Download Hyperthermal Vapor Deposition of Copper: Reflection and Resputtering

Surface Science 431 (1999) 58–73
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Hyperthermal vapor deposition of copper:
reflection and resputtering effects
X.W. Zhou, H.N.G. Wadley *
Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Virginia,
Charlottesville, VA 22903, USA
Received 23 November 1998; accepted for publication 2 February 1999
Abstract
Three-dimensional molecular dynamics simulations of hyperthermal copper atom impacts with copper surfaces
have been used to investigate the effects of incident atom energy upon atomic reflection and resputtering during
physical vapor deposition. No reflection or resputtering has been observed for incident energies below 10 eV. However,
as the incident energy was increased to 20 eV and above, the likelihood of both adatom reflection and sputtering of
predeposited atoms rapidly increased. The probability of reflection increased with the angle of incidence and was
greatest for oblique (glancing) angle impacts. The reflected adatoms were strongly forward scattered and retained a
large fraction of their initial incident energies. The resputtering yield was highest for incident angles around 40° to
the surface normal. The resputtered atoms were typically ejected with significantly smaller energies than those of the
incident atoms, and were preferentially ejected in the forward direction with a maximum probability at an angle of
about 45° to the surface normal. These results have been compared with the published experimental data for low
energy ion impact. The dependence of the reflection probability, the resputtering yield, as well as the angular and
energy distributions of both reflected and resputtered atoms upon the adatom’s incident energy and angle have been
obtained and fitted to simple relations suitable for incorporation in models of vapor deposition. © 1999 Elsevier
Science B.V. All rights reserved.
Keywords: Atom–solid interactions; Copper; Growth; Metallic films; Models of surface kinetics; Molecular dynamics; Sputtering;
Sticking
1. Introduction
The morphology and microstructure of physical
vapor deposited (PVD) materials can be significantly modified by changing the incident energy
of the depositing atoms [1–7]. The atomistic mechanisms responsible for these incident energy effects
are thought to include: (i) local transient surface
heating which induces athermal diffusion; (ii)
* Corresponding author. Fax: +1-804-982-5677.
E-mail address: [email protected] (H.N.G. Wadley)
adatom skipping across the growth surface in the
impact direction leading to biased adatom diffusion; (iii) adatom reflection; and (iv) adatom
induced resputtering [7–17]. A detailed understanding of these mechanisms and their dependence upon incident energy and angle is a
precursor in unraveling the complex dependence
of film morphology and microstructure upon PVD
process conditions. Predictive models that incorporate the effects of incident energy and angle upon
the morphology and microstructure of films might
eventually aid the design of improved vapor deposition techniques.
0039-6028/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved.
PII: S0 0 39 - 6 0 28 ( 99 ) 0 03 3 6 -2
X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
An atom impact model based upon a threedimensional molecular dynamics (MD) analysis
has recently been developed and used to investigate
impact atom induced diffusional processes during
the deposition of hyperthermal atoms [18]. This
impact model used an embedded atom method
( EAM ) potential to calculate the interaction forces
between metal atoms during impacts. It was used
to analyze the local surface heating responsible for
athermal diffusion and the momentum effects that
caused biased diffusion of adatoms. The results
indicated that the local transient heating induced
by a hyperthermal adatom impact is often sufficient
to activate atomic diffusion and the reconstruction
of locally defective structures. They also revealed
that long-range adatom biased diffusion readily
occurs. The bias diffusion distances sometimes
exceed 100 Å, especially when incident energies are
above ~20 eV and incident angles are above 70°.
As a result, increasing the incident energy is
expected to reduce the defect concentrations and
to promote a flatter surface morphology for thin
films deposited under kinetically limited conditions
(i.e. at low temperatures or high deposition rates).
Both the impact induced local heating and the
biased diffusion results were fitted to empirical
equations, simplifying their incorporation in the
various modeling schemes utilized for the simulation of vapor deposition [19].
Experimental studies have shown that hyperthermal adatoms with incident energies of 20 eV or
above can also be reflected and/or induce sputtering of predeposited atoms (resputtering) [6 ]. These
reflection and resputtering processes can have
important consequences for the manufacture of
thin films and the metal interconnects used in
large-scale integrated circuits [7]. To increase the
device density, narrow conductive lines are used
for interconnecting individual devices. As a result,
metals must be deposited into deep narrow (i.e.
high aspect ratio) trenches. However, when the
aspect ratio is high, the deposit often covers the
trench opening before fully filling it. This results
in large voids becoming trapped within the
interconnect, and the premature failure of the
device [6,7]. Reflection and resputtering may be
able to retard the formation of overhangs at the
trench top and promote more even coverage of
59
the trench walls. Since these processes only occur
for energetic atom impacts, interest has grown in
the use of high incident energy deposition techniques such as bias sputter deposition [7–10,20]
or thermal evaporation with sputter etching [11].
The sputtering of metals by atomic bombardment of their surface has been widely investigated
using various experimental approaches [21]. The
focus of much of the work has been the sputtering
of metal targets by high energy (~1–10 keV ) inert
gas ions in order to investigate the process that
are normally used to create a metal atom flux for
subsequent deposition [21]. Recently, Doughty
et al. at Oak Ridge National Laboratory have
measured the angular distribution of copper atoms
ejected by helium, argon and xenon ions incident
on copper surface at incident angles of 30, 45, and
60° with low incident energies of 40, 160 and
600 eV [22]. The sputtering yields of silicon surface
by low energy (25–200 eV ) argon ion bombardment were calculated by Kubota et al. [23]. While
these data are useful for assessing some aspects of
low energy impacts, they are inadequate for a
quantitative analysis of the contribution of reflection and resputtering to hyperthermal metal atom
(or metal ion) deposition. These processes remain
poorly characterized and are only superficially
understood.
Atomistic modeling provides an alternative
approach to the study of atom impact processes.
At high incident energies, sputtering has been
reasonably simulated using a Monte Carlo method
based upon a binary atomic collision approximation [24]. However, at the lower incident energies
of interest here, many-body collision effects
become important, and the binary collision
approximation fails. Collisions must therefore be
simulated using methods that better account for
the many-body nature of the interaction. In a
molecular dynamics simulation, the trajectories of
atoms within the interaction field of all the other
atoms can be traced by solving Newton’s equation
of motion using a predefined interatomic potential.
If electronic excitation and chemical reaction
effects can be ignored, the MD method provides a
tractable approach to the analysis of an adatom–
substrate impact process. MD simulations have
been extensively used to investigate the ion sputter-
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X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
ing of metals [25]. The reflection of a 40 eV silicon
atom from a (111) silicon surface at an incident
angle of 12° has been simulated using MD [16,17],
but no work has sought to establish a detailed
understanding of the adatom reflection and resputtering mechanisms that are active during deposition of hyperthermal atoms.
Here, a MD vapor atom impact model developed earlier to analyze impact induced diffusion
[18] was extended to investigate atomic reflection
and resputtering as a function of the incident
energy and angle of the depositing atoms. The
work concentrates on the reflection and resputtering of copper from a copper surface because of
the importance of copper in integrated circuits
[26 ], its widespread use in GMR devices [27–30],
and the availability of a highly validated interatomic potential of copper [31].
2. Computational method
Atomic reflection and resputtering during atom
impacts with low index {100}, {110} and {111}
copper surfaces have been studied. The computational crystals and the MD scheme used for the
simulations of single atom impacts with crystal
surfaces are identical to those reported previously
[18]. The geometry of the crystals and the basic
directions and angles are schematically shown in
Fig. 1. As in the previous work, periodic boundary
conditions were used along the x- and z-directions.
Atoms within d of the bottom surface were fixed
0
at the equilibrium positions of the bulk crystal,
the region d (identified by the darker atoms in
T
Fig. 1) was kept at a fixed substrate temperature,
while the atoms above the thermostatically controlled volume were left free.
The impact process was simulated by using
molecular dynamics to calculate the positions and
velocities of atoms for 2 ps following the arrival
of a copper adatom at the cut-off distance of the
interatomic potential above the crystal surface.
The copper adatom was assigned an initial speed
corresponding to a far-field ‘incident’ kinetic
energy, E , and an incident direction. The initial
i
direction of the impacting copper atom was constrained to lie in the x–y plane and could therefore
be defined by a single incident angle, h, Fig. 1. The
trajectories of the reflected or resputtered atoms
are generally not confined to the x–y plane, and
hence two angles, h and h , were used to specify
1
2
their directions. 50 MD runs were performed for
each condition to obtain a reliable estimate of the
Fig. 1. Schematic geometry of the computational crystal and definitions of directions and angles.
X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
61
Fig. 2. Trajectories of reflected and resputtered atoms during a 50.0 eV adatom impact. Adatom, resputtered atom, and other atoms
are marked by dark, grey and light balls, respectively: (a) reflection at an incident angle of 70°; (b) resputtering at an incident angle
of 45°.
reflection probability and resputtering yield (the
number of resputtered atoms per adatom impact),
and to permit analysis of the angular and energy
distributions of the ejected atoms. Incident energies
ranging from 0 to 50.0 eV and incident angles
ranging from 0 to 90° were investigated. All the
simulations were conducted with a fixed substrate
temperature of 300 K.
3. Time resolved impacts
To investigate the basic mechanisms responsible
for hyperthermal atomic reflection and resputtering, time resolved results for a 50.0 eV atom impact
with a {100} copper surface at impact angles (h)
of 70° and 45° are shown in Fig. 2a and b, respectively. In Fig. 2, the adatoms (the reflected atom
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X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
is also the adatom), the resputtered atom, and
other crystal atoms are marked with black, grey
and lightly shaded balls, respectively. The crystals
are displayed by atomic positions at the time of
impact, and the trajectories of the incident,
reflected and resputtered atoms are revealed by
marking their positions at time steps of either
0.05 ps (for reflection) or 0.1 ps (for resputtering).
velocity component normal the surface, reflection
is most significant for oblique angles of incidence.
At oblique angles of incidence, the adatom’s velocity component parallel to the surface remains large
with respect to its velocity component normal to
the surface after impact, and as a result, the
reflection angle is large and the atom was often
seen to be reflected in an almost specular manner.
3.1. Reflection
3.2. Resputtering
Fig. 2a shows the reflection of a 50.0 eV hyperthermal atom impacting a surface at an oblique
angle of incidence (h=70°). It can be seen that the
reflection occurred with only a small penetration
of the adatom into the surface. The reflected atom
retained about 60% of its incident energy. It was
reflected with an angle (h ) of about 73°. The
1
reflection angle was therefore close to the incident
angle. About 40% of the incident energy was
transferred to the lattice. This transferred energy
was partitioned amongst the vibration modes of
the lattice near the impact site and caused a
thermal spike near the impact site similar to that
previously observed and analyzed [18].
During an atom impact with a surface, the
incident atom is subject to force components
normal and parallel to the surface. For a successful
atom reflection, the incident atom must reverse its
velocity component normal to the surface. For
impacts with a low normal velocity component
(e.g. h=70°), recoil forces are able to rapidly
reverse this velocity component during the impact
and, as indicated above, a moderate fraction of
the impact energy was transferred to the crystal.
As the velocity component normal to the surface
increases (i.e. as h0°), the incident atom penetrates into the surface more, and velocity reversion
is only achieved after multiple collisions. This
results in more energy transfer to the crystal.
For an atom to completely escape from a surface
after impact, its initial energy must be higher than
the sum of the surface binding energy E (E
b b
ranges from 2.5 to 3.5 eV for different crystallographic surfaces of copper [18]), and the energy
E dissipated by energy transfer. Since a decrease
a
of E can be achieved by increasing the adatom’s
a
in-plane velocity component and/or decreasing its
Fig. 2b shows a 50.0 eV hyperthermal atom
impacting a surface at an incident angle of 45°. In
this case, the impacting atom fully penetrated the
crystal surface and eventually occupied one of the
surface lattice sites. This process caused a large
transient lattice distortion and energy transfer to
neighboring atoms. While the initial momentum
of the incident atom pointed into the crystal, some
of the nearby surface atoms achieved significant
momentum out of the surface due to multiple
collisions. Fig. 2b shows that one of these surface
atoms was ejected at an angle near 45° to the
surface normal, and a resputtering event occurred.
In Fig. 2b it can be seen that the spacing between
two ‘consecutive’ snapshots of the resputtered
atom is much shorter than that of the incident
adatom, indicating that the resputtered atom had
a much lower velocity, or energy (about 4.9 eV for
the collision shown in the figure) than that of the
incident atom.
The observations above indicate that a successful resputtering event requires sufficient energy and
momentum transfer to a lattice atom for it to
overcome the binding force in a direction out of
the crystal surface. Energy transfer is more likely
for lower incident angles since the impacting atom
can then more easily penetrate the crystal.
However, as the incident angle falls toward zero,
the velocity component of the first knock-on surface atoms more directly points into the crystal,
which is less favorable for escape and thus resputtering. The trade-off between energy transfer and
momentum vector conversion results in a resputtering yield peak at an intermediate incident angle.
The large difference in both the energies and
angles of the reflected and resputtered atoms are
likely to result in different effects on film growth.
X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
63
Reflection and resputtering are therefore separately
analyzed and parameterized.
4. Atomic reflection
Suppose the adatom arrival rate is uniform
across a surface. The local growth rate then scales
with the adatom’s sticking probability, Y .
st
Sticking is related to adatom reflection,
Y =1−Y , where Y is the adatom’s reflection
s
rf
rf
probability. In some cases (e.g. deposition into a
trench), the reflected atoms are sometimes deposited again. The positions where these reflected
atoms redeposit are determined by the reflected
angles and the film geometry. Depending on the
energy and propagation direction, the redeposition
of the ‘reflected’ atoms may induce athermal
and/or biased diffusion [18]. The ‘reflected’ atoms
retain a high energy, and they can also cause a
second reflection and/or resputtering event. These
processes can significantly affect the evolution of
a thin film’s surface morphology and microstructure. It is therefore important to characterize the
incident energy and incident angle dependence of
reflection probability, as well as the angular and
energy distributions of the reflected atoms for the
range of energies and angles encountered in vapor
deposition processes.
4.1. Reflection probability
MD simulations of a copper atom impact with
the {100}, {110} and {111} surfaces of copper
crystal were conducted for incident angles between
0 and 90°, and for incident energies between 0.0
and 50.0 eV. Impact results of the type shown in
Fig. 2a were analyzed to determine the reflection
probability. Results for the three surfaces as a
function of incident angle at a fixed (high) incident
energy of 50.0 eV are given in Fig. 3. For the
reasons discussed above, the reflection probability
is seen to be negligible at low incident angles, but
becomes much more significant as the incident
angle approaches 60°. The reflection probability
was close to unity between 65 and 80°, and then
decreased at incident angles above 80°. Similar
Fig. 3. Reflection probability as a function of incident angle at
a fixed incident energy of 50.0 eV.
reflection probability verses incident angle trends
were observed at lower incident energies.
Since a maximum reflection probability
occurred at incident angles between about 65 and
80°, a fixed incident angle of 80° was selected to
illustrate the dependence of the reflection probability upon incident energy, Fig. 4. Fig. 4 shows
that the reflection probability was close to zero for
incident energies less than a threshold value, E ,
ic
of about 10 eV. As the incident energy increased
from 10 eV, the reflection probability rapidly
increased. The results shown in Figs. 3 and 4
indicate that the reflection probability was relatively insensitive to the crystallographic type of
surface.
The reflection was significant for impacts with
oblique angles. However, the reflection probability
Fig. 4. Reflection probability as a function of incident energy
at a fixed incident angle of 80°.
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X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
decreased rapidly as the incident angle was
increased beyond 80°. Examination of simulations
indicated that incoming atoms that propagated
almost parallel to the surface interacted with the
surface weakly, and their velocity component parallel to the surface could not be converted into a
direction for escape. As a result, adatoms would
gradually shed their energy to the crystal and
many were eventually captured by the surface.
To parameterize the incident angle dependence
of the reflection probability shown in Fig. 3, two
angles, h and h , are introduced. h represents the
c
m
c
threshold incident angle at which the reflection
probability starts to rise. h is the incident angle
m
at which the reflection probability is a maximum.
The probability of reflection from a general flat
surface as a function of incident angle h at an
incident energy of 50.0 eV was then fitted by an
appropriate equation and the result is listed as Eq.
(1) in Table 1. The curve of Eq. (1) is also shown
in Fig. 3.
Based on the observation that the reflection
probability approached unity at large incident
energies, the reflection probability for a flat surface
as a function of incident energy, E , at a constant
i
incident angle of 80° was fitted and the result is
listed as Eq. (2) in Table 1. In order for Eq. (2)
to be consistent with Eq. (1), the relation
Y (h=80°)=Y (E =50 eV ) was used to determine
rf
rf i
the parameters. The line corresponding to Eq. (2)
is included in Fig. 4.
The similar shape of the reflection probability
vs. incident angle curves for various incident energies enables the incident angle and energy dependent reflection probability, Y (h, E ), to be
rf
i
approximated by multiplying Y (h), defined by
rf
Eq. (1), with Y (E ), given by Eq. (2), and normalrf i
izing the result at E =50 eV. Y (h, E ) defined in
i
rf
i
this way is listed as Eq. (3) in Table 1. Since the
relation Y (h=80°)=Y (E =50 eV ) has been conrf
rf i
sidered in fitting Eqs. (1) and (2), Eq. (3) returns
to Eq. (1) at E =50 eV and to Eq. (2) at h=80°.
i
4.2. Angular distribution of reflected atoms
Variations in the exact impact point within a
unit cell and the stochastic nature of lattice vibration result in statistical variation of the incident
atom’s reflected angle. However, the average angle
of the reflection depends on the incident energy,
the incident angle of the incoming atom, and the
surface type. MD data were therefore analyzed to
deduce normalized probability density distributions for both h and h (see Fig. 1) in terms of
1
2
incident energies, incident angles and types of
surface. It was found that the surface type had
only a minor effect on the angular distribution of
reflected atoms, and so only results obtained for
the {100} surface are shown.
Examples of the h distribution for reflected
1
atoms following impact at an energy of 50.0 eV
and different incident angles of 65 and 75° are
shown in Fig. 5a. Examples of the h reflection
1
distribution at an incident angle of 80° and
different energies of 30.0 and 50.0 eV are shown
in Fig. 5b. The h distribution and its dependence
2
on the incident angle are shown in Fig. 6. Figs. 5
and 6 clearly indicate that the h distribution
1
peaked at a reflected angle approximately equal to
the incident angle h, while the h distribution fell
2
within a fairly narrow range between ±40°, with
a sharp peak at about 0°. These results indicate
that reflection often occurred in a near specular
manner. The reflected atoms were strongly forward
directed with small lateral spreading (no backward
scattering), consistent with a usually modest inelastic interaction with the substrate.
Examination of Fig. 5b indicates that increasing
the incident energy at a fixed incident angle shifted
the h distribution to higher angles. As the incident
1
energy of the adatom was increased, its velocity
components both normal and parallel to the surface increased. Because a larger fraction of the
energy associated with the normal velocity component was transformed during the reflection,
increasing the incident energy increased the
reflected angle. Careful analysis of the data indicated that in general, h could be described as
1
distributed in a range between h and 90°, with a
1L
peak at an angle h . Both h and h depend on
1p
1L
1P
the incident energy and the incident angle. An
incident angle and energy dependent h probability
1
density function for reflected atoms was constructed based on the values of h and h . The
1L
1p
fitted function is listed as Eq. (4) in Table 1. The
X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
65
Table 1
Best fit equations for reflection probability, and angular and energy distribution of reflected atoms
Equations
Parameters
(1) Reflection probability as a function of h at E =50.0 eV:
i
h−h l
c
,
h≥h
Y (h)=min 1, p+p sin −90.0+180.0
c
rf
h −h
m
c
h =22.0°, h =72.0°, p=0.59, and l=1.70
c
m
(2) Reflection probability as a function of E at h=80°:
i
E −E l
i
ic
,
E ≥E
Y (E )=1.0−exp −
i
ic
rf i
p
E =10.0 eV, p=25.4, and l=2.42
ic
G
C
A
CA
B DH
BD
(3) Reflection probability as a function of incident angle and
incident energy:
Y (E )
rf i
Y (E , h)=Y (h)
rf i
rf
Y (E =50 eV )
rf i
(4) h distribution of reflected atoms as a function
1
of incident angle and energy:
r(h )=p (h −h )a(90.0−h )b,
1
n 1
1L
1
where:
a=
p =normalization (integral of r equals 1) factor,
n
and b=1.62
h ≥h
1
1L
b(h −h )
1p
1L
90.0−h
1p
A
h =max 0.0, h+5.0−
1L
6.0×104
E2
i
B
A
3.2(E −40.0+|E −40.0|)
i
i
h =min 90.0, h+
1p
E −40.0+|E −40.0|+2.0
i
i
B
(5) h distribution of reflected atoms as a function of incident angle:
2
r(h )=p exp(−ch4h2 )
2
n
2
c=−1.9×10−10
(6) Energy distribution of reflected atoms as a function of incident
angle and energy:
c=1.10, E =−13.06, h =47.0, b=1.65 for the {100} and
0
0
{111} surfaces; and c=1.04, E =−12.76,
0
h =47.5, b=1.5 for the {110} surface
0
r(E )=p Ea(E −E)b
n
i
where:
a=
bE
p
E −E
i
p
G
E =max 5, (cE +E ) sin
i
0
p
C
90.0(h−h )
0
90.0−h
0
DH
66
X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
curves calculated using Eq. (4) are also included
in Fig. 5a and b.
Because the change of the velocity component
parallel to the surface is small, the reflected atoms
are expected to be strongly forward directed with
a h distribution peaking sharply at 0°. Decreasing
2
the incident angle led to a broader h distribution,
2
Fig. 6. The calculations revealed that the breadth
of the h distribution was insensitive to the incident
2
energy. With incident energy and surface type
effects ignored, the h distribution and its incident
2
angle dependence can be well described by an
exponential expression listed as Eq. (5) in Table 1.
The curves corresponding to Eq. (5) are included
in Fig. 6.
4.3. Energy distribution of reflected atoms
Fig. 5. h probability density of reflected atoms: (a) incident
1
angle effect; (b) incident energy effect.
Fig. 6. h probability density of reflected atoms.
2
The effects of incident angle and incident energy
on the energy distribution of the atoms reflected
from a {100} surface are shown in Fig. 7a and b.
The energy spectra in Fig. 7a were obtained using
a single incident energy of 50.0 eV and different
incident angles of 65 and 85°. Fig. 7a also shows
the energy loss. It indicates that the most probable
energy loss was about 10 eV at 85°, but it rose to
about 25 eV near 65°. This rise occurred because
at lower incident angles, the adatoms had higher
normal velocity components and so they penetrated into the surface more. This induced more
multiple collisions and energy transfer. The energy
spectra in Fig. 7b were obtained at a single incident
angle of 80° and different incident energies of 30.0,
40.0 and 50.0 eV. In this case the energy loss was
about 10 eV for all three different incident energies.
Because the most probable energy loss decreased
with incident angle, Fig.7 indicates that the
reflected energy increased with both incident
energy and incident angle. Similar energy distribution spectra were observed for the atoms reflected
from the {111} and {110} surfaces.
The energy spectrum of reflected atoms exhibited a peak at an incident angle and incident energy
dependent energy, E , between 0 and E . The
p
i
energy distribution of the reflected atoms was fitted
to an equation and the result is listed as Eq. (6)
in Table 1. The corresponding curves calculated
from Eq. (6) are also given in Fig. 7.
X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
67
energy and angle of the resputtered atoms at the
site of redeposition determine the extent of impact
induced (athermal and biased ) diffusion [18]. To
better understand the effects of resputtering on
thin film morphology and microstructure, it is
necessary to characterize the conditions under
which resputtering occurs, and to establish the
resputtering yield, the angular and the energy
probability density distribution of the resputtered
atoms, all as a function of the angle and energy
of the incident atom.
5.1. Resputtering yield
Fig. 7. Energy probability density of reflected atoms from the
{100} surface: (a) incident angle effect; (b) incident energy
effect.
Fig. 2b shows a resputtering event that resulted
in the emission of one atom (i.e. a resputtering
yield of unity). The resputtering yields from flat
{100}, {110} and {111} copper surfaces were calculated, and are shown in Fig. 8 as a function of
incident angle for a fixed incident energy of
50.0 eV. As discussed above, resputtering was most
significant when the incident angle was in the range
of about 30–45°. This is consistent with experimental measurements and observations of sputter
etched facets on metal surfaces which are often
about 45° to the incident direction [22]. The
resputtering yields for the {100} and {110} type
surfaces were found to be similar, but that for the
{111} surface was always lower. Fig. 8 indicates
that the peak yield from a {111} surface was about
half that of either the {100} or {110} surface.
Fig. 9 shows the calculated resputtering yield as
5. Atomic resputtering
Energetic vapor deposition processes such as
bias sputter and ion beam deposition all involve
atomic impacts with sufficient energy to cause
significant sputtering of already deposited materials. In contrast to atomic reflection, resputtering
events often occur after multiple collisions of the
adatom with the crystal and extensive energy
transfer. As a result, the resputtered atoms are
likely to possess lower energies and a broader
range of ejection angles than those of the reflected
atoms. The ejection angles determine where the
resputtered atoms are redeposited. The incident
Fig. 8. Resputtering yield as a function of incident angle at a
fixed incident energy of 50.0 eV.
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X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
Fig. 9. Resputtering yield as a function of incident energy at a
fixed incident angle of 40°.
a function of incident energy for an incident angle
of 40° (close to the maximum probability for
resputtering). A threshold energy was required for
resputtering. This threshold energy is about 17 eV
for the {100} and {110} surfaces and near 20 eV for
the {111} surface. It can be seen from Fig. 9 that
resputtering yield rapidly increased with incident
energy above the threshold value. These findings
are generally consistent with the experimental
results for low energy inert ion sputtering [21].
The existence of a high threshold energy for
resputtering is consistent with the need to transfer
sufficient energy to a surface atom for it to escape
the surface. The energy transferred to the atom to
be resputtered must therefore be sufficient to overcome its binding energy (i.e. the latent heat of
vaporization) to the surface. Molecular statics
calculations were carried out and the results indicated that the binding energies of copper atoms to
a flat {100}, {110} and {111} copper surface are
4.12, 3.79, and 4.24 eV, respectively. The higher
threshold energy and lower resputtering yield of
the {111} surface is therefore consistent with its
higher binding energy. It should be noted that in
addition to the binding energy of the surface, the
energy threshold and sputtering yield are also
dependent on the efficiency with which a single
surface atom can acquire sufficient momentum
pointing out of the surface.
Since the resputtering yield as a function of
incident angle exhibited a maximum at an incident
angle, h , a sinusoidal function was used to fit the
m
resputtering yield data. The fitted result for a fixed
incident energy of 50.0 eV is listed as Eq. (7) in
Table 2. Since Fig. 8 shows virtually no resputtering at high incident angles, a higher bound on h
is defined in Eq. (7). The calculated curves with
Eq. (7) are also displayed in Fig. 8.
Fig. 2b indicates that the bombarding atom
penetrated into the surface during a sputtering
event. The value of the resputtering yield at very
high incident energy is therefore likely to be
bounded because when the impacting atom deeply
penetrates into the solid, it transfers its energy to
the bulk atoms rather than a greater number of
near surface atoms that could then be rejected. To
a good approximation, the resputtering yield as a
function of incident energy can be represented by
a function with a near zero slope at large incident
energies. In view of this constraint, the resputtering
yield was fitted as a function of incident energy at
a fixed incident angle of 40°, and the result of this
fitting is shown as Eq. (8) in Table 2. In order for
Eq. (8) to be consistent with Eq. (7), the relation
Y (h=40°)=Y (E =50 eV ) was used for deterrs
rs i
mining the parameters. The curves defined by Eq.
(8) are also given in Fig. 9. Following the same
procedure described above, an approximate equation for the resputtering yield as a function of
both incident angle and incident energy is listed as
Eq. (9) in Table 2.
5.2. Angular distribution of resputtered atoms
The locations where the resputtered atoms
eventually redeposit can be determined from angular probability density functions for the resputtered
atoms. The MD data were therefore analyzed to
determine the (h and h ) distributions for the
1
2
resputtered atoms for various incident energies,
incident angles and surface types. To illustrate,
the h and h probability density functions are
1
2
plotted in Figs. 10 and 11 for the atoms resputtered
from the {100} surface at an incident energy of
50.0 eV and an incident angle of 30°.
Fig. 10 shows that the h angular probability
1
density for resputtered atoms peaked at a value of
~45°. The probability density was near zero at 0°
and 90°. This type of distribution can be approxi-
X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
69
Table 2
Best fit equations for resputtering yield, and angular and energy distribution of resputtered atoms
Equations
Parameters
(7) Resputtering yield as a function of h at E =50.0 eV:
i
h l
,
Y (h)=p+p sin h +(90.0−h )
0
0 h
rs
m
270.0−h 1/l
0
h≤h
m 90.0−h
0
h =40.0°, h =−57.5°, p=0.31, and l=1.61 for the {100} and
m
0
{110} surfaces; and h =35.0°, h =−54.1°, p=0.17,
m
0
and l=1.18 for the {111} surface
(8) Resputtering yield as a function of E at h=40°:
i
E l
Y (E )=p exp − f
rs i
E
i
p=1.02, E =36.0 and l=2.08 for the {100} and {110} surfaces;
f
and p=0.58, E =39.86 and l=2.35 for the {111} surface
f
A
C
B
A BD
C A BD
(9) Resputtering yield as a function of
incident angle and incident energy:
Y (E )
rs i
Y (E , h)=Y (h)
rs i
rs
Y (E =50 eV )
rs i
(10) h distribution of resputtered atoms:
1
r(h )=c exp[−l(h −45.0)2]
1
1
c=3.0×10−2 and l=3.0×10−3
(11) h distribution of resputtered atoms:
2
r(h )=r +c exp(−lh2 )
2
0
2
r =7.0×10−4, c=4.3×10−3 and l=1.0×10−4
0
(12) Energy distribution of resputtered atoms
as a function of incident energy:
E =4.92 eV, a =1.68, c=207.7, l=1.236×10−1 for
m
0
the {100} surface; E =6.88 eV, a =2.05, c=68.5,
m
0
l=9.03×10−2 for the {110} surface; and E =4.28 eV,
m
a =1.41, c=8.83, l=4.06×10−2 for the {111} surface
0
A
B
a
E
r(E )=p Ea exp −
n
E
m
where:
a=a +c exp(−lE )
0
i
mately represented by a cosine distribution of the
solid angle H, which is consistent with the sputtering experiments [27]. The data for the h angular
1
distribution were fitted to a normal distribution
function, listed as Eq. (10) in Table 2. The fitted
curve is included in Fig. 10.
During high energy bombardment, the angular
distribution of sputtered atoms is always symmetric about the surface normal because the collision
cascade is so large that many knock-on atoms are
involved and hence the ‘memory’ of the initial
impingement direction is lost [32]. However,
during the low energy impacts analyzed here, the
sputtered atoms retain some ‘memory’ of the initial
direction of the bombarding particle and the distribution becomes tilted in the forward direction. In
a three-dimensional situation, the forward tilting
is characterized by the h distribution. It can be
2
seen from Fig. 11 that for a 50.0 eV impact at an
incident angle of 30°, h distributed between −180
2
and 180°, with a probability density peak at 0°.
While the majority of the resputtered atoms were
preferentially ejected in the forward direction,
integration of the distribution curve over |h|>90°
70
X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
5.3. Energy distribution of resputtered atoms
Representative energy distribution curves for
incident energies of 40.0 eV and 50.0 eV and a
normal angle of incidence are shown in Fig. 12a–
c for the {100}, {110} and {111} surfaces. The
effect of incident energy on the average resputtered
energy is illustrated in Fig. 13 for the normal
impact on the {100} surface. It can be seen that
the energy of resputtered atoms peaked sharply at
a value, E , between 4 and 7 eV. Few atoms had
m
energies of 20 eV or above. This result is similar
to the experimental measurements of inert gas ion
induced sputtering [32]. Increasing the impact
Fig. 10. h probability density of resputtered atoms.
1
Fig. 11. h probability density of resputtered atoms.
2
indicated that about 25% were emitted back along
the direction of impact. These results are generally
in agreement with the experimental observations
[22].
For the incident energy range of significant
resputtering (i.e. 20.0–50.0 eV ), calculations indicated that the h and h distributions were not
1
2
sensitive to the surface type, the incident angle,
and the incident energy. The data in Fig. 11 were
best fitted by a normal distribution function, listed
as Eq. (11) in Table 2. The curve represented by
Eq. (11) is also shown in Fig. 11.
Fig. 12. Energy probability density of resputtered atoms: (a)
{100} surface; (b) {110} surface; (c) {111} surface.
X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
Fig. 13. Average resputtered energy as a function of incident
energy for the normal impact on the {100} surface.
energy slightly increased the average energy of
resputtered atoms, but the position of the peak
was almost unaffected. While the resputtered
energy in general increased as more energy was
deposited on the surface, it did not directly scale
with the incident energy because the ‘memory’ of
the initial impact energy was increasingly attenuated by ensuing multiple collisions. Fig. 12 also
indicates that the energy of resputtered atoms was
lowest for the {111} surface, consistent with the
highest binding energy on {111} surface. The
energy distribution of resputtered atoms was found
to be insensitive to the incident angle.
The energy distribution data of resputtered
atoms was fitted to an expression that gives the
correct value of E and the skewed response shown
m
in Fig. 12. The fitted equation is listed as Eq. (12)
in Table 2. The curves calculated by Eq. (12) are
also plotted in Fig. 12.
6. Incident energy effects on thin film morphology
and microstructure
Vapor deposition techniques such as RF diode
sputtering, bias sputtering and ion beam assisted
deposition are being developed for the physical
vapor deposition of materials. These methods provide a metal flux whose energy can be distributed
from about 0.1 eV to 100 eV [33]. The reflection
probability and resputtering yield can therefore be
71
significant for some of these deposition processes.
Under some conditions, reflection and resputtering
could significantly modify thin film microstructures
and surface morphology. The reflection and
resputtering results obtained above, together with
those for adatom induced diffusion [18], provide
a starting point for an understanding of these
energetic vapor deposition processes. For example,
the microstructures of DC diode sputter deposited
films of various metals have been reported by
Thornton as a function of substrate temperature
and background argon pressure [1]. These results
indicate that at a fixed relatively low deposition
temperature T~0.5T (where T is the absolute
m
m
melting temperature), and background argon pressure above 30 mTorr, the film microstructure is
porous, containing voids trapped between tapered
crystallites. However, the films become densely
packed fibrous grains as the argon pressure is
decreased from 30 to 3 mTorr. These fibrous grains
develop into column grains as the argon pressure
is further decreased to below 3 mTorr.
In Thornton’s copper deposition experiments,
adatoms collided with the lower energy background argon gas atoms during transportation
from target to substrate. Their energy therefore
decreased as the argon pressure increased. For a
target–substrate distance of 50 mm, direct simulation Monte Carlo calculations [34] indicated that
as the argon pressure is increased from 1 to 10
and then to 30 mTorr, the average incident energies
of deposited atoms at the substrate drop from
about 100% to 15% and then to 3% of their
energies at the target. Taking the average kinetic
energy of the atoms emitted at the target to be
about 20 eV (some atoms may have energies significantly higher) [35], the average incident energies of adatoms at the substrate are therefore
about 20, 3, and 0.6 eV for argon pressures of 1,
10 and 30 mTorr. The incident angles also become
more isotropically distributed as the pressure
increases [34].
At an incident energy of 0.6 eV, effects such as
biased diffusion, reflection and resputtering are all
negligible. However, the latent heat release and
the additional 0.6 eV of incident energy are likely
to cause a local temperature rise to more than
1000 K for about 0.5 ps [18]. This can result in
72
X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
additional surface diffusion, but is not sufficient to
reconstruct bulk vacancy defects or eliminate voids
created during earlier deposition [18]. As a result,
films deposited at 30 mTorr remained porous and
contain voids.
When the incident energy is increased to 3 eV,
the local temperature reaches 2000 K or above
[18]. This leads to significant athermal diffusion
and a much higher probability for atoms to fill in
vacant lattice sites. This is generally consistent
with two-dimensional molecular dynamics simulations of nickel deposition which indicated that the
vacancy concentration was greatly reduced when
the incident energy was increased to about 2.0 eV
[2]. As a result, vacancies and voids were reduced
by reducing the argon pressure to 10 mTorr.
At incident energies of 20 eV and above, biased
diffusion, adatom reflection and resputtering all
begin to become significant. During oblique angle
impact, adatoms can skip on the surface for a
distance in excess of 0.01 mm [18]. This is likely to
promote a more equilibrium structure because the
probability for the adatoms to find more stable
sites (e.g. the sites along the edge of a ledge) is
increased by skipping. In addition, the probability
for adatom reflection is about 10% at an incident
energy of 20 eV and an incident angle of 80°, while
the resputtering yield is about 3% at the same
energy but an incident angle of 40°. The resulting
reflection and resputtering can eliminate surface
asperities and promote flatter surface growth. As
a result, dense column structures were seen at the
lowest argon pressures or under biased deposition
conditions.
Reflection and resputtering can cause significant
surface morphology effects during deposition of
metals into trenches [6,7]. The results above indicate that reflection and resputtering are likely to
retard the formation of overhangs at trench tops
or to etch them away once they are formed. The
strongly forward directed beam reflected from the
sidewalls of the trench helps the depositing atoms
reach the bottom of the trench and hence improve
the filling. On the other hand, the slightly forward
directed beam resputtered from the trench top is
likely to be redeposited in nearby areas, promoting
the pinch-off of the overhangs and consequent
void formation inside the trench. The exact evolu-
tion of surface morphology during trench deposition depends on the degree of reflection and
resputtering, where the redeposition of the reflected
or resputtered atoms occurs, and the local surface
geometry, etc. Clearly, this is a complicated process
to predict, but the results obtained above enable
a quantitative kinetic Monte Carlo simulation of
the effects of athermal and biased diffusion, the
reflection and resputtering upon thin film microstructure and surface morphology. The kinetic
Monte Carlo study of the energy effects during
deposition on flat and featured surfaces will be
published in subsequent papers [19].
7. Conclusions
Molecular dynamics simulations of adatom
impacts during copper deposition have been used
to explore reflection and resputtering during hyperthermal vapor deposition. Empirical equations
have been obtained to describe the reflection probability, the angular and energy distribution of the
reflected atoms, the resputtering yield, and the
angular and energy distribution of the resputtered
atoms as functions of incident angle, incident
energy and surface type. The results indicate the
following.
1. Reflection only occurs when the incident energy
is above about 10 eV. Above this threshold, the
reflection probability increases with incident
energy and incident angle (up to 80°).
2. Reflected atoms are strongly forward directed,
and retain a majority of their initial incident
energy.
3. Resputtering occurs for incident energies above
about 15 eV. The resputtering yield increases
with incident energy and exhibits a peak for
intermediate angles of impact.
4. Resputtered atoms are slightly forward directed
with an energy distribution that peaks between
4 and 7 eV. The average energy of resputtered
atoms has a weak dependence upon incident
energy.
Acknowledgements
We are grateful to the Defence Advanced
Research Projects Agency (A. Tsao, Program
X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73
Manager) and the National Aeronautics and Space
Administration for support of this work through
NASA Grants NAGW1692 and NAG-1-1964.
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