Compound Formation in Bulk Couples and Thin Films:

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Part 8 Thin Film Reactions
?Compound Formation in Bulk Couples and Thin
Films
In bulk diffusion couples, often one or two of
the compounds were missing. This has become a
dominant factor in thin film reactions.
Question why are compounds missing? One
example Au-Al In bulk diffusion couple,
interdiffusing Au and Al at 460oC for 100 min
? five compounds were observed. If the system
is annealed at 200oC, the AuAl2 and AuAl is
not observed. In the case of thin film, at low
T, there may be only one phase formed ?
Bulk and thin film reaction sequence is
different!
Au
Al
460oC 100 min
AuAl
Au5Al2
Au4Al
Au2Al
AuAl2
2
tAu
Al
Next example is Si-Ni system In the bulk
diffusion couple, heated to 850oC for 8 hr.
Au
tAl
Au5Al2 Au2Al
Si
NiSi
Au2Al
Ni3Si2
Temperature, Time
tAu lt tAl
tAu gt tAl
Ni2Si
Au2Al
Ni5Si2
Au2Al
Ni
T ? 100oC
Au5Al2
See Textbook for real optical micrograph.
Several compounds form simultaneously.
T ? 150oC
Au4Al
AuAl2
S.U. Campisano, et. al., Phil. Mag., 31, 903
(1975).
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In the case of thin film, if we deposit a Ni
film on Si and anneal at 250oC for one hour,
it will form Ni2Si. Increasing time ? thicker
Ni2Si layer.
Ni
For a Ni thin film on top of Si wafer, the
first phase formed is Ni2Si. When the Ni is
consumed, then NiSi is formed and after that
will form NiSi2. For a Si thin film on Ni
substrate, the first phase is still Ni2Si, but
the subsequent phases are different and there
are rich in Ni.
Si
Ni2Si
From the phase diagram, if one has a Ni film
on Si, the composition of the whole sample is
Si rich and we should have NiSi2 in
equilibrium with Si. ? one can not predict
whats happening just by looking at the phase
diagram. The first phase is determined
kinetically.
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In the following, the reaction processes
controlled by kinetics is discussed.
?Thin film reactions Diffusion and Reaction
Control To explain the missing compound
phenomenon and in turn the single-phase growth
in thin film reactions, the concept of a
critical thickness of growth is crucial. First
define that in a kinetic process if the
process is in the diffusion controlled regime.
On the other hand, if ,
the process is in the reaction controlled
regime. J flux C concentration A schematic
atomistic picture of the reaction controlled
process is shown in the next page. Assume the
driving force is small ( ) ?
the net frequency of forward jump
(see part 3). The interfacial
velocity v is given by
and the flux J is
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Interface
A
A in A?B
v0
v0
If F is constant, we have
?
?1
?2
mobility
In equilibrium
the process is interfacial reaction
controlled. K interfacial reaction
controlled constant. cm/sec a measure
of the mobility of the atoms or an
interface. A diffusion controlled layer growth
will show parabolic relationship between the
growth rate and time. An interfacial
reaction-controlled growth will show linear
relationship.
Ni
Ni2Si
v
v-
?Gf
F
During reaction
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?Growth of a Layer Compound In the following,
the growth of a layer compound controlled
by both diffusion and interfacial reaction
will be considered. Consider the growth of
a layered compound of A?B between A?B and
A?B (For pure A represented by A?B, ? ?
for pure B represented by A?B, ? 0).
Assume the concentration of A in A?B and B in
A?B are flat.
A?B
A?B
A?B
(1)
CA
(2)
x?
x
x??
x??
(1) and (2) are concentration profiles without
and with interface reaction barrier.
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If there is reaction barriers at the
interfaces, say at the A?B/A?B interface, the
incorporation of A from A?B to A?B is slow
(any A breaks away from the interface can
rapidly diffuse away) ? the interfacial
concentration at the A?B side is smaller than
the equilibrium concentration without reaction
barrier. ? C?? lt If the incorporation of
A atoms into the A?B/A?B interface takes place
as soon as atoms arrived, the equilibrium
concentration can be maintained. If the
interfacial process is slow ? A atoms will
accumulate in front of the surface ? C?? gt
Lets consider the interface is moving with a
velocity v,
v
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0
Conc. profile is flat!
In the compound A?B, we could assume a linear
concentration gradient
If one considers the case to be reaction
controlled process
K?? interfacial reaction constant
K?? measures the rate of removing A from the
interface. If C?? , the concentration
across the interface is smaller, yet the
interface velocity is greater and vice versa.
Similarly, at the A?B/A?B interface
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0
and also
adding
also define
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Now calculate the thickening rate of A?B
G? concentration parameter for A?B.
Define a change-over thickness x?
i.e. x? ? t
i.e. x?2 ? t
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The above shows An interfacial reaction
controlled growth x? ? t A
diffusion-controlled growth x? ? t1/2 A
reaction controlled growth will always change
over to a diffusion controlled growth if the
layer thickness x? has grown sufficiently
large that x? gtgt x?,
x?
x?
Reaction controlled
Diffusion controlled
Time
Time
?Growth of Two Layered Compounds The case is
that there are two compounds A?B and A?B
growing between A?B and A?B. The equilibrium
concentration and non-equilibrium
concentration Cij at
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the interfaces xij following the previous
figures. At the x?? interface
A?B
A?B
A?B
A?B
x?
x?
x
At the x?? interface
C??
C??
C??
C??
x?
x?
x??
x??
x??
At the x?? interface
A?B
A?B
A?B
The thickening of A?B
x??
x??
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The thickening of A?B
The two layers could grow simultaneously and
in some case one of the layer could vanish due
to competition.
For the two interfaces of A?B, we have
For the two interfaces of A?B, we have
Similar to the case for the one layer growth,
one can derive
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where
The condition for the A?B layer to growth or
shrink
Grow
Shrink
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Similar condition for the A?B layer to growth
or shrink
Grow
Shrink
One could use assumption to estimate r1 and
r2. The concentration parameter
The concentration of A in A?B is ?/(1?). If
we assume
In most case, C?? C?? is less than a few .
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(? - ?) gt (? - ?) (? - ?)gt(? - ?)
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Now if
both layers grow together
A?B shrinks, A?B grows
A?B grows, A?B shrinks
Next consider a special case where one layer
shrinks away completely. Three combinations
for the growth process of these two layers
(1) Both are diffusion controlled, (2) both are
interfacial reaction controlled, and (3) one
is diffusion controlled and the other is
interfacial reaction controlled. Take the last
case and assume that A?B is interfacial
reaction controlled and A?B is diffusion
controlled.
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Consider three regions of the ratio
A?B grows, A?B shrinks
Region I
? x? decrease until the ratio r2, then A?B
will stop shrinking and both layers grow
together!
both A?B and A?B grow!
Region II
Region III
A?B shrinks, A?B grows,
If x? is below a critical thickness defined by
A?B can shrink away entirely in the case that
layer A?B has grown to the critical thickness
before A?B shrinks
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away, then both layers could coexist and grow
together
A
B
A?B
A?B
When x? is small,
x?
x?
As x? increases,
Until x? larger than the critical thickness,
x? ? t
x? ? t1/2
The critical thickness is on the order of
microns. For typical thin film diffusion
couples having thickness in hundreds of nm, we
see only a single layer compound growth. In
the case of a metal deposited on Si wafer, such
as Ni on Si. We need to discuss the second
phase growth from the viewpoint of
supply-limitation or source-exhaustion. If
the first phase formed is A?B and the end element
B has been consumed (J?A 0).
? x? shrink and x? grow!