr 1d 1 φ ( χPR( 1−ρ( r1, 1 φ ) ) + χ ( AR) ρ( r1, 1 φ ) ) 2 r r2 ( h + r1 −r ) 1 1 X 2 dr1 ⎡ r 2 ⎛r ⎤ 1⎞ ⎢1+ ⎜ ⎟ ⎥ ⎢⎣ ⎝h⎠ ⎥⎦ 2 1 2 Surface “1” Copyright ©2008, Mentor Graphics. 2 8 =
Mass-balance Differential equation for radical distribution at the flux-BC surface • averaging the diffusion equations along the plasma thickness (L), • using the flux BC • and assuming that diffusion is much faster than the gas flow Flux BC: Radical fluxes Γ i 0 coming from plasma impinges a wafer surface. Fluxes impinged a PR surface and an etched feature are consumed with different probabilities: χ i PR and χ i (χ i is AR dependent parameter). Density of consumed flux of neutrals, which is the difference of the densities of incoming and reflected fluxes depends on the PD: Γ C dS 2 = r Γi = 2 πh ( r ) N ∫ R i r c 4 ( r ) r χ i h π r 2 2π R ∫∫ ( r + r ) ρ( r , φ ) 1 0 0 i i r1dr 1dφ1 ( χ PR ( 1− ρ( r1 , φ1) ) + χ ( AR) ρ( r1 , φ1) ) 2 r r 2 ( h + r1 − r ) 1 1 2 dr1 ⎡ r 2 ⎛ r ⎤ 1 ⎞ ⎢1 + ⎜ ⎟ ⎥ ⎢⎣ ⎝ h ⎠ ⎥⎦ 2 2 = ( r, φ) 2 2 ⎪⎧ ⎡∂ n ⎤⎪⎫ i 1 ∂ ni 1 ∂ni nicF 0 = D⎨⎢ + ⋅ + ⋅ − 2 2 2 ⎥⎬ ⎪⎩ ⎣ ∂r r ∂φ r ∂r ⎦⎪⎭ 4L 2 r r r r r d r ′ F( r, φ) = ∫ ˆ χ( r ′ + r ) ρ( r ′ + r ) r 2 2 ⎛ r ′ ⎞ ⎜ ⎜1+ ⎟ 2 ⎝ h ⎠ + γ − kV n r ⎧χ ⎫ ˆ χ( r ′ ) = ⎨ ⎬ ⎩χ PR ⎭ Stenger, AIChE Journal, 33, 1187-1190 (1987) Y φ 1 r r 1 dS 1 X Θ r r δδ Ω = sin Θ Θδδ Θ Θδϕ δϕ 2 r r r 12 r r r r = r − r 1 Surface “2” dS 2 Surface “1” Copyright ©2008, Mentor Graphics. 2 9 i
Page 1 and 2: Design Design Design specific speci
Page 3 and 4: Etch Step in Pattern Transfer Simul
Page 5 and 6: Effects of Aspect Ratio & Microload
Page 7: • Neutral radical generation •
Page 11 and 12: Radical Flux to the Feature � Whe
Page 13 and 14: Die-level analysis: Calculation of
Page 15 and 16: Thin & Thick Polymer Regimes T. Tat
Page 17 and 18: Approximation of “Thin Polymer”
Page 19 and 20: Etch Stop Condition � Etch stops
Page 21 and 22: VCE Input/Output Copyright ©2008,
Page 23 and 24: Calculation of Gas Kinetic Paramete
Page 25 and 26: Calibration Methodology � The maj
Page 27 and 28: VCE Capability Based on accurate ca
Page 29 and 30: VCE Capability Across-die etch hot-
Page 31 and 32: APPLICATIONS of VCE Copyright ©200
Page 33 and 34: Process-Aware Design Optimization v
Page 35 and 36: Process optimization • VCE predic
Page 37 and 38: F Concentration, mass fraction Redu
Page 39 and 40: Averaged pattern density R=1000µm
Page 41 and 42: OBSERVATION: FIB inspection of 0.26
Page 43 and 44: CF2 flux F flux SEMbar (1) in all01
Page 45 and 46: Calibration/Prediction - Resist Mod
Page 47 and 48: Calibration/Prediction - Main Etch
Page 49: Mentor Graphics Corp., San Jose, CA

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