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

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

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


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SLIDE 1

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/

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SLIDE 2

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
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SLIDE 3

Deposition processes

From ordinary life to advanced materials

…coatings, nanomaterials, MEMS…

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

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SLIDE 4

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

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

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SLIDE 5

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

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

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SLIDE 6

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…

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SLIDE 7

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

slide-8
SLIDE 8

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

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SLIDE 9

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)

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SLIDE 10

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

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

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SLIDE 11

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

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SLIDE 12

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

Engineering Analysis

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SLIDE 13

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

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

( )

2 i i i i i

Y D Y R S ∇⋅ ρ = ∇ + + v

Species Equation:

i

Y

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SLIDE 14

Mathematical model Numerical approximation/ Code implementation

Partial Differential Equations (conservation laws) Discretization

finite element method finite volume method

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Computer-aided Analysis

Algorithms (solvers) High-performance machines

Cost-effective computations Reliability of solutions (Validation)

Discretization refinement Comparison with experiments

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SLIDE 15

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

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SLIDE 16

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

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SLIDE 17

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)

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SLIDE 18

High performance computing (cont’d)

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

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

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SLIDE 19

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)

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SLIDE 20

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

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SLIDE 21

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

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

ANSYS/FLUENT CFD package

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SLIDE 22

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

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SLIDE 23

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

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

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SLIDE 24

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

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SLIDE 25

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

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SLIDE 26

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

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

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SLIDE 27

On the showerhead design

design A design B design C

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

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

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SLIDE 28

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

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SLIDE 29

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 ∆

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

slide-30
SLIDE 30

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

slide-31
SLIDE 31

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)

slide-32
SLIDE 32

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

slide-33
SLIDE 33

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

slide-34
SLIDE 34

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

slide-35
SLIDE 35

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

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

slide-36
SLIDE 36

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 →

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

slide-37
SLIDE 37

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)

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

slide-38
SLIDE 38

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

slide-39
SLIDE 39

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

slide-40
SLIDE 40

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

slide-41
SLIDE 41

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

slide-42
SLIDE 42

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

slide-43
SLIDE 43

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

slide-44
SLIDE 44
  • 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