Nuclear Instruments and Methods in Physics Research B 234 (2005) 441–457
www.elsevier.com/locate/nimb
Low energy sputtering of nickel by normally
incident xenon ions
X.W. Zhou *, H.N.G. Wadley, S. Sainathan
Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Virginia,
116 Engineers Way, Charlottesville, VA 22903, USA
Received 11 June 2004; received in revised form 14 February 2005
Available online 18 April 2005
Abstract
New sputter deposition processes, such as biased target ion beam deposition, are beginning to be used to grow metallic superlattices. In these processes, sputtering of a target material at ion energies close to the threshold for the onset of
sputtering can be used to create a low energy flux of metal atoms and reflected neutrals. Using embedded atom method
potentials for fcc metals and a universal potential to describe metal interactions with the inert gas atoms used for sputtering, we have used molecular dynamics simulations to investigate the fundamental phenomena controlling the emitted
vapor atom and reflected neutral fluxes in the low energy sputtering regime. Detailed simulations of low energy, normally incident Xe+ ion sputtering of low index nickel surfaces are reported. The sputtering yield, energy and angular
distributions of sputtered atoms, together with the reflection probability, energy and angular distributions of reflected
neutrals were deduced and compared with available experimental data. The average energy of sputtered metal atoms
can be controllably reduced to 1–2 eV as the Xe+ ion energy is reduced to 50–100 eV. Normally incident Xe+ ion sputtering in this energy range results in reflected Xe energies that are narrowly distributed between 2 eV and 6 eV. These
fluxes are ideally suited for the growth of metallic multilayers.
2005 Elsevier B.V. All rights reserved.
PACS: 79.20.R; 71.15.D
Keywords: Sputtering; Molecular dynamics
1. Introduction
*
Corresponding author. Tel.: +1 434 9825672; fax: +1 434
9825677.
E-mail address: [email protected] (X.W. Zhou).
Nanoscale multilayers have many important
applications. For instance, Cr/Sc multilayers are
critical X-ray optics materials [1] that can be used
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.nimb.2005.02.016
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X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
for microscopy [2], astronomy [3], lithography [4]
and microanalysis [5]. Multilayers composed of
ferromagnetic metal layers separated either by thin
conductive metal or dielectric (tunneling barrier)
layers are giant magnetoresistive (GMR) [6–8]
and are being used for read head sensing [9,10]
and magnetic random access memory (MRAM)
[11–13]. The performance of devices utilizing these
metallic multilayers are optimized by minimization
of both the interfacial roughness and interlayer
mixing at each interface within the multilayer
stack [1,14–17].
These metallic superlattices have been grown by
a wide variety of vapor deposition techniques
[1,6,17,18]. Hyperthermal processes such as magnetron sputtering and ion beam deposition (IBD)
that utilize metal atoms with average translational
energies of several electron volts or more have
been found to produce better multilayers than
those made by molecular beam epitaxy (MBE)
where the vapor atoms have energies of around
0.1 eV [19]. Numerous efforts have sought to
experimentally optimize the IBD process for
growth of GMR multilayers [18,20,21]. The best
GMR films were obtained when the energy of
the inert gas ions used for sputtering lay between
500 eV and 700 eV. In this ion energy range, the
average kinetic energy of the atoms sputtered from
the target is close to or greater than 10 eV [22].
Atomistic simulations of multilayer growth indicate that hyperthermal atom impacts activate surface flattening mechanisms resulting in smoother
growth surfaces [23–25]. However, as the impact
energy is increased, significant interlayer mixing
by an impact induced atomic exchange (layer
alloying) mechanism begins to occur [23–25]. Reflected (inert gas) neutrals and assisting ion fluxes
have been shown to induce similar effects [26].
These simulations indicated that the best tradeoff between interfacial roughness and interlayer
mixing occurs at an atom impact energy of 2–
3 eV [24], in agreement with the experiments [17].
Atomistic simulations also indicate that further
improvements in film perfection are possible if the
atoms are modulated from a low (<1 eV) to a
higher (5–10 eV) energy during the growth of each
layer [23–25]. The use of a low energy to deposit
the first few monolayers of a new material layer reduces mixing at the interface, but at the expense of
forming high roughness. Switching to a higher energy as the layer thickness increases enables the
layer surface to be flattened without intermixing
at the now buried interface.
Implementation of the deposition concepts
identified by the simulations requires a process
where the metal and the reflected neutral atom energy can be controlled in the 1–5 eV range. The
average metal atom kinetic energy in conventional
(700–2000 eV ion energy) IBD appears to be much
higher than the ideal energy predicted by atomistic
simulations. Reducing the ion energy is expected
to decrease the average metal atom energy. However, the use of ion energies below 300 eV results
in ion beam de-focusing (which causes overspill
contamination by sputtering of the target holder
and chamber walls) and a reduction in the deposition rate due to a reduction of sputtering yield
(which results in increased contamination by residual gas species) [27]. A recently developed biased
target ion beam deposition (BTIBD) technique
has sought to extend the IBD process to a much
lower ion energy range by resolving both the overspill contamination and deposition rate problems
[28]. Preliminary studies of the growth of GMR
multilayers using BTIBD at an ion energy of
300 eV has resulted in significantly improved
GMR properties compared to identical multilayers
grown using conventional IBD with an ‘‘optimized’’ ion energy of 600 eV [27].
The ion bombardment of a metal surface creates energetic reflected (inert gas) neutrals in addition to sputtered metal atoms [29–32]. These
neutrals can potentially reach the growth surface,
altering the structure and hence the properties of
the deposited films [33]. They can also reach other
hardware, such as chamber walls, where they sputter off undesired materials that contribute to contamination. The metal and reflected neutral
fluxes created by very low ion energy bombardment of a target are not as well understood as
those of conventional sputtering, which has been
widely studied since the 1950s [34–37]. A complete
characterization of the fluxes includes the sputtering yield, reflection (inert gas neutral) probability
X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
and the energy/emission angular distributions of
both fluxes. For practical applications, such as
X-ray optics [1] and GMR devices [9], many different materials (Sc, Cr, Ta, Ni, Fe, Cu, Co, etc.) are
involved. In principle, a characterization of the
sputtering fluxes of all of these materials is required for each ion species, ion incident energy
and incident angle of practical interest. The experimental collection of this sputtering data is difficult
and prohibitively time consuming. An alternative
atomic scale simulation approach is used here to
explore the sputtering of nickel by xenon ions.
The wide availability of compatible interatomic
potentials for the many metals [23,38] and sputtering gases [39] makes the approach readily extendable to other systems of interest.
Our simulation approach extends considerably
past theoretical efforts to understand and simulate
the sputtering of metals by inert gas ion bombardment. In sputtering, the impinging ions transfer
their energy and momentum to the target atoms
upon collision. These primary knock-on target
atoms then transfer their energy and momentum
to other atoms via secondary recoils. This process
repeats until a near surface atom receives a sufficiently high, outwardly-directed impulse that it
overcomes its binding to the surface and is sputtered. A major advance in the theoretical analysis
of sputtering was made by Sigmund in the 1960s
[40]. His analytical theory assumed that sputtering
proceeded by a linear collision cascade mechanism. High speed computing subsequently enabled
linear-cascade sputtering processes to be simulated
using Monte Carlo techniques and a binary collision approximation. These frequently utilized
Monte Carlo methods include the codes MARLOWE [41] and TRIM [42,43]. They have a well
developed physical picture behind them and often
give a good representation of experimental results
[43]. However, these methods suffer from several
drawbacks. First, they need a number of ad hoc input parameters that cannot be obtained fundamentally. For instance, the results of simulations
are very sensitive to the surface binding energies
[42,43], which are poorly defined and often need
to be modified to match experimental sputtering
data [44]. Second, the simulations cannot address
443
the phenomena outside the linear-cascade regime,
such as cluster sputtering and the occurrence of
high energy density (spike) zones. The binary collision approximation has also been found to fail
at low incident energies [45,46]. Finally, these
Monte Carlo approaches are not easily extended
to alloyed or compound targets or to cases where
more complex sputtering molecules or particles
are used.
The emergence of increasingly high fidelity
interatomic potentials and computationally efficient molecular dynamics (MD) algorithms led to
a widespread interest in the use of MD methods
for investigations of sputtering [47–49]. In MD
simulations, atom positions are deduced using
NewtonÕs equation of motion where the interaction among all the atoms is treated simultaneously.
MD therefore better captures the physics of sputtering. The applicability of MD approaches to
sputtering has been limited in the past by high
computational cost arising from (a) the large computational crystal that must be used to encompass
the heat zone generated during a sputtering event,
(b) the very short time step that must be used to
correctly reflect both the lattice vibration and the
energetic particle bombardment and (c) the duration of the sputtering processes, which can be significant compared to the time step. Modern
desktop computers now enable MD simulations
to handle 5000 or more atom crystals and allow
real time simulation periods that exceed the time
duration of low ion energy sputtering events (typically <2 · 1012 s) [47].
MD has been used to simulate the sputtering
during hyperthermal (5–400 eV) Ne, Ar and Xe
atom impacts on crystalline Cu surfaces [50]. Here
we use an MD approach to simulate the sputtering
of low index ({1 1 1}, {1 1 0} and {1 0 0}) nickel
(target) surfaces by normally incident, low energy
xenon ions. The sputtering yield, the energy and
angular distributions of the sputtered nickel
atoms, together with the reflection probability,
the energy and angular distributions of the reflected xenon atoms are all quantified for xenon
ion incident energies between 50 eV and 1000 eV.
Time-resolved simulations are also used to show
mechanisms of low ion energy sputtering.
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2. Computational methods
2.1. Interatomic potentials
Realistic MD simulations require high fidelity
interatomic potentials to calculate interatomic
forces. For metal systems, especially the fcc transition metals such as nickel, the embedded atom
method (EAM) potential originally developed by
Daw and Baskes has been widely used [51]. In addition to pair potentials, EAM potentials include an
embedding energy term, which effectively incorporates the local environment dependence of atomic
interactions and allows for a realistic description
of interatomic binding near defective lattice regions, such as free surfaces and interfaces. EAM
has been shown to correctly predict the energy distribution of high ion energy sputtered atoms [52].
The standard EAM functions of nickel determined
by Foiles et al. [53] were used here for the sputtering simulations. The cut-off distance chosen for the
potentials (4.95 Å) was larger than the third neighbor spacing in nickel (4.31 Å). This ensured a realistic representation of the energetics specific to fcc
structures, including the stacking fault energy.
Sputtering occurs when atoms escape the surface by overcoming the surface binding energies.
The binding energies for the {1 1 1} Ni surface were
calculated using the EAM potential. The binding
energy for a single Ni adatom on top of the
{1 1 1} surface is about 3.3 eV. The binding energy
for a Ni atom in the {1 1 1} surface plane is about
5.4 eV. An energy barrier is associated with the
outward motion of a Ni atom in the next plane below the surface. This energy barrier is about 7.0 eV.
A pairwise universal potential [39] was used to
describe interactions between inert gas ions and
metal atoms. In the universal potential, the pair
energy (in unit eV), Eij, between two atoms i and
j, can be expressed as:
Eij ¼ 14.4
4
ZiZj X
bk exp½ck rij ðZ i0.23 þ Z j0.23 Þ;
rij k¼1
ð1Þ
where Zi and Zj are atomic numbers of species i
and j, rij is the separation distance between i and
j (in unit Å), and coefficients b1 = 0.181, b2 =
0.5099, b3 = 0.2802, b4 = 0.02817, c1 = 6.8323,
c2 = 2.0113, c3 = 0.8600, c4 = 0.4303. The
coefficients of the universal potential have been fitted to experimental data for low energy ion bombardment of solid surfaces [39] and hence well
represent the interactions between atoms of a solid
surface and inert gas atoms/ions in the vapor
phase.
2.2. Molecular dynamics model
The sputtering of three low index nickel surfaces {1 1 1}, {1 1 0} and {1 0 0} was studied, Fig.
1(a)–(c). Periodic boundary conditions were used
in the x- and z-directions and free boundary conditions were used in the y-direction. Trial runs were
carried out to determine the crystal sizes that reasonably encompassed the lattice distortion zone
caused by the highest energy ion impacts studied.
The crystal with the {1 1 1} surface has 48 (224Þ
planes in the x-direction, 20 (1 1 1) planes in the
y-direction and 28 (220Þ planes in the z-direction.
The crystal with the {1 1 0} surface has 20 (0 0 2)
planes in the x-direction, 34 ð220Þ planes in the
y-direction and 28 (2 2 0) planes in the z-direction.
The crystal with the {1 0 0} surface has 20 (2 0 0)
planes in the x-direction, 24 (0 2 0) planes in the
y-direction and 20 (0 0 2) planes in the z-direction.
To prevent ion impact induced crystal shifting,
the positions of the bottom monolayer of (gray)
atoms were fixed in the simulations. An initial substrate temperature of 300 K was assumed by
assigning the other atoms velocities based upon
the Boltzmann distribution. During a simulation,
drag forces were applied to a thin layer of (black)
atoms above the fixed region so that the temperature in this zone was kept constant at 300 K.
To initiate a simulation (of a xenon impact), the
velocity distribution among the crystal atoms was
first equilibrated by solving for the motions of all
atoms for 0.1 ps. A xenon ion with the desired kinetic energy was then injected towards the surface
from a random point in the x–z plane far above
the crystal. The initial ion velocity vector was normal to the solid crystal surface. The ensuing sputtering process was then simulated by solving for
the motions of both the xenon ion and all the
nickel atoms using the Nordsieck numerical inte-
X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
445
Fig. 1. Geometry of atomic crystals. (a) a {1 1 1} surface, (b) a {1 1 0} surface and (c) a {1 0 0} surface.
gration algorithm [54]. For vapor deposition
processes where adatom energies are only a few
electron volts, this algorithm ensures stable simulations even a numerical time step as large as 4 fs
is used. Because the bombarding ion simulated
here moves at a high speed, a smaller time step
of 0.2 fs was used to ensure a reliable numerical
integration of the high energy impacts. The beginning of an ejection was defined as the moment
when an atom or atoms that moved away from
the surface no longer interacted with other metal
atoms on the surface. Once a metal or xenon
atom ejection was detected, the ejected atom was
removed and its kinetic energy, E, and ejection
angle components, h and / (see Fig. 1) were
recorded. Our intention was to gain some understanding of the sputtering of polycrystalline surfaces. Although a specific surface (crystalÕs y
orientation) needs to be used for the simulation,
/ can be defined with respect to an in-plane direc-
tion (x 0 ) that can be randomly chosen in each impact. The results from many such simulations then
mimic a surface composed of ‘‘polycrystalline’’
grains that have the same surface normal but their
in-plane orientations are random.
Histograms of the time at which each sputtering
event occurred were first constructed by simulating
many impacts on the three Ni surfaces {1 1 1},
{1 1 0} and {1 0 0} and three incident ion energies
300, 600 and 1000 eV. We found that the majority
of sputtering events occurred between 0.4 ps and
1.2 ps. Statistical analysis indicated that less than
3.5% of sputtering events occurred more than
2 ps after ion impact. For efficient calculations reported below, each impact was therefore simulated
for about 2 ps. Once one impact was finished, another impact with the remaining Ni crystal was
then initiated after the displaced atom coordinates
were re-assigned to their equilibrium nickel lattice
sites and the temperature re-equilibrated at 300 K.
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X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
The process was repeated until sufficient sputtering
and reflection events were recorded to enable a
reasonable statistical analysis. If insufficient sputtering events occurred within 50 impacts (about
0.04 ions/Å2 fluence), the simulations were restarted with a perfect nickel crystal. This simulation approach was intended to accurately capture
the average sputtering phenomena that may occur
in experiments during the first 0.04 ions/Å2 fluence
of ion impacts. It was not designed to reveal the effect of surface topography that may significantly
change with a further increase in ion fluence.
3. Results
3.1. Nickel sputtering yield
Sputtering of the three Ni surfaces were simulated at Xe+ ion incident energies of 50–1000 eV,
with most simulations carried out in the low energy end (50–300 eV). The sputtering yield was
determined as a function of incident Xe+ ion energy. Similar data have also been experimentally
measured [55–58]. The simulated and the experimental data are compared in Fig. 2. It can be seen
that the incident ion energy dependence of the
sputtering yield obtained from simulations is close
for the three Ni surfaces and agrees well with
experimental measurements for a polycrystalline
surface [57]. Fig. 2 also indicates the existence of
Ni sputtering yield (atoms/ion)
3.0
2.5
polycrystalline surface, experiments [57]
(111) surface
2.0
(110) surface simulations
(100) surface
}
Eq. (A1)
1.5
1.0
0.5
0.0
a sputtering threshold ion energy of 25 eV, below
which no sputtering occurs.
Sigmund first derived a formula for sputtering
yield as a function of incident ion energy for the
normal ion incident angle [40]. The formula has
since been improved by numerous authors [57–
59]. With four material dependent parameters fitted to sputtering data at selected high ion energies,
the formula enables an estimate of the threshold
energy for sputtering and the sputtering yield at
other ion energies [58]. Good agreement with
experimental high ion energy sputtering data has
been reported [57,59] and the formula has been
used to tabulate sputtering yield data [57,58].
Using the standard formula [58], we fitted the four
free parameters to our simulated data and the results are shown as Eq. (A1) in Table 1 of Appendix
A. A sputtering threshold energy of 24.5 eV was
obtained from this fit, in good agreement with
experiments where a sputtering threshold ion energy of 20 eV has been reported for normal Xe+
ion incidence [60]. The curve calculated using this
empirical formula is plotted in Fig. 2. It can be
seen that this empirical formula predicts the low
incident ion energy sputtering yield data well.
Fig. 2 shows that as the ion energy is increased
from the threshold to about 200 eV, the sputtering yield rapidly rises to about 0.5. Further increases in ion energy to 1000 eV continuously
increase the sputtering yield, though the rate of increase gradually declines. It can be seen that a
reduction of the ion incident energy from
1000 eV to 100 eV results in a reduction in sputtering yield (and hence a reduction in deposition rate
for a fixed ion flux) by a factor of about 20. The
reduction is about a factor of 3 when the ion energy is reduced from 600 eV to 200 eV. The low
ion energy BTIBD processes are able to significantly increase the ion flux (compared to conventional IBD processes) and therefore compensate
for this yield drop [28].
3.2. Nickel atom energy distribution
0
200
400
600
800
1000
Xe ion incident energy (eV)
Fig. 2. Nickel sputtering yield as a function of xenon ion
incident energy.
Experiments show that the average kinetic energy of metal atoms sputtered using 600–1000 eV
incident ions [18,20,21] is in the 10 eV range [22].
This is much higher than the desired energy for
X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
Average sputtered Ni atom energy (eV)
growing metallic superlattices. The calculated average energy of the sputtered atoms from the simulation is shown in Fig. 3 as a function of ion energy (a
sufficient number of impacts was simulated so that
at least 30 sputtered events were used in the average
energy calculation even for the lowest sputtering
yield condition considered). Like the sputtering
yield data shown in Fig. 2, the average energy of
sputtered Ni atoms is insensitive to the surface
type. The standard deviation of the sputtered Ni
atom energy (averaged over all the three surfaces)
is shown as the gray bars in Fig. 3. Because a large
number of data from different surfaces is averaged,
the error bars are very small (even smaller than the
range of data of the three surfaces).
The average energy was found to increase rapidly to 6 eV as the Xe+ ion energy was increased
from the sputtering threshold (about 25 eV) to
200 eV. The rate of increase then slows as the incident ion energy is further increased and the average
energy reaches a plateau value of about 11 eV at an
ion energy of 800 eV. The observation of an energy
plateau is in good agreement with higher ion energy
experiments [61]. The average energy of sputtered
atoms versus incident energy data shown in Fig. 3
can be well fitted by an exponential function, Eq.
(A2), shown in Table 1 of Appendix A. The solid
curve plotted in Fig. 3 was calculated using this formula (the dotted line extended from the calculated
curve is used only to guide the eye).
Following an ion impact, the probability that a
sputtered atom is ejected with an energy, E, is
15.0
12.0
Eq. (A2)
9.0
6.0
(111) surface
0.0
}
(110) surface simulations
(100) surface
3.0
0
200
400
600
800
1000
Xe ion incident energy (eV)
Fig. 3. Average energy of sputtered nickel atoms as a function
of xenon ion incident energy.
447
described by a distribution function q(E). This
energy spectrum is important to characterize since
the atomic scale structure of a thin film can be affected by individual adatom impacts. Extensive
studies indicated that for high ion energy sputtering, the sputtered atom energy distribution peaked
between 1 eV and 5 eV but had a tail extending to
high energies that diminished as E2 [61–64].
Using a binary cascade model, Thompson derived
a probability distribution function of the form
[61,62,65]:
E
qðEÞ /
;
ð2Þ
3
ðE þ U Þ
where U is a surface binding energy. Eq. (2) has
since been very successfully applied [36,37,63,64].
Maximum energy of sputtered atoms should be
bounded. For instance, the energy of sputtered
atoms should not exceed the ion bombarding energy. The exact value of the upper bound energy
of sputtered atoms depends on ion bombarding
energy and surface properties. To incorporate a
reasonable energy bound Eu, Eq. (2) is truncated
at Eu by multiplying a truncating term:
"
4 #
E
E
qðEÞ /
.
ð3Þ
a 1
Eu
ðE þ U Þ
Notice that for a parameter of a = 3, Eq. (3) is
equivalent to Eq. (2) when E Eu. It decays to
zero only when E approaches Eu, effectively implementing the distribution truncation. The incident
ion bombarding energy dependence of the sputtered atom energy distribution can also be addressed using Eq. (3) by simply allowing Eu to
vary as a function of ion bombarding energy Ei.
Analysis of the energy spectrum data indicated
that the three low index surfaces had similar q(E)
distributions, and as a result, no distinction was
made for different surfaces. The surface binding
energy of Ni in the (1 1 1) Ni surface is 5.4 eV, so
we assumed U = 5.4 eV. We further used a value
of a = 3.2 to approximate closely ThompsonÕs
equation. By requiring Eq. (3) to predict the
same average energy of sputtered atoms as shown
in Fig. 3 and Eq. (A2), the function Eu(Ei)
was determined. The resultant energy distribution
is described in Eq. (A3) in Table 1 of Appendix
A, where the distribution density function is
X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
3.3. Angular distribution of sputtered nickel atoms
The operation of many nanoscale devices requires precise layer thickness control. The layer
thickness uniformity across a sample can be a limiting factor in selection of a growth process. The
(a) Empirical function and simulated data
0.1
Probability density (eV-1)
Xe+ ion energy 600 eV
0.8
0.6
Eq. (A3)
0.4
0.2
0.0
0
10
20
30
40
50
Sputtered atom energy (eV)
(b) Empirical function and simulated data in logarithm scale
0.1
Probability density (eV-1)
normalized so that its integration over the energy
space equals unity.
We compare the modified energy distribution
curve predicted by Eq. (A3) with data from simulations in Fig. 4(a) at an ion incident energy of
600 eV. Recalling that the curve was deduced from
only the average energy without a direct fitting to
the data, the agreement between the simulated
data and the curve is excellent. To more clearly
show the decay rate of the distribution density,
the data are further compared in Fig. 4(b) using
double logarithmic scales. Fig. 4(b) indicates that
for the sputtered atom energy between 8 eV and
30 eV, the distribution function is approximately
linear with energy in logarithmic scales. At the
higher energy range, the distribution density drops
quickly due to the application of the truncation
function.
The data were sparser at lower incident energies
due to the much lower sputtering yield and it became impractical to compute the energy spectrum
directly from MD simulations with available computational resources. However, the availability of
the empirical function, Eq. (A3), enables us to
examine the energy distribution density functions
at low ion incident energies. The energy distributions for ion energies of 50, 100, 300 and 600 eV
predicted by the empirical function are shown in
Fig. 4(c). It can be seen from Fig. 4(c) that the energy distribution densities at relatively high incident ion energies, such as 300 and 600 eV, are
very similar. They have a peak close to 2–3 eV
and a broad high energy tail. Because energy distribution is insensitive to ion bombarding energy,
the average energy of sputtered atoms is also
insensitive to incident ion energy. This is in agreement with the plateau region in Fig. 3. The sputtered atom energy becomes increasingly narrowly
distributed at the low energy end when the incident
ion energy is decreased to 100 eV and then to
50 eV.
Eq. (A3)
Xe+ ion energy 600 eV
0.01
0.001
1
10
100
Sputtered atom energy (eV)
(c) Effects of Xe+ ion energy
0.80
Eq. (A3)
0.70
Probability density (eV-1)
448
0.60
Xe+ ion energy 50 eV
0.50
0.40
0.30
0.20
Xe+ ion energy 100 eV
Xe+ ion energy 300 eV
0.10
0.00
0
Xe+ ion energy 600 eV
10
20
30
40
50
Sputtered atom energy (eV)
Fig. 4. Energy distribution of sputtered nickel atoms. (a)
Comparison between the empirical function and the simulated
data obtained at a 600 eV Xe+ ion energy (statistics from all
three surfaces), (b) comparison similar to that shown in (a), but
using logarithm scales and (c) effects of Xe+ ion energy
predicted by the empirical function.
deposition thickness uniformity at the substrate
is related to the angular distribution of sputtered
X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
atoms, which can be defined by h and / distributions. In general, non-uniform h and / distributions are expected during sputtering from an
anisotropic single crystalline surface. To simulate
polycrystalline surfaces, / was measured from an
in-plane direction x 0 randomly chosen for each impact. In this polycrystalline approximation scenario, the / distribution is uniform and can be
ignored.
The h distribution predicted by SigmundÕs theory has a cosine form when the sputtering ion incident direction is perpendicular to the surface [36].
However, many experimental results deviate from
this [66,67]. The simulated data obtained here are
not sufficient to separately determine the h distribution at each ion energy on each surface. Instead,
the sputtering data collected for all ion energies
and surfaces were used to construct a relative flux
density distribution for atoms sputtered within
±2.5 of an ejection angle h, Fig. 5. Using a Fourier expansion analysis, a functional form for the
angular distribution was obtained, Eq. (A4) in
Table 1 of Appendix A. The curve calculated using
this empirical function is also shown in Fig. 5. It
can be seen that the empirical function correctly
represented the simulated data. The results in
Fig. 5 indicate that a relatively high sputtering flux
density was obtained at h = 0, but the maximum
emission occurred at about h = 25. Similar results
have been observed in experiments [68]. The sputtered flux was found to quickly decrease as the
0.1
Probability density (deg.-1)
Normal Incidence
0.8
Eq. (A4)
0.4
0.2
0.0
10
20
30
40
50
60
ejection angle increased above 40. A negligible
atom flux was ejected at angles h > hmax 66.
Finally, it should be noted that the results discussed here pertain to a point source. In practical
applications, uniform ion illumination over a large
target area can be used to improve the uniformity
of the flux over a growth surface.
3.4. Xenon reflection probability
Our simulations indicated that for incident ion
energies below 150 eV, almost all of the incident
Xe+ ions were reflected within the period of the
calculation (2 ps). However, as the ion energy
was increased, the reflection probability appeared
to decrease and approached zero at the highest
simulated energy of 1000 eV. More detailed analysis indicated that as the ion energy was increased,
the reflection events increasingly occurred later
during the simulation. We extended the simulation time to 6 ps for the 1000 eV ion impacts but
still observed a zero reflection probability. The
1000 eV ions were found to deeply penetrate the
surface and were buried in the bulk of the target
and unable to dynamically escape. We note, however, that during real deposition, the target is continuously etched away and the previously buried
inert gas species are likely to be later exposed at
the surface while new impacting ions are continuously buried. These exposed inert gas atoms are
eventually released from the surface and reappear
as ‘‘reflected’’ neutrals. Dynamic equilibrium can
be reached during a long sputtering process. The
inert gas flux that leaves the surface then matches
the incoming ion flux, and the apparent reflection
probability approaches 100%.
3.5. Energy distribution of reflected xenon neutrals
0.6
0
449
70
80
90
Sputtered atom ejection angle (deg.)
Fig. 5. Angular distribution of sputtered nickel atoms (statistics from all incident energies and surfaces studied).
Using the prompt Xe reflection simulation data
(reflections that occur within the calculated time of
2 ps), the average energy of the dynamically reflected Xe atoms was calculated for the various
incident ion energies for the three low index Ni
surfaces, Fig. 6. Again at least 30 reflection events
were used to calculate the average energy. It can be
seen that the average energy of the reflected atoms
is similar for each of the Ni surfaces and is
X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
0.12
10.0
(111) surface
}
Probability density (deg.-1)
Average reflected Xe atom energy (eV)
450
(110) surface simulations
(100) surface
8.0
6.0
4.0
2.0
0.0
0
100
200
300
400
500
600
Normal Incidence
0.10
0.08
0.06
Eq. (A6)
0.04
0.02
0.00
0
5
10
15
20
25
30
Reflected atom ejection angle (deg.)
Xe+ ion incident energy (eV)
Fig. 6. Average energy of reflected xenon neutrals as a function
of xenon ion incident energy.
Fig. 8. Angular distribution of reflected xenon neutrals (statistics from all incident energies and surfaces studied).
independent of the incident ion energy. As in Fig.
3, the standard deviation of the average reflected
energy from all three surfaces is displayed as the
gray bar. Again small error bars were obtained.
For all incident ion energies, the average reflected
Xe atom energy is about 3.7 eV, Fig. 6. This is different from the reflected neutrals during oblique
incident angle impacts where their energies can approach that of the incident ions [69].
A composite (all ion energies/Ni surfaces) reflected atom energy distribution was calculated
and the result is shown in Fig. 7. The energy of
most reflected Xe atoms lies between 2 eV and
6 eV. The energy was found to be well approximated by a normal distribution, Eq. (A5) in Table
1 of Appendix A. The curve calculated by this
equation is shown in Fig. 7 and is in good agreement with the simulated data.
3.6. Angular distribution of reflected xenon neutrals
Analysis of the simulation data indicated that
the angular (h) distribution of the reflected neutrals was insensitive to the incident ion energy or
crystal surface type. A composite angular distribution result is shown in Fig. 8. Unlike the sputtered
flux, which is broadly distributed, the relative reflected flux quickly decays as the ejection angle increases. Such a distribution was well fitted by a
normal distribution density function and is listed
as Eq. (A6) in Table 1 of Appendix A. The corresponding curve is shown in Fig. 8, which matches
the simulated data well.
0.5
Probability density (eV-1)
Normal Incidence
4. Discussion
0.4
4.1. Collision mechanisms
0.3
0.2
Eq. (A5)
0.1
0.0
0.0
2.0
4.0
6.0
8
10.0
Reflected atom energy (eV)
Fig. 7. Energy distribution of reflected xenon neutrals (statistics from all incident energies and surfaces studied).
The low energy sputtering has been well
established to proceed through a single-knock-on
mechanism [34]. MD simulations enable the detailed sputtering mechanisms to be visualized.
Here we examine several representative low energy
(100 eV) impacts and their collision sequence
resulting in low energy sputtering phenomena.
During ion impacts at energies above the sputtering threshold, significant displacement of atoms
X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
Fig. 9. Examination of a 100 eV Xe+ ion impact that resulted in
sputtering.
451
occurs. To analyze the collective motion of many
atoms is not a simple task. The collision sequences
can be more clearly revealed if only a few of the
‘‘most important’’ atoms are traced. This approach
is used in Figs. 9 and 10 to examine the motion of
the incoming Xe+ ion, the reflected Xe neutral and
four Ni atoms that underwent the largest displacements during the collision. To view the collision
processes inside the bulk of the crystals, a part of
the Ni crystal was removed. In Figs. 9 and 10, the
silver Ni atoms are at their lattice sites prior to
the impact, the trajectories of the incoming Xe+
ion (black), the reflecting Xe neutral (red) and the
four traced Ni atoms ‘‘a’’ (blue), ‘‘b’’ (green), ‘‘c’’
(yellow) and ‘‘d’’ (cyan) are shown by their time-resolved positions at a 0.03 ps time interval.
Fig. 9 shows the common sputtering mechanism
observed in the low energy (100 eV) sputtering
simulations. Upon impact, atom ‘‘d’’ (cyan) was
Fig. 10. Examination of four additional 100 eV Xe+ ion impacts that did not result in sputtering. (a) Impact 2, (b) impact 3, (c) impact
4 and (d) impact 5.
452
X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
first displaced. Because off-center, many-body collisions had been involved before energy was transferred to the cyan atom, the momentum acquired
by the cyan atom had been significantly redirected
from that of the incident ion so that it had a large
component directed out of the surface. The cyan
atom then collided with the overlying atom ‘‘c’’
(yellow), which in turn collided with the overlying
atom ‘‘a’’ (blue) at the surface. This blue atom acquired sufficient energy to overcome its surface
binding energy and was sputtered. In this case, it
retained a kinetic energy of 3.25 eV after fully
escaping the surface. It should be noted that because only the four Ni atoms that underwent the
largest displacements are traced, the collision sequences shown in the figure do not necessarily include all the atoms involved. We also point out
that although the low energy sputtering predominantly occurred through a sequential collision
mechanism, the energy and momentum transfer
deviated from the binary collision approximation
due to the strong many-body character of the collisions at the low impact energies.
Fig. 10(a)–(d) show four low energy impacts
where no sputtering occurred. The sputteringenabling sequential collision series similar to that
described above also occurred in many of these
cases. In Fig. 10(a), for example, the incident
ion ! yellow ! green atom collision series and
the incident ion ! blue atom collision series occurred. During these collisions, the green and blue
atoms respectively acquired a momentum with a
large component pointing out of the surface. Both
atoms attempted to escape from the surface. However, the energies they acquired were not sufficient
to overcome the binding energy (3–6 eV) of the
surface. As a result, they both fell back after traveled a short distance across the surface. Similarly,
the green and blue atoms in Fig. 10(b) and the
cyan atom in Fig. 10(c) all attempted to escape
during the collision series but failed due to their
insufficient energies.
Fig. 10(a)–(d) can be used to understand why
sputtering did not occur in some of the impacts.
In Fig. 10(a), the impact ion was able to transfer
energy to the cyan atom deep below the surface
without causing significant displacement of atoms
above. This is likely to occur when the collision is
along a hard atomic row. Because energy was
deposited deep inside the crystal, the probability
for surface atoms to acquire sufficient energy for
the sputtering was reduced. In addition, the impact
also initiated multiple (double) sequential collision
series. Although each series is potentially sputterenabling, the probability for any one series to result in a sputtering was reduced due to the splitting
of energy among these series. The doubling
sequential collision series also occurred in Fig.
10(b). In Fig. 10(c), the blue atom transferred a
momentum to the cyan atom in a direction nearly
parallel to the surface. Because only the momentum component normal to the surface enables
the atom to escape, the cyan atom was not sputtered. Finally, Fig. 10(d) is a typical example
where the incident momentum was not converted
to a direction pointing out of the surface. As a result, the collision was transferred toward the bulk
of the crystal rather than cause the sputtering.
The observations above agree well with the single-knock-on sputtering mechanism [34]. They account for the dependence of sputtering yield and
energy distribution of sputtered atoms on the
incident ion energy seen in Figs. 2–4. During an
incident ion impact, numerous binary collision
sequences are induced. Each sequence can potentially result in sputtering by transferring the energy
and rotating the direction of the momentum. The
energy and momentum that are eventually transferred to the surface atom statistically vary from
each collision sequence. At the threshold energy
(
25 eV) of sputtering, the incoming momentum
can be rotated sufficiently and energy transferred
to a surface atom can narrowly surpass its surface
binding energy (
5.4 eV). But this requires highest
momentum and energy transfer efficiency, which in
turn requires the collision sequence to occur along
few precise routes. As a result, the events are statistically rare, and a low sputtering yield is obtained.
Because almost all energies acquired by the surface
atoms are used to overcome the surface binding
energies, the energies of sputtered atoms are narrowly distributed in a low energy range. When
the incident ion energy is increased from the
threshold energy to, say, 100 eV, the energy deposited in the top few surface layers linearly increases
because the incident ion only penetrates the top
X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
With the energy deposited in the surface region
saturated, the sputtering yield, the average energy
of sputtered atoms and the peak distribution of energy all approach to near constants.
In all the cases shown in Figs. 9 and 10, the incident ion only penetrated the top surface layer (2
{2 2 0} layers were counted as 1 {1 1 0} layer) before being reflected. This is significantly different
from sputtering at higher energies, where we found
the impacting ion deeply penetrated the surface
(e.g. more than seven layers below the surface at
600 eV).
surface layer. As a result, more binary collision sequences that result in sputtering are activated, and
the sputtering yield linearly increases. Some of
these collision sequences are more efficient in
transferring energy, resulting in high energies of
sputtered atoms. Some of these are less efficient,
resulting in relatively low energies of sputtered
atoms. Most of the routes are intermediately efficient, resulting in a peak distribution at an intermediate energy for the sputtered atoms. In this
ion energy regime, the average energy of sputtered
atoms almost linearly increases with ion energy.
When the incident ion energy is further increased
to a high energy range, say, between 600 and
1000 eV, the penetration of the incident ion into
the bulk starts to increase with incident ion energy.
As a result, the energy deposited into the surface
region becomes less sensitive to the incident ion energy because any increase in ion energy is virtually
deposited into a deeper region below the surface.
4.2. Origins of sputtered atoms
MD simulations allow the origin of the sputtered
atoms to be revealed. The relative probabilities for
atom sputtering from each of the top four monolayers of the {1 1 1}, {1 1 0} and {1 0 0} Ni surfaces
were calculated and are shown in Fig. 11(a)–(c),
Distance below surface (Å)
0.00
2.03
4.06
6.09
Relative probability of sputtering
Relative probability of sputtering
Distance below surface (Å)
1.0
EXe = 300 eV
EXe = 600 eV
0.8
0.6
0.4
0.2
0.0
1
2
3
453
4
0.00
1.24
2.49
3.73
1.0
EXe = 300 eV
EXe = 600 eV
0.8
0.6
0.4
0.2
0.0
1
2
3
4
Number of planes below surface
Number of planes below surface
(b) {110} surface
(a) {111} surface
Relative probability of sputtering
Distance below surface (Å)
1.0
0.00
1.76
3.52
5.28
EXe = 300 eV
EXe = 600 eV
0.8
0.6
0.4
0.2
0.0
1
2
3
4
Number of planes below surface
(c) {100} surface
Fig. 11. Depth origin of sputtered nickel atoms. (a) {1 1 1} surface, (b) {1 1 0} surface and (c) {1 0 0} surface.
454
X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
respectively. In each of the figures, data obtained
from a relatively low (300 eV) and a relatively high
(600 eV) incident ion energy are compared. Fig. 11
indicates that for the {1 1 1} and {1 0 0} surfaces, all
the sputtered atoms came from the top two surface
monolayers, while for the {1 1 0} surface, all the
sputtered atoms came from the top two monolayers
at 300 eV ion energy. However, when the ion energy
was increased to 600 eV, atoms from the top four
monolayers were sputtered from the {1 1 0} surface.
Increasing the ion energy therefore resulted in sputtering of more deeply buried atoms. In all cases, the
sputtered atoms resided near the free surface. In the
case of the {1 1 0} surface, the spacing between adjacent {2 2 0} layers is appreciably smaller (1.24 Å)
than that between either {1 1 1} or {2 0 0} layers
(2.03 and 1.76 Å, respectively). As a result, even
the fourth {2 2 0} layer below the surface is still very
close (
4 Å) to the surface. These results are similar
to those found in other studies [70,71].
Fig. 11 clearly indicates that the probability for
atoms to be sputtered decreases sharply as their
distance from the surface is increased. This phenomenon is seen to become more obvious as the
ion incident energy is decreased. It also suggests
that the sputtering more easily occurs when a surface atom receives a momentum in a direction
pointing out of the surface. Although it is possible
for a large momentum pointing out of the surface
to be transferred to an atom below the surface, a
high energy is required for that atom to first penetrate the overlying layer of atoms through lattice
interstices and then to retain enough energy for the
escape. This becomes increasingly likely as the incident ion energy is increased. As a result, the probability for a subsurface atom to be sputtered is
increased by increasing the incident ion energy.
of sputtered atoms, as well as reflection probability, average energy, energy and angular distributions of reflected neutrals, were all quantified
as general incident ion energy dependent empirical equations. The following results have been
obtained:
• Similar sputtering yields were observed for the
three low index Ni surfaces studied. As the incident Xe+ ion energy was decreased from 600 eV
to 100 eV, the sputtering yield was found to
decrease by about a factor of 10.
• In conventional sputtering techniques using an
incident ion energy in excess of 600 eV, the
average energy of sputtered atoms is above
10 eV. The use of low incident ion energies in
the range between 100 eV and 200 eV enabled
the average energy of sputtered atoms to be
reduced to 2–5 eV.
• Unlike relatively high energy (300 eV or above)
sputtering where the energy distribution of
sputtered atoms peaks at a near constant 3 eV
with a long tail extending to a high energy
range, an energy distribution that is narrowly
distributed at a low energy range was obtained
when the ion incident energy was reduced to
below 100 eV.
• The angular distribution of sputtered atoms
deviated from cosine distribution. The peak
sputtering flux was shifted to an ejection angle
of 25.
• The energy of reflected neutrals was narrowly
focused about an average energy of 3.7 eV for
incident ion energies from 50 eV to 1000 eV
and the most probable reflection angle was normal to the surface.
• Sputtering was mainly caused by the sequential
collision processes at low incident ion energies.
5. Conclusions
Acknowledgments
MD simulations have been used to study the
low energy (50–1000 eV) normal incident Xe+ ion
sputtering on low index Ni surfaces. The study focused on the low energy end (50–300 eV) exploited
by new deposition technologies, such as biased target ion beam deposition. The sputtering yield,
average energy, energy and angular distributions
We are grateful to the Defense Advanced
Research Projects Agency and Office of Naval
Research (C. Schwartz and J. Christodoulou, Program Managers) for support of this work through
grant N00014-03-C-0288. We also thank S.A.
Wolf for numerous helpful discussions.
X.W. Zhou et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 441–457
455
Appendix A
See Table 1.
Table 1
Equations characterizing sputtered Ni and reflected Xe atoms
Eq. no.
Equations
(A1)
Sputtering yield Y(Ei) (atom/ion) as a function of incident ion energy Ei (eV) (standard function [58] with
parameters Q = 0.51, Us = 3.12 eV, W = 1.33 and s = 4.1 derived in the present work):
qffiffiffiffi4:1
pffiffiffi
0:1889 Ei lnð0:1372105 Ei þ2:718Þ 1
Eth
Ei
;
3=2
Y ¼ ð1þ0:7443102 pffiffiffi
Ei 0:2343105 Ei þ0:1106107 Ei Þð1þ0:4464105 E0:3
i Þ
0;
(A2)
Ei > Eth
Ei 6 Eth
where the threshold energy for sputtering Eth = 24.4782 eV
Average energy E (eV) as a function of incident ion energy, Ei (eV):
E ¼ 10:89½1 expð0:8703 103 E1:27
Þ
i
(A3)
Normalized probability density q(E) (eV1) of sputtered Ni atoms with energy E (eV) and its dependence
on incident ion energy Ei (eV):
"
4 #
cE
E
1
q¼
;
Eu
ðE þ 5:4Þ3:2
where
Þ
Eu ¼ 49:5158½1 expð1:0829 104 E1:5536
i
and c is a normalization factor such that
Z Eu
cE
dE ¼ 1
ðE þ U Þa
0
(A4)
(A5)
Normalized probability density q(h) (deg1) of sputtered Ni atoms whose flux was measured at the ejection angle h (deg):
0:0111 þ 0:0121 cosð2hÞ 0:0022 cosð4hÞ 0:0040 cosð6hÞ; h < hmax
q¼
0;
h P hmax
where the approximate maximum ejection angle hmax = 65.96 deg
Normalized probability density q(E) (eV1) of reflected Xe neutrals with energy E (eV):
q ¼ 0:484 exp½0:735ðE 3:71Þ2 (A6)
Normalized probability density q(h) (deg1) of reflected Xe neutrals whose flux was
measured at the ejection angle h (deg):
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