Scaling-up and bridging scales in process engineering Andreas G. - - PowerPoint PPT Presentation

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Postgraduate Program "Mathematical Modeling in Modern Technologies and Finance“, NTUA, 2 Dec. 2015

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/

A scale-up triumph: Penicillin Production

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

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 Scaling-up of penicillin production became a top-priority program

• f complexity and size rivaling that of the Manhattan Project

Deposition processes

From ordinary life to advanced materials

…coatings, nanomaterials, MEMS…

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Metal-organic Chemical Vapor Deposition of Aluminum (Al - MOCVD)

Precursor: DMEAA

Metal-organic CVD

 high conformal coverage of complex-in-shape substrates  low deposition temperature  convenient handling of gaseous byproducts  high throughput

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Chemical Vapor Deposition: Transport + Reaction

I R Lamps cooling I NLET OUTLET

susceptor wafer

surface diffusion

• f film precursors

adsorption forced – convection region transport to surface + gas phase reactions desorption

• f adsorbed

species surface reaction

CVD reactor CVD process

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H3C Al H H H N C2H5 CH3 Al H H H H3C N C2H5 CH3

+

Al + 3/ 2H2

Dimethylethylamine alane (DMEAA) Alane Dimethylethyleamine (DMEA)

In the “test tube” : A typical chemist’s prospective…

The engineer’s prospective... Scale-up: from the “test tube” to production

CIRIMAT-CNRS, ENSIACET, Toulouse

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Showerhead Wafer Pump Trap

P DMEAA

MFC

T

Τ N 2

P

MFC

Test tube

Chemical Vapor Deposition: Transport (+ Reaction)

Xenidou et al., Surface Coatings Technology 201, 8868 (2007)

T(Κ)

Temperature

U(m/ s)

Velocity

U(m/ s)

(Aluminum deposition)

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

CH3 H3C N C2H5 CH3 H3C N C2H5 H2 Al Al H H H Al H H H CH3 H3C Al H H H N C2H5 CH3 H3C Al H H H N C2H5 CH3 H3C N C2H5

+

Al H H H

Gas-phase reaction Surface reactions

H2

Yun et al., J. Vacuum Sci. Technol. 16, 419 (1998); Jang et al., Thin Solid Films 333, 137 (1998)

Chemical Vapor Deposition: (Transport +) Reaction

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

dimethylethylamine alane (DMEAA) dimethylethylamine (DMEA) + alane (AlH3)

(Aluminum deposition)

The key engineering motivation: Determine “operating windows”

Reactor operating conditions

• pressure
• temperature
• flow rates, …

Film properties

• deposition rate
• thickness uniformity
• film composition, …

Reactor design

 high deposition rates  thickness uniformity  economic use of

the reactants

Industrial demands

substrate substrate

Layer thickness control

uniform layer non-uniform layer

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The engineering analysis outcome: Reliable Process Design

Temperature effect on Aluminum growth rate

Al Growth Rate (Α/min)

50 100 150 200 250 300 5 10 15 20 25 model experiment 50 100 150 200 250 300 5 10 15 20 25 model experiment 50 100 150 200 250 300 5 10 15 20 25 model experiment

T = 160oC T = 200oC T = 220oC T = 260oC

50 100 150 200 250 300 5 10 15 20 25 model experiment

Xenidou et al., Surface Coatings Technology 201, 8868 (2007)

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

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

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Engineering Analysis

Transport Processes Modeling Summary

(N species, single phase)

• 3 + N Physical (conservation) Laws – 3 + N differential equations

) ( t = ρ ⋅ ∇ + ∂ ρ ∂ v

] p t p [ ) T k ( ] T t T [ cp ∇ ⋅ + ∂ ∂ + ∇ ⋅ ∇ = ∇ ⋅ + ∂ ∂ ρ v v

τ ⋅ ∇ + ∇ − ρ = ρ ⋅ ∇ + ρ ∂ ∂ p ) ( ) ( t g vv v

Mass: Momentum: Energy:

• 3 + N Unknowns: p, v, T,

ρ = ρ(p, T), e.g. ρ=p/RT (ideal gases)

{ }

T

) ( . g . e ), ( v v v ∇ + ∇ µ = τ τ = τ

(Newtonian fluids) plus constitutive equations

• Boundary and initial conditions

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( )

2 i i i i i

Y D Y R S ∇⋅ ρ = ∇ + + v

Species Equation:

i

Y

Mathematical model Numerical approximation/ Code implementation

Partial Differential Equations (conservation laws) Discretization

finite element method finite volume method

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Computer-aided Analysis

Algorithms (solvers) High-performance machines

Cost-effective computations Reliability of solutions (Validation)

Discretization refinement Comparison with experiments

Governing Equations

2-D Axisymmetric Geometry – Cylindrical coordinates

( ) ( ) ( )

1 1 1 2 1 2 3

x x r x x r x

u u u p r u u r u u r u r g r x r r x r x x r r r x ρ ρ µ µ ρ  ∂   ∂  ∂ ∂ ∂ ∂ ∂ ∂     + = − + − ∇⋅ + + −         ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂         

Momentum Equations

( ) ( ) ( ) ( )

2 2

1 1 1 1 2 2 3 2 2 3

x r r x r r r r

u u u p r u u r u u r r u r x r r r r x x r r r r u u u r r r

θ

ρ ρ µ µ µ µ ρ  ∂  ∂  ∂  ∂ ∂ ∂ ∂ ∂     + = − + + + − ∇⋅ −         ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂         − + ∇⋅ +  

( ) ( )

x r r

u u u x r r ρ ρ ρ ∂ ∂ + + = ∂ ∂

Continuity Equation

( ) ( )

3 2

1 1 1

r x r

u u u u r u u r u u r r r x r r x x r r r r r

θ θ θ θ θ

ρ ρ µ µ ρ ∂   ∂ ∂ ∂ ∂ ∂     + = + −       ∂ ∂ ∂ ∂ ∂ ∂      

( )

i i i i

uY J R S ρ ∇⋅ = −∇⋅ + +   

Species Equation

[ ]

( )

i i i

u E p k T h J ρ   ∇⋅ + = ∇⋅ ∇ −    

∑

 

Energy Equation

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

FLUENT CFD package

Discretization – Finite Volume Method

( ) ( )

CV CV CV

div u dV div dV S dV ρ

Φ Φ

Φ = Γ ∇Φ +

∫ ∫ ∫



Integration over each volume of the mesh:

Divergence Theorem:

( )

CV A

div a dV n adA = ⋅

∫ ∫

  

( )

A A CV

n u dA n dA S dV ρ

Φ Φ

⋅ Φ = ⋅ Γ ∇Φ +

∫ ∫ ∫

  

Integral Form convection diffusion sources

( ) ( ) div u div grad Sφ ρ Φ = Γ Φ + 

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Versteeg & Malalasekera “Introduction To Computational Fluid Dynamics-The Finite Volume Method”, Longman, 1995

Substitution yields algebraic equations with only center values involved. Subscript NB refers to neighboring cells.

C C NB NB NB

a a S Φ = Φ +

∑

C

A b Φ =

A: Matrix of coeffients ΦC: Unkowns at cell centers b: sources

Assembly of the system to be solved

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Discretization (conl’d)

High performance computing (cont’d)

[http://febui.chemeng.ntua.gr/pegasus.htm]

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MOCVD: Aluminum deposition

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

• Collaborative project: CIRIMAT/ENSIACET, Toulouse – NTUA, Athens

Main objectives

 optimum process parameters (temperature, flow rates, …)  optimum reactor configuration (showerhead-substrate distance, shower-plate, …) Teams: Athens: A. Boudouvis, I. Aviziotis, N. Cheimarios, D. Xenidou Toulouse: C. Vahlas, T. Duguet, N. PrudHomme

Xenidou et al., Surface Coatings Technology 201, 8868 (2007); Xenidou et al. J. Electrochemical Soc. 157, D633 (2010)

Typical operating conditions

Parameter Typical value Ν2 diluent flow rate

305 sccm

Ν2 carrier flow rate 25 sccm

DMEAA bubbler temperature 9 οC DMEAA flow rate 1.4 sccm Inlet gas temperature 65 oC Substrate temperature 200 oC Walls temperature 25 oC Total pressure 10 Torr Deposition time 120 min

Αντλία P DMEAA

MFC

T

Τ Θερμοστοιχείο τύπου S Παγίδα συμπύκνωσης Μανόμετρο N2

P

MFC

P Td Tb Fd Fc Tin Tw Fp

MOCVD reactor

9 mm 16 mm 20 mm 24 mm

Growth Rate Measurement

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Numerical Solution

Reactor discretization

Computational details

• Finite Volume Method
• SIMPLEST pressure

correction scheme

• Upwind differencing

scheme

• TDMA solver
• Grid: 33.000 cells

(105 x 315 (NX x NZ))

• 120 min CPU time

(2.8GHz Pentium IV/1.GB RAM)

12.7 mm 290mm 20 mm 15mm 83 mm 58 mm 60 mm 110mm 10mm

y x

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ANSYS/FLUENT CFD package

Model predictions at typical operating conditions

T(Κ)

Temperature

Model predictions

−

Temperature filed is uniform above the substrate; this means that conduction is dominant compared to convection

−

The isotherms follow the shape

• f the showerhead, due to heat

transfer through the walls

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Model predictions at typical operating conditions

U(m/ s)

Model predictions

Velocity

−

The recirculation zone may be attributed to the local pressure drop

−

The recirculation zone will trap the mixture inside the showerhead and cause precursor condensation

−

It may provide premixing of the gas mixture, which is beneficially to the thickness uniformity

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0,7 0,85 1 1,15 1,3 5 10 15 20 25

Distance in radial direction (mm) Normalized species mass fractions

N2 DMEAA H2 DMEA

Model predictions

Chemical species distribution at typical operating conditions

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Comparison of experiments and predictions

Arrhenius plot of Al growth from DMEAA

160 200 220 260

1000/T (1/K) T(oC)

50 100 150 200 250 300 1,8 1,9 2,0 2,1 2,2 2,3 2,4 experiment model

Growth Rate (Α/min) Growth Rate (Α/min)

−

Growth rate decreases above 200oC, due to DMEAA dissociation in the gas-phase

−

Kinetically-controlled regime extends below 200oC, while above 200oC growth takes place in the transport-controlled regime

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Al Growth Rate (Α/min)

Distance in radial direction (mm)

50 100 150 200 250 300 5 10 15 20 25 model experiment 50 100 150 200 250 300 5 10 15 20 25 model experiment 50 100 150 200 250 300 5 10 15 20 25 model experiment

T = 160oC T = 200oC T = 220oC T = 260oC

50 100 150 200 250 300 5 10 15 20 25 model experiment

Comparison of experiments and predictions

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On the showerhead design

design A design B design C

84mm 7mm 10mm 6mm 3mm 50mm 7mm 44mm 101mm

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Velocity at typical operating conditions

On the showerhead design

design A design B design C

Umax = 12.8m/s Umax = 9.6m/s Umax = 6.4m/s

NATIONAL TECHNICAL UNIVERSITY OF ATHENS Andreas G. Boudouvis VIMA/ RTRA-STAE @ Toulouse, 4 July 2014

On the showerhead design

Distribution of the reactants over the substrate

1,38E-02 1,40E-02 1,42E-02 1,44E-02 1,46E-02 1,48E-02 1,50E-02 5 10 15 20 25 30 35 Distance in the radial direction of the substrate (mm) DMEAA mass fraction small medium large

design A design B design C design A design B design C

DMEAA mass fractions Distance in radial direction (mm)

Design Δω(%) * A 5.870 B 6.268 C 6.444 * Non-uniformity Δω(%) is calculated through

the maximum, minimum and average values:

average min max

ω ω − ω = ω ∆

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Ongoing work

New design

7 mm 1.30 mm 1.5 mm 0.76 mm 10 mm

Actual design Investigation of the shower-plate

On the showerhead design (ongoing)

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Copper CVD: Mixed chemical kinetics

0 exp d

E k k RT

α

  = −    

[ ] [ ]

1 2

0.07 / , 0.01 / k m s k m s = =

Inhibition effect from H(amd)

Arrhenius plot

( ) ( ) ( )

( )

2 2 2 2

1 1 2

2

d H Cu amd d H H amd Cu amd

k k C C r k C k C k C

       

= + +

( )

2 2

H Cu amd

E r k C C RT

α    

  = −    

10 1 2

66 / , 1.33 10 / E kJ mol k s kmol m s

α − 

 = = ×  

Langmuir-Hinshelwood 1-st order

Aviziotis et al., Surf. Coat. Tech. (2014)

Multiscale modeling in CVD

Manipulation of the events in the micro/nano scale

Deposition in a predefined topography Surface nano-morphology

by macro CVD reactor operating conditions Physical phenomena in micro/nano

5 nm

Hamers et al., Ultramicroscopy (1989)

void

0.2 μm

Kinoshita et al., Jpn. J. Appl. Phys. (2005)

823 K 873 K

• A. G. Boudouvis

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Micro- topography corresponding to a boundary cell @ the wafer

Macro- scale (cm) (Reactor Scale Model) Micro- scale (μm) (Feature Scale Model)

Coupling (bi-directional exchange of info) of scales Correction of the boundary condition for the species equation.

effective reaction rate: ε effective reactivity factor

Single scale (macro-) computations: Multiscale computations:

Multiscale modeling of CVD: Wafer with micro-topography

cannot use the same models to describe the physical phenomena in macro- & micro- scale Macro- scale Kn < 1 Micro- scale: Kn > 1

reaction rate

, i i i i s eff macro

r D Y M ρ γ ⋅∇ = n

s i i i i

D Y M r ρ γ ⋅∇ = n

, s s eff macro

r r ε = ⋅

s

r

Jensen et al., Curr. Opin. Solid St. M. (1998). Cale et al., Comput. Mater. Sci. (2002)

National Technical University of Athens School of Chemical Engineering

• A. G. Boudouvis

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Momentum Equations

( ) ( )

x r r

u u u x r r ρ ρ ρ ∂ ∂ + + = ∂ ∂

Continuity Equation

( )

i i i

uY J R ρ ∇⋅ = −∇⋅ +   

Species Equation

[ ]

( )

i i i

u E p k T h J ρ   ∇⋅ + = ∇⋅ ∇ −    

∑

 

Energy Equation

x r

FLUENT

( ) ( ) ( )

1 1 1 2 1 2 3

x x r x x r x

u u u p r u u r u u r u r g r x r r x r x x r r r x ρ ρ µ µ ρ  ∂   ∂  ∂ ∂ ∂ ∂ ∂ ∂     + = − + − ∇⋅ + + −         ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂         

( ) ( ) ( ) ( )

2

1 1 1 1 2 2 3 2 2 3 ρ ρ µ µ µ µ  ∂  ∂  ∂  ∂ ∂ ∂ ∂ ∂     + = − + + + − ∇⋅ −         ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂         − + ∇⋅  

x r r x r r r r

u u u p r u u r u u r r u r x r r r r x x r r r r u u r r

Reactor Scale Module (RSM)

7183 cells

boundary condition (surface reactions)

, s i i i i eff macro

D Y v M r ρ ⋅∇ = n Xenidou et al., J. Electrochem. Soc. (2010).

Volumetric reactions

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Calculation of the local fluxes and sticking coefficients

{ }

, ,

( ) ( ) 1 ( ) ( ) ( ) ( , ) ( )

c

i i direct E i 1 2 N i i

S , ,..., Q dA

Α

Γ Γ Γ Γ Γ Γ   ′ ′ ′ ′ ′ ′ = + −  

∫∫

x x x x x x x x i=1,2, …, N

SE,i: Sticking coefficient of species i Γi,direct (x): direct flux, shadowing effects Qi(x, x’): geometrical term which incorporates the reemission mechanism of species i

Kokkoris et al., J. Vac. Sci. Technol. A (2004) Osher, S. and R. P. Fedkiw, Springer (2003)

Flux of species i in elementary area on point x :

Reemission Shadowing

Kn > 1

Feature Scale Module (FSM) : Ballistic transport

+ | | 0, ( , 0) ( ), ,

t F

t q ∇ = = = ∈ x x x ϕ ϕ ϕ Ω

Profile evolution algorithm/Level Set Method

φ: level set function F: normal velocity to the moving boundary F | ∇φ| = H: Hamiltonian

www.phietch.org

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Coupling RSM with FSM

FLUENT Ballistic model n = n +1 Yi , ρ,T Film growth for Δt Yes Level set method No

Correction of the surface reaction rate term in the BC for the species equation

@ A

( )

,

' 1

n

s s eff m ro A ic

r r dA A =

∫

s

r

( ) ( )

( ) ,

n n

s n s eff macro

r r ε =

• Boundary condition:

( )

,

n

s i i i i eff macro

D Y M r ρ γ ⋅∇ = n

( ) ( ) ( )

, , , 2

n n n

s s eff macro eff micro s eff macro

r r tol r − <

Cheimarios et al., Chem. Eng. Sci. (2010)

( ) ( )

, ( 1) ( ) ,

n n

s eff micro n n s eff macro

r r ε ε

+ =

Yi , ρ,T

j

ε

@

s i

A r Γ →

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Case study: Multiscale modeling of Si CVD

Sticking coefficients:

4 2 4 2

, ,

( , , ) 1

E SiH w H SiH E SiH

S g T S = Γ Γ =

(constant)

Kleijn, J. Electrochem. Soc. (1991)

Volumetric reaction: SiH4 ↔ SiH2 + Η2

( )

4

0 exp(

)

V a SiH

E r k f C RT = − (Arrhenius type) SiH4 → Si(s) + 2Η2 SiH2 → Si(s) + Η2 Surface (deposition) reactions:

, 4 2

, ,

s i E i i

r S i SiH SiH = Γ =

(Eley-Rideal type)

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Results: Coupling RSM with FSM

(thickness top) (thickness bottom)

t b

d d Θ =

Conformality (Θ) inside long rectangular trenches Base case  decreasing Tw  decreasing fSiH4 (inlet)  increasing Pop Effect on conformality by: Pop= 133 Pa Tw = 1050 K fSiH4 = 0.1 (inlet)

4 2 4 2

, , 7 9 3

3.5 10 1 0. 4.18 10 . 10 91 2 9

s s SiH E S E SiH Si H H i

S r S r

− − −

= ⋅ = Θ = = ⋅ = ⋅

dt db

t = 0s t = 192s

16 trenches per 32 μm, initial depth = 3 μm, initial width = 1 μm

• A. G. Boudouvis

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Conformality (Θ) inside long rectangular trenches Base case

4 2 4 2

, , 7 9 3

3.5 10 1 0. 4.18 10 . 10 91 2 9

s s SiH E S E SiH Si H H i

S r S r

− − −

= ⋅ = Θ = = ⋅ = ⋅

Decreasing Tw

2 4 2 4

5 , 11 8 ,

9.00 1 2.37 1 1 5.0 10 1

s E Si SiH s SiH E SiH H

r S r S

− − −

= ⋅ = = ⋅ ⋅ Θ = =

Pop= 133 Pa Tw = 1050 K fSiH4 = 0.1 (inlet)

• Tw = 900 K
• t = 0s

t = 0s t = 192s t = 2340s

Results: Coupling RSM with FSM (cont’d)

National Technical University of Athens School of Chemical Engineering

• A. G. Boudouvis

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Conformality (Θ) inside long rectangular trenches Base case

4 2 4 2

, , 7 9 3

3.5 10 1 0. 4.18 10 . 10 91 2 9

s s SiH E S E SiH Si H H i

S r S r

− − −

= ⋅ = Θ = = ⋅ = ⋅

Decreasing fin,SiH4

2 2 4 4

12 2 , 9 ,

8 1.5 1 9.9 5 .0 .6 1 1 7 8 10

E S s SiH s SiH E SiH iH

r S S r

− − −

= ⋅ = Θ = ⋅ = = ⋅

• fSiH4 = 0.001 (inlet)

t = 0s t = 192s t = 0s t = 15600s

Pop= 133 Pa Tw = 1050 K fSiH4 = 0.1 (inlet)

Results: Coupling RSM with FSM (cont’d)

• A. G. Boudouvis

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Conformality (Θ) inside long rectangular trenches Base case

4 2 4 2

, , 7 9 3

3.5 10 1 0. 4.18 10 . 10 91 2 9

s s SiH E S E SiH Si H H i

S r S r

− − −

= ⋅ = Θ = = ⋅ = ⋅

Increasing Pop

4 2 4 2

7 7 4 , ,

6.0 10 6.66 10 1.19 .85 1 10

E S E SiH s SiH s Si iH H

S S r r

− − −

= = ⋅ Θ = = = ⋅ ⋅

Pop= 1033 Pa

• t = 0s

t = 192s t = 185s t = 0s

Pop= 133 Pa Tw = 1050 K fSiH4 = 0.1 (inlet)

Results: Coupling RSM with FSM (cont’d)

• A. G. Boudouvis

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Results: Coupling RSM with FSM (cont’d)

with micro- topography no micro- topography

• Effect on the Arrhenius plot

National Technical University of Athens School of Chemical Engineering

• A. G. Boudouvis

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

void

0.2 μm

Kinoshita et al. Jpn. J. Appl. Phys. (2005)

823 K 873 K

t = 0s t = 192s t = 0s t = 2340s

900 K 1050 K

43

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Model vs Experiment

• Multiscale modeling of MOCVD – Experiments & computations

Ongoing research

Aluminum deposition in rectangular trenches (courtesy of Dr. C. Vahlas, CIRIMAT/Toulouse)

Challenge Coupling of the three scales (macro-, micro-, nano- ) roughness development in the features

National Technical University of Athens School of Chemical Engineering

• A. G. Boudouvis

NATIONAL TECHNICAL UNIVERSITY OF ATHENS