JOURNAL OF APPLIED PHYSICS 104, 034310 共2008兲
Atomic assembly of Cu/Ta multilayers: Surface roughness, grain structure,
misfit dislocations, and amorphization
M. F. Francis,1,a兲 M. N. Neurock,1 X. W. Zhou,2,b兲 J. J. Quan,3 H. N. G. Wadley,4 and
Edmund B. Webb III5
1
Chemical Engineering Department, University of Virginia, Charlottesville, Virginia 22904, USA
Mechanics of Materials Department, Sandia National Laboratories, Livermore, California 94550, USA
3
Seagate Technology, Bloomington, Minnesota 55435, USA
4
Materials Science and Engineering Department, University of Virginia, Charlottesville,
Virginia 22904, USA
5
Computational Materials Science and Engineering Department, Sandia National Laboratories,
Albuquerque, New Mexico 87185, USA
2
共Received 7 March 2008; accepted 11 June 2008; published online 8 August 2008兲
Molecular dynamics simulations and selected experiments have been carried out to study the growth
of Cu films on 共010兲 bcc Ta and the deposition of CuxTa1−x alloy films on 共111兲 fcc Cu. They
indicate that fcc Cu films with a 共111兲 texture are always formed when Cu is deposited on Ta
surfaces. These films are polycrystalline even when the Ta substrate is single crystalline. The grains
have one of two different orientations and are separated by either orientational or misfit dislocations.
Periodic misfit dislocations and stacking faults develop within these grains to release structure
difference induced misfit strain energy. The Cu film surface roughness was found to decrease with
increase in the adatom energy for deposition. When CuxTa1−x is deposited on Ta, the films always
have a higher Cu composition than that of the vapor mixture. This arises from a surface segregation
phenomenon. When the Cu and Ta fractions in the films are comparable, amorphous structures form.
The fundamental origins for the segregation and amorphization phenomena are discussed.
© 2008 American Institute of Physics. 关DOI: 10.1063/1.2968240兴
I. INTRODUCTION
The atomic scale structure of interfaces plays a critical
role in many materials with high interfacial area to volume
ratios. For instance, the creation of a bimodal distribution of
grain boundaries in nanocrystalline metals 共e.g., copper, aluminum, etc.兲 significantly improves both strength and ductility of these materials.1 Control of interfacial structures is also
essential for vapor phase synthesized multilayered thin film
solar cells with high photovoltaic efficiency.2 Other vapor
deposited multilayer structures, such as giant magnetoresistance multilayers,3–5 magnetic tunnel junction multilayers,6–8
x-ray
mirror
multilayers,9
and
microelectronic
10,11
multilayers,
all require chemically sharp planar interfaces
for best performance. In many of these systems, the individual layers are polycrystalline resulting in the presence of
grain boundaries perpendicular to the film and dislocations
that accommodate misfit strain at the interfaces between the
layers.12 The atomic scale structures of these interfaces are
determined by complicated thermodynamic and kinetic processes and are extremely sensitive to processing conditions,
material properties, surface chemistry, and crystal orientations.
The copper/tantalum 共Cu/Ta兲 bilayer system is a good
model problem for study. This system is also of practical
interest for two important reasons. First, Ta is an effective
barrier to Cu diffusion. The insertion of a thin Ta layer between Cu and semiconductors enables Cu to be used as an
a兲
Electronic mail: [email protected].
Electronic mail: [email protected].
b兲
0021-8979/2008/104共3兲/034310/12/$23.00
interconnect in large scale integrated circuits without Cu diffusion into the junction region of semiconductor devices.13
Second, amorphous films can be obtained during growth of
Cu/Ta multilayers,14–16 which may result in high strength and
highly corrosion resistant films.17–19 The optimized structures
for these two situations are quite different. Copper interconnects require sharp crystalline Cu/Ta interfaces, while the
amorphous systems require highly intermixed interfaces.
Both types of interface can be synthesized through physical
vapor deposition by varying the growth conditions 共e.g., adatom energy, adatom incident angle, substrate temperature,
growth rate, and inert gas ion assistance兲. Because these two
applications of this system require knowledge of the fundamental assembly mechanisms acting over a wide range of
atomic scale length scales, its study provides insights that
may be of broad utility to nanotechnology.
Several groups have already begun to use atomistic modeling methods to investigate the interfaces in the Cu/Ta system. Gong and Liu20,21 have used a Finnis–Sinclair potential
in molecular dynamics 共MD兲 simulations to explore the relative stability of the various interfaces between Cu and the
共100兲, 共110兲, and 共111兲 atomic planes of Ta. They found that
the energy of unstable interfaces can be sufficiently large that
it drives interdiffusion and causes solid state amorphization.
MD simulations of the growth of Cu/Ta multilayers have
also been carried out.22 The approach created more realistic
interfaces than these studies by Gong and Liu20,21 and has
shed significant light on the atomic assembly mechanisms
during growth. However, the severe computational demands
of these simulations made it difficult to investigate all the
104, 034310-1
© 2008 American Institute of Physics
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J. Appl. Phys. 104, 034310 共2008兲
Francis et al.
relevant atomic assembly phenomena. The present work carries out large scale MD simulations of the growth of Cu on a
Ta surface and exploits selected experiments to validate the
conclusions. The study extends the earlier work22 by investigating the formation of a wide range of Cu/Ta interface
morphologies and grain structures as the process conditions
are changed. It also investigates the deposition of Ta on a Cu
surface enabling exploration of the factors controlling interface roughness, grain structure, misfit dislocation structures,
and mixing induced amorphization.
II. EMBEDDED ATOM METHOD POTENTIAL
The interatomic interactions between metal atoms can be
described by embedded atom method 共EAM兲 potentials.23
The approach used here was based on an EAM interatomic
potential database that was previously formulated for different metal elements 共Cu, Ag, Au, Ni, Pd, Pt, Al, Pb, Fe, Mo,
Ta, W, Mg, Co, Ti, Zr, and their alloys兲.24,25 This potential
database has been applied to simulate the growth of a number of metal multilayers.25,26 The potential was fit to the lattice constants, cohesive energy, elastic constants, and vacancy formation energy of elements 共Ta and Cu兲.24,25 The
cross pair potentials between dissimilar species were not fit.
Instead, they were constructed based on an alloy EAM
model.27 Because of this, the heat of mixing prediction was
not optimized. We found that by multiplying the Ta–Cu cross
pair potential of the original EAM potential with a factor of
0.9, better heat of mixing prediction can be achieved. This
adjustment does not change any properties of Ta and Cu
elements, nor does it have any effects on the separation distance that gives the energy well of the Ta–Cu cross pair
potential. The heat of mixing predicted by both the original
and the adjusted EAM potentials are discussed in the following.
A series of fcc substitutional CuxTa1−x 共0 ⱕ x ⱕ 1兲 crystals were used as initial configurations to evaluate possible
phase transformations. The computational cell was assumed
to be cubic with low indices along the edge crystal orientations 共i.e., x = 关100兴, y = 关010兴, z = 关001兴兲. Each lattice contained a total of 13 500 atoms. The three systems were
treated as infinite bulk samples by using periodic boundary
along all three coordinate directions. To ensure full relaxation of the systems, a two-step simulation was used. First,
constant atom number, pressure, and temperature 共NPT兲 MD
simulation of annealing was carried out for a nanosecond of
simulated 共real兲 time in which the system was slowly cooled
from an initial temperature of 800–300 K under zero pressure. By using a high thermal energy to allow the system to
sample many configurations that would be otherwise unlikely to reach if the system is initially in a metastable state,
the simulated annealing effectively identifies the global minimum energy configuration against system volume and atom
positions. The crystal obtained from a simulated annealing,
however, contains thermal energy that causes atoms to
slightly deviate from the equilibrium positions. We therefore
further minimized the system potential energy against volume and atom positions using a conjugate gradients
method28 where kinetic energy of atoms was kept at zero.
(a) Cu
(b) Ta
(c) Cu0.6Ta0.4
FIG. 1. Atomic structures of 共a兲 fcc Cu, 共b兲 bcc Ta, and 共c兲 a fcc Cu0.6Ta0.4
alloy after a two-step energy minimization simulation.
Figures 1共a兲–1共c兲 show the structure of the Cu, Ta, and
Cu0.6Ta0.4 structures, respectively, after the energy minimization simulations using the original EAM potential. The results obtained with the adjusted EAM potential are similar. It
can be seen that not all systems maintained their original
crystal configurations. While Cu remained a perfect fcc
phase 关Fig. 1共a兲兴, the initial fcc Ta transformed into multiple
domains separated by boundaries 关Fig. 1共b兲兴. A detailed
analysis showed that these domains were bcc-structured
crystalline grains consistent with bcc Ta having a lower cohesive energy compared to the fcc structure. The Cu0.6Ta0.4
system was found to transform into an amorphous structure
关Fig. 1共c兲兴. The radial distribution function of a material g共r兲
provides a measure of the structure of a system. It is defined
by the following equation:
g共r兲 = n共r兲/␳␲r2⌬r,
共1兲
where n共r兲 is the mean number of atoms in a shell of width
⌬r a distance r away from an atom, and ␳ is the mean atomic
density. In a radial distribution function, well defined peaks
are indicative of a crystalline structure, while smoother and
ill-defined peaks are indicative of an amorphous state without long range order. Figure 2 plots the three radial distribution functions obtained respectively from the three configurations shown in Fig. 1. The peak-to-peak distances shown in
Fig. 2 clearly indicate that Cu remained a fcc crystal and Ta
transformed into a bcc structure. The broad peaks of the
Cu0.6Ta0.4 distribution indicate that it has no long range order
and is amorphous.
Simulations were further carried out to quantify the heat
of mixing as a function of composition. This requires the
calculation of cohesive energy of the equilibrium CuxTa1−x
crystal phase at different compositions x. The discussion
6
Radial distribution (#)
034310-2
5
Cu
4
Cu0.6Ta0.4
3
2
Ta
1
0
2
3
4
5
6
Radius (Å)
FIG. 2. Radial distribution functions for selected bulk phases. Data are
shown for pure Cu 共light solid兲, pure Ta 共dashed兲, and Cu0.6Ta0.4 共heavy
solid兲.
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034310-3
J. Appl. Phys. 104, 034310 共2008兲
Francis et al.
Heat of mixing (eV/atom)
0.10
0.08
CuxTa1-x initially fcc
CuxTa1-x initially bcc
0.06
0.04
0.02
0.00
-0.02
-0.04
original EAM
adjusted EAM
-0.06
-0.08
0.0
0.2
0.4
0.6
0.8
1.0
Cu mole fraction, x
FIG. 3. Heat of mixing as a function of composition.
above shows that phase transformation occurs if the initial
input crystal used in the simulations is not the equilibrium
phase. In such a case, even the two-step energy minimization
cannot fully relax the system as some defects such as grain
boundaries will remain. We therefore conducted two sets of
calculations using respectively fcc and bcc CuxTa1−x initial
crystals. Both the fcc and bcc systems were in the cubic
orientations, with the former containing 4000 atoms and the
latter containing 2000 atoms. The cohesive energy of the
equilibrium CuxTa1−x phase was then taken as the lower
value of the two results obtained respectively from the two
sets of calculations. With the cohesive energy as a function
of known composition, heat of mixing ⌬Hmix was calculated
using the following relation:
⌬Hmix = ECuxTa1−x − xEfcc Cu − 共1 − x兲Ebcc Ta ,
共2兲
where ECuxTa1−x, Efcc Cu, and Ebcc Ta are the cohesive energies
共potential energies per atom兲 of CuxTa1−x, fcc Cu, and bcc Ta
phases, respectively, and x is the copper mole fraction. The
heat of mixing values thus calculated using both the original
and the adjusted EAM potentials are shown in Fig. 3.
Figure 3 shows that the original EAM potential predicts
a negative heat of mixing over a wide range of composition.
However, the adjusted EAM potential predicts correctly a
positive heat of mixing.15,20
III. MD METHOD OF GROWTH
In the present work, the deposition of a Cu film on the
共010兲 bcc Ta surface was simulated to explore the growth of
Cu interconnects on a Ta diffusion barrier, and deposition of
a CuxTa1−x alloy film 共0 ⱕ x ⱕ 1兲 on the 共111兲 fcc Cu substrate surface was simulated to investigate solid state amorphization. Growth on 共111兲 fcc Cu was chosen because the
fcc crystal is the lowest energy phase of Cu and its 共111兲
surface has the lowest energy. The lowest energy phase of
bulk Ta is the tetragonal ␤ phase. However, experiments indicate that for thin films, the ␤-Ta phase is destabilized and
transforms into the ␣ phase.29 We therefore simulated the
growth of Cu on a 共010兲 bcc Ta surface.
Sandia’s parallel MD code LAMMPS 共Ref. 30兲 was used
for the simulations. Computations were performed using the
Thunderbird cluster, which consists of 4480 3.6 GHz processors with 6 Gbyte random access memory. A computational
substrate was first created by assigning positions of atoms
according to crystal structure, equilibrium lattice constant,
and crystallographic orientation of the substrate. The bcc Ta
substrate included 180 共200兲 planes in the x-direction, 5
共020兲 planes in the y-direction, and 180 共002兲 planes in the
z-direction. This Ta substrate 共the blue region in Fig. 4兲 contained 40 500 Ta atoms with a lattice parameter of 3.30 Å.
Two fcc Cu substrates were used for the study of Ta
alloy deposition. One contained 232 共22̄0兲 planes in the
x-direction, 4 共111兲 planes in the y-direction, and 402 共2̄2̄4兲
planes in the z-direction, and the other contained 232 共22̄0兲
planes in the x-direction, 13 共111兲 planes in the y-direction,
and 402 共2̄2̄4兲 planes in the z-direction. These two initial Cu
substrates contained 62 176 and 202 072 Cu atoms, respectively. The horizontal dimensions of the Ta and Cu substrates
were around 300⫻ 300 Å2. However, the thicknesses of the
two Cu substrates were about 8 and 27 Å, respectively, compared to that of the Ta substrate of about 8 Å. The thicker
Cu substrate increased the distance between the Ta/Cu interface and the bottom boundary so that mixing across the interface between the deposited film and the Cu substrate could
be more realistically studied.
An initial substrate temperature was introduced by assigning velocities to atoms based on a Boltzmann distribution. Periodic boundary conditions were used in the two horizontal 共x- and z-兲 coordinate directions so that the simulated
systems can be viewed as large planes in the x-z dimension.
A free boundary condition was used in the vertical 共y−兲 coordinate direction to allow for surface growth.
During simulations, adatoms were continuously injected
at the top of the simulation cell in y. Atom types were statistically assigned to match the desired composition of the
vapor. The adatom injection frequency was assigned to
match the desired growth rate. Newton’s equations of motion
were then used to solve for the positions of all system atoms
as a function of time. A constant system volume condition
was used so that the system size matched that of a simulated
thick substrate. To prevent the shift of the computational system due to the impact of the adatoms with the top surface,
the positions of two bottom atomic plane of atoms were fixed
during simulations.
Due to the remote kinetic energy of adatoms and the
latent heat release during adatom condensation, the system
temperature rises. To mimic isothermal growth conditions, an
intermediate region above the fixed region but several atomic
planes below the surface was maintained at a desired substrate temperature using a Nóse–Hoover algorithm.31 This
leaves a free surface zone that realistically captures various
events induced during adatom impacts. It also naturally introduces a heat conduction zone through which the energy
created at the surface during impacts is conducted to the
temperature controlled region for dissipation. To maintain
the distance between the temperature controlled region and
the free surface, the temperature controlled region was expanded as the surface grew. In simulations where significant
roughness emerged, growth of the temperature controlled region was made slow compared to that of the surface to avoid
rising above any surface boundary. For most simulations,
about 30 Å thick films were grown. This corresponded to
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034310-4
J. Appl. Phys. 104, 034310 共2008兲
Francis et al.
y
z
x
(a) adatom energy 0.1 eV
(b) adatom energy 0.5 eV
nm
4
nm
4
nm
4
0
nm 30
0
30 nm
0
nm 30
20
10
0
10
20
nm
4
20
10
0
10
20
10
0
10
20
0
30 nm
(d) adatom energy 2.0 eV
(c) adatom energy 1.0 eV
0
nm 30
nm
4
20
nm
4
nm
4
0
30 nm
0
nm 30
(e) adatom energy 3.0 eV
nm
4
20
10
0
10
20
0
30 nm
(f) adatom energy 4.0 eV
nm
4
nm
4
nm
4
nm
4
0
nm 30
0
30 nm
0
nm 30
0
30 nm
20
10
0
10
20
20
10
0
10
20
FIG. 4. 共Color online兲 Cu-on-Ta surface morphology obtained from MD simulations with adatom energies of 共a兲 0.1, 共b兲 0.5, 共c兲 1.0, 共d兲 2.0, 共e兲 3.0, and 共f兲
4.0 eV. Blue indicates Ta substrate and other atoms are colored based on their y coordinate.
roughly 200 000 deposited atoms. All simulations were carried out at room temperature using a deposition rate of about
0.5 nm/ns. The simulations therefore cover about 6 ns period
of accelerated growth.
IV. EXPERIMENTS
Experimentally, 30 nm Cu on 30 nm Ta bilayer films
were deposited on 6 in. silicon-silicon oxide wafers at room
temperature using a biased target ion beam deposition
共BTIBD兲 technique.32 A base pressure of about 3
⫻ 10−8 torr, a working pressure of about 8 ⫻ 10−4 torr, a depositing flux direction perpendicular to the growth surface, a
fixed Ta sputtering energy of 400 eV, and various Cu sputtering energies between 400 and 1200 eV were used. According to previous analyses,33,34 the applied sputtering energy
range results in emitted atoms whose average translational
energy roughly corresponds to the simulated adatom energy
共between 0.1 and 4.0 eV兲. Depending on the depositing material and sputtering energy, the growth rate was found to
roughly lie between 0.4⫻ 10−10 and 1.5⫻ 10−10 nm/ ns.
X-ray diffraction 共XRD兲 measurement was used to characterize the film texture. A tapping mode atomic force microscope 共AFM兲 was used to analyze film surface morphology
and the root-mean-square 共rms兲 surface roughness.
V. GROWTH OF COPPER ON TANTALUM
Synthesis of Cu interconnects is done by first depositing
a thin Ta diffusion barrier layer on semiconductor devices
and then depositing the Cu interconnecting layer on the Ta
layer. Properties of the system are sensitive to the atomic
structure of the Cu-on-Ta bilayer. For good performance, Cuon-Ta interface must be chemically sharp and atomically uniform. High purity, high density, and high crystallinity are
essential for the Cu layer to exhibit a high electrical conductivity. This also means that concentrations of defects, such as
surface roughness, growth islands, grain boundaries, voids,
and dislocations, must all be low. The control of surface
roughness and growth island density is critical because they
can result in the formation of other defects such as grain
boundaries, voids, and dislocations. Island coalescence may
also result in stress generation.35 Here, the growth of Cu on
Ta is first explored. Because similar results were obtained
from both potentials, we will focus our discussion using the
original EAM potential. This was based on two considerations: 共a兲 a negative heat of mixing accelerates the mixing
process and therefore provides a more stringent test for the
formation of sharp interfaces and 共b兲 an accelerated mixing
process counteracts the kinetics-limiting effect due to the
short time scale used in the simulation.
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034310-5
J. Appl. Phys. 104, 034310 共2008兲
Francis et al.
(a) AFM at 400 eV sputtering energy
(b) AFM at 600 eV sputtering energy
nm
(c) AFM at 800 eV sputtering energy
nm
nm
10
10
10
5
5
5
nm
nm
0
nm
nm
0
nm
0
100
100
100
200
0
100
200
200
300
300
400
nm
0
100
100
200
200
300
0
300
300
400
400
200
500
300
400
400
500
(d) AFM at 1000 eV sputtering energy
400
500
(e) AFM at 1200 eV sputtering energy
nm
nm
10
10
5
5
nm
0
nm
nm
0
100
nm
0
100
100
200
0
100
200
200
300
200
300
300
400
300
400
400
400
500
500
FIG. 5. 共Color online兲 AFM images of Cu-on-Ta surface morphology obtained from experiments with sputtering energies equal to 共a兲 400 eV, 共b兲 600 eV, 共c兲
800 eV, 共d兲 1000 eV, and 共e兲 1200 eV.
A. Observations of atomic structures as a function of
adatom energy
A series of MD simulations was carried out to grow Cu
films on Ta at different adatom energies between 0.1 and 5.0
eV. The resulting atomic images of the deposited films are
shown in Figs. 4共a兲–4共f兲 at selected adatom energies, where
blue indicates the Ta substrate and other atoms are colored
according to their y coordinate to clearly show Cu film surface morphology. Figure 4 indicates that as the adatom energy is increased, the surface roughness decreases. To verify
this observation, a series of Cu films was experimentally
grown on Ta using BTIBD technique at different sputtering
(b) AFM RMS roughness vs. sputtering energy
3.2
9.0
3.0
8.0
RMS roughness (Å)
RMS roughness (Å)
(a) MD RMS roughness vs. adatom energy
energies between 400 and 1200 eV. AFM was used to measure the surface morphology of the deposited films. The results, which are shown in Fig. 5, indicate that the Cu film
surface roughness decreases with increasing adatom energy.
While both simulations and experiments show that the
Cu surface roughness decreases with increasing adatom energy, simulations were obtained at a deposition rate of about
0.5 nm/ns, whereas experiments were done at a deposition
rate of about 0.5⫻ 10−10 nm/ ns. In addition, the horizontal
dimension scale used in Fig. 4 is at least one order of magnitude smaller than that used in Fig. 5. The accelerated deposition rate used in simulations significantly reduced the time
2.8
2.6
2.4
2.2
2.0
1.8
0
1
2
3
adatom energy (eV)
4
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0
200
400
600
800
1000
1200
sputtering energy (eV)
FIG. 6. 共a兲 MD roughness as a function of adatom energy; and 共b兲 AFM roughness as a function of sputtering energy.
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034310-6
J. Appl. Phys. 104, 034310 共2008兲
Francis et al.
that surface atoms could diffuse before they were buried by
new adatoms. The buried defects such as surface roughness,
therefore, exhibit shorter length scales. Considering such
scaling arguments, the MD results shown in Fig. 4 agree well
with AFM results shown in Fig. 5.
y [010] Ta
x [100] Ta
orientation A
orientation B
B. Surface roughness as a function of adatom energy
To quantify the effects of adatom energy on morphology,
the rms deviation of surface atoms from their mean height 共y
coordinate兲 was calculated from the atomic configurations of
simulated Cu-on-Ta films as a function of adatom energy.
The results of the calculations are shown in Fig. 6共a兲. Figure
6共a兲 indicates that the rms roughness of the Cu films decreases as adatom energy increases from 0.1 to 4.0 eV, with
the rate of decrease higher at small adatom energies and
lower at high adatom energies. rms roughness was also measured experimentally from AFM samples. The results are
shown in Fig. 6共b兲 as a function of sputtering energy. A
similar trend to that shown in Fig. 6共a兲 was obtained. In
particular, the surface roughness decreases with increasing
sputtering energy, and the rate of decrease is higher at small
sputtering energies and lower at high sputtering energies.
Quantitatively, smaller roughness is obtained in the MD
simulations than in experiments. This is consistent with a
much smaller thickness of the simulated films. The adatom
energy effect on surface roughness has been well studied.25,34
When an adatom with high incident energy impacts a surface
with a local asperity, the impact is more likely to cause the
collapse of the asperity, resulting in a flattening of the surface.
The impact-induced flattening does not have to be
caused by depositing atoms. It can be introduced by high
energy inert gas ions using an ion beam assisted deposition
process.36 Because inert gas ions do not adhere to the surface, they do not change the film composition. This provides
a convenient means to control the morphology of a growth
surface. Combined MD simulations and experiments have
been used to study the morphology of a Cu-on-Ta surface
grown with the impact of various inert gas ions.37 Both simulations and experiments indicated that when using argon as
the inert gas species, the ion assistance at a sufficiently high
ion to metal ratio 共say 10 or above兲 and a high ion energy
共say 20 eV or above兲 can reduce the roughness of the Cuon-Ta films by 50% through the impact-induced flattening
mechanism.
adatom energy 4.0 eV
z [001] Ta
FIG. 7. 共Color online兲 Four consecutive atomic planes inside a Cu film
deposited on Ta at 4.0 eV adatom energy.
Our test simulations indicated that when relatively small
horizontal dimensions 共e.g., 50 Å兲 were used, the simulated
Cu films usually contained only one grain in the simulated
film area. Small systems are not realistic even when the use
of periodic boundary conditions removes the surfaces in the
x- and z-directions. This is because the periodic boundary
condition imposes constraints on the motion of atoms near
cell boundaries. For our systems that contained about 300 Å
horizontal dimension, polycrystalline Cu films were observed in all of our simulations of Cu growth on a single
crystalline Ta. The grain structure was found to be relatively
insensitive to adatom energy. As an example, Fig. 7 shows
four consecutive atomic planes inside a Cu film deposited on
Ta at an adatom energy of 4.0 eV, where four different colors
are used to distinguish y coordinates 共planes兲. Clearly, the
film exhibits two grains: one in orientation marked as “A”
and the other in orientation marked as “B.” Both grains have
fcc stacking with a 共111兲 surface. One interesting discovery
is that all of our simulated Cu films contained only the two
orientations shown in Fig. 7.
Further examinations of grain structures were carried
out. Figure 8 shows an example of a Cu film deposited at 0.1
eV, where several consecutive atomic planes inside the Cu
film are viewed at a tilted angle from top with different colors showing the y coordinate of the atoms. It can be seen that
multiple grains were formed. These multiple grains appeared
to result in the formation of grain boundary junctions where
three “grain” boundaries meet. Normally, grain boundary
junctions require that the three joining boundaries are be-
x [100] Ta
translational boundary
C. Grain structure observation
void
Examination of atomic images indicated that crystalline
Cu films were obtained in all of our simulations. A detailed
analysis was carried out to identify the atomic stacking of the
Cu films. It was discovered that only the first atomic plane of
Cu was somewhat epitaxial to the 共100兲 bcc Ta substrate
surface. Starting from the second plane, Cu quickly evolved
into a fcc phase. In all simulations, Cu films grew in a 关111兴
direction. Our subsequent XRD experiments using BTIBD
samples verified that Cu films deposited on Ta were fcc crystals with a very strong 关111兴 texture.
orientation boundary
stacking fault
z [001] Ta
FIG. 8. 共Color online兲 Tilted top view of a few consecutive atomic planes
inside a Cu film deposited on Ta at 0.1 eV adatom energy. Circles mark
grain boundary junctions where three grain boundaries meet.
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034310-7
J. Appl. Phys. 104, 034310 共2008兲
Francis et al.
(a) adatom energy 0.1 eV
y
view from top
(b) time 2030.7 ps
Cu film
x
z
Ta substrate
x
z
(c) time 2487.6 ps
(d) time 2995.3 ps
sizes are not too small because the migration of grain boundaries requires significant reconstruction of atoms. The translational grain boundary is also seen to be stable in the MD
simulations. Furthermore, we noticed that very thin films
were usually absent in translational grain boundaries and
only after the films grew beyond a critical thickness were
translational boundaries 共dislocations兲 nucleated within an
otherwise relatively perfect grain. This is similar to the formation of misfit dislocations to release the misfit strain energy when the film thickness exceeds a critical value.12,38
Because the translational boundary corresponds to a lower
misfit strain energy, it is relatively stable.
D. Grain structure formation mechanisms
FIG. 9. 共Color online兲 Grain structure formation during deposition: 共a兲
three-dimensional geometry; 共b兲 planar view at 2030.7 ps; 共c兲 planar view at
2487.6 ps; and 共d兲 planar view at 2995.3 ps.
tween grains with different orientations with respect to each
other. As pointed out above, only two orientations were observed in the Cu films. Careful examination of Fig. 8 indicates that only two boundaries at the grain boundary junctions are the regular orientational boundaries that separate
grains with different orientations. The remaining boundary,
however, is a translational boundary that separates “two”
grains with the same orientation except that they are translationally shifted with respect to each other. As a result, such a
boundary originated from a dislocation. In addition to grain
structures, Fig. 8 reveals the presence of other defects such
as voids and stacking faults 共bounded by dislocations兲. The
change in color within the stacking fault bands suggests that
these stacking fault planes are tilted from the surface plane.
It should be noted that the translational boundary, which is
essentially a dislocation, should also cause a stacking fault.
In this case, however, the stacking fault plane coincides with
the surface plane.
Figures 7 and 8 reveal the grain structures that form
during accelerated deposition of Cu on 共010兲 bcc Ta. It is not
clear how stable these grain structures are and if they would
exist in films grown at a significantly decreased rate. To address these issues, the time evolution of grain configurations
was studied. Figure 9 examines a Cu film deposited at an
adatom energy of 0.1 eV, where Fig. 9共a兲 is a threedimensional view of the film; Figs. 9共b兲–9共d兲 are time evolution snapshots of planar view of a narrow layer of material
inside the Cu film as indicated in Fig. 9共a兲. No deposition
occurs during ⬃1 ns of simulation shown and it can be seen
from Figs. 9共b兲–9共d兲 that little change in the grain structure
occurred during this time period. Results shown in Fig. 9
indicate that the observed grain structures were fairly stable;
however, we cannot rule out long time reconstruction based
on these MD results. Nonetheless, it is not surprising that an
orientational grain boundary is stable at least when the grain
The results discussed above showed mainly two grain
phenomena: 共a兲 the formation of grains with two characteristic orientations and 共b兲 the formation of stable translational
boundaries 共dislocations兲. Atomistic simulations allow us to
explore fundamental mechanisms for these two phenomena.
As a representative example, a Cu film deposited at an adatom energy of 3.0 eV is examined in Fig. 10. In Fig. 10共a兲, a
planar view of three consecutive atomic planes inside the Cu
film is displayed using different colors to distinguish different planes. A periodic band structure is seen. In the relatively
dark bands, atoms with all three different colors are shown,
indicating a local ABCABC¯ hexagonal stacking in the
关111兴 fcc 共growth兲 direction. In the relatively bright bands,
only atoms with two different colors are shown, indicating a
local ABAB¯ stacking in the 关111兴 fcc direction. As a result,
these bands are periodic stacking faults on the surface plane.
In fcc Cu, these stacking faults are separated by partial dislocations with Burgers vectors 61 具112典a, where a is the lattice
constant of Cu. It can be seen that these partial dislocations
are not only present at the translational grain boundaries but
also inside each grain. High resolution scanning tunneling
microscopy 共STM兲 experiments revealed similar periodic
stacking faults on a Cu-on-共0001兲Ru surface39 关Fig. 10共b兲兴,
which has been elucidated using simulations.40
In order to examine the structure in more detail, the circular region marked in Fig. 10共a兲 is magnified and shown in
Fig. 10共c兲. The orientation of a grain can be visually represented by a triangle drawn through, for instance, six red atoms on the hexagonal 共111兲 surface. It can be seen that the
two grains on the left side have the same orientation as they
are represented by the same orientation of triangles, whereas
the grain on the right has a different orientation as it is represented by a different orientation of triangle. As a result,
boundary A between left and right grains is an orientational
boundary and boundary B between the two left grains is a
translational boundary. Furthermore, we superimpose the two
different orientations of the triangle identified in Fig. 10共c兲
over the square symmetry of the 共010兲 bcc Ta, and display
the result in Fig. 10共d兲, where the light shaded squares represent the 共010兲 symmetry of the bcc Ta, and the dark shaded
triangles represent the 共111兲 symmetry of the fcc Cu. We can
see that one side of the triangle, which is a 具110典 fcc Cu
direction, is always parallel to the diagonal of the square,
which is a 具110典 bcc Ta direction. The parallel relationship
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034310-8
J. Appl. Phys. 104, 034310 共2008兲
Francis et al.
(a) overall top view
x
(b) STM image of Cu on Ru
E = 3.0 eV
z
stacking fault
(c) local top view
A
B
A
(d) film-substrate symmetry relation
<1
10
>C
u/
/<
11
0>
Ta
Ta
0>
11
/<
u/
>C
10
<1
q ~ 15o
q ~ 15o
FIG. 10. 共Color online兲 Grain orientation: 共a兲 overall top view of three deposited Cu atomic planes near the Cu-on-Ta interface; 共b兲 high resolution STM image
of a Cu film deposited on local 共0001兲 Ru surface 共Ref. 39兲; 共c兲 local view 关circular region in 共a兲兴 of a trigrain boundary juncture; and 共d兲 film-substrate
symmetry relation, where dark area shows 兵010其 bcc Ta symmetry and light area shows 兵111其 fcc Cu symmetry.
between 具110典 fcc Cu and 具110典 bcc Ta is not surprising as
both directions are close packed when projected on the surface plane. It can now be seen from Fig. 10共d兲 that because
there are only two diagonal directions of the square, there are
only two orientations for the triangles 共therefore, grains兲. As
the two diagonals are perpendicular, the two Cu grain orientations are related by a 90° rotation.
During growth simulations using small horizontal dimensions, new grains are nucleated at locations close to the
existing grains. This creates high energy configurations and
new grains are likely to be eliminated 共coarsened away兲 by
the existing grains at the nucleation stage. As a result, simulated films often exhibited a single crystal. Figure 11 shows
nucleated Cu islands obtained at an early deposition time of
around 0.8 ns using an adatom energy of 3.0 eV. For clarity,
atoms below the islands are not shown. It can be seen that
during growth of the Cu films on a large plane of Ta surface,
Cu grains are nucleated at random locations. The probabilities of forming either of the two orientations are exactly the
same when the nucleated grains are far apart and therefore
are independent. When these grains grow to meet each other,
the grain sizes are already big and, therefore, relatively stable
orientational boundaries are formed. This explains why two
and only two grain orientations were observed in all simulations.
x
E = 3.0 eV, t = 0.8 ns
z
FIG. 11. 共Color online兲 Origin of misfit dislocations. 共a兲 stacking geometry
of a 共111兲 fcc Cu grain on the 共010兲 bcc Ta substrate; and 共b兲 magnified view
of the white dashed triangle shown in 共a兲.
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034310-9
J. Appl. Phys. 104, 034310 共2008兲
Francis et al.
(a) hexagonal Cu over square Ta
(b) blow-up of the white dashed trangle in (a)
_1
<112>a
6
periodicity
b=
The analysis above indicates that the formation of polycrystalline Cu films, translational boundaries, and periodic
stacking fault bands/dislocations lower the system energy.
We conclude they are therefore relatively stable and can be
expected to exist in films grown via experiment. Because
they are not metastable defects created under kinetically constrained conditions, they are difficult to eliminate by controlling kinetic growth conditions or by using high quality single
crystalline substrates.
VI. GROWTH OF CUXTA1−X ON CU
FIG. 12. Top views of the first three atomic planes of CuxTa1−x films deposited on Cu at an adatom energy of 3.0 eV. 共a兲 Ta on Cu; 共b兲 Cu0.2Ta0.8 on
Cu; 共c兲 Cu0.4Ta0.6 on Cu; and 共d兲 Cu on Cu.
The observed periodic stacking faults/partial dislocations
were caused by lattice mismatch. Unlike the misfit dislocations that accommodate the size difference between the two
layers with the same crystal structure,12,38 the observed misfit
dislocations must accommodate both size and structure differences between bcc Ta and fcc Cu. The origin of the observed misfit dislocation configurations is explored in Fig.
12, where in Fig. 12共a兲, the alternate dark and light shaded
squares represent a 共010兲 bcc Ta surface, and the triangles
represent a 共111兲 Cu plane in the orientation of the two left
grains shown in Fig. 12共c兲. In Fig. 12共b兲, a magnified view of
the white dashed triangle in Fig. 12共a兲 is shown. In the figure, the relative size of the triangles with respect to that of
the squares matches the real material lattice constants so that
misfit is accurately reflected. To examine the periodicity of
共111兲 Cu on 共100兲 Ta, two of the triangles are marked black
in Fig. 12共a兲 and the lower black triangle is aligned 共corner
on corner兲 with the underlying square. It can be seen from
Fig. 12共a兲 that perfect 共111兲 Cu on 共100兲 Ta does not have
short range periodicity along the vertical direction in the
page. As a result, the misfit energy becomes large as the
feature size increases. However, if the upper-left part of the
共111兲 plane is shifted with respect to the lower-right part of
the plane by a vector marked inside the white dashed triangle, a periodicity of a length of six squares is created.
Figure 12共b兲 indicates that this shift vector corresponds to
the Burgers vector of a partial dislocation 61 具112典a of the Cu
lattice. As a result, the long range misfit strain energy is well
released by the creation of lower energy partial dislocations.
The dislocation line direction seen in Fig. 12共a兲 matches the
stacking fault band direction shown in Fig. 10共c兲, and the
periodicity identified in Fig. 12共a兲 gives a stacking fault band
width slightly shorter than that seen in Fig. 10共c兲. Because
the precise structure of both dislocations and stacking faults
depend on balancing various energy contributions, it is expected that the actual stacking fault band width 共misfit dislocation separation distance兲 will differ from the one shown
in Fig. 12共a兲. Figure 12 identifies only one dislocation 共line
and Burgers vector兲 characteristic of one grain orientation.
Because there are two perpendicular grain orientations, two
perpendicular arrays of stacking fault bands/dislocations are
seen in Fig. 10共a兲, with each array coming from one grain
orientation.
The diffusion barrier application requires only the
growth of Cu on Ta. Simulations of Ta on Cu are motivated
by the experimental discovery that alternate electron beam
deposition of Cu and Ta under Ar ion assistance can produce
amorphous films around a film composition of Cu0.3Ta0.7.15
In the experiment, the film composition was controlled by
the relative thickness of the deposited Cu and Ta layers. This
means that extensive mixing occurred either during deposition of Cu on Ta or Ta on Cu. This mixing can be caused by
high energy Ar impacts.41–44 Simulations discussed above
show that in the absence of Ar assistance, little mixing occurs during growth of Cu on Ta. It is not clear if mixing can
occur during growth of Ta on Cu. Our bulk simulation results
shown in Figs. 1 and 2 indicated that crystalline metals are
readily formed when the material is either Cu 共or Cu-rich兲 or
Ta 共or Ta-rich兲. In these cases, crystallization is difficult to
inhibit as the kinetics is extremely fast in metals. When mixing occurs, especially when the Cu and Ta compositions in
the alloy 共solid solution兲 are comparable, an amorphous
phase is likely to form. This is because the lattice mismatch
strain energy is so large that it cannot be fully released by
any crystal-maintaining density of defects such as misfit dislocations. This effect is predicted in Figs. 1共c兲 and 2. To form
amorphous films, it is therefore critical to create highly
mixed regions and inhibit separation to Cu-rich and Ta-rich
phases.
Mixing can be driven by a negative heat of mixing. It
can also be driven by other factors. For instance, previous
studies25,26,34 have indicated that when the underlying surface is composed of atoms with a lower cohesive energy, a
larger lattice spacing, and a lower surface energy with respect to the depositing atoms, the depositing atoms are more
likely to penetrate the underlying surface through the lattice
interstices and the underlying atoms are more likely to be
exchanged to the surface to lower both surface stress and
surface energy. A continuous surface segregation of the underlying atoms to the surface then causes them to be mixed
into the overlying deposited layer. Although the radius of Cu
is smaller than that of Ta, the cohesive energy of Cu,
−3.54 eV/ atom, is significantly smaller in magnitude 共less
negative兲 than that of Ta, −8.09 eV/ atom. This suggests that
Cu atoms are likely to segregate to the Ta surface to release
the high surface energy 共which is caused by broken Ta
bonds兲, and that the depositing Ta atoms are likely to penetrate a weakly bonded Cu surface and cause Cu–Ta exchange. This observation suggests that there could be a significant mixing across the Ta-on-Cu interface. If this is the
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J. Appl. Phys. 104, 034310 共2008兲
Francis et al.
x
5
(b) Cu0.20Ta0.80 on Cu
(a) Ta on Cu
E = 4.0 eV
radial distribution
034310-10
z
disordered region
4
Ta on Cu
3
2
Cu0.4Ta0.6
1
0
-1
(c) Cu0.40Ta0.60 on Cu
Cu on Cu
2
3
(d) Cu on Cu
4
5
6
radius (Å)
FIG. 14. Front view of a Cu0.4Ta0.6 film deposited on Cu at an adatom
energy of 3.0 eV.
FIG. 13. 共Color online兲 Radial distribution functions for selected films.
case, it provides an avenue for the synthesis of amorphous
films. An alternative approach that offers control of the film
composition is to deposit CuxTa1−x films on Cu, with x somewhere between 0 and 1. Considering that surface segregation
and phase separation may occur during the growth, it is not
clear how the film composition relates to the vapor phase
composition. The atomic assembly mechanisms during
growth of Ta on Cu can therefore provide useful insights that
lead to better design concepts. Here we explore the formation
of amorphous films by simulating the growth of CuxTa1−x
films on Cu using a variety of compositions x. Both original
and adjusted EAM potentials were used in the simulations.
Extensive mixing was observed in both cases. In the following, we focus our discussion with the adjusted EAM potential. This was also based on two considerations: 共a兲 it provides a more stringent test for the formation of mixing
because it eliminates the possibility that the mixing is incorrectly driven by a 共wrong兲 negative heat of mixing, and 共b兲
the “adjusted” Ta–Cu cross pair contribution becomes significant when mixing occurs.
A. Atomic structure observations
A series of MD simulations was carried out to grow
CuxTa1−x films on Cu at a constant adatom energy of 4.0 eV
and various compositions of x, 0 ⱕ x ⱕ 1. Here the composition x refers to the vapor composition, and the actual film
composition is likely to be different considering that Cu atoms in the underlying Cu substrate may be mixed into the
deposited film. Examples of atomic configurations of deposited films are shown in Fig. 13, where planar views of a
small area of three consecutive atomic planes inside the deposited films are shown in Figs. 13共a兲–13共d兲 for four selected
film compositions x = 0.0, 0.2, 0.4, and 1.0. It can be seen that
at x = 0.0 关Fig. 13共a兲兴, the growth of Ta on Cu resulted in a
film that is mostly composed of crystalline grains. Following
the same analysis above, we found that all the Ta grains have
a 共110兲 plane parallel to the 共111兲 Cu substrate surface. The
grain orientation can be represented by a rectangle connecting the eight red 共orange兲 atoms. The short side of the rectangle is parallel to the 具100典 bcc Ta direction, and the long
side of the rectangle is parallel to the 具100典 bcc Ta direction.
We further found that for all of the Ta grains, one of the
具100典 bcc Ta direction is parallel to one of the 具110典 fcc Cu
direction. Because there are only three nonequivalent 具110典
directions on the hexagonal Cu surface, only three Ta grain
orientations were discovered in all of our simulations. An
additional finding in Fig. 13共a兲 is that the regions between
grains are disordered, which is a characteristic of an amorphous phase. The width of these disordered regions increased
toward the Ta-on-Cu interface. These observations indicate
that the amorphization is driven by a combination of lattice
mismatch across the Ta/Cu interface and the grain boundaries.
Figure 13共b兲 shows that the structure of the Cu0.2Ta0.8
film is very similar to that of the Ta film. However, when the
film composition was increased to x = 0.4 关Fig. 13共c兲兴, the
area of disordered regions increased significantly. These regions essentially formed a considerable volume fraction of
an amorphous structure. Finally, when the composition is x
= 1, the growth of Cu on Cu resulted in the formation of a
relatively perfect fcc Cu single crystalline film on Cu substrate 关Fig. 13共d兲兴. To verify the observation from Fig. 13,
radial distribution functions were calculated for films deposited at different compositions. Selected results are shown in
Fig. 14. Comparison between Figs. 2 and 14 indicates that
the Cu film on Cu exhibited a fcc crystalline structure, the Ta
film on Cu was dominated by a bcc crystalline structure, and
the Cu0.4Ta0.6 film on Cu was dominated by an amorphous
structure.
B. Interlayer mixing
The amorphization of binary metals is believed to be
driven mainly by heat of mixing, atomic size difference, and
crystal structure difference.16,45–47 When the heat of mixing
is high, the system tends to be separated into two elemental
phases. Only when the heat of mixing is low, a highly mixed
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034310-11
J. Appl. Phys. 104, 034310 共2008兲
Francis et al.
zy
:Cu
:Ta
Cu0.40Ta0.60 on Cu
x
FIG. 15. Composition profile.
solid solution forms. Amorphization then occurs if significant atomic size and crystal structure differences result in a
significant misfit energy that sufficiently destabilizes a crystalline structure. Compared to bulk synthesis methods, vapor
deposition offers unique means to create mixed film composition even in systems with a positive heat of mixing. Interlayer mixing created during vapor deposition is hence important to understand.
The film compositions marked in Figs. 13 and 14 are the
nominal 共vapor兲 compositions used in simulations. Due to
effects such as surface segregation, the actual local composition in the film differs from the vapor composition. Obviously, amorphization is a result of local composition in the
film. To show the possible composition distributions expected in the films, the front view of a Cu0.4Ta0.6 film deposited on Cu at an adatom energy of 4.0 eV is shown in Fig. 15,
where darker spheres represent Ta atoms and lighter spheres
are Cu atoms. It can be seen that Cu has a strong surface
segregation effect, consistent with its lower cohesive and surface energies. Due to this surface segregation, the Cu composition near the surface becomes significantly higher than
that deep inside the film.
In order to quantify composition profiles, the growth of
Ta on Cu was simulated using a thicker initial Cu substrate.
The composition profiles were calculated for such simulations and the results are shown in Fig. 16.
Figure 15 indicates that intermixing formed during deposition of Ta on Cu is insensitive to adatom energy. The composition profiles shown for 0.1 and 4.0 eV two adatom energies are very close 共composition distribution at 4.0 eV does
appear to be slightly broader, if any兲. This is different from
previous observation in Ni/Cu and Co/Cu multilayer growth
where mixing was found to increase with adatom energy due
to an impact-induced atom exchange mechanism.34 Significant Cu mixing into the overlying Ta layer occurs at a low Ta
adatom energy because Cu has a strong tendency to segregate to the surface of Ta due to its significantly lower surface
and cohesive energies compared to those of Ta. Because this
mixing effect saturates at a low Ta adatom energy, a further
increase in energy does not increase the mixing correspond-
ingly. The simulations indicate that while the growth of Cu
on Ta and Ta on Cu both create a Cu/Ta interface, the atomic
structure is very different. When Cu is deposited on Ta, the
lower surface energy of Cu keeps Cu on the surface, reducing mixing; whereas when Ta is deposited on Cu, Cu surface
segregation causes intermixing. Previous work also showed
that intermixing is low during deposition of Cu on Ta at
various adatom energies even when inert gas ion impacts
were used during deposition.42
The key to create amorphous structure is to induce mixing. Due to the Cu surface segregation effect, Cu tends to
mix into subsequently deposited Ta films. As a result, depositing Ta on Cu helps create a mixed interface. This accounts
for why an alternate deposition of Cu and Ta can be used to
experimentally synthesize thicker amorphous films. Experimentally, the use of Ar ion assistance is also beneficial to
increase the depth of the mixing zone near the surface. On
the other hand, directly depositing CuxTa1−x alloy films offers a useful means to better control the film composition.
However, due to Cu surface segregation, Cu composition
tends to increase as the film thickness increases when using
this approach. In addition, phase separation may occur.
Simulations indicated a need to use experimental approaches
to identify the growth of amorphous films using the CuxTa1−x
alloy vapor flux.
VII. CONCLUSIONS
MD simulations and selected microscopic experiments
have been performed to study the growth of fcc Cu films on
共010兲 bcc Ta substrate and CuxTa1−x alloy films on 共111兲 fcc
Cu substrate. The following results have been obtained.
共a兲
共b兲
共c兲
Atomic fraction
1.0
0.8
0.6
0.4
0.2
0.1 eV:
4.0 eV:
Ta
共d兲
Cu
Ta
Cu
0.0
10
20
30
40
position along film thickness (Å)
FIG. 16. Composition profile.
50
共e兲
The roughness of Cu films deposited on Ta decreases
as adatom energy is increased due to an impactinduced flattening mechanism.
Cu deposited on 共010兲 Ta always forms fcc polycrystalline films with a 共111兲 texture. The crystalline grains
only have two orientations and are separated by either
orientational boundaries or translational boundaries
共dislocations兲. The formation of two crystal orientations is due to crystalline symmetry between Cu film
and Ta substrate. The formation of translational boundaries is due to misfit dislocations.
A characteristic array of periodic stacking fault bands/
misfit dislocations is formed within each Cu grain orientation to release misfit strain energies. Two grain orientations then resulted in two perpendicular arrays of
stacking fault bands/misfit dislocations in polycrystalline Cu films.
Cu has a strong surface segregation effect when Ta is
deposited on Cu. This causes underlying Cu to float up
and mix in subsequently deposited Ta or CuxTa1−x
films. As a result, the Cu composition in the CuxTa1−x
layer is always higher than vapor composition.
Amorphous phase can form when the Cu and Ta compositions in the deposited films are comparable. This
can be achieved by either both alternatively depositing
Cu and Ta with inert gas ion assistance or directly de-
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034310-12
positing CuxTa1−x alloy films with controlled vapor
composition and highly kinetically constrained growth
conditions or combination of both.
While the work revealed the fundamental mechanisms
for the formation of defects—such as surface roughness,
grain boundaries, misfit dislocations, stacking faults, and
amorphization—further studies are needed to investigate the
links between these defects and atomic size difference, heat
of mixing, crystal structure, and crystal orientation in order
to develop methods to reduce these defects.
ACKNOWLEDGMENT
Sandia is a multiprogram laboratory operated by Sandia
Corporation, a Lockheed Martin Co., for the United States
Department of Energy’s National Nuclear Security Administration under Contract No. DEAC04-94AL85000.
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