- The document provides information on chemical vapor deposition (CVD) growth of silicon and germanium films, including elementary surface reactions and rate equations. - It also discusses catalyst deactivation kinetics and models, types of catalyst deactivation including sintering, fouling, and poisoning. Equations are provided for modeling the decay in catalyst activity over time. - The document reviews the design and modeling of a moving-bed reactor, where catalyst deactivation occurs and spent catalyst is continuously regenerated while maintaining steady-state operation. Rate equations are developed to model the reactor performance.

1. L18b-1
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Review: Growth of Silicon Film by CVD
Write out elementary reactions and assume a rate-limiting step
 
2 2
SiH g S SiH S
 
1. Adsorption
Rate of adsorption = rate of attachment – rate of detachment
AD SiH SiH v SiH SiH
2 2 2 2
r k P f k f

  SiH2
AD SiH SiH v
2 2
SiH2
f
r k P f
K
 
  
 
 
 
2. Surface reaction:  
2 2
SiH S Si S H g
  
S S SiH S Si H v
2 2
r k f k C P f

 
Si H v
2
S S SiH2
S
C C f
r k f
K
 
  
 
 
Si Si Si Si
Si
H
H
Si Si Si Si
Si
H
H
Si Si Si Si
Si
adsorption
Surface
reaction
fv & fSiH2: fraction of the surface covered by vacant sites or SiH2, respectively
Surface coverage is in terms of fraction of surface, not conc of active sites

2. L18b-2
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Gas-phase dissociation 4(g) 2(g) 2(g)
GeCl GeCl Cl

Adsorption (1)
kA
2(g) 2
k A
GeCl S GeCl S

 
Adsorption (2)
kH
2(g) k H
H 2S 2H S

 
Surface reaction    
kS
2
GeCl S 2H S Ge s 2HCl g 2S
   
  
Surface reaction is believed to be the rate-limiting step:
ks: surface specific reaction rate (nm/s)
fH2: Fraction on the surface occupied by H2
fGeCl2: fraction of the surface covered by GeCl2
Review: Growth of Germanium Films
by CVD
Germanium films have applications in microelectronics & solar cell fabrication
" 2
Dep S GeCl H
2
r k f f

Rate of Ge deposition (nm/s):
*Surface coverage is in terms of fraction of surface, not conc of active sites

3. L18b-3
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Review: Catalyst Deactivation Kinetics
• Adjustments for catalyst decay need to be made in the design of reactors
• Catalyst activity a(t) is used as a quantitative specification
 
'
A
'
A t 0
r (t)
a t
r 



Catalyst activity at time t:
Reaction rate for catalyst used for time t
Reaction rate for fresh, unused catalyst
For fresh, unused catalyst, t 0
a 1


 
0 a t 1
 
     
A A, B
r' a t k T fn C C ,....etc
 
Rate of consumption of reactant A on catalyst used for time t is:
a(t): time-dependent catalyst activity k(T): T-dependent specific rate constant
fn(CA, CB…etc): function of gas-phase conc. of reactants, products &
contaminants
Rate of catalyst decay:      
d d A B
da
r p a t k T h C ,C ,...,etc
dt
    
 
Function of activity
Temperature-dependent specific decay constant
Functionality of rd on reacting
species conc. h=1: no conc
dependence; h=Cj: linearly
dependent on concentration

4. L18b-4
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Review: Types of Catalyst Deactivation
3. Poisoning: molecules (product, reactant or impurity) irreversibly bind
to the active site
1. Sintering (aging): loss of active surface due to high temperature
Second-order decay of reaction rate with respect to present activity:
2
d d
r k a

 
d
1
a t
1 k t


Catalyst activity at time t:
  d
d d 0
0
E 1 1
k k T exp
R T T
 
 
 
 
 
 
 
Sintering decay constant:
2. Coking or fouling: carbonaceous material (coke) deposits on surface
n
C
C At

Concentration of carbon
on surface (g/m2):   m
1
a t
1 k't


Catalyst activity at time t:
A, n & m: fouling parameters
'
kd
P S N S
 
 
 
d d P
da
r a t k' C
dt
  
a(t): time-dependent catalyst activity
kd: specific decay constant
CP: concentration of the poison

5. L18b-5
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
•Reactant & catalyst enter at top of reactor
•Reactant & catalyst flow down the length of
the reactor together as a plug
•Product and spent catalyst (black) flow out of
reactor outlet
•Spent catalyst is regenerated by passing it
through a separate regeneration unit, and
newly regenerated catalyst is fed back into
the top of the reactor
Review: Moving-Bed Reactor
• When catalyst decay occurs at a significant rate, they require frequent
regeneration or replacement of the catalyst
• Moving-bed reactor enables continuous regeneration of spent catalyst
• Operates in the steady state, like a PBR

6. L18b-6
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Review: Moving-Bed Reactor Design
Reactants
u0 (dm3/s)
fresh
catalyst
US (g/s)
Z
Z + DZ
W
W + DW
Products & coked catalyst
Catalyst flow US << reactant flow u0
As far as the reactants are concerned,
the reactor acts like a PBR:
A
A0 A
dX
F r'
dW
 
n
d
da
Assume the decay rate law is: k a
dt


Find -da/dW and dXA/dW. Will need dt/dW.
Relate t to US:
S
W
t
U

S
dW
dt
U
 
Multiply dt/dW by -da/dt to get –da/dW:
S
dt 1
dW U
 
n
d
S
da dt 1
k a
dt dW U
 
  

   
   
n
d
S
k
da
a
dW U

 
If the rate of consumption of A for catalyst used for time t:      
A j
r' a W k T fn C
 
A A
A0
dX r '
dW F


    j
A
A0
a W k T fnC
dX
dW F
 
 
 
X W
A
A0 A
j
0 0
F dX
a W dW
k T fnC
 
 

7. L18b-7
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Guidelines for Deducing Mechanisms
• More than 70% of heterogeneous reaction mechanisms are surface
reaction limited
• If a species appears in the numerator of the rate law, it is probably a
reactant
• If a species appears in the denominator of the rate law, it is probably
adsorbed in the surface

8. L18b-8
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Suggest a mechanism and rate-limiting step that is consistent with the rate law
E
E
E
E
H
kP P
r '
1 K P
 

The overall reaction for the hydrogenation (H) of ethylene (E) over a cobalt-
molybdenum catalyst to form ethane (A) is H2(g) + C2H4(g) → C2H6 (g) and the
observed rate law is:
PE appears in the denominator of the observed rate eq, so PE is adsorbed on
the surface. Neither PH or PA are in the denominator, so neither H or A are
adsorbed on the surface.
We’ll assume that the surface reaction is rate limiting
E S
AD A E V
AD
C
Adsorption: E S E S r k P C
K

 
   
 
 
E
S S
S H
Surface rxn: E S H A S r k C P

    
No desorption step - PA isn’t in the
denominator. Eliminate conc of
occupied & vacant sites on surface:
AD
E
A AD
E S
V
C
0 P
k
C
r
K

   V S
AD E
EC
K P C 
 
V E
t S
site balance: C
C C 
  A V
t D E
V K C
C C P
  
t
V
AD E
C
C
1 K P
 

E
S H
S
SC
r k P

 S t
AD
E H
E
AD
S
k P C
1 K
P
r
P
K

  t
S AD E
ADC
K
k k & K K
  E H
S
E E
kP P
r
1 K P
 


9. L18b-9
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The experimental data for
the gas-phase, catalytic,
irreversible reaction A +
B→C is given in the table.
Suggest a rate law &
mechanism consistent with
the data.
Run PA (atm) PB (atm) PC (atm) -r’A(mol/g∙s)
1 0.1 1 2 0.073
2 1 10 2 3.42
3 10 1 2 0.54
4 1 20 2 6.80
5 1 20 10 2.88
6 20 1 2 0.56
7 1 1 2 0.34
8 1 20 5 4.5
Approach: Use graphs to
show how -r’A varies with
Pi when Pj and Pk are held
constant
0
0.2
0.4
0.6
0 10 20
-r'
A
PA (atm)
0
2
4
6
8
0 10 20
-r'
A
PB (atm)
0
2
4
6
8
0 5 10
-r'
A
PC (atm)
We need to use these graphs to determine whether A, B, & C are in
the numerator, denominator, or both.

10. L18b-10
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The experimental data for
the gas-phase, catalytic,
irreversible reaction A +
B→C is given in the table.
Suggest a rate law &
mechanism consistent with
the data.
Run PA (atm) PB (atm) PC (atm) -r’A(mol/g∙s)
1 0.1 1 2 0.073
2 1 10 2 3.42
3 10 1 2 0.54
4 1 20 2 6.80
5 1 20 10 2.88
6 20 1 2 0.56
7 1 1 2 0.34
8 1 20 5 4.5
Approach: Use graphs to
show how -r’A varies with
Pi when Pj and Pk are held
constant
0
0.2
0.4
0.6
0 10 20
-r'
A
PA (atm)
-r’A increases rapidly at low PA (means its in the
numerator), but it levels off at high PA (means its in
the denominator)→ PA in numerator & denominator
of -r’A
A
A
A
kP ...
r '
1 kP ...
 


11. L18b-11
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The experimental data for
the gas-phase, catalytic,
irreversible reaction A +
B→C is given in the table.
Suggest a rate law &
mechanism consistent with
the data.
Run PA (atm) PB (atm) PC (atm) -r’A(mol/g∙s)
1 0.1 1 2 0.073
2 1 10 2 3.42
3 10 1 2 0.54
4 1 20 2 6.80
5 1 20 10 2.88
6 20 1 2 0.56
7 1 1 2 0.34
8 1 20 5 4.5
Approach: Use graphs to
show how -r’A varies with
Pi when Pj and Pk are held
constant
0
0.2
0.4
0.6
0 10 20
-r'
A
PA (atm)
0
2
4
6
8
0 10 20
-r'
A
PB (atm)
-r’A increases linearly as
PB increases → PB is
only in the numerator
A B
A
A
kP P ...
r '
1 kP ...
 

A
A
A
kP ...
r '
1 kP ...
 


12. L18b-12
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The experimental data for
the gas-phase, catalytic,
irreversible reaction A +
B→C is given in the table.
Suggest a rate law &
mechanism consistent with
the data.
Run PA (atm) PB (atm) PC (atm) -r’A(mol/g∙s)
1 0.1 1 2 0.073
2 1 10 2 3.42
3 10 1 2 0.54
4 1 20 2 6.80
5 1 20 10 2.88
6 20 1 2 0.56
7 1 1 2 0.34
8 1 20 5 4.5
Approach: Use graphs to
show how -r’A varies with
Pi when Pj and Pk are held
constant
0
2
4
6
8
0 10 20
-r'
A
PB (atm)
0
2
4
6
8
0 5 10
-r'
A
PC (atm)
A B
A
A
kP P ...
r '
1 kP ...
 

-r’A ↓ with ↑PC→ rnx is
irreversible so PC must
be in the denominator
of -r’A. Therefore, C is
adsorbed on surface
A B
A
A A C C
kP P
r '
1 K P K P
 
 

13. L18b-13
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The rate law suggested for the experimental data given for the gas-phase,
catalytic, irreversible reaction A + B→C is:
Suggest a mechanism for this rate law.
A B
A
A A C C
kP P
r '
1 K P K P
 
 
PA and PC are in the denominator. A (reactant) and C (product) must be
adsorbed on the surface, but B is not adsorbed on the surface:
A S A S
  AD A A V A A S
r k P C k C
 
  A S
AD A A V
A
C
r k P C
K

 
  
 
 
C S C S
  DC D C S D C v
r k C k P C
 
  C V
DC D C S
D
P C
r k C
K

 
  
 
 
Adsorption of reactant A:
Desorption of product C:

14. L18b-14
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The rate law suggested for the experimental data given for the gas-phase,
catalytic, irreversible reaction A + B→C is:
Suggest a mechanism for this rate law.
A B
A
A A C C
kP P
r '
1 K P K P
 
 
PA and PC are in the denominator. A (reactant) and C (product) must be
adsorbed on the surface, but B is not:
A S A S
  AD A A V A A S
r k P C k C
 
  A S
AD A A V
A
C
r k P C
K

 
  
 
 
C S C S
  DC D C S D C v
r k C k P C
 
  C V
DC D C S
D
P C
r k C
K

 
  
 
 
Adsorption of reactant A:
Desorption of product C:
Surface reaction step: B is not adsorbed on the surface, so B must be in the
gas phase when it reacts with A adsorbed on the surface.
The overall reaction is irreversible, so this step is likely irreversible.
A S B C S
    S S A S B
r k C P



15. L18b-15
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The rate law suggested for the experimental data given on slide 14 for the
gas-phase, catalytic, irreversible reaction A + B→C is:
Suggest a mechanism for this rate law.
A B
A
A A C C
kP P
r '
1 K P K P
 
 
A S A S
 
A S
AD A A V
A
C
r k P C
K

 
 
 
 
C S C S
  C V
DC D C S
D
P C
r k C
K

 
 
 
 
Adsorption of reactant A:
Desorption of product C:
A S B C S
    S S A S B
r k C P


Surface reaction:
Postulate that the surface reaction is the rate limiting step since that is true
the majority of the time. Check if that is consistent with the observed kinetics
A S S B
A S
r ' r k C P

   Eliminate CA∙S & Cv
from rate eq
AD
A V
A A
A S
r
0 P
k K
C
C 
   A
A
A
S
V
C
P
K
C 
  V
A A A S
C
K P C 
 
A C S
t v S
C C
C
C  
  
C
DC C
D D
V
S
C
r C
P
0
k K

   C
C
D
V
S
P
C
K
C

  Insert into site balance
and solve for Cv

16. L18b-16
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
The rate law suggested for the experimental data given on slide 13 for the gas-
phase, catalytic, irreversible reaction A + B→C is:
Suggest a mechanism for this rate law.
A B
A
A A C C
kP P
r '
1 K P K P
 
 
A S A S
 
A S
AD A A V
A
C
r k P C
K

 
 
 
 
C S C S
 
C V
DC D C S
D
P C
r k C
K

 
 
 
 
Adsorption of reactant A: Desorption of product C:
A S B C S
   
S S A S B
r k C P


Surface reaction:
Postulated surface
reaction is rate limiting
A S
A S S B S V
A B
A
r ' r k P
C K P C
k P

    A A V
S A
C K P C
 
A C S
t v S
C C
C
C  
  
C S C V D
C P C K
 
A A
t
D
v V
C V
C C
K
C
C
P
K
P
   
t
v
A A C D
C
C
1 K P P K




S t
A A
B
C D
A
S
A
k P
C
1 K P K
P
r
K
P
 
 
A S
A S S B S V
A B
A
r ' r k P
C K P C
k P

   
C
D
1
K
K
 S t
A
k k K C
 A B
S
A A C C
P P
r
1 K P K P
k
 
 