scaling-up and bridging scales in process engineering -...
TRANSCRIPT
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 of complexity and size rivaling that of the Manhattan Project
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)
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
Chemical Vapor Deposition: Transport + Reaction
IR Lamps
cooling
INLET
OUTLET susceptor
wafer
surface diffusion
of film precursors adsorption
forced – convection region
transport to surface
+
gas phase reactions
desorption of adsorbed species
surface reaction
CVD reactor
CVD process
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
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
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
The engineering analysis outcome: Reliable Process Design Temperature effect on Aluminum growth rate
Al G
row
th R
ate
(Α/m
in)
0
50
100
150
200
250
300
0 5 10 15 20 25
modelexperiment
0
50
100
150
200
250
300
0 5 10 15 20 25
modelexperiment
0
50
100
150
200
250
300
0 5 10 15 20 25
modelexperiment
T = 160oC T = 200oC
T = 220oC T = 260oC
0
50
100
150
200
250
300
0 5 10 15 20 25
modelexperiment
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
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
Engineering Analysis
Transport Processes Modeling Summary (N species, single phase)
3 + N Physical (conservation) Laws – 3 + N differential equations
0)(t
=ρ⋅∇+∂ρ∂ v
]ptp[)Tk(]T
tT[cp ∇⋅+
∂∂
+∇⋅∇=∇⋅+∂∂
ρ vv
τ⋅∇+∇−ρ=ρ⋅∇+ρ∂∂ p)()(t
gvvv
Mass:
Momentum:
Energy:
3 + N Unknowns: p, v, T, ρ = ρ(p, T), e.g. ρ=p/RT (ideal gases)
T)(.g.e),( vvv ∇+∇µ=ττ=τ (Newtonian fluids) plus constitutive equations
Boundary and initial conditions
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
( ) 2i i i i iY D Y R S∇⋅ ρ = ∇ + +vSpecies Equation:
iY
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
Governing Equations 2-D Axisymmetric Geometry – Cylindrical coordinates
( ) ( ) ( )1 1 1 2 123
x x rx x r x
u u upr u u r u u r u r gr x r r x r x x r r r x
ρ ρ µ µ ρ ∂ ∂ ∂∂ ∂ ∂ ∂ ∂ + = − + − ∇⋅ + + − ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂
Momentum Equations
( ) ( ) ( )
( )2
2
1 1 1 1 223
223
xr rx r r r
r
uu upr u u r u u r r ur x r r r r x x r r r r
uu ur r r
θ
ρ ρ µ µ
µµ ρ
∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + = − + + + − ∇⋅ − ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂
− + ∇ ⋅ +
( ) ( ) 0x r ru u ux r rρ ρ ρ∂ ∂
+ + =∂ ∂
Continuity Equation
( ) ( ) 32
1 1 1 rx r
u u u ur u u r u u r rr x r r x x r r r r r
θ θ θθ θρ ρ µ µ ρ∂ ∂ ∂ ∂ ∂ ∂ + = + − ∂ ∂ ∂ ∂ ∂ ∂
( ) ii i iuY J R Sρ∇⋅ = −∇ ⋅ + +
Species Equation
[ ]( ) i ii
u E p k T h Jρ ∇ ⋅ + = ∇ ⋅ ∇ −
∑
Energy Equation
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
FLUENT CFD package
Discretization – Finite Volume Method
( ) ( ) CV CV CV
div u dV div dV S dVρ Φ ΦΦ = 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 dVρ Φ Φ⋅ Φ = ⋅ Γ ∇Φ +∫ ∫ ∫
Integral Form
convection diffusion sources
( ) ( ) div u div grad Sφρ 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.
0 0C C NB NBNB
a a SΦ = Φ +∑
CA bΦ =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]
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
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
ΤΘερμοστοιχείο
τύπου SΠαγίδα
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
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
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
of 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
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
0,7
0,85
1
1,15
1,3
0 5 10 15 20 25
Distance in radial direction (mm)
Nor
mal
ized
spe
cies
mas
s fr
actio
ns
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
160200220260
1000/T (1/K)
T(oC)
0
50
100
150
200
250
300
1,8 1,9 2,0 2,1 2,2 2,3 2,4
experimentmodel
Gro
wth
Rat
e (Α
/min
)G
row
th R
ate
(Α/m
in) − 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 G
row
th R
ate
(Α/m
in)
Distance in radial direction (mm)
0
50
100
150
200
250
300
0 5 10 15 20 25
modelexperiment
0
50
100
150
200
250
300
0 5 10 15 20 25
modelexperiment
0
50
100
150
200
250
300
0 5 10 15 20 25
modelexperiment
T = 160oC T = 200oC
T = 220oC T = 260oC
0
50
100
150
200
250
300
0 5 10 15 20 25
modelexperiment
Comparison of experiments and predictions NATIONAL TECHNICAL UNIVERSITY OF ATHENS
On the showerhead design
design A design B design C
84mm
7mm
10mm
6mm 3mm
50mm
7mm
44mm
101mm
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
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
0 5 10 15 20 25 30 35
Distance in the radial direction of the substrate (mm)
DM
EAA
mas
s fr
actio
n
small
medium
large
design A design B design Cdesign A design B design C
DM
EAA
mas
s fr
actio
ns
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
minmax
ωω−ω
=ω∆
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
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 expdEk kRT
α = −
[ ] [ ]1 20.07 / , 0.01 /k m s k m s= =
Inhibition effect from H(amd)
Arrhenius plot
( )
( ) ( )( )22
22
1
1 22
d HCu amd
d HH amdCu amd
k k C Cr
k C k C k C
=+ +
( ) 220 HCu amd
Er k C CRT
α
= −
10 1 2066 / , 1.33 10 /E kJ mol k s kmol m sα
− = = ×
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 is
eff macrorD Y Mρ γ⋅∇ =nsi i i iD Y M rρ γ⋅∇ =n
,s s
eff macror rε= ⋅sr
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
( ) ( ) 0x r ru u ux r rρ ρ ρ∂ ∂
+ + =∂ ∂
Continuity Equation
( ) ii iuY J Rρ∇⋅ = −∇ ⋅ +
Species Equation
[ ]( ) i ii
u E p k T h Jρ ∇ ⋅ + = ∇ ⋅ ∇ −
∑
Energy Equation
x
r
FLUENT ( ) ( ) ( )1 1 1 2 12
3x x r
x x r xu u upr u u r u u r u r g
r x r r x r x x r r r xρ ρ µ µ ρ ∂ ∂ ∂∂ ∂ ∂ ∂ ∂ + = − + − ∇⋅ + + − ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂
( ) ( ) ( )
( )2
1 1 1 1 223
223
ρ ρ µ µ
µµ
∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + = − + + + − ∇⋅ − ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂
− + ∇ ⋅
xr rx r r r
r
uu upr u u r u u r r ur x r r r r x x r r r r
u ur r
Reactor Scale Module (RSM)
7183 cells
boundary condition (surface reactions)
,s
i i i i eff macroD Y v M rρ ⋅∇ =n
Xenidou et al., J. Electrochem. Soc. (2010).
Volumetric reactions
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
Calculation of the local fluxes and sticking coefficients
, ,( ) ( ) 1 ( ) ( ) ( ) ( , ) ( )ci i direct E i 1 2 N i iS , ,..., 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 xϕ 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
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
( )
, '1ns seff m ro
Aicr r dA
A= ∫
sr
( ) ( )( ),
n ns n seff macror rε=
•Boundary condition: ( )
,
nsi i i i eff macroD Y M rρ γ⋅∇ =n
( ) ( )
( )
, ,
, 2
n n
n
s seff macro eff micro
seff macro
r rtol
r
−<
Cheimarios et al., Chem. Eng. Sci. (2010)
( )
( )
,( 1) ( )
,
n
n
seff micron ns
eff macro
r
rε ε+ =
Yi , ρ,T
jε
@si ArΓ →
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
Case study: Multiscale modeling of Si CVD
Sticking coefficients:
4 2 4
2
,
,
( , , )
1E SiH w H SiH
E SiH
S g T
S
= Γ Γ
= (constant)
Kleijn, J. Electrochem. Soc. (1991)
Volumetric reaction:
SiH4 ↔ SiH2 + Η2
( )40 exp( )V aSiH
Er k f CRT
= −
(Arrhenius type)
SiH4 → Si(s) + 2Η2
SiH2 → Si(s) + Η2
Surface (deposition) reactions:
, 4 2, ,si E i ir S i SiH SiH= Γ =
(Eley-Rideal type)
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
Results: Coupling RSM with FSM
(thickness top)(thickness bottom)
t
b
dd
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
sSiH
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
sSiH
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
0
0
1
s
E Si
SiH
sSiH
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
sSiH
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
0
5
.0
.6
1
1
0
7
8
0
10
E S
sSiH
sSiH
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
sSiH
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
0
E S
E SiH
sSiH
sSi
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