Atomistic simulations of deep submicron interconnect metallization
Y. G. Yang,a) X. W. Zhou, R. A. Johnson, and H. N. G. Wadley
Department of Materials Science and Engineering, University of Virginia, Charlottesville, Virginia 22903
共Received 27 July 2001; accepted 14 January 2001兲
Damascene approaches are widely used for creating microelectronic interconnects. Successful
implementation of the process is reliant upon the deposition of a refractory metal or metal nitride
liner coating. It functions as a diffusion barrier layer to suppress transport of subsequently deposited
interconnect metals into the surrounding dielectric. The development of vapor-phase processes for
the deposition of uniform thickness liner layers has been problematic. Flux collimation and
energetic deposition approaches have been attempted with mixed results as the feature size is
decreased. Here, a modified kinetic Monte Carlo 共KMC兲 method has been used to explore the
physical vapor deposition of liner coatings. To incorporate the many effects associated with
energetic metal fluxes, the results of molecular dynamics calculations of incident atom reflection,
resputtering, surface biased diffusion, and athermal relaxations have been introduced into the KMC
algorithm. The method has been applied to investigate the effects of the incidence flux’s angular
distribution and kinetic energy upon the liner coating coverage. It has been found that trench step
coverage uniformity increases with increasing atom kinetic energy above a threshold energy value
of 20 eV. Atom resputtering/reflection are found to be the most important mechanisms responsible
for improvements in the step coverage. Sputtering of already deposited material is found to be the
most important mechanism for transporting the flux to the most difficult to coat lower sidewall
region of a trench. Energetic deposition processes that activate these mechanisms are therefore
preferred. The simulations reveal the existence of an optimal incident angular distribution to
maximize coverage uniformity. For a flux with a kinetic energy of 70 eV, a cosine angular
distribution within the collimation angle of ⫾15°–25° provided the best balance of direct and
resputtered/reflected fluxes to maximize coating uniformity. © 2002 American Vacuum Society.
关DOI: 10.1116/1.1458952兴
I. INTRODUCTION
In a damascene interconnect manufacturing process,1–3
trenches or vias are etched in a flat dielectric and a conducting metal is then placed in the cavities. The process is followed by chemical mechanical polishing to planarize the embedded conductors. This approach is dramatically different
from earlier approaches, which were based on the reactive
ion etching of blanket metal films followed by dielectric
deposition and planarization.3 The recent transition to copper
as the interconnect metal also requires the use of a thin,
conformal layer on the inner surface of the patterned dielectric to promote adhesion and facilitate nucleation and growth
of the best interconnect microstructure in addition to functioning as a barrier layer that prevents copper diffusion
through the dielectric.1,2 This layer also plays a role in inhibiting chemical reactions between the deposited metal conductor and the dielectric.2 Various barrier layer materials including titanium, titanium nitride, and various refractory
metals and compounds are used for the diffusion barrier.2
These coatings are known generically as ‘‘liner’’ films, since
their role is to conformally line the sidewalls and bottoms of
the various trenches and vias used to create the interconnect
structure. To achieve the functions above, it is critical that
the liner layer is continuous and free of pinholes. Since it is
also desirable to maximize the cross sectional area of the
a兲
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interconnect 共for current flow兲, the thinnest possible pinhole
free coating is needed. Both are achieved by a coating of
uniform thickness.
Liner films are usually deposited by sputtering—a simple,
relatively low cost physical vapor deposition 共PVD兲
process.1 At typical process pressures, PVD is a geometrical
line-of-sight deposition process. A simple view factor model
presented in the Appendix reveals that the direct flux incident
upon the interior of a trench is nonuniform. Thus thickness
nonuniformity within the trench is a significant problem.1–7
This has been particularly true for high aspect ratio structures
and as result, the development and optimization of the PVD
process is becoming correspondingly more difficult as feature widths 共but not depths兲 decrease. Additional complexity
results from the high kinetic energy of the impacting metals
in a low pressure sputtering2 or ionized PVD process.1 High
energy impacts can result in atom reflection and resputtering
共to regions out of the line of sight of a target兲 and activate
athermal modes of atom diffusion.8 –11 This has stimulated
our interest in the use of simulation techniques that can predict thin film thickness given as an input, the angular distribution of the atomic flux, its kinetic energy, and the aspect
ratio of a trench.
Many simulation approaches have been explored for this
class of problems.4 –7,12–17 They can be classified into two
types: those based upon continuum methods4 –7,12 and those
that utilize atomistic techniques.13–17 The continuum ap-
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Yang et al.: Atomistic simulations of deep submicron metallization
proaches first calculate the speed with which the material is
added to, or removed from a small region of the surface 共a
node or cell兲. This depends on the net effect of deposition,
etching 共resputtering兲, and diffusive flow on the films
surface.5 A moving front algorithm such as the string,6 shock
wave,7 or level set12 method is then used to incrementally
advance the surface. To approximate the effects of the impacting atoms kinetic energy, a simple sticking coefficient
approximation is often made. While continuum methods can
reasonably predict the topography of the growth surface during a metallization process, the method is less suited to the
analysis of individual device features that have entered the
deep submicron region where atomic reflection/resputtering
can redistribute the flux and athermal diffusion distances can
approach the dimensions of the feature.5
Most atomistic approaches applied to metallization are
based on either the SIMBAD method13 or a Monte Carlo
technique.14,15 In the SIMBAD method, the effect of thermally
activated surface diffusion is approximated by a ‘‘mobility’’
factor. The mobility factor allows a landed disk 共i.e., an atom
cluster兲 to move a specified distance once before stopping for
good. A higher deposition temperature is modeled by a
longer distance. The technique does not address the change
in mobility that accompanies changes to the atomic scale
surface roughness. The effects of an adatom’s kinetic energy
such as atom resputtering have been attempted to be incorporated by using data from experimental measurements. Often the experimental data for a specific metal under the required conditions is unavailable and approximations have to
be made to fit the materials and conditions of the case of
interest.13 This subclass of model has additional problems
when used to link film morphology to process conditions.
Since diffusion of any one of the atoms in the system is
allowed only once, the constant rearrangement of the atomic
ensemble configuration during deposition cannot be simulated, and since time is also not explicitly included, the role
of the deposition rate cannot be quantitatively analyzed nor
its tradeoff against deposition temperature. Kinetic Monte
Carlo methods that more realistically treat thermally activated atom jumps have been developed and used to investigate deposition on flat and patterned surfaces.14,15 While
these approaches do allow the role of temperature, flux incident angle distribution, and deposition rate to be reasonably
well evaluated, the role of the incident atoms kinetic energy
has until recently not been addressed. In one recent approach
molecular dynamics 共MD兲 simulations of impacts have been
followed by kinetic Monte Carlo 共KMC兲 relaxation.18 However, the great computational cost of such an approach precludes its use for the study of liner deposition where many
thousands of impacting atoms must be examined.
In an alternative to the direct MD/KMC method,18 a KMC
approach has recently been extended to energetic atom deposition by incorporating the results of off-line MD simulations
of energetic incident atom interactions with substrate
atoms.19 Reflection, resputtering, biased, and athermal diffusion were examined and their dependence upon the impact
energy and angle catalogued. A modified 共hyperthermal兲
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KMC algorithm was then developed and used to simulate the
PVD of metals on a flat surface.19 The energy incorporated
KMC method avoids the computational demanding direct
combination of KMC and MD,18 while still addressing energy dependent phenomena such as reflection and
resputtering,8 biased surface diffusion, and thermal spike induced atomic relaxation at the impact site.9 It is important to
include surface biased diffusion and athermal relaxation
since they can have significant effects upon film coverage,
especially when atomic mobility is limited by a low substrate
temperature and/or a high deposition rate. For example, surface biased diffusion was reported to be the cause of a layer
by layer 共step flow兲 growth mode at cryogenic temperature
where island growth 共and pinhole formation兲 is more usually
expected.20
Here, we briefly review the fundamentals of hyperthermal
incident atom impacts and the design of a KMC technique
for simulating atomic self assembly following a hot atoms
impact with a surface. The technique is then applied to analyze the deposition of thin metal films on the interior surface
of a trench. The technique can be used to investigate the
effect upon coating thickness uniformity of the many adjustable PVD process parameters including the substrate temperature, the deposition rate, the atomic kinetic energy, truncation of the incident metal atom angle distribution, and the
aspect ratio of the feature.
II. METHODOLOGY
To simulate the deposition of thin films from energetic
metal fluxes both impact energy and thermally activated
atomic diffusion must be addressed. When interconnect
deposition takes place under conditions that result in zone I
or zone II of the structure zone model,21 surface diffusion
dominates the evolution of the film profile. The contribution
of bulk diffusion in this regime is negligible. The first step is
to identify an appropriate surface diffusion model to track
the constant rearrangement of atoms in the simulated system.
Kinetic Monte Carlo methods appear to be the best approach
for
simulating
competing
thermally
activated
processes.14,22–24 In this approach atomic configurations
evolve by identifying and executing all available thermally
activated jumps. The likelihood that an atom jumps from one
lattice site to another depends upon its local configuration,
which can be characterized by an activation energy and/or a
jump attempt rate. The details of the simulation approach
used here can be found in Ref. 14. Briefly, it first deduces the
set of jump rates for every allowed jump path using precalculated activation energies and then executes jumps according to their relative probabilities. After a jump is executed,
time is advanced by the residence time of the system, i.e., the
reciprocal of the sum of the jump rates for all the allowed
jump paths of the system. This process is then repeated until
the time between atom arrivals is exhausted. A new atom is
then added and the algorithm iterated.
The second step is to incorporate interactions of energetic
incident atoms with the growing film. This interaction includes incident atom reflection, resputtering, biased diffu-
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Yang et al.: Atomistic simulations of deep submicron metallization
sion, and athermal rearrangement induced by the thermal
spike that arises from partitioning of the impacting atoms
velocity and heat of condensation among the lattice vibrational modes near the impact site.8,10,11 The impact energy/
angle dependence of these processes has recently been investigated by MD10,11 and their effects incorporated in a
hyperthermal KMC code. A detailed description of the impact atom energy dependent implementation can be found in
Ref. 19. The essential concept is recognition that impact energy induced processes are completed in a few picoseconds,
whereas thermally activated hopping occurs intermittently
with quiescent times in the nano- to microsecond range. In a
simulation, energy dependent mechanisms of transport can
therefore be implemented instantaneously followed by thermally activated assembly.
Briefly, the reflection and resputtering is incorporated by
first identifying the incident atom’s impact angle and kinetic
energy. The probability of either reflection, resputtering, or
both is then deduced from the results of previous 共off-line兲
MD calculations.11 The relevant atoms’ next movement direction and residual energy are also determined from results
of the same calculations. The reflected and/or resputtered
atom is then ballistically translated until it either again impinges with the surface or is removed from the system 共if no
surface is encountered兲. To incorporate biased diffusion, the
diffusion distance is first deduced from a MD simulation.10
Steps and ledges can arrest the process and so the distance to
the nearest ledge or step from the impact site is deduced. If
this is greater than the MD computed bias diffusion distance,
the MD precalculated distance is used. Otherwise, the atom
is allowed to reach the ledge or step and then arrest. The
remote atoms kinetic energy and its heat of condensation are
both partitioned among the local modes of vibration near an
atoms impact point. This rapidly heats the surface near the
impact site, allowing thermally activated jumps to occur before cooling to the quiescent background. This jumping rate
depends weakly on the background temperature and is
termed athermal diffusion.10 The athermal relaxation rate depends upon both the atoms’ acquired energy 共or equivalently
the temporary rise of temperature兲 for each atom in the
neighborhood of the impact and the activation barriers for
rearrangement near the impact site. The atom with the highest energy and the lowest energy activation barrier is taken to
have the highest probability to jump to a lower surface energy site. We characterize it by a jump probability, P i
⫽(E/Q) n , where E is the energy of an atom in the thermal
spike zone precalculated from MD simulations,10 Q is the
activation energy for a jump pathway,14 and n is an adjustment parameter that is found by fitting hyperthermal KMC
results to MD simulation. A jump is allowed when P i ⬎ P, a
jump index number also deduced from MD simulations. If an
atom has a pathway meeting the above condition, it is then
said to have a finite probability of jumping to a new place
through that path. When many atoms have a nonzero probability to jump along different paths, the jump simulation is
conducted in such a way that the probability for the jump in
the ith pathway scales with P i . Once the jump is made, P i is
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FIG. 1. Schematic geometry for deposition from an extended source over a
featured substrate used in the simulations. The trench parameters and the
placement of the flux monitors on it are also shown. Each monitor had a
length of L/10.
updated for all the paths. This procedure is then iterated until
no atoms have a finite probability to move.
Simulations have been carried out with a two-dimensional
共2D兲 lattice using periodic boundary condition applied in the
horizontal direction. The substrate had a width of 200 atoms.
The trench was set to be 100 atoms in width. The activation
barriers for atomic jumps on this surface were taken to be
those for nickel.14 The atoms were randomly introduced from
a target surface above the substrate with a 共sometimes truncated兲 cosine distribution,1 Fig. 1. When the flux was highly
collimated, the simulation was analogous to that encountered
in ionized PVD.2 The kinetic energy was assumed to be uniform within a simulation run and was varied between runs to
investigate the effect of the kinetic energy. The substrate
temperature was fixed at a 2D homologous temperature of
T/T m ⫽0.3, which corresponds to 350 K and the deposition
rate R fixed at 1.0 ␮m/min. A total of 15 000 atoms were
deposited and generally took less than 1 h on RS/6000 machines to execute. 共The execution time expects to increase
exponentially with increasing substrate temperature.兲 The
step coverage was used to characterize each run. It was defined as the relative thickness at a point on the trench surface
scaled by the thickness of the film on the top areas of the
trench2 and was recorded at three monitor positions on the
sidewall and at the center of the bottom surface, Fig. 1.
It is worth pointing out that the energy dependent phe-
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Yang et al.: Atomistic simulations of deep submicron metallization
FIG. 2. Effect of incident energy E on step coverage. The substrate temperature was 350 K (T/T m ⫽0.3), the deposition rate R was 1.0 ␮m/min, the
incidence flux had a cosine angular distribution within the collimation angle
␪ of ⫾25°. The aspect ratio of the trench was 5. 15 000 atoms were used for
the simulations. The black regions correspond to the deposited coating.
nomena 共sputtering yields, etc.兲 were obtained from threedimensional MD simulations and hence should correctly reflect the incidence flux and deposition rate. Because
metallization geometries are mostly symmetric, the growth is
simulated using a 2D model, which constrains atomic relaxations on a plane and reduces the number of diffusional
paths. However, the differences should only have minor effects on the model’s qualitative predictiveness on surface
morphological evolution.
III. SIMULATION RESULTS
The effect of atom energy upon the coverage of a trench
with an aspect ratio of 5 is shown in Fig. 2. When the energy
was 20 eV 共or less兲 关Fig. 2共a兲兴 the liner deposited on the
sidewalls had a rough columnar-like structure prone to the
formation of pinholes. The upper sidewall part of the coating
had a greater thickness than that of the lower part. The pinholes were most prevalent close to the trench bottom. Coverage on the sidewalls was improved when the energy was
increased to 40 eV 关Fig. 2共b兲兴. The surface was also
smoother on all inner surfaces and no pinholes were present.
When the energy was increased to 70 eV 关Fig. 2共c兲兴, the
coating thickness in the lower part of the trench increased to
nearly that of the mid section. The coverage on the bottom
was also thicker. This trend of coverage change with increasing atom energy has found excellent agreement with the
experiments.2
The step coverage dependence upon atom energy is summarized in Fig. 3 for each monitor position. As the energy
was increased from zero, the upper trench wall and bottom
coverage both initially decreased. Above 20 eV, step coverage at all monitor positions increased with increasing atom
energy. The step coverage at the bottom was always greater
than that on the sidewalls. The rate of increase in thickness
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FIG. 3. Effect of incident energy on step coverage.
for the bottom and the upper sidewall appear similar but are
noticeably greater than that for the mid and the lower parts.
The amount of material left at the trench top decreases
sharply with increasing atom energy above 20 eV 共Fig. 2兲.
The decrease in bottom and upper sidewall coverage as the
energy increases from 0 to 20 eV is a result of biased diffusion of material above the trench. This process transports
material into the trench throat resulting in strong shadowing.
Increasing the energy further induces sputtering of this material, which then reopens the trench throat and reduces shadowing of the trench interior. It is interesting to note that the
increase of step coverage at all inner surface locations arises
from material that, at low energy, would otherwise have assembled at the trench top to create the 共flux shadowing兲 overhang at the trench throat.
Figure 4 shows the effect of the truncating the flux incident angle distribution 共collimation兲 on the liner coating process at a fixed atom energy of 70 eV. At a 5° cutoff 关Fig.
4共a兲兴 the majority of the middle sidewalls are sparsely coated
and pinholes were present. At the lower corners, however, an
extraordinary thick coating can be seen. Since incident atoms
rarely reach this location directly and surface diffusion is not
sufficient at this deposition temperature, the extra deposit
must originate from energy induced redistribution mechanisms discussed above. This, in particular, agrees well with
the experimental observations1 and would not be possible
without including the energy effects into the KMC model. As
the width of the distribution was increased by increasing the
truncation angle to 25° 关Fig. 4共b兲兴 considerably better sidewall coverage was seen, and the amount of material deposited at the bottom of the trench was significantly decreased.
These deposition conditions are close to the best for achieving uniformity of deposition. As the distribution was allowed
to broaden by increasing the truncation angle to 45° 关Fig.
4共c兲兴, the lower sidewall coating thickness decreased while
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Yang et al.: Atomistic simulations of deep submicron metallization
FIG. 4. Effect of collimation angle ␪ on step coverage. The substrate temperature was 350 K (T/T m ⫽0.3), the deposition rate R 1.0 ␮m/min, the
incident kinetic energy E was 70 eV, and the trench aspect ratio was
5.15 000 atoms were used for the simulations. The black regions correspond
to the deposited coating.
that at the upper sidewall increased. Atom accumulation on
the upper sidewalls was consistent with the greater probability of direct atom impact near the trench top because of the
inclusion of more of the obliquely incident flux. The results
in Fig. 4 indicate the existence of an optimal incident collimation angle for the most uniform liner coating. To better
explore this, additional results were obtained and are plotted
in Fig. 5. It can be seen that the most uniform sidewall coverage occurs at a truncation angle between 15° and 25°. It is
apparent that the coverage at the bottom of the trench decreases with broadening of the incident angle distribution but
626
FIG. 6. Effect of trench aspect ratio on step coverage. The substrate temperature was 350 K (T/T m ⫽0.3), the deposition rate R was 1.0 ␮m/min, the
incidence flux had a cosine angular distribution within the collimation angle
␪ of ⫾25°, and the incident kinetic energy E was 70 eV. 15 000 atoms were
used for the simulations. The black regions correspond to the deposited
coating.
is always significantly greater than that of the sidewalls.
However, this may not be a significant issue for the manufacture of interconnects since the resulting loss of conductor
area could be compensated by a minor increase in the depth
of the trench etch.
The observations above are sensitive to the aspect ratio of
the trench. Figure 6 shows the effect of the trench aspect
ratio on coating thickness. It can be seen that at an aspect
ratio of 3 关Fig. 6共a兲兴 the coating thickness along the sidewalls
is very uniform. As the aspect ratio was increased to 5 关Fig.
6共b兲兴 and then 7 关Fig. 6共c兲兴, the coating at the lower half of
the sidewalls and on the trench bottom thinned. This thinning
was sufficient to result in pinhole formation when the aspect
ratio was increased to 7 关Fig. 6共c兲兴. The coating thickness
trends with aspect ratio are shown in Fig. 7. It can be seen
that coverage at all interior surface locations decrease monotonically with increasing aspect ratio. The most noticeable
decrease appears at the bottom of the trench. Little change in
thickness occurs at the upper sidewall, which remains in the
direct line of sight of a majority of the flux.
IV. DISCUSSION
FIG. 5. Effect of collimation angle on step coverage.
J. Vac. Sci. Technol. B, Vol. 20, No. 2, MarÕApr 2002
In a liner coating process the objective is to obtain a uniform, pinhole free layer across the full interior of the trench.
Since the upper part of the trench is closer to the vapor
source material, it is always well positioned to directly receive more of the incident atoms. Shadowing by the upper
part of the trench reduces the flux directly incident upon the
lower parts of the trench. This inevitable effect increases
with trench depth and divergence in the angular flux distri-
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Yang et al.: Atomistic simulations of deep submicron metallization
FIG. 7. Effect of trench aspect ratio on step coverage.
bution. The problem is dynamic in the sense that the buildup
of material at the trench throat increases the extent of shadowing.
Two approaches have been experimentally explored to
improve coating uniformity. One utilizes surface diffusion by
increasing the substrate temperature 共thermal reflow兲.2 The
high temperature enables diffusion over distances comparable to the trench dimensions. Different curvature of the
surface then drives mass transport. However, this strategy is
difficult to implement for liner deposition because of the use
of refractory materials which require the use of too high a
temperature.2
The second approach is to use energetic deposition in
combination with flux collimation. Ignoring the role of energetic working gas ion bombardment, we have seen that energetic incident atoms can undergo reflection and cause resputtering of previously deposited material at the impact
site.8,11 The simulations above indicate that both help to redeposit material to regions that otherwise would be shadowed. This reduces accumulation 共and shadowing兲 at the upper areas of the trench 关Figs. 2共b兲 and 2共c兲兴. As seen in Fig.
2共a兲, when the energy is low, the atoms do not trigger these
desired interactions. Instead only biased and athermal diffusion occurs and these are insufficient to avoid material accumulation at the trench throat.
The simulations indicate that the local thickness of the
liner layer is governed by the flux directly incident upon the
surface and that which is retransported by energy dependent
transport mechanisms. To more completely understand the
role of each, we have developed a simple view factor model
to predict the local flux incidence upon the interior surfaces
of the trench, while ignoring reflection, resputtering, and the
assembly mechanisms discussed above. This flux illumination model and its analysis can be found in the Appendix.
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627
FIG. 8. Effect of incident cutoff angle on step coverage. The curve was
predicted from the view factor analysis. The symbols represent simulated
data at various positions inside the trench. The simulations were done with
the substrate temperature of 350 K (T/T m ⫽0.3), deposition rate of 1.0
␮m/min, aspect ratio of 5, kinetic energy of 0 eV, and 15 000 atoms.
Figures 8 and 9 show comparisons of the flux illumination
model 共solid lines兲 and full Monte Carlo solutions for incident atom energies of 0 and 70 eV. For the low energy case
共Fig. 8兲, the retransport mechanisms discussed above are ab-
FIG. 9. Effect of cutoff angle on step coverage. The curve was predicted
from the view factor analysis. The symbols represent simulated data at various positions inside the trench. The simulations were done with the temperature of 350 K (T/T m ⫽0.3), deposition rate of 1.0 ␮m/min, aspect ratio
of 5, kinetic energy of 70 eV, and 15 000 atoms.
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Yang et al.: Atomistic simulations of deep submicron metallization
sent. The model shows that the flux incident upon the bottom
of the trench decreases rapidly as the flux cutoff angle is
increased. The decrease is particularly rapid as the cutoff
angle is increased from 10° to 30°. This is accompanied by
an increase in the flux incident upon the upper sidewall,
which increases linearly with increasing cutoff angle. The
flux incident upon the mid and the lower sidewalls both initially increase and then decrease as the cutoff angle increases. Deviations between the flux illumination model and
the Monte Carlo results are a manifestation of flux shadowing by previously deposited material. For highly divergent
fluxes this effect is large. It also has important effects for
highly collimated fluxes. The flux illumination model and
Monte Carlo model indicate that a compromise cutoff angle
of 12°–15° provides the best sidewall coverage.
Figure 8 also shows the full KMC simulation results for
an incident atom energy of 0 eV. In this, the biased diffusion
distance as well as the reflection and resputtering probabilities are close to zero since thermal diffusion results in little
transport. The results therefore show the effects of the dynamic nature of flux shadowing due to the buildup of material near the trench top. The evolving shadowing has the
most significant effect at the upper sidewall and is most important for small cutoff angles. The results indicate the need
for a flux cutoff angle of at least 12° to avoid shadowing at
the top sidewall monitor position.
Figure 9 shows a comparison between the view factor
model and KMC simulation for atoms with an energy of 70
eV. Significant differences can be seen. The KMC predicted
coverage at the bottom of the trench exceeded that of the
incident flux model for the high cutoff angle. This is shown
below to result from reflection and resputtering from the
sidewalls. A similar increase was seen at the upper walls for
small cutoff angles and also resulted from the sputtering and
reflection.
To investigate more quantitatively the role of the various
assembly mechanisms we have performed simulations in
which the mechanisms of material redistribution have been
selectively turned off. Detailed simulation results are shown
in Fig. 10 and a summary is presented in Fig. 11. Using an
energy of 70 eV and flux cutoff angle of 25°, Fig. 10共a兲
shows the configuration when all energy induced assembly
mechanisms and thermal diffusion were enabled. Adequate
coverage at both the sidewalls and at the bottom can be seen.
In Fig. 10共b兲, energy induced reflection was suppressed
while all other mechanisms remained intact. It can be seen
that the thickness at the lower part of the sidewalls and at the
bottom are noticeably thinner. This is a clear indication that
reflection helps redirect a significant fraction of the incident
atoms to the lower part of the trench bottom. The narrowing
of the trench opening 共a manifestation of material accumulation at the trench opening兲 when reflection was absent is a
graphic indication of the importance of the reflection mechanism. In Fig. 10共c兲, the sputtering was suppressed while all
other mechanisms remained intact. The lower parts of the
sidewalls are now even thinner than that of Fig. 10共b兲,
whereas the thickness at the bottom compares favorably to
J. Vac. Sci. Technol. B, Vol. 20, No. 2, MarÕApr 2002
628
FIG. 10. Contributions of each impact energy induced mechanism to step
coverage. For all four cases the substrate temperature was 350 K (T/T m
⫽0.3), the deposition rate R was 1.0 ␮m/min, the incidence collimation
angle ␪ was ⫾25°, the aspect ratio was 5.0, and the incident kinetic energy
E was 70 eV: 共a兲 all energy induced mechanisms are present, 共b兲 reflection
suppressed, 共c兲 self-resputtering suppressed, and 共d兲 both reflection and selfresputtering mechanisms suppressed.
that of the full treatment 关Fig. 10共a兲兴. Self sputtering is therefore seen to have the most significant effect upon coverage of
the lower sidewall area of the trench where undesirable pinhole formation is most likely. This discovery has been confirmed by experiments25 and illustrates the usefulness of
modeling in explaining phenomena that are otherwise elusive. In Fig. 10共d兲, both the reflection and self-resputtering
mechanisms have been turned off. The coating at the lower
FIG. 11. Contributions of each impact energy induced mechanism to step
coverage. Test mode: 共1兲 all energy induced mechanisms are present; 共2兲
reflection suppressed; 共3兲 self-resputtering suppressed; and 共4兲 both reflection and self-resputtering mechanisms suppressed.
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Yang et al.: Atomistic simulations of deep submicron metallization
sidewalls is much thinner, that at the bottom is reduced, and
the trench throat is much narrower, which contributes to a
more severe self-shadowing effect.
The results shown above have been summarized in Fig.
11. The discrete numbers on the abscissa are the test modes
in the same order presented in Fig. 10. The shaded areas in
the histograms are scaled to represent the step coverages at
the different locations. Obviously, the full treatment represented by test mode 1 is the best. Simulation approaches that
do not include the reflection and resputtering effects 共test
mode 4兲 are clearly unlikely to be adequate. Test modes 2
and 3 indicate that reflection transfers more atoms into the
trench than resputtering. However, at the lower sidewall
monitor position 共the site most vulnerable to pinhole formation兲, resputtering is the most important mechanism for improving uniformity.
The results of the KMC simulation indicate that a complex interplay occurs between the energy and incidence angle
distribution of an atomic flux and the geometry of a trench
whose interior is being coated. Uniformity in thickness at all
locations within the trench appears an elusive goal. But uniformity of the sidewalls and a thicker trench bottom coating
appears viable in the deep submicron regime. The best results are found when the incident energy is high 共within the
limit of 70 eV used in this work兲 and a flux cutoff angle of
between 15° and 25° is used.
ACKNOWLEDGMENTS
The authors are grateful to Dr. Steve Rossnagel 共IBM兲 for
helpful discussions concerning interconnect manufacturing.
The Defense Advanced Research Projects Agency 共A. Tsao
and S. Wolf, Program Managers兲, and the National Aeronautics and Space Administration supported this work through
NASA Grant Nos. NAGW1692 and NAG-1-1964.
APPENDIX: FLUX ARRIVAL DISTRIBUTION AT
TRENCH
To obtain arrival distributions of incident flux on all surfaces inside a trench, we assume no kinetic energy induced
reflection and resputtering and every atom sticks to its initial
impinging position. We further assume the incident flux to be
a cosine distribution 共it can be any other type of distribution
function兲 which may be truncated using a collimator. Figure
1 shows a sketch of a trench with an incidence distribution
truncated by ␪. Arbitrary feature width and unit are used in
the view factor analysis. Flux illumination at the top is normalized to be 1.0 and would thus be correspondingly smaller
on all other surfaces.
For flat surface like the trench top having open space
above, the net flux illumination at an arbitrary position can
be expressed as
f 共 x 兲⫽
V. CONCLUSIONS
A comprehensive energy dependent kinetic Monte Carlo
method has been developed to simulate the PVD application
of a refractory metal trench liner. Important impact energy
dependent atom–substrate interaction events, including reflection, resputtering, surface biased diffusion, and athermal
relaxation, are precalculated using a MD method and the
results formulated as analytical expressions. A modified form
of kinetic Monte Carlo modeling is then used to incorporate
these hot atom effects into an atomistic treatment of thermally activated atomic assembly.
It has been found that interior trench coverage uniformity
increases with increasing atom kinetic energy when the energy is greater than a threshold value of 20 eV. Energy induced atom resputtering is most responsible for improving
step coverage at the lower sidewall region. Reflection is responsible for a significant transport from the trench mouth
region to the interior of the feature. The simulations indicate
the existence of an optimal incident atom angle distribution
at which the incident flux onto the sidewalls and the bottom
can be balanced against that due to resputtering and reflection. For 70 eV fluxes used to coat the interior of trenches
with aspect ratios in the 5:1 range, a cosine flux truncated
between 15° and 25° results in relatively uniform sidewall
coverage. This condition leads to thicker trench bottom coverage, but this may be less of an issue since it can be easily
compensated for by increasing the depth of the trench.
JVST B - Microelectronics and Nanometer Structures
629
冕
␪
⫺␪
cos ␣ d ␣ ,
共A1兲
where cos(␣) is the distribution function and 关⫺␪, ⫹␪兴 the
incident flux range. For all trench horizontal surfaces including the trench bottom, the general expression becomes
f 共 x 兲⫽
冕
␪u
␪l
cos ␣ d ␣ ,
共A2兲
where ␪ l ⫽⫺⍀ 1 ␪ ⫺⍀ 2 •arc tan(x/H) and ␪ u ⫽⍀ 3 ␪ ⫹⍀ 4
•arc tan(L⫺x)/H; H is the height, L the width of the trench,
and x the position away from the left sidewall at the bottom
共Fig. 1兲. The range of expressions of 关 ␪ l , ␪ u 兴 are due to the
geometrical shadowing effect of the sidewalls. The coefficients ⍀ i (i⫽1 – 4) taking values of either 1 or 0 are used to
indicate if a position x is under the effect of the sidewalls or
not and have the following forms:
⍀ 1 ⫽int
⍀ 2 ⫽int
⍀ 3 ⫽int
and
⍀ 4 ⫽int
冉
冉
冉
冉
L⫺x
H•tan ␪
冊冒再 冉
冊冒再 冉
冊冒再 冉
H•tan ␪
L⫺x
冊冒再 冉
x
H•tan ␪
H•tan ␪
x
冊 冎
冊 冎
冊 冎
int
x
⫺␦ ,
H•tan ␪
int
H•tan ␪
⫺␦ ,
x
int
L⫺x
⫺␦ ,
H•tan ␪
int
冊 冎
H•tan ␪
⫺␦ ,
L⫺x
630
Yang et al.: Atomistic simulations of deep submicron metallization
where int is an integer function and ␦ a small fraction number. The position-dependent incidence illumination at the top
and the bottom of the trench upon integration of Eq. 共A2兲
becomes
冉
f 共 x 兲 ⫽sin ⍀ 1 ␪ ⫹⍀ 2 •arc tan
冉
x
H
⫹sin ⍀ 3 ␪ ⫹⍀ 4 •arc tan
冊
冊
L⫺x
.
H
共A3兲
Considering that the sidewalls are perpendicular to the
bottom, a slightly different expression for y-dependent incidence illumination along the sidewalls can be similarly obtained:
冉
f 共 y 兲 ⫽1.0⫺cos ⍀ 5 ␪ ⫹⍀ 6 •arc tan
where
⍀ 5 ⫽int
and
⍀ 6 ⫽int
冉 冊冊
L
y
,
冉
L
y•tan ␪
冊冒再 冉
L
⫺␦
y•tan ␪
冉
y•tan ␪
L
冊冒再 冉
y•tan ␪
⫺␦ .
L
int
int
共A4兲
冊 冎
冊 冎
Using Eqs. 共A3兲 and 共A4兲 the flux arrival illumination on
all trench surfaces can be obtained for the cosine distribution
共and any different distribution兲.
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