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

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Mass-balance Differential equation for across-die distribution of the radicals Due to complex character of dependency of the introduced parameters on the plasma recipe as well as the difference in generation rates of different radicals it is reasonable to introduce a dimensionless form for radical concentration: This transformation leads to the dimensionless form of the mass balance equation: 2 γ ⎛ γλ ⎞ cn0 n0 = andθ 0 = n0 / = Here: k ⎜ V D ⎟ ⎝ ⎠ 3γλ Solution of these mass balance equations generates across-die distributions of concentrations of all radicals participating in etch reactions. Gas-kinetic properties of radicals (D, λ, c) are calculated based on Chapman-Enskog kinetic theory. Approximate solution of the mass-balance equation clearly demonstrates that an across-die distribution of radicals is characterized by a complex PD dependency, more complicated than the “traditional” reverse PD: 1/PD. n θ = 2 ⎛ γλ ⎞ ⎜ ⎟ ⎝ D ⎠ r ⎡ 1 3 λ r ⎤ r 1−θ ( r) ⎢ + F ⎥ r ⎣θ0 4 L ⎦ 2 ( r ) + λ ∆θ ( ) = 0 Approximate solution 2 ⎡ 1 3 λ r ⎤ 1− λ ∆⎢ + F( r ) ⎥⎦ r ≈ ⎣θ0 4 L θ ( r ) ⎣θ0 4 L θ ( r ) ≈ ⎦ ⎡ 1 3 λ r ⎤ ⎢ + F( r ) ⎥⎦ ⎣θ0 4 L F = ∫ r r r r PD – GDSII 2r d r′ r 2 ⎛ r′ ⎞ ⎜1+ ⎟ 2 ⎝ h ⎠ ( r, φ) ˆ χ( r′ + r ) ρ( r′ + r ) 2 Sticking coefficients Visibility factor Copyright ©2008, Mentor Graphics. 10
Radical Flux to the Feature � When a radical distribution across “effective reactive” surface is known we can determine a flux coming to the feature from a small area of the “effective reactive” surface and to integrate it through the all area of visibility. λ π λ ∫ ϕ ∫ ( ϕ ) 2 r d 1 N r1 , 1 r1dr 1 3 0 0 2 c Γ = 8π r r 2 r r 2 ( h + r + r1 ) Output of the Microloading Analysis Consumption Flux Copyright ©2008, Mentor Graphics. 11
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 and 8: • Neutral radical generation •
Page 9: Mass-balance Differential equation
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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