The influence of surface defects on the pinhole formation in silicide thin film
The growth of the CoSi layer was considered within the framework of the grain boundary diffusion model. The time dependences of the temperature due to the exothermic reaction of silicide formation as well as the dependences of the CoSi layer thickness were calculated for various values of the reacti...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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| Zitieren: | The influence of surface defects on the pinhole formation in silicide thin film / I.V. Belousov, A.N. Grib, G.V. Kuznetsov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 3. — С. 29-34. — Бібліогр.: 19 назв. — англ. |
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irk-123456789-1216152017-06-16T03:03:31Z The influence of surface defects on the pinhole formation in silicide thin film Belousov, I.V. Grib, A.N. Kuznetsov, G.V. The growth of the CoSi layer was considered within the framework of the grain boundary diffusion model. The time dependences of the temperature due to the exothermic reaction of silicide formation as well as the dependences of the CoSi layer thickness were calculated for various values of the reaction activation energy. It was shown that the heat release at high reaction velocities can lead to the considerable increase of the temperature up to melting of the silicide and covering Co layers. The model of pinhole formation in cobalt silicide films was proposed on the basis of local melting in the reaction area at crystal defects of the silicon surface. 2006 Article The influence of surface defects on the pinhole formation in silicide thin film / I.V. Belousov, A.N. Grib, G.V. Kuznetsov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 3. — С. 29-34. — Бібліогр.: 19 назв. — англ. 1560-8034 PACS 68.35Fx, 68.55Ln, 82.65.Dp http://dspace.nbuv.gov.ua/handle/123456789/121615 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The growth of the CoSi layer was considered within the framework of the grain boundary diffusion model. The time dependences of the temperature due to the exothermic reaction of silicide formation as well as the dependences of the CoSi layer thickness were calculated for various values of the reaction activation energy. It was shown that the heat release at high reaction velocities can lead to the considerable increase of the temperature up to melting of the silicide and covering Co layers. The model of pinhole formation in cobalt silicide films was proposed on the basis of local melting in the reaction area at crystal defects of the silicon surface. |
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Article |
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Belousov, I.V. Grib, A.N. Kuznetsov, G.V. |
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Belousov, I.V. Grib, A.N. Kuznetsov, G.V. The influence of surface defects on the pinhole formation in silicide thin film Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Belousov, I.V. Grib, A.N. Kuznetsov, G.V. |
| author_sort |
Belousov, I.V. |
| title |
The influence of surface defects on the pinhole formation in silicide thin film |
| title_short |
The influence of surface defects on the pinhole formation in silicide thin film |
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The influence of surface defects on the pinhole formation in silicide thin film |
| title_fullStr |
The influence of surface defects on the pinhole formation in silicide thin film |
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The influence of surface defects on the pinhole formation in silicide thin film |
| title_sort |
influence of surface defects on the pinhole formation in silicide thin film |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2006 |
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http://dspace.nbuv.gov.ua/handle/123456789/121615 |
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The influence of surface defects on the pinhole formation in silicide thin film / I.V. Belousov, A.N. Grib, G.V. Kuznetsov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 3. — С. 29-34. — Бібліогр.: 19 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 29-34.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
29
PACS 68.35Fx, 68.55Ln, 82.65.Dp
The influence of surface defects on the pinhole formation
in silicide thin film
I.V. Belousov1, A.N. Grib2, G.V. Kuznetsov1
1Taras Shevchenko Kyiv National University, 64, Volodymyrska str., 01033 Kyiv, Ukraine
2Kharkiv National University, 4, Svobody sq., 61077 Kharkiv, Ukraine
Abstract. The growth of the CoSi layer was considered within the framework of the
grain boundary diffusion model. The time dependences of the temperature due to the
exothermic reaction of silicide formation as well as the dependences of the CoSi layer
thickness were calculated for various values of the reaction activation energy. It was
shown that the heat release at high reaction velocities can lead to the considerable
increase of the temperature up to melting of the silicide and covering Co layers. The
model of pinhole formation in cobalt silicide films was proposed on the basis of local
melting in the reaction area at crystal defects of the silicon surface.
Keywords: formation of silicide, activation energy, zone of reacting, local melting,
defects on surface.
Manuscript received 05.04.06; accepted for publication 23.10.06.
1. Introduction
Thin films of CoSi2 have a wide application both in the
semiconductor technology and for buffer layers to grow
new materials such as high-temperature superconductors
due to their good epitaxial and electrical properties [1-8].
However, the principal difficulty in obtaining films with
needed properties remains the problem of film roughness
(formation of pinholes) [2]. To solve this problem,
considerable efforts were applied but the reason of origin
of this pinhole formation has not been found till now. It
was shown that pinhole formation was promoted by
decreasing the surface and interface energies [3]. On the
other hand, experimental investigations show that the
kinetic processes are important in this case [2]. The
supposition was made that some diffusion channels are
activated in the film, permitting a significant mass
transport to the surface during the rapid thermal process
[2]. Moreover, the density of pinholes correlates with the
density of structural defects on the Si surface [1]. These
experimental data allow to suppose that structural
defects play a considerable role in the pinhole formation.
Due to the high diffusion coefficient inside the defect
and the high reaction ability of atoms on the walls, a
considerable increase of the layer growth velocity can be
expected. Besides, increasing the temperature owing to
exothermic reactions of silicide formation have to be
taken into account. Investigations show that Co2Si, CoSi
and CoSi2 layers can be formed in silicide [4]. Formation
of these chemical compositions is an exothermic
reaction with a considerable heat effect [5]. At high
diffusion coefficients and velocities of the chemical
reaction, this heat release can result in increase of the
temperature in the silicide layer.
In this work, we describe the formation of the
silicide layer in a two-dimensional structural defect such
as a boundary of a grain or a dislocation. We show that
Co diffusion into the defect leads to growing the heat
release and to melting both the silicide and Co layers due
to the low activation energy for the silicide formation
reaction. The melted alloy is extracted by capillary
forces of spills onto the surface of the Co film and
crystallizes creating CoSi2. This process of the pinhole
formation can exist when the thickness of the Co layer
reaches up to 10 nm.
2. The model
The investigation of nucleation stage of the cobalt
silicide phases revealed the local formation of the
crystallites of the silicide phase surrounded by the
unreacted Co film (Fig. 1a, b, d, e). The local origin of
the Co silicide phases was found in structural defects on
the silicon surface at the initial stage of the Co-Si
interaction [1]. The coalescence of the lateral cobalt
silicide crystallites is supposed to be the preferable mode
of the growth during the silicide layer formation on the
Si surface with high density of structural defects
(Fig. 1d, e). Therefore, account must be taken of the
diffusion processes into the crystal defects at the Co/Si
interface for the adequate description of the silicide
phase growth. The Fisher model [9-11] allows to
describe a diffusion process in two-dimensional defects
such as the grain boundaries or dislocations. In the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 29-34.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
30
frames of this model, the defect is considered as the
plate with high diffusion coefficient which is implanted
between boundaries of the bulk Si material (Fig. 2). The
Co atoms penetrate into the defect (plate) from the top
thin Co film on the silicon and forming the Co-Si
mixture. For simplicity, suppose that the chemical
reaction Co + Si = CoSi occurs only at the interface
between Co-Si mixture and silicon inside the plate; the
opposite Si atom flux in the top Co film is neglected. In
the present model, the system is instantly heated from
the room temperature up to T0 = 1000 K when the
Co + Si chemical reaction begins.
According to the Fisher model, for the diffusion of
Co atoms into the dislocation the displacement of atoms x
(Fig. 2) is proportional to the fourth root of time t:
,4
1
Atx =
D
DA
2
πδ ′
= , (1)
where δ is the thickness of the plate, D is the Co
diffusion coefficient in the bulk material (Si). D' is the
diffusion coefficient of Co atoms into the plate as well as
into the Co-Si mixture formed into the plate. As the
silicide is formed between grains it is assumed that
D'/D ∼ 104…105 [11].
The diffusion time of Co atoms between the
Co/Co-Si and Co-Si/Si interfaces in Fisher’s model is
determined from Eq. (1). The full time of the layer
growth is the sum of the time of diffusion and the time
of the chemical reaction:
v
x
A
xt
′
+= 4
4
, (2)
where v' is the velocity of the chemical reaction Co + Si
after Co atom crossed the boundary between Co-Si
mixture and Si. The thickness of the layer after the
arbitrary time t can be found as the root of the fourth
degree from Eq. (2):
.04
4
4 =−
′
+ tAx
v
Ax (3)
The velocity of the layer growth V is also found from
equation (2) by differentiation:
1
4
3 14
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
′
+==
vA
x
dt
dxV . (4)
The limiting cases of (4) are V = v' if 4x3v' << A4 and
3
4
4x
aV = at 4x3v' >> A4. The change of these cases
occurs when 3
4
4v
Ax
′
≈′ . Comparing this expression with
the characteristic thickness x1 of changing the growth
mechanisms, which follows from the usual diffusion
[12-15]
v
Dx ≈1 (v is the constant of layer growth in the
kinetic regime for the homogeneous layer), we can see
that at large v and v' the first expression allows to get
much more thickness than in the usual case. For
example, at D ≈ 10−14 m2/s, δ ≈ 10−8 m and D' ≈
10−10 m2/s we obtain A ≈ 3⋅10−6 that at v' ≈ 10−2 m/s
gives x′ ≈ 1.3 ⋅ 10−7 m instead of x1 ≈ 1⋅10−12 m at the
same value of v. The high velocities of the chemical
reaction can exist due to the dependence of the
activation energy on the density of the surface charge
[12] which can be high within the boundaries of the
structural defects or Si cracks.
Let us estimate the temperature of the CoSi layer
during the exothermic reaction Co + Si = CoSi at the
CoSi/Si interface. Consider the case when this interface
has the width δ and is placed between the boundaries of
the defect. Assuming a low thickness of Co layer above
the defect (∼1 nm) and supposing that t ≤ 10−7 s (the
distance of temperature diffusion x'' = 2 at is lesser
than the thickness of the Si sample (a is the temperature
conductivity coefficient, a ≈ 10−5 m2/s) and we can
consider the quasi-one-dimensional case of heating the
edge of the Si half-infinite rod. The functional solution
of the thermal conductivity equation in this case gives
the temperature on distance r from the CoSi/Si interface
at chosen moment τ [16]:
( ) ( )[ ] ( )
( )∫ −
+=
−
−τ
0ε
0 τπ
,02τ,
τ4
2
dz
z
ezTq
K
TrT
za
r
, (5)
where 222 ρλ cK =ε , with the thermal conductivity
λ2, the heat capacity c2 and density ρ2 of Si; q[T(0, z)] is
the heat flux in J/m2 on the CoSi/Si interface due to the
exothermic reaction:
( )[ ] ( )τ,ρ~τ,0 1 TVQTq = , (6)
ρ1 is the concentration of Co at the interface, Q~ is the
heat effect of the reaction. The temperature at the
interface can be obtained from this relation:
( ) ( )[ ]
( )∫ −
+=
τ
0ε
0 τπ
,02τ,0 dz
z
zTq
K
TT . (7)
The change of the factor
τ4
2
a
r is small, and further we
will suppose that the interface does not move in the
process of the reaction. Then, we can solve the system
(3), (4), (6), (7) using the numerical method proposed in
[17, 18] for mm z ττ 1 <<− :
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 29-34.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
31
Fig. 1. AFM images (a, b), surface profile (c) and SEM image (d) for the Co/Si structure after vacuum annealing at 873 K. The
scheme of the lateral silicide crystallites and pinholes formation (e).
a b
3 μm
d
Crystal defects
Si-substrate
CoxSiy nuclei pinhole
e
c
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 29-34.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
32
Co/Si interface Co film
single crystal Si single crystal
δ
Co,
D, V
Co,
D, V
X
Co
distribution
Si
Co
D’, V’
Fig. 2. Fisher's model for the diffusion of Co atoms into the
dislocation and Co atom displacement x.
( ) ( )[ ]
( )
( )[ ]
( )
.
τπ
1τ,02
τπ
,02τ,0
τ
τ
1
τ
0ε
0
1
1
∫
∫
−
−
−
+
+
−
+=
−
m
m
m
dz
zK
Tq
dz
z
zTq
K
TT
m
m
ε
(8)
The temperature dependence of the velocity of layer
growth is determined by the temperature dependences of
the velocity constants
kT
U r
evv
−
= 0 , kT
U
g r
evv
−
′=′ 0 (9)
and coefficients of diffusion:
kT
Ud
eDD
−
= 0 , kT
U
eDD
def
0
−
′=′ , (10)
where v0, v'0, D0, D'0 are pre-exponential factors, Ur is
the activation energy of the reaction, Ud is the diffusion
energy barrier, Udef is the energy barrier on the diffusion
inside the defect, g is a factor 0 < g < 1.
3. Results and discussion
The dependences D(T) and D'(T) were chosen as
follows: ,10
eV9.1
5 kTeD
−−= kTeD
eV9.1
5
3
510
⋅−−=′ . The
value Ud = 1.9 eV was experimentally found in [4] for
the CoSi layer growth. Because there are no
experimental data on the linear growth of layer in Co-Si
system, we used the expression kT
g
ev
eV9.1
310
−
=′ , which
at 1000 K and g = 1 gives the same velocity 10−7 m/s as
was found experimentally for the system Ni-Si [19].
Using the factor g in this expression, we can model the
change of the reaction activation energy due to the
surface charge inside the defect. The initial temperature
T0 = 1000 K was chosen. The energy effect of the
reaction Q~ is equal to 1.15⋅106 J/kg [5]. Dependences
T(0, t) are shown in Fig. 3 for various values of g and δ
parameters. At small δ, the sufficient exponential growth
of the interface temperature is reached only at great
velocities (or small values of g, Fig. 3a, curves 1, 2).
Then the temperature decreases due to the transfer to the
diffusion growth of the layer. The decrease of the
temperature obeys the t−1/4 law accordingly to the chosen
model. At larger values of g, the growth of the layer is
slow (Fig. 3a, curves 3, 4), and the temperature
decreases after peaking which does not reach the melting
point of Si (∼1696 K).
0 2 4 6 8 10
1000
1500
2000 a
t, 10 - 8 s
4
3
2
1
T(
0,
t),
K
0 2 4 6 8 10
1000
1500
2000
2500 b
5
4
3
2
1
T(
0,
t),
K
t, 10 - 8 s
0 2 4 6 8 10
1000
1500
2000
2500 c
5
4
3
2
1
T
(0
,t)
, K
t, 10 - 8 s
Fig. 3. Dependences of the CoSi/Si interface temperature
T(0, t) on time at various values of the parameters δ and g:
a) δ = 10−8 m, g = 0.18 (1), 0.25 (2), 0.32 (3), 0.40 (4); b) δ =
= 10−7 m, g = 0.30 (1), 0.35 (2), 0.38 (3), 0.40 (4), 0.42 (5);
c) δ = 5⋅10−7 m, g = 0.40 (1), 0.41 (2), 0.42 (3), 0.43 (4),
0.44 (5). Lines denote the CoSi melting temperature
Tmelt=1737 K.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 29-34.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
33
0 2 4 6 8 10
0
1
2
3
4
5
6 a
3
2
1
x,
1
0 -
8
m
t , 10 - 8 s
0 2 4 6 8 10
0
5
10
15
20
b
5
4
3
2
1
x,
1
0 -
8
m
t , 10 - 8 s
0 2 4 6 8 10
0
10
20
30
40 c
5
4
3
2
1
x,
1
0 -
8
m
t , 10 - 8 s
Fig. 4. Dependences of the CoSi layer thickness x on time at
various values of the parameters δ and g: a) δ = 10−8 m, g =
0.18 (1), 0.32 (2), 0.40 (3); b) δ = 10−7 m, g = 0.30 (1),
0.35 (2), 0.38 (3), 0.40 (4), 0.42 (5); c) δ = 5⋅10−7 m, g =
= 0.40 (1), 0.41 (2), 0.42 (3), 0.43 (4), 0.44 (5).
Increasing the parameter δ leads to increase of g at
which the transition to high temperatures occurs
(Figs 3b, c). The peak in the T(t) dependences is shifted
to large times and decrease of the temperature is
moderate. The range of the parameters g in which the
change of temperature regimes appears is reduced
(Δg ≈ 0.2 at δ = 10-8, Δg ≈ 0.12 at δ = 10-7 and Δg ≈ 0.04
at δ = 5⋅10−7). The dependence of the thickness of the
CoSi layer x on time is shown in Fig. 4. At δ = 10−8 and
small g, the thickness obeys the t1/4 law, as it follows
from Eq. (3) (Fig. 4a, curve 1). While the parameter g
increases, the dependence x(t) turns to the exponential
growth at small t and t1/4 growth at large t (Fig. 4a,
curves 2, 3). The increase of the parameter δ leads to
significant enhancement of the layer thickness
(Fig. 4b, c).
The temperature of the interface can reach the
melting temperatures of CoSi, Si and Co especially at
larger values of δ = (1…5)⋅10−7 m (Fig. 3b, c). If the
activation energy of the reaction is small, the
temperature in the reaction area at the interface increases
to very high values (Fig. 3b, curves 1-3) and decays with
small decrement, which leads to melting of the CoSi
layer during this time. Moreover, the Co layer with the
thickness ~10 nm will be melted too, accordingly to the
chosen model of heating of the half-infinite rod. At
larger thickness of the Co layer, the exponent in the
equation (5) has to be taken into account, and the
temperature of the Co layer will be lower than that inside
the defect. Note that, when the temperature of the
reaction area will reach the melting points of Co, Si and
CoSi phases, the chosen model will not describe heating
the interface because the specific heats of melting do not
take into consideration. It means that the temperature in
the reaction area will not increase higher then in melting
points or will decrease when the reaction will be
finished. Calculations show that the melted CoSi is
extracted by capillary forces on the Co surface for
~10−7 s and after the process of crystallization CoSi2 is
formed on the top Co film. Thus, the melting of the CoSi
layer arises during the exothermic reaction because of
the small activation energy of the reaction in the
structural defect and as a result of this local melting
process the pinhole channel is formed.
4. Conclusions
We considered the growth of the cobalt silicide layer in
the frames of the model of grain boundary diffusion. The
diffusion front of Co in this model shifts obeying the
t1/4 law. Because of this law, the layer thickness can
grow up to 0.1 μm at large velocities of the chemical
reaction. This growth rate leads to a great extraction of
heat due to the exothermic reaction at the CoSi/Si
interface. We calculated the time dependence of the
temperature of the reaction area at the interface CoSi/Si
and found that for t ∼ (10−8…10−7) s the temperature can
increase to the melting points of Co, Si and CoSi. The
liquid alloy spills out on the top of the Co film and
pinholes are formed into silicide film as well as lateral
silicide crystallites.
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