NATIONAL TECHNICAL UNIVERSITY OF ATHENS Scaling-up and bridging scales in process engineering Andreas G. Boudouvis Professor & Dean School of Chemical Engineering NTUA, Athens, Greece http://www.chemeng.ntua.gr/dep/boudouvis/ Postgraduate Program "Mathematical Modeling in Modern Technologies and Finance“ , NTUA, 2 Dec. 2015
NATIONAL TECHNICAL UNIVERSITY OF ATHENS A scale-up triumph: Penicillin Production Scaling-up of penicillin production became a top-priority program of complexity and size rivaling that of the Manhattan Project Sir Alexander Fleming holding a petri dish with Penicillium notatum culture, 1928 (Left) and inspecting a 15,000 gallon “deep tank” used in penicillin production at a Squibb plant in New Brunswick, NJ, June 1945 (Right). The project was completed in a very short time 1939: Florey (Oxford University) produces enough penicillin to test it on mice. But, he cannot produce enough for human clinical trials. 1943: A dose of penicillin cost: $20. 1946: A dose of penicillin cost: 55 cents. Submerged fermentation process is still the dominant production technique for penicillin
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Deposition processes From ordinary life to advanced materials …coatings, nanomaterials, MEMS…
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Metal-organic Chemical Vapor Deposition of Aluminum (Al - MOCVD) Metal-organic CVD high conformal coverage of complex-in-shape substrates low deposition temperature convenient handling of gaseous byproducts high throughput Precursor: DMEAA
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Chemical Vapor Deposition: Transport + Reaction forced – convection region gas phase reactions + desorption transport to adsorption of adsorbed surface of film precursors species CVD reactor cooling surface diffusion surface reaction I NLET wafer OUTLET CVD process susceptor I R Lamps
A typical chemist’s prospective… In the “test tube” : Dimethylethylamine alane (DMEAA) Alane Dimethylethyleamine (DMEA) C 2 H 5 H 3 C CH 3 H N C 2 H 5 Al H + H 3 C CH 3 H Al N H H H Al + 3/ 2H 2
NATIONAL TECHNICAL UNIVERSITY OF ATHENS The engineer’s prospective... Scale-up: from the “test tube” to production MFC MFC T P N 2 Showerhead DMEAA Wafer P Τ Pump Trap Test tube CIRIMAT-CNRS, ENSIACET, Toulouse
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Chemical Vapor Deposition: Transport (+ Reaction) (Aluminum deposition) Temperature Velocity T (Κ) U(m/ s) U(m/ s) Xenidou et al., Surface Coatings Technology 201, 8868 (2007)
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Chemical Vapor Deposition: (Transport +) Reaction (Aluminum deposition) dimethylethylamine alane (DMEAA) dimethylethylamine (DMEA) + alane (AlH 3 ) C 2 H 5 H 3 C CH 3 Al C 2 H 5 N H 3 C CH 3 + H H H Al N Gas-phase H H H H 2 reaction C 2 H 5 Surface H 3 C CH 3 reactions C 2 H 5 H 3 C CH 3 N H 2 N C 2 H 5 H 3 C CH 3 Al N H H H H H Al Al H Al H H H Yun et al., J. Vacuum Sci. Technol. 16, 419 (1998); Jang et al., Thin Solid Films 333, 137 (1998)
NATIONAL TECHNICAL UNIVERSITY OF ATHENS The key engineering motivation: Determine “operating windows” Industrial demands high deposition rates Layer thickness control thickness uniformity economic use of substrate substrate the reactants uniform layer non-uniform layer Reactor design Reactor operating Film conditions properties - pressure - deposition rate - temperature - thickness uniformity - flow rates, … - film composition, …
NATIONAL TECHNICAL UNIVERSITY OF ATHENS The engineering analysis outcome: Reliable Process Design Temperature effect on Aluminum growth rate 300 300 T = 160 o C T = 200 o C 250 250 200 200 150 150 100 model 100 Al Growth Rate (Α /min) model 50 experiment 50 experiment 0 0 0 5 10 15 20 25 0 5 10 15 20 25 300 300 T = 220 o C T = 260 o C 250 250 model 200 200 experiment 150 150 100 100 model 50 experiment 50 0 0 0 5 10 15 20 25 0 5 10 15 20 25 Xenidou et al., Surface Coatings Technology 201, 8868 (2007)
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Engineering Analysis The goal : Computer-aided process analysis based on first-principles – An enabling tool The means : Realistic model development – Input from experiment Validation – Comparison with experiment The benefits : Understanding mechanisms Savings on experimental cost and manpower Improve experimental design Guided experiments
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Transport Processes Modeling Summary (N species, single phase) ● 3 + N Physical (conservation) Laws – 3 + N differential equations ∂ ρ + ∇ ⋅ ρ = Mass: ( ) 0 v ∂ t ∂ Momentum: ρ + ∇ ⋅ ρ = ρ − ∇ + ∇ ⋅ τ ( ) ( ) p v vv g ∂ t ∂ ∂ T p ρ + ⋅ ∇ = ∇ ⋅ ∇ + + ⋅ ∇ c p [ T ] ( k T ) [ p ] Energy: v v ∂ ∂ t t ( ) ∇⋅ ρ = ∇ + + 2 Y D Y R S Species Equation: v i i i i i ● 3 + N Unknowns: p, v , T, Y i ρ = ρ( p, T), e.g. ρ= p/RT (ideal gases) plus constitutive equations { } τ = τ τ = µ ∇ + ∇ T ( ), e . g . ( ) (Newtonian fluids) v v v ● Boundary and initial conditions
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Computer-aided Analysis Partial Differential Equations Mathematical (conservation laws) model Numerical Discretization finite element method approximation/ finite volume method Code implementation Algorithms (solvers) Cost-effective High-performance machines computations Reliability of Discretization refinement solutions Comparison with experiments (Validation)
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Governing Equations 2-D Axisymmetric Geometry – Cylindrical coordinates FLUENT CFD package Momentum Equations ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ 1 1 p 1 u 2 1 u u ( ) ( ) ( ) ρ + ρ = − + µ − ∇⋅ + µ + − ρ 2 x x r r u u r u u r u r g ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ x x r x 3 r x r r x r x x r r r x ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ 1 1 1 1 2 p u u u ( ) ( ) ( ) ρ + ρ = − + µ + + µ − ∇⋅ − r x r r u u r u u r r 2 u ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ x r r r 3 r x r r r r x x r r r r µ 2 2 u ( ) u − µ + ∇⋅ + ρ θ 2 r u 2 3 r r r ∂ ∂ ∂ ∂ ∂ ∂ 1 1 u 1 u u u ( ) ( ) ρ + ρ = µ θ + µ θ − ρ θ 3 r r u u r u u r r θ θ ∂ ∂ ∂ ∂ ∂ ∂ x r 2 r x r r x x r r r r r Continuity Equation ( ) ( ) ∂ ρ ∂ ρ ρ u u u + + = x r r 0 ∂ ∂ x r r Species Equation ( ) ∇⋅ ρ = −∇⋅ + + uY J R S i i i i Energy Equation [ ] ∑ ∇⋅ ρ + = ∇⋅ ∇ − ( ) u E p k T h J i i i
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Discretization – Finite Volume Method ρ Φ = Γ Φ + ( ) ( ) div u div grad S φ convection diffusion sources Integration over each volume of the mesh: ( ) ( ) ∫ ∫ ∫ ρ Φ = Γ ∇Φ + div u dV div dV S dV Φ Φ CV CV CV ( ) ∫ ∫ = ⋅ div a dV n adA Divergence Theorem: CV A Integral Form ( ) ∫ ∫ ∫ ⋅ ρ Φ = ⋅ Γ ∇Φ + n u dA n dA S dV Φ Φ A A CV Versteeg & Malalasekera “Introduction To Computational Fluid Dynamics-The Finite Volume Method”, Longman, 1995
NATIONAL TECHNICAL UNIVERSITY OF ATHENS Discretization (conl’d) Assembly of the system to be solved Substitution yields algebraic equations with only center values involved. Subscript NB refers to neighboring cells. ∑ Φ = Φ + a a S C C NB NB 0 0 NB Φ = A b C A: Matrix of coeffients Φ C : Unkowns at cell centers b: sources
NATIONAL TECHNICAL UNIVERSITY OF ATHENS High performance computing (cont’d) [http://febui.chemeng.ntua.gr/pegasus.htm]
NATIONAL TECHNICAL UNIVERSITY OF ATHENS MOCVD: Aluminum deposition ● Collaborative project: CIRIMAT/ENSIACET, Toulouse – NTUA, Athens Teams: Athens: A. Boudouvis, I. Aviziotis, N. Cheimarios, D. Xenidou Toulouse: C. Vahlas, T. Duguet, N. PrudHomme Main objectives optimum process parameters (temperature, flow rates, …) optimum reactor configuration (showerhead-substrate distance, shower-plate, …) Xenidou et al., Surface Coatings Technology 201, 8868 (2007); Xenidou et al. J. Electrochemical Soc. 157, D633 (2010)
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