JOURNAL OF APPLIED PHYSICS
VOLUME 88, NUMBER 10
15 NOVEMBER 2000
Low energy ion assisted control of interfacial structure: Ion fluence effects
X. W. Zhoua) and H. N. G. Wadley
Department of Materials Science and Engineering, School of Engineering and Applied Science,
University of Virginia, Charlottesville, Virginia 22903
共Received 21 June 2000; accepted for publication 15 August 2000兲
Multilayered thin films consisting of high electrical conductivity copper layers sandwiched between
pairs of low coercivity ferromagnetic alloys can exhibit giant magnetoresistance. The magnitude of
the magnetoresistance increases with the structural and chemical perfection of the interfaces. Recent
atomistic modeling and experimental observations have shown that nickel and cobalt atoms in the
ferromagnetic layer readily exchange with underlying copper atoms during the deposition of the
ferromagnetic layer upon the copper spacer. This results in mixing at the ferromagnetic metal on
copper interface. Low energy 共1–20 eV兲 inert gas ions can be used during deposition to flatten the
surface of layers, in some cases without causing interlayer mixing. Here we use the molecular
dynamics simulation method to investigate the effects of the assisting ion fluence upon the surface
roughness and interlayer mixing of a model Ni/Cu/Ni multilayer system. The results reveal that the
surface roughness initially drops rapidly with ion fluence and then approaches a limiting roughness
that is dependent upon the surface type, the ion energy, and the ion mass. For a Cu on Ni surface
irradiated by 2.0 eV Xe⫹ ions, the flattening transition occurs at a fluence of about 0.2 ions/Å2
共corresponding to an ion to metal deposition flux ratio of about 5兲. The same transition was seen at
a similar fluence for a Ni on Cu surface, but at a higher Xe⫹ ion energy of 14.0 eV. Threshold
energies for flattening and mixing were identified for various surfaces. The probabilities of both
flattening and mixing were found to increase with ion fluence and ion energy. Because the threshold
energy for mixing was lower than that for smoothing, significant interfacial mixing was only seen
during ion assisted flattening of the Ni on Cu interface. Simple models have been developed to
establish the functional dependence of interfacial structural parameters upon the assisting ion
fluence. © 2000 American Institute of Physics. 关S0021-8979共00兲06022-9兴
I. INTRODUCTION
magnetic field, and increasing the thermal stability. These
performance parameters depend upon the material system
and the conditions used for growth. The best magnetoresistive performance for a particular material system is achieved
when the interfacial roughness and the interlayer chemical
mixing are minimized during growth by vapor
deposition.11,12
Interfacial roughness in multilayers grown under kinetically limited diffusion conditions is determined by the surface roughness of each layer at the start of the next layer’s
overgrowth. This is controlled by a combination of thermodynamic and kinetic factors. A simple thermodynamic argument 共Fig. 1兲 can be used to analyze the growth of an A/B/A
multilayer 共where B is deposited on A and vice versa兲. In Fig.
1共a兲, B atoms completely wet an A surface. This requires that
the A and B surface energies, ␥ A and ␥ B , as well as the B/A
interface energy ␥ AB satisfy the relation: ␥ B ⫹ ␥ AB ⬍ ␥ A . In
the absence of kinetic constraints, atoms of B will then attach
to ledges and epitaxially cover the A surface. However, under this condition, A atoms cannot completely wet a B surface since ␥ A ⫹ ␥ AB ⬎ ␥ B ⫹2 ␥ AB ⬎ ␥ B . As Fig. 1共b兲 indicates, this promotes stable islands of A on a B surface
because a nonzero angle ␪ can be defined from
Magnetic metal multilayers are the basis for several new
magnetoelectronic devices.1 For instance, films composed of
thin 共⬃60 Å兲 ferromagnetic metals 共such as Ni80Fe20 or Co兲
sandwiching a thin 共⬃20 Å兲 electrically conductive 共e.g.,
Cu兲 metal layer can exhibit a large change in electrical resistance when a magnetic field is applied.2–5 This giant magnetoresistive 共GMR兲 effect results from a change in electron
spin dependent electron scattering due to a shift in the alignment of the magnetic moment of one of the magnetic
layers.6–8 The effect can be sensed when a small electrical
current is propagated either in the plane 共CIP兲 or perpendicular to the plane 共CPP兲 of the multilayers.1 A few repeats of
the basic sandwich structure are used in CIP GMR multilayers to create spin valves.9 These structures have been used to
build a new generation of read heads for magnetic hard
drives, which is responsible for much of the recent increase
in hard drive capacity.1,9,10 Several groups are attempting to
use many repeats of the sandwich structure in a CPP architecture as a potential route to the creation of nonvolatile
magnetic random access memory.1 The performance of either device is improved by increasing the GMR ratio 共defined as the maximum resistance change divided by the resistance at magnetic saturation兲, lowering the saturation
cos共 ␪ 兲 ⫽
a兲
This thermodynamic argument can also be understood atom-
Author to whom correspondence should be addressed.
0021-8979/2000/88(10)/5737/7/$17.00
␥ B ⫺ ␥ AB
2 ␥ AB
⬍1⫺
⬍1.
␥A
␥A
5737
© 2000 American Institute of Physics
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J. Appl. Phys., Vol. 88, No. 10, 15 November 2000
FIG. 1. Growth modes at the interfaces between strongly bound A and a
weakly bound B atoms. In 共a兲 step flow growth of B is promoted. It results
in the lowest surface energy configuration. In 共b兲 the strong bonds between
the A atoms encourage the growth of A islands and formation of a rougher
surface.
istically. For the case discussed in Fig. 1, the bond energy
between A – A atoms is higher than that between B – B atoms
because bond energy scales with surface energy. If A and B
atoms are of the same size, then B wets A because the more
strongly bound A atoms can pull B atoms onto their surface
关Fig. 1共a兲兴. This promotes B layer growth by step flow across
the surface, and the development of a smooth B surface.
However, A will not then wet B because it is energetically
unfavorable for the relatively weakly bound B atoms to break
the strongly bound A clusters 关Fig. 1共b兲兴.
The analyses above indicate that during the deposition of
A/B/A multilayers with little kinetic constraints, only one of
the layers can nucleate and grow by the step flow growth
mechanism. As a result, the potential for an asymmetric interfacial roughness always exists in nanoscale multilayered
systems, especially when the surface energy difference is
large. Significant stress driven surface roughness can also
occur in systems where there is an atomic size difference,
even when bond strength considerations favor step flow
growth. Increasing the opportunity for atomic reassembly toward equilibrium by raising the substrate temperature or decreasing the deposition rate cannot then improve the smoothness of both the A on B and B on A interfaces in nanoscale
multilayers. Such a strategy has not enhanced the performance of vapor deposited GMR films.13,14
However, the use of hyperthermal adatoms can reduce
the roughness of the A on B surface by breaking A – A bonds
in the A islands and providing an opportunity for the A atoms
to attach to the B surface. This is not the thermodynamically
favored condition, but when this is done under thermally
constrained diffusion conditions, the resulting A – B bonds do
not break to reform islands of A. This appears to be one
reason why some energetic sputter deposition processes14–17
have produced better GMR films than those grown by molecular beam epitaxy where the atoms have low energies during impact with surface.18
Sputter deposition experiments have indicated that both
the interfacial roughness and the interlayer mixing are sensitive to the adatom energy used for the deposition.14–17 The
X. W. Zhou and H. N. G. Wadley
lowest interfacial roughness and intermixing usually occur at
an intermediate atom impact energy in the 1–3 eV range.
Atomistic simulations have revealed the fundamental mechanisms of these incident energy effects.19 They indicated that
increasing the incident energy reduced surface roughness because the energetic adatom impacts break strongly bound
surface asperities, resulting in local nonequilibrium flat configurations. However, high incident atom energy also promotes interlayer mixing by an atomic exchange mechanism.
These atomistic simulations have enabled an effective exploration of many deposition conditions that have not been addressed experimentally, including adatom incident angle and
substrate rotation.20 The work has led to a proposal for the
use of a modulated energy deposition strategy to improve
both roughness and mixing during GMR multilayer
deposition.19,20 Simulations indicated that multilayers with
flat interfaces and almost no intermixing could be grown
over a wide range of incident angles if a low energy 共⬃0.1
eV兲 was used to deposit the first few monolayers of each new
material layer and a higher energy 共⬃5 eV兲 was used for the
completion of that layer. These novel growth strategies may
be particularly important for the growth of CPP
multilayers.21 In these systems several hundred layers are
deposited to create a device with an easily measured resistance. However, because surface roughness increases with
the number of layers, it is essential to seek processes that
reduce the surface roughness without causing interlayer mixing.
Ion assistance provides a second approach to controlling
the interfaces of nanoscale multilayered systems. In this approach energetic inert gas ion impacts are used to break
atomic scale clusters and to smooth a surface grown under
conditions where thermal diffusion is limited. Atomistic
simulations22,23 have again been used to explore the effects
of inert gas ion assistance during multilayer deposition. The
results indicated that low energy 共⬍20 eV兲 ion impacts can
effectively reduce the surface roughness, and provided the
energy is sufficiently low, no mixing would occur. They also
indicated the existence of two threshold energies above
which there exists a high probability of either smoothing or
mixing. Obviously, the extent of the smoothing or the intermixing is likely to depend upon the ion fluence.
Here, a molecular dynamics simulation approach has
been used to investigate the effects of ion fluence on surface
smoothing and interfacial intermixing. To bypass complexities associated with the variable surface roughness of each
layer during a simulation of vapor deposition, we examine
the effects of individual ion impacts with a model rough
surface using the methodology developed in Ref. 23. For
consistent comparisons with the previous work,23 we analyze
model Ni/Cu/Ni multilayers with a 共111兲 surface.
II. COMPUTATION METHOD
The molecular dynamics model for simulating the effects of inert gas ion impacts during multilayer deposition
has been described in an earlier article.23 Examples of the
computational crystals prior to the impacts are shown as
parts 共a兲 in Figs. 2 and 3. Cu and Ni crystals containing
J. Appl. Phys., Vol. 88, No. 10, 15 November 2000
X. W. Zhou and H. N. G. Wadley
5739
TABLE I. Threshold energy 共eV兲 of flattening for various surfaces and
ions.a
Material system
Impact ion
Ar⫹
Xe⫹
a
Cu on Cu
Cu on Ni
Ni on Cu
Ni on Ni
4
3
2
1
14
12
8
6
See Ref. 23.
72(224̄) planes in the x direction, eight 共111兲 planes in the y
FIG. 2. Evolution of Cu islands on Ni surface as a function of ion fluence
during 2 eV normal angle ion impacts.
direction, and 42(22̄0) planes in the z direction were generated at the equilibrium lattice sites to represent a previously
deposited layer. Arrays of either Cu or Ni pyramids were
then created on top of these crystals to simulate a defined
rough surface. The four possible materials scenarios corresponding to Cu on Cu, Cu on Ni, Ni on Cu, and Ni on Ni
were all considered. To minimize the effects of small crystal
size, periodic boundary conditions were used in the x and z
directions and a fixed boundary condition was used for the
two monolayers of atoms at the bottom y surface. This effectively extended the crystal scales both in the lateral and in
the vertical dimensions. By using a temperature control algorithm, the three monolayers of atoms above the fixed region were kept at a fixed substrate temperature of 300
K.19,20,22,23 Inert gas ions with a given incident energy E
were injected at a normal incident angle to the top y surface
from random locations far above. A Cu–Ni alloy embedded
atom method potential developed by Foiles24 was used to
calculate the force between metal atoms and a universal pair
potential25 was used to define the interaction between inert
gas ions and metal atoms. The surface reconstruction following ion impacts was determined by solving the trajectories of
both the metal atoms and the impacting ions using Newton’s
equations of motion. To enable the system to relax between
ion impacts, a low ion injection frequency of 2 ions/ps was
used. Surface structures were analyzed at different ion fluences.
III. EFFECTS OF ION FLUENCE ON SURFACE
ROUGHNESS
A. Atomic configurations
FIG. 3. Evolution of Ni islands on Cu surface as a function of ion fluence
during 14 eV normal angle ion impacts.
For the four surfaces 共i.e., Cu on Cu, Cu on Ni, Ni on
Cu, and Ni on Ni兲, simulations were carried out for both Ar⫹
and Xe⫹ ion impacts at various ion energies from 0.1 to 20
eV. The threshold energies for the flattening of these four
surface have been determined,23 and are tabulated in Table I.
The atomic configurations at different ion fluences were analyzed. Selected atomic configurations for the Cu on Ni and
the Ni on Cu surfaces are shown in Figs. 2 and 3 as a function of Ar⫹ and Xe⫹ ion fluences. The results for the Cu on
Ni surface shown in Fig. 2 were obtained at an ion energy of
2 eV, while the results for the Ni on Cu surface shown in
Fig. 3 were obtained at a much higher ion energy of 14 eV.
This is because the threshold energy for flattening of rough
Ni surfaces is much higher than that for flattening of rough
Cu surfaces 共Table I兲. Figures 2 and 3 clearly show that the
extent of the flattening due to the ion assistance depended
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J. Appl. Phys., Vol. 88, No. 10, 15 November 2000
X. W. Zhou and H. N. G. Wadley
FIG. 4. Cu on Cu surface roughness as a function of ion fluence.
FIG. 6. Ni on Cu surface roughness as a function of ion fluence.
upon ion fluence 共or ion metal flux ratio during deposition兲.
The surface roughness generally decreased as the ion fluence
increased. Xe⫹ ion impacts produced a more significant flattening effect at a given ion fluence.
energy above the threshold energy is quite similar for different cases. The 1 eV Ar⫹ ion impacts with the Ni on Ni
surface shown in Fig. 7 indicates that when the ion energy
was below the threshold energy of flattening, the surface
roughness remained at unity regardless of the ion fluence.
For ion energies above the threshold, the surface roughness
was seen to decrease with ion fluence and ion energy. It
appeared that most of the surface roughness reduction was
achieved as the ion fluence was increased to between 0.2 and
0.3 ions/Å2; the roughness reduction with further fluence increase became relatively minor. At sufficiently high ion energies, the surface roughness approached zero with increasing ion fluence. Examination of Figs. 4–7 shows that at a
given ion energy and ion fluence, Xe⫹ ion impacts resulted
in a lower roughness for all the surfaces.
B. Functional dependence
The surface roughness of the crystals studied here can be
quantified by the fraction of atoms remaining above the first
共bottom兲 monolayer of the islands.23 This normalized surface
roughness value was calculated as a function of ion fluence
at several selected ion energies for both Ar⫹ and Xe⫹ ion
impacts. The results for the Cu on Cu, Cu on Ni, Ni on Cu,
and Ni on Ni systems are shown in Figs. 4–7 using filled and
unfilled squares and circles 共the curves in these figures were
obtained using a continuum model described below兲. Results
using higher ion energies are shown for the Ni islands. This
choice complied with the threshold energies for the flattening
of the different surfaces 共Table I兲. Figures 4–7 indicate that
while impacts with different surfaces by different ions were
associated with different threshold ion energies of flattening,
the surface roughness dependence upon the ion fluence at an
FIG. 5. Cu on Ni surface roughness as a function of ion fluence.
IV. EFFECTS OF ION FLUENCE ON INTERLAYER
MIXING
A. Atomic configurations
Figure 2 indicates that at a low ion energy of 2 eV, no
mixing of the Cu island atoms with the underlying Ni atoms
FIG. 7. Ni on Ni surface roughness as a function of ion fluence.
J. Appl. Phys., Vol. 88, No. 10, 15 November 2000
X. W. Zhou and H. N. G. Wadley
TABLE II. Threshold energy 共eV兲 of mixing for various surfaces and ions.a
Material system
Impact ion
⫹
Ar
Xe⫹
a
Cu on Cu
Cu on Ni
Ni on Cu
Ni on Ni
9
5
15
10
9
5
15
10
See Ref. 23.
occurred at any fluence during either the Ar⫹ or Xe⫹ ion
impacts. The earlier study23 identified a material and ion specific threshold energy for mixing. These threshold energies
are tabulated in Table II for different surfaces. It can be seen
from Table II that in fact, no mixing occurs for the Cu on Ni
surface until the ion energy is above 10 eV. However, Fig. 3
indicates that at the 14 eV ion energy necessary to flatten the
Ni on Cu surface, significant mixing between the surface Ni
atoms and the underlying Cu atoms occurred. The degree of
mixing was higher for Xe⫹ ion impacts than for Ar⫹ ion
impacts, and increased with ion fluence. These are all consistent with Table II that the threshold energy for mixing on
the Ni on Cu surface is 9 eV for Ar⫹ ion impacts and 5 eV
for Xe⫹ ion impacts.
B. Functional dependence
The extent of mixing can be quantified by the probability
of atomic exchange during the ion impacts. Since the ion
energy required for surface flattening exceeded the threshold
energy of mixing only for the Ni on Cu surface, the mixing
probability of surface atoms on this surface was calculated.
The calculated data points at some selected ion energies for
both Ar⫹ and Xe⫹ ion impacts are displayed in Fig. 8 as a
function of ion fluence using filled and unfilled squares and
circles 共the curves were again obtained from a continuum
model described below兲. It can be seen that mixing increased
almost linearly with ion fluence. At a relatively low ion energy of 6 eV, both Ar⫹ and Xe⫹ impacts caused little mix-
5741
ing. At a higher energy of 14 eV, significant mixing occurred. At this energy Xe⫹ ions caused much more mixing
than Ar⫹ ions.
V. DISCUSSION
Figures 4–8 indicate that the surface type, the ion species, and the ion energy all affect the functional dependence
of the normalized surface roughness R and mixing M upon
the ion fluence F. An increasingly higher ion energy is required to flatten the Cu on Ni, the Cu on Cu, the Ni on Ni,
and the Ni on Cu surfaces. By studying the energy contour
over facets of various pyramids on the fcc surfaces and examining the trajectories of adatoms deposited on these facets
using molecular dynamics, Halstead and DePristo have
found that the surface morphology during growth is predominantly determined by the ratio of the diatomic binding
energy to the bulk cohesive energy of the depositing
species.26 Our work on the assisting ion energy effects indicated that the threshold ion energy of flattening decreased as
ion mass was increased or the 共net兲 energy change associated
with the ‘‘rough to flat’’ cluster transition was decreased.23
More significant mixing was observed when the surface atoms were strongly bound 共e.g., Ni兲 and the underlying atoms
were weakly bound 共e.g., Cu兲 than vice versa.23
To evaluate the contributions of different atomic mechanisms to the results of Figs. 4–8, simple models were developed to predict surface roughness and mixing parameter as a
function of ion fluence. To simplify the calculation of surface flattening, it was assumed that a nonplanar atom in a
given surface asperity would become a planar atom during
an ion impact when it is within a flattening distance r 0 from
the impact site. The flattening distance r 0 is dependent upon
the ion energy. For example, r 0 ⫽0 at an ion energy below
the threshold energy of flattening because even a head-on
collision will not cause the flattening. In general, r 0 increases
as ion energy is increased. Suppose that the ion fluence during a short time interval t to t⫹dt is dF, then the probability
for a particular nonplanar atom to be flattened scales with
dF• ␲ r 20 . Because the surface roughness is essentially the
fraction of the nonplanar atoms, then the change of surface
roughness dR caused by dF during random ion irradiation
can be written as the fraction of flattened atoms
dR⫽⫺R ␲ r 20 dF.
共1兲
Integration of Eq. 共1兲 yields a dependence of the roughness
upon ion fluence
R⫽exp共 ⫺ ␲ r 20 F 兲 .
FIG. 8. Mixing of Ni on Cu surface as a function of ion fluence.
共2兲
Equation 共2兲 can be used for constant energy ion impacts
where island configurations remain constant. Figures 2 and 3
indicate that islands generally grow during ion irradiation.
As the surface islands became bigger, the threshold energy of
flattening increased. As a result, an ion energy can be above
the threshold energy of flattening at the start of ion impacts,
but can fall below it when the size of all the islands exceed a
critical value S. To develop a simplified model to account for
this, it was assumed that all surface asperities can be divided
into two types: type one with size below S, and type two with
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J. Appl. Phys., Vol. 88, No. 10, 15 November 2000
X. W. Zhou and H. N. G. Wadley
size above S. Type one asperities can be flattened, and their
average flattening distance is assumed to be r 0 . Type two
asperities cannot be flattened. The overall surface roughness
can then be expressed as R⫽R 1 ⫹R 2 , where R 1 and R 2 correspond to the fractions of nonplanar atoms in type one and
type two surface asperities, respectively. By accounting for
the conversion of asperities from type one to type two during
ion impacts, the change of R 1 and R 2 , dR 1 and dR 2 , due to
a change of ion fluence dF can be approximated as
dR 1 ⫽⫺R 1 ␲ r 20 dF⫺dR 2
共3兲
dR 2 ⫽ ␯ R 1 dF,
共4兲
where ␯ is an ion energy dependent parameter accounting for
the rate at which the conversion occurs. The solutions of
Eqs. 共3兲 and 共4兲 were combined to give
␲ r 20
␯
R⫽ 2
⫹
•exp关 ⫺ 共 ␲ r 20 ⫹ ␯ 兲 •F 兴 .
␲ r 0 ⫹ ␯ ␲ r 20 ⫹ ␯
共5兲
If R s ⫽ ␯ /( ␲ r 20 ⫹ ␯ ) is used to represent the saturation surface
roughness at a large ion fluence, and ␯ 0 is used to represent
the ratio ␯ /R s , then Eq. 共5兲 becomes
R⫽R s ⫹ 共 1⫺R s 兲 •exp关 ⫺ ␯ 0 F 兴 .
共6兲
The two parameters R s and ␯ 0 in Eq. 共6兲 are both dependent
upon ion energy E. Physically R⬅R s ⬅1 if E is very small,
and when E becomes very large, R s drops to zero and the
saturation is achieved at a small F. This indicates that R s
⫽1 and ␯ 0 equals 0 when E⫽0, and R s ⫽0, and ␯ 0 becomes
large when E is large. Hence, R s and ␯ 0 can be fitted, respectively, to
R s⫽
exp共 ⫺ ␣ E 兲
1⫹ ␤ E n
␯ 0⫽ ␥ E m.
共7兲
共8兲
Equations 共7兲 and 共8兲 define five parameters ␣, ␤, n, ␥, and
m. By fitting to the energy dependent saturation surface
roughness data reported earlier,23 ␣, ␤, and n can be obtained. Here only ␥ and m are left to be determined. From
Figs. 4–7, we assumed that the surface roughness is approximately saturated at the ion fluence of 0.5. With this as a
condition, we only used additional surface roughness data at
F⫽0.2 to calculate both ␥ and m. The values of ␣, ␤, n, ␥,
and m are listed in Table III for various surfaces and ion
species. The surface roughness as a function of ion fluence is
then calculated using Eq. 共6兲, and the results are shown as
lines in Figs. 4–7. It can be seen that the model captures well
the effects of ion fluence on surface roughness.
Table I indicates that the energy required to collapse a
surface asperity depends on the type of the surface. The relatively strongly bound Ni islands have higher threshold flattening energies than the relatively weakly bound Cu islands.
The same islands have a slightly higher threshold flattening
energies when the underlying crystal is weakly bound Cu
than strongly bound Ni. These account for the observation in
Figs. 4–7 that the surfaces in the sequence of increasing ion
energy for their flattening are Cu on Ni, Cu on Cu, Ni on Ni,
and Ni on Cu.
TABLE III. ␣, ␤, n, ␥, and m for different surfaces and ions.
Impact ion
␣
Ar⫹
Xe⫹
0.00
0.24
Ar⫹
Xe⫹
0.16
0.96
Ar⫹
Xe⫹
0.00
0.00
Ar⫹
Xe⫹
0.00
0.18
␤
n
Cu on Cu system
0.39
2.02
1.07
2.90
Cu on Ni system
0.01
9.64
51.70
12.78
Ni on Ni system
0.02
3.18
0.29
2.89
Ni on Cu system
7.2⫻10⫺2
1.60
8.2⫻10⫺4
3.13
␥
m
6.71
5.24
6.7⫻10⫺2
0.60
3.50
8.05
1.65
1.31
3.57
4.54
0.44
0.39
4.49
0.85
0.21
1.15
When the ion energy is below the threshold flattening
energy of smallest surface asperity, no flattening occurs and
the roughness remains at 1 at various ion fluence 共Fig. 7兲. If
the ion energy is higher than the threshold energy of the
largest asperities, surface roughness continuously decreases
with continuous ion impacts and eventually approaches zero
at a very large ion fluence 共Figs. 4 and 5兲. Because the probability for ions to impact surface asperities decreases as the
asperity density drops, the ion fluence dependence of roughness also decreases with ion fluence. All the curves shown in
Figs. 4–7 roughly reached the saturation roughness at an ion
fluence between 0.2 and 0.3 ions/Å2. This characteristic ion
fluence value is of practical importance. It is determined by
the statistics of random ion impact sites. For the present extreme case where all the 120 deposited metal atoms formed
the pyramids, this ion fluence corresponded roughly to an ion
to metal flux ratio of 5. In general, it will depend upon the
propensity for roughing, which in turn depends upon material system, substrate temperature, and metal atoms flux.
Nonetheless, it is clear that rough surfaces can be flattened
using an appropriate low energy ion fluence.
To explore the effects of ion fluence upon mixing parameter at the Ni on Cu surface, we considered a surface
monolayer that contains N Ni Ni atoms and N Cu Cu atoms,
and has a total area of S. If the total number of atoms on this
monolayer is N 0 (⫽N Ni⫹N Cu), then the number of ions impacting with Ni atoms during an ion fluence of dF can be
approximated by
dN⫽
N Ni0共 1⫺M 兲
N Ni
•SdF⫽
•SdF,
N0
N0
共9兲
where N Ni0 is number of Ni surface atoms before ion impacts, and the mixing parameter M can be viewed as the
fraction of exchanged 共mixed Ni兲 atoms. Each ion impacting
a Ni atom has a probability p for the exchange between the
Ni atom and an underlying Cu atom. Obviously, p increases
as ion energy is increased. The change of mixing dM due to
dF, can then be approximated by
dM ⫽p•
dN
共 1⫺M 兲
⫽ p•
•SdF.
N Ni0
N0
共10兲
Integration of Eq. 共10兲 yields an expression for the mixing
parameter:
J. Appl. Phys., Vol. 88, No. 10, 15 November 2000
X. W. Zhou and H. N. G. Wadley
TABLE IV. ␦ and ⑀ for the Ni on Cu surface and different ions.
Impact ion
⫹
Ar
Xe⫹
␦
␧
0.27
0.44
28.64
17.42
M ⫽1⫺exp共 ⫺uF 兲 ,
subsequent exchange probability. The mixing probability
was much higher when the underlying crystal was Cu rather
than Ni.
Heavier Xe⫹ ions produced more smoothing and mixing
because of their more efficient momentum transfer to the
metal atoms per impact.
共11兲
where u⫽(p/N 0 )•S. Because p is small when E is below a
threshold value and p can be assumed to be unity when E is
large, u is well fitted by
u⫽
S
exp关 ␦ 共 E⫺ ⑀ 兲兴
•
.
1⫹exp关 ␦ 共 E⫺ ⑀ 兲兴 N 0
5743
共12兲
For the crystals used here, S⫽2.86⫻103 Å 2 , and N 0 ⫽504.
Equation 共12兲 involves only two unknown parameters ␦ and
⑀. By fitting to the ion energy dependent mixing parameter
data,23 the values of ␦ and ⑀ were obtained and are listed in
Table IV. Using these data, the mixing parameter was calculated as a function of ion fluence for Ar⫹ and Xe⫹ ion impacts with the Ni on Cu surface, and the results are shown in
Fig. 8. It can be seen that the continuum calculations resulted
in good agreement with those obtained with full molecular
dynamics simulations. Table II indicates that the heavier
Xe⫹ ions have a lower threshold energy for mixing than Ar⫹
ions. The results here indicated that at a given ion energy,
Xe⫹ ions caused much higher degrees of mixing at various
ion fluences, especially when the ion energy is high.
VI. CONCLUSIONS
Molecular dynamics simulations of the Ar⫹ and Xe⫹ ion
impacts with various rough surfaces formed during the Ni/
Cu/Ni multilayer growth indicated that:
At low ion energies, surface roughness was independent
of ion fluence. At high ion energies, the surface roughness
decreased with ion fluence and approached zero.
For ion energies below 20 eV, most of the flattening was
achieved when the ion fluence had reached 0.2 ions/Å2. This
corresponded to an ion to metal flux ratio of 5.
The flattening dependence upon ion fluence was determined by the probability of ion impact with surface asperities and the threshold energies for breaking asperities. The
threshold energy increased in going from Cu on Ni, Cu on
Cu, Ni on Ni, to Ni on Cu surfaces.
The ion fluence dependence of mixing between surface
B atoms and underlying A atoms was mainly dependent upon
the probability of ion impact with surface B atoms and the
ACKNOWLEDGMENTS
The authors are grateful to the Defense Advanced Research Projects Agency 共A. Tsao and S. Wolf, Program Managers兲 and the National Aeronautics and Space Administration for support of this work through NASA Grant Nos.
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