Surface & Coatings Technology 185 (2004) 283 – 291
www.elsevier.com/locate/surfcoat
Physical vapor deposition on cylindrical substrates
D.D. Hass a,*, Y. Marciano b, H.N.G. Wadley a
a
Department of Materials Science and Engineering, School of Engineering and Applied Science, 116 Engineers Way, University of Virginia,
Charlottesville, VA 22903, USA
b
Nuclear Research Center-Negev, Beer-Sheva 84190, Israel
Received 27 June 2003; accepted in revised form 19 December 2003
Available online 5 June 2004
Abstract
It is well established that low pressure physical vapor deposition processes such as thermal evaporation and the many variants of
sputtering utilize nearly collisionless vapor transport to a substrate. This results in line-of-sight deposition. The deposition of uniform
coatings on complex shapes using these approaches therefore requires substrate rotation or a multiple evaporation source strategy. In many
cases, the line-of-sight requirement precludes the use of these processes entirely. Recently, developed rarefied gas jet based deposition
processes, however, operate at much higher pressures where many gas phase collisions occur. Vapor scattering from a laminar flow that
propagates around a non-planar substrate provides opportunities for non-line-of-sight deposition. Experiments indicate that the coating
thickness around the circumference of a stationary, non-rotated fiber placed perpendicular to the axis of a gas jet containing aluminum atoms
is sensitively dependent upon the jet’s Mach number and the chamber pressure near the substrate. By employing gas jets having low Mach
numbers (< 0.1), highly uniform coatings of aluminum on cylindrical fibers have been achieved without fiber rotation. Direct simulation
Monte Carlo (DSMC) simulations have been used to understand the fundamental phenomena involved and to identify the role of the process
conditions on the coating’s uniformity.
D 2004 Published by Elsevier B.V.
Keywords: Thickness uniformity models; Electron beam evaporation; Aluminum
1. Introduction
Vapor deposition processes capable of uniformly depositing coatings on fibers have many potential applications
including the deposition of metallic alloys on structural
fibers to create metal matrix composites [1 –5] and low
shear strength coatings on the fibers used to create ceramic
matrix composites [6 –11]. The deposition of metals and
solid electrolyte thin films on fibers is also of interest for
synthesizing solid state fiber batteries. These processes
could be used for the deposition of metals on sacrificial
fiber templates to create hollow fibers as well [12,13]. More
generally, vapor deposition processes that allow the deposition of conformal coatings on non-planar substrates are of
great technological interest. For example, the deposition of
reaction inhibiting coatings into the vias and trenches used
* Corresponding author. Tel.: +1-434-982-5678; fax: +1-434-982-5677.
E-mail address: [email protected] (D.D. Hass).
0257-8972/$ - see front matter D 2004 Published by Elsevier B.V.
doi:10.1016/j.surfcoat.2003.12.027
for microelectronic interconnects [14], the growth of coatings on the ligaments of stochastic foam structures [15] and
the application of various coatings to medical implants such
as stents [16,17] are all rapidly growing in importance.
Several vapor phase deposition options for creating coatings of this type exist. They include chemical vapor deposition (CVD) [1,18] and physical vapor deposition (PVD)
approaches such as thermal evaporation [18 –21] and the
many variants of sputtering [18,22]. In CVD, uniform
coating thicknesses on a fiber are easily achievable because
the flux is uniformly distributed over the fiber surface [18].
However, the deposition process requires the use of toxic
(and frequently expensive) precursor materials [18]. In
addition, the chemical vapor deposition of the multi-component metallic alloys required for metal matrix composites
is very difficult. In most PVD based processing approaches,
it is not possible to uniformly coat non-planar substrates
without sophisticated substrate translation/rotation or the
use of multiple, spatially distributed sources (e.g. cylindrical
magnetron sputtering [22]). This arises because the vapor
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D.D. Hass et al. / Surface & Coatings Technology 185 (2004) 283–291
atoms are created in a high vacuum that results in nearly
collisionless vapor transport to the substrate. As a result,
only regions in the line-of-sight of the vapor source are
coated.
Novel high pressure PVD processes utilizing rarefied gas
jets have recently begun to appear [23 – 27]. They entrain
the atomic flux created by an evaporation process in a
rarefied, trans-sonic gas jet. Fig. 1 shows as an example the
directed vapor deposition (DVD) approach [25]. In this
case, material is vaporized in a low vacuum environment
with a continuous electron-beam (the electron beam gun is
modified to allow its use in a low vacuum environment).
The vapor is entrained in a helium gas jet created by
expansion through a nozzle and is directed towards a
substrate. High local vapor densities near the substrate result
in high ( > 10 Am min1) deposition rates and a sometimes
high materials utilization efficiency [26].
The gas jets used in these processes are created by
maintaining a high pressure, Pu, upstream of a nozzle
opening and a lower downstream (or chamber) pressure,
Po. The pressure ratio, Pu/Po, and the specific heat of the gas
determine the jets Mach number as it expands into the
chamber. Typically, these jet-based processes use pressure
ratios greater than 2 to create jets having supersonic speeds
(M >1) near the nozzle exit. The Mach number gradually
slows as it approaches the substrate, consequently, the
Reynolds number remains sufficiently low so that little or
no turbulence is created when the jet interacts with a
substrate. As a result, the laminar flow remains attached to
the substrate and streamlines can extend around a nonplanar substrate. In addition, when high pressures are
employed in these processes, the mean-free-path between
collisions of the vapor and gas jet atoms is reduced. The
vapor atoms become entrained in the flow and this, combined with the ability to flow the carrier gas over the surface
of a complex shaped object, sets up the possibility of nonline-of-sight coating (NLOS) by scattering of the vapor from
the streamlines onto the substrate surface.
Here, we explore the hypothesis proposed above and
investigate the affect of a gas jet’s flow characteristics upon
the uniformity of coatings applied to stationary, non-rotated,
cylindrical substrates orientated perpendicular to the axis of
the jet. We use a model system consisting of a DVD process,
an aluminum vapor, a helium gas jet and a 380 Am diameter
stainless steel fiber substrate. Altering the pressure ratio, and
thus the jet speed will be shown to dramatically change the
coating thickness uniformity around the circumference of a
stationary cylindrical substrate. The lowest pressure ratios
lead to the most uniform coatings. A direct simulation
Monte Carlo (DSMC) modeling technique is used to simulate the interactions between the helium gas jet, the vapor
atoms in the flow and the cylindrical substrate. It enables the
fundamental mechanisms responsible for coating uniformity
to be identified.
2. Experimental results
2.1. DVD setup
Design details of the DVD system used for deposition
can be found elsewhere [25 –27]. Aluminum vapor was
created by electron beam evaporation from a 12.7 mm
diameter (five 9’s) Al source rod and deposited on a 380 Am
diameter, 13.0 cm long stainless steel fiber positioned 15.0
cm from the nozzle exit. The midsection of the fiber was
located directly above the center of the vapor source. The
chamber pressure was 16 Pa and the nozzle opening
diameter was 300 mm for all experiments. Coatings were
produced with pressure ratios of 7.0, 4.5 or 2.0 (see Table 1)
by altering the pumping rate of the chamber. Aluminum
was evaporated at a rate of 67 mg/min, 58 mg/min and
53 mg/min for the three pressure ratios, respectively. A
beam current of 70 mA was used. The deposition rate
varied from 2 to 30 Am/min on the front side of the fiber
(i.e. the side that faced the evaporation source) and 0.2 to
2 Am/min on the backside.
2.2. Experimental observations
Fig. 1. Schematic illustration of a directed vapor deposition coating system.
Scanning electron microscope (SEM) micrographs of
the cross section of the fibers coated with aluminum are
D.D. Hass et al. / Surface & Coatings Technology 185 (2004) 283–291
285
Table 1
Summary of the deposition time and evaporation rates used for each experiment. The frontside thickness on the fiber is given for each case, as is the thickness
normalized by the evaporation rate
Pressure
ratio
Deposition
time (min)
Evaporation
rate (mg/min)
Frontside
thickness (Am)
Normalized
frontside thickness
(Am/mg/min)
7.0
4.5
2.0
3
6
12
67
58
53
87
59
31
1.29
1.01
0.58
shown in Fig. 2 for the three pressure ratio conditions. In
each case, the micrographs are taken from the midpoint of
the wire and therefore correspond to the structure created
on the axis of the jet. This location led to the lowest
uniformity of any point on the fiber, see Table 2. In Fig. 3,
the relative coating thicknesses are plotted as a function of
the position around the periphery of the fiber. Note that
when the pressure ratio was high (i.e. 7.0) the backside
coating thickness was less than 10% of the frontside.
When the pressure ratio was reduced to 4.5, the backside
coating thickness increased and at the lowest pressure
ratio, 2.0, the backside coating thickness was greater than
70% of the frontside thickness. The maximum thickness
of the coatings on the frontside (normalized by the
amount of material evaporated in each case) was also
reduced when the pressure ratio was decreased from 7.0 to
2.0, Table 1.
3. Simulations
3.1. Direct simulation Monte Carlo methodology
A DSMC code (Icarus) developed at Sandia National
Laboratories [28,29] was used to determine the velocity
field of the gas jet for the three test conditions. It was also
used to analyze the interaction between the gas jet, the
vapor flux and a polygonal approximation to a cylindrical
fiber. We first simulated the expansion of a helium gas jet
from a choked nozzle in the absence of a cylindrical
substrate. The flow field was determined at the substrate
location and used in a second model to analyze the
interaction of the flow with the cylindrical substrate. The
inputs to the substrate interaction model were the velocity
of the gas flow and the vapor flux at the position of the
substrate (determined from the preceding analysis). Previous simulations have indicated that the vapor atoms reach
the velocity of the gas jet a short distance from the source
[30] and thus the aluminum vapor atoms were input at the
same velocity as the helium. The average trajectories of
the helium and aluminum atoms and the helium velocity in
the axial direction were determined for a region near the
cylindrical substrate.
The jet flowfield was calculated by defining the geometry, boundary conditions and collision properties representative of the DVD process environment [31]. Fig. 4a shows
the grid used for this analysis. A second DSMC grid, Fig.
4b, was used to simulate the flow in the vicinity of a fiber. In
both cases, the simulated area was divided into regions that
were then subdivided into cells. The cell size was chosen to
be small enough to represent the gradients in gas pressure,
speed and temperature that existed in the flow field [32,33].
The nozzle diameter for all cases was taken to be 30 mm.
For a pressure ratio of 2.0, a helium flow rate of 2.811024
atoms/m2-s was input across an area 2.83103 m2 located
0.0445 m upstream of the nozzle opening. This resulted in
the experimental measured upstream pressure of 32 Pa. By
altering this flow rate (from 2.811024 to 9.841024 atoms/
Fig. 2. SEM micrographs showing cross sections of aluminum coatings deposited onto stainless steel fiber substrates (380 Am diameter) using a pressure ratio
of (a) 7.0, (b) 4.5 and (c) 2.0. Note the dramatic increase in the coating thickness on the backside of the fibers as the pressure ratio was decreased.
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Table 2
Ratio of the frontside coating thickness to the backside coating thickness for
a given distance from the jet axis
Distance from jet axis (cm)
Pressure ratio=2.0
0.0
1.0
2.0
3.0
4.0
5.0
0.72
0.73
0.75
0.76
0.77
0.88
m2-s) the upstream pressure was varied from 32 to 112 Pa.
The chamber pressure was maintained at a prescribed
pressure of 16 Pa so that the desired pressure ratio (2.0 to
7.0) and chamber pressure could be maintained. The number
of He particles simulated in each case was adjusted so that a
minimum of 20 particles/cell were present in all cells. A
time step of 0.1 As was used in order to ensure that particles
did not travel further than their mean free path during a time
step. A variable hard sphere model was used to determine
the scattering angles of collision events [32]. The molecular
diameter of helium was taken to be 0.233 nm at a reference
temperature of 300 K [32]. The viscosity index was set at
0.66 [32]. The aluminum collision parameters were estimated using an approach proposed by Fan [34]. The molecular
diameter was taken to be 1.0182 nm at 300 K. The viscosity
index was taken to be the same as that of helium. The fiber
surface was set so that all aluminum atoms adhered to the
surface upon impact. The helium atoms all reflected from
the fiber surface.
Fig. 4. DSMC grid used to determine (a) the Mach number of helium gas jet
in the area near the fiber and (b) the helium and aluminum atom trajectories
near the fiber.
3.2. Simulation results
The affect of altering the pressure ratio on the properties
of the carrier gas flow is shown in Fig. 5. Results for the
axial velocity component of the helium gas jet are plotted
for the three pressure ratio conditions experimentally investigated. The Mach number of the gas jet in the region of the
flow where the gas would have impinged upon the fiber (i.e.
15 cm from the source) steadily increased with pressure
ratio, Table 3. The Mach number is related to the jet velocity
by the following relationship [32]:
U
M ¼ pffiffiffiffiffiffiffiffiffiffi
cRs T
Fig. 3. Plot showing the relative coating thickness as a function of radial
position on the fiber using a pressure ratio of (a) 7.0, (b) 4.5 and (c) 2.0.
Note that when the pressure ratio was 2.0 the coating thickness on the back
side of the fiber is greater than 70% of the front side.
ð1Þ
where M is the Mach number, U is the gas velocity (m/s), c
is the ratio of specific heats (5/3 for helium), Rs is the
specific gas constant (i.e. the universal gas constant divided
by the molecular mass of the gas, 2077 J/kg K for helium)
and T is the temperature (modeling results indicate gas
temperatures of f298 K in the region of the fiber).
The average helium trajectories (shown by the streamlines) and the axial component of the helium velocity field
D.D. Hass et al. / Surface & Coatings Technology 185 (2004) 283–291
287
Fig. 5. Axisymmetric DSMC simulations of the helium gas jet expansion from a choked nozzle. Shown is the helium velocity in the Z-direction using a
pressure ratio of (a) 7.0, (b) 4.5 and (c) 2.0. The Mach number of the helium gas jet steadily decreased as the pressure ratio was reduced.
in the vicinity of the substrate are shown in Fig. 6 for the
case of the highest gas jet Mach number (M=0.433). For this
case, the mean free path for He –He collisions are on the
order of a millimeter. The He –Al collisions are estimated to
be a factor of 4 lower. Note that the helium carrier gas flows
around the fiber in a laminar manner and remains attached
to the substrate. As the carrier gas atoms approach the front
of the substrate, their axial velocity decreases. The axial
velocity at a point directly behind and 30 Am away from the
substrate surface (termed the backside velocity, VB) was
recorded, Table 3. Note that this velocity was substantial for
the highest Mach number and decreased to 9 m/s for the
lowest Mach number.
The average aluminum atom trajectories are plotted in
Fig. 7 for all three cases. At a gas jet Mach number of 0.433,
Fig. 7a, the aluminum trajectories were similar to those of
the helium (i.e. the aluminum flowed around the substrate
and followed the laminar streamlines of the helium flow).
However, as the Mach number was decreased, significant
deviations between the aluminum and helium trajectories
began to be observed. At the lowest Mach number,
M=0.039, Fig. 7b, the average aluminum atom trajectories
were observed to deposit on both the front and the backside
of the substrate. The aluminum trajectory simulations also
reveal that the lateral distance of the vapor flux that could be
captured by the substrate increased as the Mach number
decreased, Fig. 7. In the low Mach number case, aluminum
atoms in streamlines well beyond the periphery of the fiber
were able to deposit on the substrate (see Table 1). The
vapor capture distance (CD) was defined as twice the lateral
distance from the fiber center within which the average
aluminum vapor atom streamlines intersected the surface of
the fiber (see Fig. 7). The vapor capture distance for atoms
that impinged upon the front surface (FCD) of the substrate
was also determined. For the highest Mach number, Fig. 7a,
CD was approximately 0.5d where d was the fiber diameter.
This was increased to 3.1d for the lowest Mach number, Fig.
7c. The fraction of atoms that deposited on the backside of
the fiber (CDFCD) also increased as the jet Mach number
decreased, Table 3.
To estimate the coating thickness around the circumference of the fiber in the simulation, we computed the
aluminum vapor density at a distance less than 10 Am
from the surface of the cylindrical substrate. This distance
was small compared to the mean free path and the fiber
diameter. The results are plotted as a function of the radial
position on the substrate’s circumference in Fig. 8. As the
Mach number was decreased, the predicted uniformity of
Table 3
Summary of DSMC simulations of the interaction of a helium/aluminum jet flow with a cylindrical substrate
Pressure
ratio
Gas jet Mach
number
Backside
velocity, VB (m/s)
FCD
width (Am)
CD
(Am)
CDFCD
(Am)
7.0
4.5
2.0
0.433
0.197
0.039
84
35
9
123
220
506
140
305
870
17
86
364
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D.D. Hass et al. / Surface & Coatings Technology 185 (2004) 283–291
Fig. 6. DSMC simulations showing (a) the average trajectories of helium gas jet atoms as they flow past a cylindrical substrate and (b) the gas jet velocity in the
z-direction in the region near the fiber for a Mach 0.433 gas jet and a 16 Pa chamber pressure.
Fig. 7. DSMC simulations showing the trajectories of aluminum vapor atoms, which originate 920 Am upstream of the fiber for a gas jet Mach number of (a)
0.433, (b) 0.197 and (c) 0.039. At the lowest Mach number, the aluminum atoms laterally diffuse onto NLOS regions of the fiber. Also, shown are the vapor
capture distance, CD and the front surface capture distance, FCD, each case. Note that both CD and FCD steadily increased as the Mach number of the flow was
reduced.
D.D. Hass et al. / Surface & Coatings Technology 185 (2004) 283–291
Fig. 8. Plot showing the relative aluminum density above the fiber surface
as a function of radial position on the fiber for a gas jet Mach number of (a)
0.433, (b) 0.197 and (c) 0.039. Note the general increase in uniformity as
the Mach number was decreased compared well with the experimental
observations.
the aluminum coating around the fiber’s circumference
improved. This result was similar to that seen in the
experimental study, Fig. 3.
289
gas jet Mach numbers (>0.3) and small Knudsen numbers
(<0.1) promote vapor atom transport close to the gas jet
atom flow trajectories since collisions between vapor and
gas jet atoms occur frequently and are energetic. This results
in limited vapor atom diffusion perpendicular to the streamline and, for the fiber case, leads to a low deposition flux
contribution via scattering. When the Mach number is
reduced and/or the Knudsen number increased (Knudsen
numbers much greater than one are not desired since vapor
atoms may then be carried past the fiber without scattering
from the streamlines), collisions between the carrier gas and
the vapor atoms occur less frequently and the momentum of
the carrier gas is lowered (Knudsen numbers much greater
than one are not desired since vapor atoms may then be
carried past the fiber without scattering from the streamlines). Thus, the ability of the carrier gas to alter the vapor
atom trajectories is also reduced. As a result, vapor atoms
develop an increasingly random walk aspect to their motion
that results in a migration perpendicular to the gas flow
streamline, Fig. 9. When this occurs near the substrate
surface, diffusion from the streamline allows vapor atoms
to deposit onto all areas of the substrate as the presence of
the surface results in the average vapor atom trajectories to
be angled towards the substrate, Fig. 10. Such diffusion
creates a mechanism for a greatly increased fraction of the
vapor flux to deposit onto a fiber. The results, Fig. 7c,
4. Discussion
The use of a rarefied gas jet to alter vapor atom
trajectories has allowed the coating of regions on a circular
cross section that were not in the line-of-sight of the vapor
source. The degree of non-line-of-sight deposition and thus
the coating thickness uniformity was a sensitive function of
the gas jet flow conditions. For a fixed background pressure
in the region of deposition, an increase in coating uniformity
was observed as the jet’s Mach number was reduced. DSMC
analysis has indicated that the observed NLOS coating is a
result of binary collisions between carrier gas and vapor
atoms in the flow. The analysis shows that gas jet streamlines flow around the substrate (see Fig. 6a). Scattering from
the carrier gas streamlines allows the aluminum vapor atoms
to diffuse out of the flow and impact parts of the substrate
that are not directly viewable from the source.
The transport of vapor atoms in a gas jet depends on
several factors: the Mach number (or kinetic energy) of the
gas jet and vapor atoms, the Knudsen number of the gas jet
and vapor atoms (The Knudsen number, Kn, is defined as
the ratio between the mean free path in a flow to the
characteristic length of a body immersed in the flow [35].
As the Mach number DVD gas jet varied from 0.433 to
0.039, Kn for Al – He scattering was estimated to change to
0.6 to 0.3) and the mass of the two atom types present. High
Fig. 9. Schematic illustration of possible vapor atom paths near a cylindrical
substrate in the presence of a gas jet flow. In (a) a vapor atom with high
momentum deposits on the front side of the substrate. In (b) a vapor atom is
directed around the fiber by the gas jet. No deposition occurs. In (c) a vapor
atom laterally diffuses onto the side of the substrate resulting in NLOS
coating. In (d) a vapor atom deposits on the backside of the substrate via
upstream diffusion. Note that atoms can deposit onto the front and side
surfaces without diffusing opposite the flow direction. Backside coating
requires upstream diffusion.
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D.D. Hass et al. / Surface & Coatings Technology 185 (2004) 283–291
helium atom trajectory and significant LOS deposition
occurred, Fig. 9. However, even for the high Mach
number case examined, the momentum of the aluminum
atoms was not sufficient to prevent some atoms from
being turned and entrained in the helium trajectories that
passed around the substrate. As a result, the capture
distance observed in the DSMC analysis was actually less
than the fiber diameter for this case.
5. Conclusions
Fig. 10. Schematic illustration showing the random walk of a vapor atom in
the presence of a gas jet with (a) no substrate and (b) a substrate present.
indicate a more than 300% increase in the capture distance
when the Mach was reduced from 0.433 to 0.039.
The flows Mach number is a critical parameter since in
order for atoms to diffuse out of the streamlines and toward
the backside of the fiber, upstream diffusion must occur for
a short distance. The axial velocity component of the carrier
gas flows into the front side and away from the backside of
the fiber. When the flow velocity is high, diffusion into the
front side of the fiber is enhanced as the axial gas jet
component carries atoms into the fiber. Diffusion onto the
backside is reduced, however, as diffusion against the
direction of flow is difficult. Thus, deposition onto the
backside of the fiber will be reduced when the backside
velocity (BSV) is significant. Coatings onto the sides of the
fiber may also be slightly reduced as atoms may be carried
downstream during lateral diffusion (see Fig. 10c). Thus, the
ratio of convective to diffusive transport (i.e. the Peclet
number) should be low for significant coating to occur on
the back of the fiber.
The mass difference between the vapor atom and the
carrier gas is also important as it determines the collision
frequency and gas jet atom momentum required to alter a
vapor atoms trajectory. This is particularly important in
regions of the flow where sudden changes in gas jet
trajectories occur (i.e. in the region near the front of a
cylindrical substrate, Fig. 6b). In the case examined here,
the ratio of the atomic masses of the jet gas (helium) and
the vapor atoms (aluminum) was 6.7. Since the velocity of
each atom type was approximately the same, the aluminum atoms had considerably more momentum than those
of the helium jet. In many cases, helium collisions with
aluminum atoms near the substrate front surface are
insufficient to entrain the vapor in the rapidly changing
Coatings of aluminum having good uniformity (backside coating thickness >70% of frontside coating thickness) have been produced on stationary, non-rotated,
cylindrical substrates using a increased pressure PVD
technique that incorporates the use of a gas jet. The
thickness uniformity around the fibers circumference was
a sensitive function of the gas jet Mach number. Low gas
jet Mach numbers led to the highest uniformity since
binary collisions between the gas jet and the aluminum
atoms promoted diffusive transport that resulting in nonline-of-sight coating.
Acknowledgements
We are grateful to Dr Timothy Bartel at Sandia National
Laboratories for use of his ICARUS DSMC code and
suggestions for its application to the problems described
here. This work has been supported by DARPA/DSO under
contract N00014-00-1-0885 monitored by Dr Leo Christodoulou (DARPA) and Dr Steve Fishman (ONR).
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