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中國機械工程學刊第二十四卷第五期第 507~515 頁(民國一百年)
Journal of the Chinese Society of Mechanical Engineers, Vol.24, No.5, pp.507~515 (2011)
Optimization of the geometry of blockage plates
to improve film uniformity in a DC magnetron
sputtering machine
Wen-Lih Chen*, Huann-Ming Chou*, Chang-Ren Chen*, and
Shi-Sung Cheng **
Keywords：sputtering, film thickness, uniformity,
blockage plate.
ABSTRACT
Inserting blockage plates in a sputtering
chamber is one of the methods to obtain better
film-thickness uniformity on the substrate.
Conventional blockage plates are flat, and they
achieve moderate improvement on film uniformity
but at a cost of seriously compromising the film
deposition rate on the substrate. In this study, a
numerical method is developed to calculate the
optimized geometry of blockage plates. With the
optimized plates in place, very high level of film
uniformity can be achieved with only moderate
reduction on the film deposition rate.
INTRODUCTION
Sputtering is a well-developed and widely used
technique to coat thin films on surfaces in many
different applications. Among currently available
sputtering methods, DC magnetron sputtering is one
of the most popular methods used in many industries.
It features advantages of low voltage to ionization
and very high film deposition rate; however, there are
also disadvantages such as low usage rate of target
material and difficulty to achieve high level of film
uniformity on the substrate. There have been many
theoretical, numerical, and experimental studies on
magnetic sputtering in open literature, e.g. Kadlec et
al (1997), Shon and Lee (2002), Sung et al. (2003),
Kwon et al. (2005), and Mahieu et al (2006). Mahieu
et al. (2006) reported the importance of the angle and
kinetic energy of the target atoms on the quality of the
film when they hit the substrate, therefore, theoretical
analysis and numerical simulation are crucial tools to
study the impacts of different control parameters
during sputtering process on the film quality.
.
Paper Received May, 2011. Revised Sepfember, 2011, Accepted
October, 2011, Author for Correspondence: Wen-Lih Chen.
* Associate Professor, Department of Mechanical Engineering,
Kun-Shan University, Tainan City, Taiwan 710, ROC.
**R&D Division Director, Allring Tech Co., Ltd, Kaohsiung City
821, ROC.
Among the numerical simulations of sputtering,
Monte Carlo method is currently the most popular
one. Despite its popularity, it is a complicated and
computer resources intensive simulation method due
to the following reasons: first, even in the highly
vacuum environment inside a sputtering chamber, the
mean free path of target atom only measured a few
millimeters. This means that a target atom will collide
with the background gas atoms tens of times before it
deposits on the substrate. In each collision, the
transfer of momentum from the target atom to
background gas atom and the deflection angle of the
target atom need to be calculated, and it is a
complicated procedure, involving spatial integrating,
to calculate both quantities. Second, a sufficient
number of target atoms need to be tracked in order to
obtain a reliable film pattern on the substrate.
According to Mahieu et al. (2006), this number has to
be at least 2×105. To trace so many target atoms and
each requiring so much computation signifies a
lengthy computing process, which is not beneficial to
shorten the design stage of a new sputtering machine.
In terms of the quality of deposited film on the
substrate, uniformity of film thickness is one of the
most crucial criteria affecting the film’s mechanical
and structural properties. Hence, achieving high level
of film uniformity is always among the most
important specifications of an industrial sputtering
machine. There have been many studies and
proposals in literature to improve film uniformity.
Ding et al. (2004) studied the effect of substrate
geometry on the uniformity of amorphous carbon
films deposited by unbalanced magnetron sputtering.
They found the thickness and hardness, the major
factors determining thin film’s lifetime, of the film on
a double V-shape substrate are strongly affected by
some geometrical ratios such as aspect ratio and
Raman ration. Other factors, the deposition pressure
and bias voltage, also play a role on the quality of the
deposited film. Their study demonstrated the
importance of film uniformity and the complexity of
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J. CSME Vol.24, No.5 (2011)
controlling it. Fu et.al (2006) reported a film
uniformity improving method by rotation and
revolution of the substrate. A relative deviation of
film thickness less than 3% within an area of 100 mm
in diameter on the substrate can be obtained when the
ratio of rotation/revolution speed is 5.3. The film
uniformity this level is impressive; however, since a
rotation and revolution system requires a very large
vacuum chamber to house, the size of substrate is
limited. Umeda et.al (2006) proclaimed the
importance of film uniformity on the mechanical and
electrical characteristics of bulk acoustic wave
devices, and improvement on film uniformity by
off-axis sputtering technique was demonstrated. An
extreme high level of film uniformity, only 0.3%
of deviation, was obtained. This technique, however,
relies on a complex rotation and control system.
In this study, a simplified numerical procedure
to calculate film thickness on the substrate with
satisfactory accuracy has been proposed. It was first
calibrated using experimental data from a circular
target then it was used to optimize the geometry of
blockage plates to improve the film uniformity on
moving substrates in an industrial sputtering machine.
The result shows extremely high level of film
uniformity can be achieved with only a moderate
decrease on the film deposition rate by adopting the
optimized blockage plates. Comparing to those
aforementioned techniques to improve film
uniformity, the use of optimized blockage plates is
straightforward, applicable to linear substrate
conveyer system, and more importantly, capable of
achieving excellent film uniformity over a large area
on the substrate.
MATHEMATICAL METHOD
The simulation procedure can be divided into
the following steps: simulation of magnetic field,
simulation of electron trajectory, simulation of the
erosion pattern on target plate, and finally simulation
of film thickness on the substrate. In the following,
the mathematical models used in each steps will be
described in detail. Here, it is assume the background
gas in the sputtering chamber is argon, and the target
material is aluminum.
Magnetic field simulation
A point magnet with magnetic intensity of m at
its pole establishes a magnetic field with the magnetic
flux intensity B at any point p in space written as:
m
B
,
(1)
4 r 2
where r is the distance between the point p and the
magnetic pole. Since the direction of a magnetic line
is from the north pole to the south pole, the north pole
can be treated as a source, whereas the south pole as a
sink. The magnetic potential Φ created respectively
by the pair of poles at point p in space can be
expressed as:
m
m
 source  
, sin k 
.
(2)
4 r
4 r
Therefore, the total magnetic potential at point p is
just a summation of the magnetic potentials by the
pair of poles:
m
m
,
(3)
p  

4 r1 4 r2
where r1 and r2 are the distances between the point p
and the two poles, respectively. Equation (3) can be
used to calculate the magnetic potential established
by the pair of magnetic poles in the entire space. With
the distributions of magnetic potential available, the
magnetic flux density vector B can be evaluated by:
B  Bx i  By j  Bz k ;
(4)



Bx 
, By 
, Bz 
x
y
z
and the magnitude of magnetic flux density B by:
B  Bx 2  By 2  Bz 2
(5)
Equations (3-5) only allow the magnetic flux density
vector created by a single pair of point magnetic
poles to be calculated. However, with the
employment of superposition method, these equations
can be extended to simulate the magnetic flux density
vector created by a magnet with an arbitrary
geometry. Taking a rectangular prism magnet with
magnetic intensity of m0 as an example, each of
magnetic pole can be treated as an assembly of n
evenly distributed point magnetic poles with equal
magnetic intensity of m0 / n . That is, the original
rectangular pole can be divided into n small cells,
each with the point magnetic pole located at its cell
center. Therefore, the magnetic potential at any point
p in space established by the rectangular magnet can
be approximated by the superposition of the magnetic
potential created by all point magnets as:
p  
i
1
4 n
n
r
i 1
m0
i
1

1
4 n
n
r
i 1
m0
i
2
,
(6)
i
where r1 and r2 are the distances between the
point p and the point magnets located at the south and
north poles, respectively. With the distribution of
magnetic potential in space available, equations (4)
and (5) can still be used to calculate the magnetic flux
density vector and magnitude. By using this method,
the magnetic field established by a magnet with
arbitrary geometry can be simulated.
Electron trajectory simulation
Since electrons in the sputtering chamber are
subjected to electromagnetic force, the distributions
of electric field intensity also need to be known
before the calculation of electron trajectory. The
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W. L. Chen et al.: Optimization of the geometry of blockage plates to improve film uniformity in a DC
magnetron sputtering machine.
electric field intensity between two electric charged
plates can be calculated by:
V
E
,
(7)
h
where V and h are the electric potential and distance
between the two electric charged plates, respectively.
The direction of electric field is from the positive
charge to the negative charge. With both magnetic
and electric fields available, the electromagnetic
force an electron is subjected to can be calculated by:

F  q E  v  B

,
(8)
where q is the electric charge of the electron, which is
1.60217 1019 coulombs. Since the mass of an
electron is 9.109 1031 kg, the acceleration of the
electron in the electromagnetic field can then be
calculated by using Newton’s second law. However,
the speed of the electron cannot be higher than the
speed of light, its mass needs to be corrected by
Lorentz factor γto enforce this speed limit. The
Lorentz factor is defined as:
C
,
(9)

2
C  v2
where C is the speed of light, and v is the velocity of
the electron. The corrected mass of the electron can
be written as:
(10)
m m .
According to Newton’s second low, the acceleration
of the electron can be expressed as:
F
.
(11)
a
m
In a three dimensional space, this translates into:
a  ax i  a y j  az k .
(12)
Assuming a free electron ejected from the surface of
the negative charged plate into the sputtering
chamber at the location  x0 , y0 , z0  and with an
initial velocity of 0, after a period of time t, its
velocity become:
v  vx i  v y j  vz k
t

vx  ax dt
0
t

v y  a y dt
,
0
t

vz  a z dt
0
and its position moves to
 xt , yt , zt  :
(13)
t

xt  x0  vx dt
0
t

yt  y0  v y dt .
(14)
0
t

zt  z0  vz dt
0
Then the trajectory of this electron within this time
period can be obtained by linking all its positions in
space from  x0 , y0 , z0  to  xt , yt , zt  . In a DC
magnetron sputtering chamber, however, a free
electron can travel back to the surface of negative
charged plate under the action of electromagnetic
force. In this case, the velocity of the electron is reset
to zero, and another tracking cycle begins. This
process continues until the time reaches a preset
ending time, or the electron finally arrives in the
positive charged plate.
Simulation of the erosion pattern on target plate
In a sputtering chamber, an argon ion is formed
because the original argon atom lost an electron due
to the collision with another high-speed free electron.
Since an argon atom can be ionized only when it
collides with a high-speed free electron, the region
where there is a larger number of high-speed free
electrons is the region where argon atoms are likely
to be ionized. That is, the number of argon ions
created in a certain region can be assumed to be
proportional to the summation of the momentum of
all free electrons within the region. To compute the
distributions of free electron momentum within a
sputtering chamber numerically, a uniform
two-dimensional grid covering the entire target
surface is first constructed, and a free electron is
assumed to be ejected from the center of each cell in
the grid. In the meantime, another three-dimensional
grid covering the space between the target and
substrate also needs to be constructed for the purpose
of computing free electron momentum within this
space. The fineness of both grids has to be
determined via a grid-independence test. Second,
using the method mentioned earlier, the trajectory of
each free electron ejected from the 2D grid on the
target surface can be calculated. By following each
electron trajectory, which cells in the 3D grid the
trajectory has past and the magnitude of electron
momentum as it passed the cell are known, and then
the summation of electron momentum in each 3D
grid cell can be performed. When the calculation of
all electron trajectories is completed, the summation
of electron momentum pe in all cells in the 3D grid
can be obtained. With the availability of this quantity,
the number of argon ions in a unit of time created in
each cell of the 3D grid can be estimated by:
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J. CSME Vol.24, No.5 (2011)
(15)
N  e pe ,
where is e a constant whose value can be
determined by calibrating with the experimental data.
As soon as an argon ion is created, it is driven
by the same electromagnetic field driving the free
electrons. Because an argon ion carries a positive
charge, the force it is subjected to is:

F  q EvB

.
(16)
The mass of an argon ion is 3.0 1026 kg which is
many orders larger than that of an electron, and under
the action of the same electromagnetic field, the
argon ion travels at much slower speed than a free
electron. In this circumstance, when compared with
the term E , the term v  B becomes too weak to
pose any effect on the motion of the argon ion; hence
the electric force dominates the trajectory of the
argon ion. Therefore, the argon ions only accelerate
almost linearly towards the target plate as soon as
they are formed. Using equations (16) and (11-14),
the trajectory of an argon ion can be calculated. This
allows us to know that a particular argon ion formed
inside a certain cell in the 3D grid will end up hitting
what location on the target plate and how large the
momentum the argon ion is when this collision takes
place. Combining with the number of argon ions
created in the cell calculated by equation (15), the
total momentum of all argon ions created in this cell
when hitting the target plate can be approximated by:
(17)
pAr i, j   NmAr v ,
where (i, j) represents a pair of cell indices on the
target grid. Repeating this calculation for all cells in
the 3D grid, the distributions of argon ion momentum
on the target plate can be obtained. We further
assume the number of target atoms knocked out by
the impact of argon ions at a particular location is
proportional to the summation of the argon ion
momentum calculated by equation (17), that is:
N Al  i, j    Ar
p Ar  i, j 
(18)
,
where  Ar is a constant to be calibrated by

data. The calculated
N Al  i, j 
function can be used to represent directly the
distributions of the erosion thickness   x, y  on the
experimental
target plate.
Simulation of film thickness on the substrate
On the target surface, it is reasonable to assume
that the number of target atoms knocked out and
flying off to the sputtering chamber at a particular
location is proportional to the erosion thickness at
that location. Once inside the sputtering chamber,
these target atoms could collide with the background
gas atoms or with other target atoms already inside
the chamber. However, according to Mahieu et al.
(2006), the number of target atoms is far less than the
number of background gas atoms in a sputtering
chamber, at a ratio of 10-2 to 10-3 in magnitude. This
suggests that the chance of collision of two target
atoms is much smaller than that of a target atom and a
background gas atom; hence the effect of
two-target-atom collision can be neglected.
Meanwhile, as the value of nAl/nAr (target
atoms/background-gas atoms) is very small, the
pressure of background gas is assumed evenly
distributed.
A target atom flies off the target surface with
very large kinetic energy, for example, about 400 eV
for an aluminum atom. This energy, however, is
gradually reduced by the successive collisions with
the background gas atoms. If too many collisions
have occurred, the energy of the target atom could be
reduced to the same level as the background gas
atoms, a situation termed “thermalized”. Then the
target atom loses its ability to adhere firmly on the
substrate. Therefore, the transport of a target atom
through the background gas is a very important factor
affecting the quality of the deposited film on the
substrate. In brief summary, simulation of the
deposited film on the substrate needs to include two
major parts: 1. characteristics of target atoms as they
fly off target surface and 2. transport of target atoms
through background gas. The details of these are
described in the following:
Characteristics of target atoms flying of target
surface
It is reasonable to assume the probability of
target atoms knocked out of the target surface is
proportional to the erosion thickness; hence the
erosion pattern calculated in Section 2.3 determines
where and how many target atoms flying off on the
target surface. To this end, a probability function can
be assumed to account for the number of target atoms
flying off the target surface at any location as:
  x, y 
p  x, y  
.
(19)
 max
Here, the value of 1 signifies the spot with the largest
number of target atoms flying off the surface,
whereas, the value of 0 implies the location with no
knocked-out target atoms. As a target atom flies off
the target surface, its initial fly path forms an angle
with the target surface shown in Fig. 1. This angle
can be divided into θ and ∅ components in a spherical
coordinate system. Some early models such as
Sigmund-Thompson model assume the initial energy
of the target atoms is independent of this initial flying
angle. Eckstein (1991), on the other hand, suggested
that the initial energy should be related to the initial
flying angle. Since the goal of this study is to develop
a simply and fast numerical procedure to shorten the
design stage for industries, the simple assumption in
Sigmund-Thompson model is adopted. Supposed a
cell with its center located at  xi , y j  in the 2D grid
emits ni,j target atoms, then the number ni,j can be
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W. L. Chen et al.: Optimization of the geometry of blockage plates to improve film uniformity in a DC
magnetron sputtering machine.
evaluated by:
ni , j  n0 p  xi , y j  Ai , j ,
(20)
where n0 is a prescribed number of target atoms, and
Ai,j is the area of the cell. The above equation implies
that no target atoms emitted from a cell with zero
probability. We further assume that these emitted
target atoms flying off the target surface uniformly in
a conical manner, and the cone is defined by azimuth
angle θ from 0 to 2π and zenith angle ∅ from -∅0 to
∅0, respectively. The value of ∅0 affects directly the
extent of the area within which target atoms spread
on the substrate surface; therefore, its value also
needs to be calibrated by experimental data.
Transport of target atoms through background gas
The transport of a target atom through the
background gas is a complex phenomenon. When a
target atom collides with a background gas atom, it
not only transfers part of its momentum to the gas
atom but also changes its direction of motion
afterwards. Hence, a simulation needs to compute the
amount of momentum transfer, loss of target atom
energy, and the new direction of its fly path in each
collision with a background gas atom, and all
quantities require some complicated calculations to
obtain (Eckstein, 1991). Furthermore, a target atom
would encounter tens of collisions (if not hundreds)
with the background gas atoms during its fly path
from the target plate to the substrate because the
length of the free path of a target atom is only a few
millimeters even in a highly vacuum sputtering
chamber. McDaniel (1964) has proposed a formula to
calculate the length of free path as:
1




P
2
Ms 2 
g
a 
  E / 
 rs  rg  1  M   . (21)
g  

 kT


The above only accounts for the tracking of a single
target atom. Overall, Mahieu et al. (2006) argued that
the number of target atoms needed to be track to form
a reliable deposition pattern on the substrate has to be
2×105 at least. With so many atoms needed tracking
and each requiring so much effort to calculate, the
amount of computation is staggering, resulting in a
huge demand on CPU time and consequently, a slow
design process. Here, a simplified method is
proposed to largely reduce the demand on computer
resources and return results with satisfactory accuracy.
As shown in Fig. 2, the method assumes all target
atoms travel in straight lines from the target surface
to substrate, and a decay factor is introduced to
account for the energy loss of the target atoms during
the collisions with background gas atoms, thus
neglecting all the complicated calculations used in
Mahieu et al. (2006). Because tracking of a single
target atom has been drastically simplified, a huge
number of target atoms, more than 10 million, can be
tracked in a very short CPU time. With some many
atoms tracked, the effect of the randomly distributed
deflection angle in any collusion can be accounted for
by the sheer number of target atoms. As mentioned
earlier, a target atom can be thermalized if much of
its energy is lost due to too many collisions with
background gas. This results in a reduction of the
number of target atoms successfully adhered on the
substrate. The decay factor also reduces the number
of target atoms reaching the substrate, mimicking the
effect of energy loss by collisions. Therefore, the
number of target atoms reaching the substrate can be
expressed as:
ns   n p ,
(22)
where ns is the number of target atoms reaching the
substrate, and np is the number of target atoms
emitting from a certain combination of θ and ∅
angles at the cell center of a 2D cell. If the target
atoms are assumed emitting uniformly in all
directions from the cell center, np can be written as:
ni , j
,
(23)
np 
N  N
where Nθ and N∅ are the numbers of discretization in
θ and ∅ directions, respectively. Finally, the decay
factor is assumed to be a function of the target atom’s
flying distance and the zenith angle as:

b

(24)
 ,


where a and b are constants to be determined by
calibrating with experimental data. The procedure of
the current simplified method can summarized as:
1. Construct a 2D grid covering the target surface
and use equation (20) to calculate the number ni,j
of target atoms emitting from the cell center of
each cell.
2. Establish a cone with the cell center as its vertex
and the ranges of 0    0 , and 0    2
in θ and ∅ directions, respectively. The azimuth
and zenith angles are discretized into Nθ and N∅
sections, forming N  N emitting angles
  r a 1 

0
within the cone. Then use equation (23) to
calculate np.
3. Construct another 2D grid on the substrate. The ns
number of target atoms travels along a particular
emitting angle will end up hitting a certain cell
Si,j of the substrate grid.
4. Tracking all the emitting angles in all cells in the
target grid, a target atom distribution function
Ts  x, y  on the substrate grid is returned. Then
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the film thickness on the substrate is assumed to
be proportional to the distribution function:
(25)
Ft  x, y   Ts  x, y  ,
where Ft  x, y  is the film thickness on the
substrate, and β is a constant requiring
adjustment by experimental data.
J. CSME Vol.24, No.5 (2011)
can be seen in Fig. 3(b). Next, a 72×80 circular grid
and another 79×79 rectangular grid are constructed
on the target and substrate surfaces, respectively. The
numbers of Nθ and N∅ are both specified as 200, that
is, there are 40,000 emitting angles in each cone at
every cell center of the circular grid, resulting in the
total number of emitting angle reaching 2.3×108,
equivalent to the tracking of the same number of
target atoms. Despite tracking this staggering
number of target atoms, the entire computation
procedure only took 300 seconds in a PC. In the
computation, the value n0 is set to 106. Fig. 4 shows
the deposition film thickness at four different
target/substrate distances. By specifying 0  70o ,
Fig. 1.
Definition of the initial flying angle of a
target atom.
a  0.05 , b=0.3,   2.4  103 , the simulated film
thickness is generally in very good agreement with
the data except the case of target/substrate distance =
130 mm, where the computation has slightly
underestimated the film thickness.
Z
substrate
X
Y
target
Fig. 2.
The flying path of a target atom.
RESULTS AND DISSCUSSIONS
(a)
10
9.8
t (mm)
Since there are a few constants in the proposed
method to be calibrated by some experimental data,
the measurements in Mahieu et al. (2006) are used to
determine their values. The experimental parameters
are as follows: DC voltage is 400 Volt between target
and substrate, the distances between target and
substrate are 70, 100, 130, and 160 mm, respectively,
the target is aluminum, and the background gas is
argon, the pressure inside the sputtering chamber
ranges from 0.3 to 1.0 Pa. The data in Mahieu et al.
(2006) show that pressure only poses slight effect on
the deposition film thickness within the range from
0.3 to 1.0 Pa; hence, the effect of pressure is not
considered in the current simulation method. Here,
the measurement with pressure fixed at 0.55 Pa is
used for the calibration of constants. Following the
procedures described in sections 2.1 to 2.3, the
erosion pattern on the target can be obtained. Fig. 3
shows the electron tracks inside the sputtering
chamber and the erosion profile on the target plate. It
can be seen from Fig. 3(a) that most electrons are
moving inside a ring-shape area above the target.
This gives rise to a circular race-track erosion
pattern on the target plate, and the erosion profile
9.6
9.4
9.2
9
-6
-4
-2
0
2
4
6
x (cm)
Fig. 3.
(b)
Electron trajectories near the target plate
and the erosion profile on the target plate; (a)
electron trajectories, and (b) target plate
erosion profile.
Fig. 5 shows the arrangement of magnets in an
industrial sputtering machine. The magnets are all
15mm×10mm×15mm in size, and they form an outer
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W. L. Chen et al.: Optimization of the geometry of blockage plates to improve film uniformity in a DC
magnetron sputtering machine.
ring measured 530mm × 60mm and an inner line
measured 442mm×20mm. The aluminum target plate
is 570mm × 70mm in size. When the sputtering
machine is in operation, the substrate moves forwards
and backwards under the target plate at a constant
speed. However, we first assume the substrate is not
moving, allowing stationary film deposition patterns
at different target/substrate distances to be observed.
The pattern of target/substrate distance = 100 mm is
shown in Fig. 6. It is noticeable that the film
thickness is thinner at the edge and reaches its
maximum at the center of the substrate. Additionally,
as the target/substrate distance is shorter, the film
thickness is more uniform at the central region of the
substrate, whereas, the film uniformity deteriorates as
the target/substrate distance becomes longer. This
implies a short target/substrate distance is beneficial
to reach better film uniformity. However, the film is
at risk of a direct bombardment by the high energy
plasma if it gets too close to the target. Next, the
situation of the substrate passing underneath the
target at a constant speed is simulated. As the target
passes under the target, it can be regarded as moving
along the y-direction at a constant speed. The film
thickness in this case can be obtained by integrating
the
stationary
film
thickness
function
the film is the thickest. Conventional blockage plates
are straight, and they only achieve limited effect with
the penalty of a large reduction on the film deposition
rate. We take the case of target/substrate distance =
90 mm as an example to demonstrate the
disadvantages of using them. When two straight
blockage plates are positioned on either sides of the
target plate, a portion of target atoms hit the blockage
plates and do not deposit on the substrate. Their
effect can be simulated by limiting the integration in
equation (26) to a smaller range at the y-direction.
That is, change the values of the lower and upper
limits y1 and y2 to form a narrower integration range.
In the case of target/substrate = 100 mm, by setting
the values of y1 and y2 to -50 mm and 50 mm,
respectively, a slightly more uniform film thickness is
returned. Fig. 8 shows the film thickness by setting
different ranges of integration. It can be seen that a
smaller integration range results in more uniform film
thickness distributions. However, the deposition rate
also decreases dramatically with the narrowing of the
integration range. In the case of setting y1 and y2 to
-50 mm and 50 mm, the maximum film thickness is
less than 50% of the case free of blockage plates.
Therefore, the geometry of blockage plates needs to
be optimized to improve their performance.
t f  x, y  along the y-direction:
25
y2
tm  x    t f  x, y dy .
(26)
16 cm exp
16 cm
13 cm exp
13 cm
10 cm exp
10 cm
7 cm exp
7 cm
20
y1
The resulted tm  x  at five different target/substrate
15
t
distances are given in Fig. 7. The distributions of
substrate film thickness confirm the previous
observation that the film thickness is more uniform as
the target/substrate distance is shorter. When the
target/substrate distance is 40 mm, the film thickness
is almost the same within the range from x=-150 mm
to 150 mm. Unfortunately, the film would be
subjected to plasma impact so close to the target plate,
rendering this distance impractical. The results also
show that the film thickness uniformity deteriorates
rapidly as the target/substrate distance increases.
Another noticeable feature is that the film thickness
decreases as the target/substrate distance increases,
signifying a reduction on the film deposition rate.
Although the results suggest that a short
target/substrate distance offers dual advantages of
high level of film uniformity and high deposition rate,
it puts the film at the risk of being damaged by
plasma. In practice, the target/substrate distance
should be at least more than 80 mm. At this distance,
however, the results show that the film thickness is
not uniform; hence some measures are needed to
improve film uniformity. One of such measures is to
place blockage plates on either sides of the target to
intercept some target atoms emitting from the central
part of the target surface, thus reducing the film
thickness at the central region of the substrate where
10
5
0
-20
-15
-10
-5
0
5
10
15
20
r
Fig. 4.
Distributions of film thickness at four
different target/substrate distances on a
stationary circular substrate.
Fig. 5.
The arrangement of magnets in an industrial
sputtering machine.
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J. CSME Vol.24, No.5 (2011)
and less towards the edges. To achieve this, they need
to be curved instead of being straight. Here, a method
is proposed to find the optimized geometry of the
blockage plates. First, a range, within which the film
thickness is uniform, on the substrate is set, say
200mm  x  200mm as an example. From Fig. 8,
the thickness of the film is 1.3 at both edges of this
range when there is no blockage plate. Therefore, the
film thickness we need to reach is 1.3 within this
range, and this can be achieved by setting the upper
limit of the following integration:
250
200
t
150
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
y (mm)
100
50
0
-50
-100
ym
1.3  2.0   t f  x, y dy ,
-150
-200
(27)
0
-250
-300
-200
-100
0
100
200
where ym is upper limit of integration.
300
x (mm)
Contours of substrate film thickness at
target/substrate distance = 100 mm.
250
200
y (mm)
Fig. 6.
3
150
100
2.5
50
thickness
2
0
-300
-200
-100
0
100
200
300
x (mm)
1.5
Fig. 9.
The profile of the optimized blockage plate.
1
0.5
Fig. 7.
-200
-100
0
100
200
2
x (mm)
Distributions of film thickness at five
different target/substrate distances on a
moving substrate.
1.5
1
0.5
3
no blockage
-150 mm <y<150 mm
-100 mm <y<100 mm
-50 mm <y<50 mm
2.5
0
-200
-100
0
100
200
x (mm)
Fig. 10. Distributions of film thickness with the use
of optimized block plates.
2
thickness
no blockage
optimized blockage
2.5
thickness
0
3
h=40 mm
h=70 mm
h=100 mm
h=130 mm
h=160 mm
1.5
As shown in Fig. 9, by solving equation (27), a
distribution
of
within
ym  x 
1
0.5
0
-200
-100
0
100
200
x (mm)
Fig. 8.
Distributions of film thickness with and
without the blockage plates.
Because the film is thickest at the center and
becomes thinner at the edges, ideal blockage plates
should block more target atoms at the central region
200mm  x  200mm is returned, and this is the
profile of the optimized blockage plate. With the
employment of optimized blockage plates, the
resulted film thickness distributions are shown in Fig.
10. It can be seen that the film thickness is almost
uniform within the specified range. Furthermore, the
thickness of 1.3 is only slightly smaller than the
maximum thickness of 1.7 in the case of no blockage
plate, suggesting only a moderate decrease on the
deposition rate. This exercise proves when the
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W. L. Chen et al.: Optimization of the geometry of blockage plates to improve film uniformity in a DC
magnetron sputtering machine.
geometry of block plates are optimized, their
performance is improved significantly. Additionally,
the optimization method developed here can be
implemented as long as a film thickness function
t f  x, y  is available. The thickness function can be
Coatings Technology, Vol. 171, pp. 178-182,
(2003).
Kwon, U.H., Choi, S.H., Park, Y.H., Lee, W.J.,
“Multi-Scale
Simulation
of
Plasma
Generation and Film Deposition in a Circular
Type DC Magnetron Sputtering System”,
Thin Solid Films, Vol. 475, pp. 17-23, (2005).
Mahieu, S., Buyle, G., Depla, D., Heirwegh, S.,
Ghekiere, P., DeGryse, R., “Monte Carlo
Simulation of the Transport of Atoms in DC
Magnetron Sputtering”, Nuclear Instruments
and Methods in Physics Research B, Vol.
243, pp. 313-319, (2006).
Ding, X.Z., Zeng, X.T., Hu, Z.Q., “Substrate
Geometry Effect on the Uniformity of
Amorphous Carbon Films Deposited by
Unbalanced Magnetron Sputtering”, Thin
Solid Films, Vol. 461, pp. 282-287, (2004).
Fu, C., Yang, C., Han, L., Chen, H., “The Thickness
Uniformity of Films Deposited by
Magnetron Sputtering with Rotation and
Revolution”,
Surface
&
Coatings
Technology, Vol. 200, pp. 3687-3689,
(2006).
Umeda, K., Takeuchi, M., Yamada, H., Kubo, R.,
Yoshino, Y., “Improvement of Thickness
Uniformity and Crystallinity of A1N Films
Prepared by Off-Axis Sputtering”, Vacuum,
Vol. 80, pp. 658-661, (2006).
Eckstein, W., Computer Simulation of Ion-Solid
Interactions, Springer-Verlag, New York,
Berlin, Heidelberg, (1991).
McDaniel, E.W., Collision Phenomena in Ionized
Gases, Wiley Series in Plasma Physics, Wiley,
New York, (1964).
calculated either by current simplified procedure or
by conventional Monte Carlo simulation, or even
obtained by measurement. This flexibility and its
simplicity make the optimization method a very
useful technique to design or improve industrial
sputtering machines.
CONCLUSIONS
In this study, a simplified method to predict the
film deposition on the substrate of a DC sputtering
machine is proposed. It requires much less CPU time
than the conventional Monte Carlo method and
returns results with comparable accuracy. The method
was first applied to predict the film thickness on a
circular stationary substrate. The predicted film
thickness is generally in good agreement with the
experiment data at four different target/substrate
distances. Then it was used, together with a simple
integration method, to find the optimized geometry of
blockage plates to improve the film uniformity in an
industrial sputtering machine. The results show that
perfect film uniformity can be achieved within a
specified range on the substrate with the optimized
blockage plates in place. This can be achieved with a
slight penalty of a moderate reduction on the film
deposition rate. In addition, the use of optimized
blockage plates is straightforward, and it applicable
to linear substrate conveyer system. Therefore, the
proposed method would be very useful for the design
of high-performance sputtering machines.
ACKNOWLEDGMENT
NOMENCLATURE
The authors are grateful for the financial
support from the National Science Council under the
project numbered: NSC-098-N-265-GOV-A-066.
a acceleration of an electron or an atom
B magnetic flux density
b constant in the decay function
REFERENCES
Kadlec, S., Quaeyhaegens, C., Knuyt, G., Stals, L.M.,
“Energy-Resolved Mass Spectrometry and
Monte Carlo Simulation of Atomic Transport
in Magnetron Sputtering,”; Surface and
Coatings Technology, Vol.97, pp.633-641,
(1997).
Shon, C.H., Lee, J.K., “Modeling of Magnetron
Sputtering Plasmas”, Applied Surface
Sciences, Vol. 192, pp. 258-269, (2002).
Sung, Y.M., Otsubo, M., Honda, C., “Studies of a
Magnetic Null Discharge Plasma for
Sputtering Application”, Surface and
C speed of light
E electric field
F
force applied to an electron or an atom
Ft  x, y  film thickness on stationary substrate
h distance between two electric charges
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i , j , k unit vector in x-, y-, z-direction, respectively
J. CSME Vol.24, No.5 (2011)
m total magnetic flux at a magnetic pole
m corrected mass of an electron
N number of argon ions created within a 3D cell in a
unit of time
ni,j number of target atoms ejected from the target
cell (i,j)
p  x, y  probability function on the target surface
pe momentum of electrons
Prof. Huann-Ming
Chou received his
Ph.D. in Mechanical
Engineering
from
NCKU
(Tainan,
Taiwan) in 1993. He
is a Professor and
currently the Dean of
Engineering Faculty in Kun-Shan University. His
major areas include heat transfer, solar energy and
green-energy technologies etc. He has hosted a
number of large academic-industrial cooperation
projects, which produced many excellent commercial
products.
Associate
Professor
Chang-Ren Chen received
his Ph.D. in Mechanical
Engineering from Univ. of
Missouri-Rolla
(UMR),
USA in 1992. Dr. Chen is
the associate professor of
Kun
Shan
University
(KSU). He is working on
the
developments
and
applications
of
Phase
Change Materials, Green Building and Solar Thermal
topics. He published thirty patents in Taiwan region
and China region. He received many awards from
International Invention Exhibition. He is the team
leader of the Solar Energy Lab., Clean Energy Centre,
KSU.
q electric charge
tm  x  film thickness on moving substrate
V electric potential
v velocity of an electron or an atom
x,y,z components in Cartesian coordinate system
 decay function
 e calibration constant
 film thickness calibration constant
Φ magnetic flux
δ erosion thickness on target surface
γ Lorentz factor
Dr.
Wen-Lih
Chen
received his Ph.D. in
Mechanical Engineering
from UMIST (Manchester,
UK) in 1996. He is an
Associate Professor of
Kun-Shan University. His
major
areas
include
conjugate heat transfer,
computations of turbulent
flow and green-energy
technologies etc. Every national science council
projects which he hosted has yielded excellent
results.
Mr. Shi-Sung Cheng was
graduated at Dept. of
Mechanical Engineering in
NCKU (Tainan, Taiwan).
He is now a senior
development engineer and
the manager of the
development department
in AllRing Tech. Co.
located
in
Southern
Science Park. He is
specialized in electro-mechanical techniques and has
been in charge of developing core technologies for
AllRing for many years.
DC 直流濺鍍機檔板最佳化
之研究
陳文立
周煥銘
陳長仁
鄭溪松
崑山科技大學機械工程學系
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W. L. Chen et al.: Optimization of the geometry of blockage plates to improve film uniformity in a DC
magnetron sputtering machine.
摘 要
在直流濺鍍機的濺鍍腔內放置擋板是達成較
好的鍍膜均勻度的方法之一。傳統的擋板是直的平
板，其效果不佳且會大幅降低鍍膜的沉積速率。本
研究之目的在於發展一種數值分析方法以設計出
最佳的擋板形狀。使用最佳化擋板將可在基板上形
成極均勻的鍍膜，而鍍膜沉積速率比起沒有擋板的
情形只有稍微下降。此分析方法對工業界設計新一
代高性能濺鍍機將有很大的幫助。
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