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Monte Carlo simulation of thermalization process of sputtered particles
L494
Surface Science 134 (1983) L494- L499 North-Holland Publishing Company
SURFACE
SCIENCE
LETTERS
MONTE CARLO SIMULATION SPUTTERED PARTICLES T. MOTOHIRO
OF THERMALIZATION
OF
and Y. TAGA
Toyota Central Research and Development Laboratories, Nagakute - cho, Atchi -gun, Aichi - ken 480 1 I, Japan Received
PROCESS
8 July 1983; accepted
for publication
Inc., 41-1, Ara Yokomichi,
17 August
Oara Nagakute,
1983
The transport process of sputtered particles in plasma sputter deposition was studied by computer simulation using the Monte Carlo method, with particular attention to the understanding of the thermalization process. Due consideration was taken of the momentum loss as well as of the energy loss of sputtered particles colliding with sputter gas molecules. The results clearly showed that with increasing target-substrate distance, the energy distribution of sputtered copper atoms arriving at the substrate shifts toward lower kinetic energies, but still contains a considerable fraction of high energy particles. In addition, it was found that the arrival rate of sputtered copper atoms at the substrate decreases exponentially with the target-substrate distance, while the return rate to the target first increases and then becomes constant. It was concluded that the present Monte Carlo simulation can be successfully used for a quantitative estimation of the transport process of sputtered particles.
Plasma sputtering is a wide-spread technique for thin film deposition. Increasing effort has been put in the study of the sputtering process as a means of depositing films, and of the interaction between the film properties and the deposition parameters [l]. In this connection, film properties such as stress and adhesion are strongly affected by the nature of sputtered particles arriving at the substrate which is expected to have a close relation with the transport process from the target to the substrate. Recently, slowing down and thermalization of sputtered particles have received an increased attention [2-51. In fact, the thermalization technique has been successfully applied for thin film preparation of high-temperature metastable superconducting compounds with so-called metallic layered ultrathin coherent structures [6,7]. In a recent paper, Meyer et al. [8] theoretically studied the thermalization of sputtered particles colliding with sputter gas molecules, and made a simple calculation of the energy distribution of the particles arriving at the substrate. On the other hand, the Monte Carlo (MC) simulation technique has been successfully applied to the study of energy and momentum distributions of particles in ion implantation [9,10], sputtering [11,12], and radiation damage. 0039-6028/83/0000-0000/$03.00
0 1983 North-Holland
T. Motohiro,
Y. Taga / Monte Carlo simulation
L495
/’ Fig. 1. A schematic
diagram
of a hard sphere collision
process.
The MC approach provides complete histories of individual particles during their collision with sputter gas molecules and can make a statistical simulation of the transport process of so many sputtered particles. However, hardly any paper has been published which deals with the MC simulation of the transport process of sputtered particles. In this paper, we describe the results of the MC simulation of the thermalization process of sputtered Cu atoms. The main emphasis of the present study is placed on the consideration of the momentum loss as well as of the energy loss of sputtered particles during the transport process. The results obtained in this study are compared with those by Meyer et al. The ejection behavior of sputtered particles at a target was assumed to obey Thompson’s formula [8], in which the energy distribution of the sputtered particles was characterized by the binding energy of a particle in the bulk, E,, and by the sputtering voltage V. The cosine ejection rule was also assumed to hold. An ejected particle runs a distance X before it collides with an ambient gas molecule. The X value is given by using a random number E, and the mean free path A,, X= -X,lne,;
(1)
X, is calculated from the sputter gas temperature T, the sputter gas pressure P, the radius of the sputter gas molecule r and the radius of the sputtered particle R. The elemental process of scattering of the sputtered particle by an ambient gas molecule is considered by the hard sphere collision model. Fig. 1 shows the situation that a sputtered atom with a velocity u is scattered by an ambient gas molecule with a scattering angle S to have a velocity U. 8 is the angle between the line which passes through the centers of the colliding two particles and the
L496
T. Motohiro,
Y. Taga / Monte Carlo simulation
momentum direction of the sputtered particle before the collision. The following relations can be obtained by the energy and momentum conservation rules: 1(= /(M--M)
’ cos26 + (M + m)’ sin26 u,
M+m
(2) (3)
The azimuthal
angle C#Iis determined
for a random
number
+=27re,,
(4)
while 8 is determined
for another
random
number
c3 as follows (5)
8 = arcsin 6. D T,S=Ocm 50-
< 0
52
PA, T
40.
=
0.01
=550
Tort
K
: Meyer
-----
et al.
a
30.
0
Lo as follows
4
8
12
16
20
Energy
.
24
28
32
36
40
ev
DT,~=3cm PA,
=
0.01 Torr
T=550
K
et al.
-----:Meyer
b
8
12
16
20
24
Energy.
eV
28
32
36
40
T. Motohiro,
Y. Taga / Monte Carlo simulation
DT,S =
6cm
PA,
0.01 Torr
=
T=550
K
-----:Meyer
*o-II
L497
et al. C
I 0 >
t
70.
I I 1
4@-
; I I
30.
;
20.
I I : , I \
lo-
,/ o-
0
4
8
Fig. 2. Energy distribution = 3 cm, (c) D,,,
(b) D,,,
12
1
16
histograms = 6 cm.
20
24
28
of Cu particles
32
arriving
36
40
at the substrate:
(a) D,,,
= 0 cm,
Eq. (5) is obtained from a consideration of the colliding point probability on the surface of the sputtered particle with the uniformly distributed ambient gas molecules, Then, the particle starts with the new kinetic energy as determined above and runs also another distance X in the new direction, before it encounters another collision. This calculation procedure is repeated until the sputtered particle comes across some boundaries such as the substrate surface, or until the energy of the sputtered particle decreases to the thermal equilibrium energy of the ambient gas molecules. Fig. 2 shows the results of the MC simulation of the energy distribution of sputtered Cu atoms arriving at the substrate. The staircase energy distribution
T. Moiohiro,
L498
Y. Taga / Monte Carlo simulation
is not substantial because it can be smoothed if the calculation number is increased. In the figure, the target-substrate distance, Dr,s, was chosen as 0, 3 and 6 cm. The conditions for the MC simulation used in this study are the same as those used by Meyer et al. and include a cut-off energy of 40 eV in the initial energy distribution of sputtered particles; the results by Meyer et al. are also shown in the figure for comparison. It is found that, with increased distance, the energy distribution of sputtered Cu atoms arriving at the substrate shifts toward lower kinetic energies. The results of the MC simulation are also found to agree well with those of the calculation by Meyer et al. It can be considered that the MC technique developed in this study is useful for a simulation of the sputter deposition process. The most prominent discrepancy between the present results and those by Meyer et al. is the sharp cut-off in the energy distribution for DT,S = 3 cm and 6 cm. So, in Meyer’s model, Cu atoms with an initial energy of 40 eV, for example, cannot have energies larger than 13 eV when Dr,s = 3 cm. As the mean free path of Cu atoms in the calculated situation is about 2.3 cm, it is quite unreasonable to assume that no Cu atoms can reach the substrate without any collisions and energy loss because the mean free path is only the mean value of free paths [13]. This can be explained as due to Meyer’s assumptions that the energy loss rate at each collision and the number of
Q
100
\
‘Y \
I
\
\
\
=
T
=550
0.01 Torr K
\ \
DT/S
3. Arrival
PA,
and return
‘cm
rates as a function
of D,,,.
T. Motohiro,
Y. Taga / Monte Carlo simulation
IA99
collisions which a sputtered particle experiences in the gas are constant, and that the momentum loss is disregarded. In the present MC simulation, however, the energy distribution profile shows a gradual decrease with increasing energy and contains a considerable fraction of high energy particles, which are expected to play an important role in film formation. Thus the Monte Carlo approach is substantially preferable to deal with these problems. Fig. 3 depicts the MC simulation results of the arrival rate of sputtered Cu atoms at the substrate as a function of D,,,.It was found that the arrival rate decreases exponentially with DT,S,while the return rate first increases and then becomes constant. These tendencies can explain the cross contamination problem in plasma sputter deposition by the use of a multi-component target. In conclusion, the MC simulation can be successfully applied for a quantitative estimation of the transport process of sputtered particles. In addition, the simulation predicts more important tendencies which cannot be expected by the conventional simple numerical calculation. Comparison between the MC simulation and experimental results is now in progress.
References [l] [2] [3] [4] (5) [6] [7] [8] [9]
T. Motohiro, Y. Taga and K. Nakajima, Surface Sci. 118 (1982) 66. R. Somekh, Proc. 7th ICVM. Tokyo, 1982, p. 17. F.J. Cadieu and N. Chencinski, IEEE Trans. Magnetics MAG-11 (1975) 227. C.T. Wu, R.T. Kampwirth and J.W. Hafstrom, J. Vacuum Sci. Technol. 14 (1977) 134. C.T. Wu, L. Kammerdiner and H.L. Luo, Appl. Phys. Letters 30 (1977) 543. I.K. Schuller, Phys. Rev. Letters 44 (1980) 1597. I.K. Schuller and C.M. Falco, Surface Sci. 113 (1982) 443. K. Meyer, I.K. Schuller and C.M. Falco, J. Appl. Phys. 52 (1981) 5803. R. Shimizu, S.T. Kang, T. Koshikawa, H. Ogata, K. Kanayama, Y. Ogata, Y. Akasaka and K. Horie, J. Appl. Phys. 48 (1977) 1745. [lo] J. Amano, A. Wagner and D.N. Seidman, Phil. Mag. A44 (1981) 199. [ll] S.T. Kang, R. Shimizu and T. Okutani, Japan. J. Appl. Phys. 18 (1979) 1717. [12] S.T. Kang, R. Shimizu and T. Okutani, Japan. J. Appl. Phys. 18 (1979) 1987. [13] T. Motohiro, Y. Taga, K. Satta and H. Morimoto, in: Proc. Intern. Ion Engineering Congr. (ISIAT ‘83 and IPAT ‘83), Kyoto, 1983.
Surface Science 134 (1983) L494- L499 North-Holland Publishing Company
SURFACE
SCIENCE
LETTERS
MONTE CARLO SIMULATION SPUTTERED PARTICLES T. MOTOHIRO
OF THERMALIZATION
OF
and Y. TAGA
Toyota Central Research and Development Laboratories, Nagakute - cho, Atchi -gun, Aichi - ken 480 1 I, Japan Received
PROCESS
8 July 1983; accepted
for publication
Inc., 41-1, Ara Yokomichi,
17 August
Oara Nagakute,
1983
The transport process of sputtered particles in plasma sputter deposition was studied by computer simulation using the Monte Carlo method, with particular attention to the understanding of the thermalization process. Due consideration was taken of the momentum loss as well as of the energy loss of sputtered particles colliding with sputter gas molecules. The results clearly showed that with increasing target-substrate distance, the energy distribution of sputtered copper atoms arriving at the substrate shifts toward lower kinetic energies, but still contains a considerable fraction of high energy particles. In addition, it was found that the arrival rate of sputtered copper atoms at the substrate decreases exponentially with the target-substrate distance, while the return rate to the target first increases and then becomes constant. It was concluded that the present Monte Carlo simulation can be successfully used for a quantitative estimation of the transport process of sputtered particles.
Plasma sputtering is a wide-spread technique for thin film deposition. Increasing effort has been put in the study of the sputtering process as a means of depositing films, and of the interaction between the film properties and the deposition parameters [l]. In this connection, film properties such as stress and adhesion are strongly affected by the nature of sputtered particles arriving at the substrate which is expected to have a close relation with the transport process from the target to the substrate. Recently, slowing down and thermalization of sputtered particles have received an increased attention [2-51. In fact, the thermalization technique has been successfully applied for thin film preparation of high-temperature metastable superconducting compounds with so-called metallic layered ultrathin coherent structures [6,7]. In a recent paper, Meyer et al. [8] theoretically studied the thermalization of sputtered particles colliding with sputter gas molecules, and made a simple calculation of the energy distribution of the particles arriving at the substrate. On the other hand, the Monte Carlo (MC) simulation technique has been successfully applied to the study of energy and momentum distributions of particles in ion implantation [9,10], sputtering [11,12], and radiation damage. 0039-6028/83/0000-0000/$03.00
0 1983 North-Holland
T. Motohiro,
Y. Taga / Monte Carlo simulation
L495
/’ Fig. 1. A schematic
diagram
of a hard sphere collision
process.
The MC approach provides complete histories of individual particles during their collision with sputter gas molecules and can make a statistical simulation of the transport process of so many sputtered particles. However, hardly any paper has been published which deals with the MC simulation of the transport process of sputtered particles. In this paper, we describe the results of the MC simulation of the thermalization process of sputtered Cu atoms. The main emphasis of the present study is placed on the consideration of the momentum loss as well as of the energy loss of sputtered particles during the transport process. The results obtained in this study are compared with those by Meyer et al. The ejection behavior of sputtered particles at a target was assumed to obey Thompson’s formula [8], in which the energy distribution of the sputtered particles was characterized by the binding energy of a particle in the bulk, E,, and by the sputtering voltage V. The cosine ejection rule was also assumed to hold. An ejected particle runs a distance X before it collides with an ambient gas molecule. The X value is given by using a random number E, and the mean free path A,, X= -X,lne,;
(1)
X, is calculated from the sputter gas temperature T, the sputter gas pressure P, the radius of the sputter gas molecule r and the radius of the sputtered particle R. The elemental process of scattering of the sputtered particle by an ambient gas molecule is considered by the hard sphere collision model. Fig. 1 shows the situation that a sputtered atom with a velocity u is scattered by an ambient gas molecule with a scattering angle S to have a velocity U. 8 is the angle between the line which passes through the centers of the colliding two particles and the
L496
T. Motohiro,
Y. Taga / Monte Carlo simulation
momentum direction of the sputtered particle before the collision. The following relations can be obtained by the energy and momentum conservation rules: 1(= /(M--M)
’ cos26 + (M + m)’ sin26 u,
M+m
(2) (3)
The azimuthal
angle C#Iis determined
for a random
number
+=27re,,
(4)
while 8 is determined
for another
random
number
c3 as follows (5)
8 = arcsin 6. D T,S=Ocm 50-
< 0
52
PA, T
40.
=
0.01
=550
Tort
K
: Meyer
-----
et al.
a
30.
0
Lo as follows
4
8
12
16
20
Energy
.
24
28
32
36
40
ev
DT,~=3cm PA,
=
0.01 Torr
T=550
K
et al.
-----:Meyer
b
8
12
16
20
24
Energy.
eV
28
32
36
40
T. Motohiro,
Y. Taga / Monte Carlo simulation
DT,S =
6cm
PA,
0.01 Torr
=
T=550
K
-----:Meyer
*o-II
L497
et al. C
I 0 >
t
70.
I I 1
4@-
; I I
30.
;
20.
I I : , I \
lo-
,/ o-
0
4
8
Fig. 2. Energy distribution = 3 cm, (c) D,,,
(b) D,,,
12
1
16
histograms = 6 cm.
20
24
28
of Cu particles
32
arriving
36
40
at the substrate:
(a) D,,,
= 0 cm,
Eq. (5) is obtained from a consideration of the colliding point probability on the surface of the sputtered particle with the uniformly distributed ambient gas molecules, Then, the particle starts with the new kinetic energy as determined above and runs also another distance X in the new direction, before it encounters another collision. This calculation procedure is repeated until the sputtered particle comes across some boundaries such as the substrate surface, or until the energy of the sputtered particle decreases to the thermal equilibrium energy of the ambient gas molecules. Fig. 2 shows the results of the MC simulation of the energy distribution of sputtered Cu atoms arriving at the substrate. The staircase energy distribution
T. Moiohiro,
L498
Y. Taga / Monte Carlo simulation
is not substantial because it can be smoothed if the calculation number is increased. In the figure, the target-substrate distance, Dr,s, was chosen as 0, 3 and 6 cm. The conditions for the MC simulation used in this study are the same as those used by Meyer et al. and include a cut-off energy of 40 eV in the initial energy distribution of sputtered particles; the results by Meyer et al. are also shown in the figure for comparison. It is found that, with increased distance, the energy distribution of sputtered Cu atoms arriving at the substrate shifts toward lower kinetic energies. The results of the MC simulation are also found to agree well with those of the calculation by Meyer et al. It can be considered that the MC technique developed in this study is useful for a simulation of the sputter deposition process. The most prominent discrepancy between the present results and those by Meyer et al. is the sharp cut-off in the energy distribution for DT,S = 3 cm and 6 cm. So, in Meyer’s model, Cu atoms with an initial energy of 40 eV, for example, cannot have energies larger than 13 eV when Dr,s = 3 cm. As the mean free path of Cu atoms in the calculated situation is about 2.3 cm, it is quite unreasonable to assume that no Cu atoms can reach the substrate without any collisions and energy loss because the mean free path is only the mean value of free paths [13]. This can be explained as due to Meyer’s assumptions that the energy loss rate at each collision and the number of
Q
100
\
‘Y \
I
\
\
\
=
T
=550
0.01 Torr K
\ \
DT/S
3. Arrival
PA,
and return
‘cm
rates as a function
of D,,,.
T. Motohiro,
Y. Taga / Monte Carlo simulation
IA99
collisions which a sputtered particle experiences in the gas are constant, and that the momentum loss is disregarded. In the present MC simulation, however, the energy distribution profile shows a gradual decrease with increasing energy and contains a considerable fraction of high energy particles, which are expected to play an important role in film formation. Thus the Monte Carlo approach is substantially preferable to deal with these problems. Fig. 3 depicts the MC simulation results of the arrival rate of sputtered Cu atoms at the substrate as a function of D,,,.It was found that the arrival rate decreases exponentially with DT,S,while the return rate first increases and then becomes constant. These tendencies can explain the cross contamination problem in plasma sputter deposition by the use of a multi-component target. In conclusion, the MC simulation can be successfully applied for a quantitative estimation of the transport process of sputtered particles. In addition, the simulation predicts more important tendencies which cannot be expected by the conventional simple numerical calculation. Comparison between the MC simulation and experimental results is now in progress.
References [l] [2] [3] [4] (5) [6] [7] [8] [9]
T. Motohiro, Y. Taga and K. Nakajima, Surface Sci. 118 (1982) 66. R. Somekh, Proc. 7th ICVM. Tokyo, 1982, p. 17. F.J. Cadieu and N. Chencinski, IEEE Trans. Magnetics MAG-11 (1975) 227. C.T. Wu, R.T. Kampwirth and J.W. Hafstrom, J. Vacuum Sci. Technol. 14 (1977) 134. C.T. Wu, L. Kammerdiner and H.L. Luo, Appl. Phys. Letters 30 (1977) 543. I.K. Schuller, Phys. Rev. Letters 44 (1980) 1597. I.K. Schuller and C.M. Falco, Surface Sci. 113 (1982) 443. K. Meyer, I.K. Schuller and C.M. Falco, J. Appl. Phys. 52 (1981) 5803. R. Shimizu, S.T. Kang, T. Koshikawa, H. Ogata, K. Kanayama, Y. Ogata, Y. Akasaka and K. Horie, J. Appl. Phys. 48 (1977) 1745. [lo] J. Amano, A. Wagner and D.N. Seidman, Phil. Mag. A44 (1981) 199. [ll] S.T. Kang, R. Shimizu and T. Okutani, Japan. J. Appl. Phys. 18 (1979) 1717. [12] S.T. Kang, R. Shimizu and T. Okutani, Japan. J. Appl. Phys. 18 (1979) 1987. [13] T. Motohiro, Y. Taga, K. Satta and H. Morimoto, in: Proc. Intern. Ion Engineering Congr. (ISIAT ‘83 and IPAT ‘83), Kyoto, 1983.