Surface Science 409 (1998) 501–511
The effect of electrical current (DC ) on gold thin films
M. Aguilar 1 *, A.I. Oliva, P. Quintana 2
Centro de Investigación y de Estudios Avanzados del EPN-Unidad Mérida, Departamento de Fisica Aplicada,
Apartado Postal 73-Cordemex, 97310 Yucatán, Mexico
Received 13 February 1997; accepted for publication 17 March 1998
Abstract
We studied changes induced by electrical current (DC ) on gold thin films by using a combination of scanning tunnelling
microscopy and grazing incidence X-ray diffraction. The results show that the process inducing device failure is based on surface
diffusion that produces the growth of microcrystals at the expense of mechanically strained microcrystals. The de-percolation and
loss of adherence to the substrate reduce the heat transfer which in turn produce an increase of film temperature. This temperature
increase induces a large mechanical stress due to the differential dilatation of substrate and film. The result of these processes is the
final failure of current conduction by the film. © 1998 Published by Elsevier Science B.V. All rights reserved.
Keywords: Au; Electromigration; STM; Thin films; XRD
1. Introduction
Very-large-scale-integration ( VLSI ) electronic
devices include metallic interconnections mainly
made of aluminium, copper, gold and Al–Cu
alloys. The electrotransport or electromigration
( EM ) in metallic interconnections produces
damage so large that it is known to be one of the
main causes of the failure of VLSI electronic
devices [1–3]. Thus, EM has vast technological
implications in the semiconductor industry. The
movement of the atoms by the friction force
exerted by the ‘‘electron wind’’ is the predominant
effect that accounts for the electrotransport in bulk
* Corresponding author. E-mail: [email protected]
1 On sabbatical leave from: Instituto Ciencia de Materiales
(C.S.I.C.), Campus Universidad Autónoma, 28049 Madrid,
Spain.
2 On leave from: Faculty of Chemistry, Universidad Nacional
Autónoma de México, México, D.F.
conductors. This movement causes voids and final
failure. In particular, the importance of surface
and stress [4] as well as the sizes and orientation
of grains on electrotransport in thin films are a
matter of research and discussion. Moreover, the
‘‘short-circuit’’ paths – as grain boundaries in
polycrystalline thin films – have not been clarified.
Most of the EM studies have concentrated on
measuring very small variations of the electrical
resistance or the electrical noise, comparing those
variations with theory and hypothesising structural
changes. However, the above mentioned factors
affecting EM are operatives on very small length
scales. Thus, microscopy is the most suited technique to understand the structural changes that
occur in EM. Pioneering studies by microscopy of
the EM process were made in the 60’s using
transmission electron microscopy ( TEM ) [5] and
scanning electron microscopy (SEM ) [6 ]. The
SEM technique is today well established and offers
0039-6028/98/$19.00 © 1998 Published by Elsevier Science B.V. All rights reserved.
PII: S0 0 39 - 6 0 28 ( 98 ) 0 02 8 2 -9
502
M. Aguilar et al. / Surface Science 409 (1998) 501–511
both large-scale and microscopic imaging with a
resolution down to about 10 nm.
The scanning tunnelling microscope (STM ) was
invented by Binnig and Rohrer [7] in the early
1980s. STM has become an important instrument
in surface science laboratories due to its capability
to obtain atomic resolution. There are several
reviews on the state of the art in STM [8,9]. The
strongest point of STM when compared with
electron microscopes is the capability of direct
three-dimensional measurements, whereas conventional microscopes are mostly dependent on twodimensional measurements. Thus, STM gives the
opportunity of imaging the surfaces with a resolution down to 0.2 nm and gives the unique possibility of three-dimensional imaging that allows one
to obtain quantitative height profiles. Also, STM
surpasses electron microscopy in resolution in
depth (height) direction, measurement accuracy,
quantification and the capability to operate in
different environments (air, vacuum, liquid). All
of these capabilities made the STM ideal for EM
studies and, in particular, to study the early stages
of EM. Thus, in 1993 the STM technique was used
for the first time to study EM. In fact, three STM
studies of EM at medium current densities
(104–106 A/cm2) in silver thin films [10,11] and
gold wires [12] were published. Those studies show
that changes in surface morphology caused by EM
can be quantitatively and qualitatively described
from the STM images. In particular, hillock
growth, void formation [12], current induced faceting and current aligned grain growth [10] were
described. However, no further works on EM by
STM have been published since then.
Although aluminium and Al alloys are the most
widely used materials for interconnections, they
have the problem of the fast oxidation process
that avoids the use of surface science techniques
and, in particular, that of STM. Thus, to try to
understand electromigration processes in metals
we have selected gold because of its resistance to
oxidation and the high quality of STM images.
However, gold film is not the best option to
undertake EM studies. In fact, it is well known
that in gold films large scale movement of atoms
occurs because of the large rate of surface diffusion
of gold atoms at room temperature, especially
under ambient conditions. Because of this fact, we
studied the stability and dynamic phenomena in
our films previously to the present work [13].
The aim of this paper is to present a procedure
to study changes induced by electrical current on
thin films by using a combination of scanning
tunnelling microscopy (STM ) and grazing incidence X-ray diffraction [14]. This combination of
techniques could yield a better understanding of
the very first steps of the electromigration process
and gives an indication of the processes that induce
the device failure. In fact, we were able to observe
electromigration induced changes in time intervals
at least 1000 times smaller than the most sensitive
technique proposed as damage indicator based on
the measurement of 1/f noise [15]. Moreover, the
results show the process that induces the final
device failure.
2. Experimental
2.1. Sample preparation
The material used for thin films’ preparation
was high-purity (99.999%) gold splatters (from
CERAC, G-1065) and the films were grown using
7059 Corning glass as a substrate. Atomic force
microscopy (AFM ) measurements of the substrate
shown an average rms-roughness of 35 Å over
surfaces of 1 mm2. The glass substrate was maintained at constant temperature (30°C ) during
sample preparation.
It is well known that gold on glass presents
structural instabilities and has large surface corrugation, in particular when grown with the substrate
at room temperature. We selected this kind of
sample because we thought that the small modifications due to electromigration will be amplified
by those instabilities and large corrugation, making
it easier to detect changes that otherwise would be
impossible to detect in good quality films (flat
surface, no strain). This assumption proved to
be correct.
Samples were prepared by free evaporation in
a conventional vacuum evaporation system
( Edwards E 306) with an oil-diffusion pump and
M. Aguilar et al. / Surface Science 409 (1998) 501–511
a liquid nitrogen trap. The chamber pressure
during evaporation was about 10−6 Torr.
The temperature of the Au source was maintained constant at 1170°C during sample preparation. The distance between substrate and source
was 4 cm. The time for film growth was 2 min,
film area was about 1 cm2 and the film thickness
3–4 mm, that is, the average growth rate was about
300 Å/s. This value is comparable with the VLSI
interconnects that have a typical thickness of about
1 mm. VLSI interconnects have widths that are
measured in microns, whereas our samples have
widths in the millimetre range. The reason for this
is the necessity to have large areas for X-ray
studies.
After preparation, the films were kept in the
chamber at vacuum for about 100 min. This was
done to ensure the film temperature uniformity so
that no thermal stress would appear when removed
from the chamber.
As usual in EM studies, the gold films were not
subsequently annealed to eliminate the intrinsic
stress because the intrinsic elastic stresses in the
film were homogeneous. Therefore, they would
not lead to gradients that would be relaxed by
material transport. This is the usual assumption in
EM studies. We will see later that this point is a
matter of discussion.
2.2. Experimental set-up
Topographic images were obtained with Park
Scientific AFM/STM, model Autoprobe CP, using
the high-resolution scanner (maximum scan length
of 5 mm). STM topographic images were obtained
in the constant current mode of operation. Tunnel
current was 0.5 nA, whereas the bias voltage
between the tip and the sample was 100 mV (tip
positive). The scan speed was 1 Hz and the image
resolution 256×256 pixels, that is, an image was
obtained in about 4 min. All the measurements
reported in this paper were obtained in air at room
temperature and atmospheric pressure.
The degree of crystallinity of the films was
studied with a SIEMENS D-5000 X-ray diffractometer with a grazing incidence geometry [14]
and Cu monochromatic radiation l=1.5418 Å
(tube voltage and current were 40 kV and 35 mA,
503
respectively). For experimental purposes, the
diffraction maxima were registered with a step size
of 0.03° and a step time of 6 s with an aperture
slit of 0.05 mm at different incidence angles. The
Diffrac AT software was used to process the gold
reflections.
To make a current flow through the sample, two
electrodes were attached to the sample by means
of silver paint and a constant voltage was applied
with a regulated HP power supply (DC source).
The value of the current was either 1 or 0.1 A.
The current density for the 1 A case was
0.25×104 A/cm2, i.e. smaller than usual in
electronic applications (at least 400 times smaller).
Thus, we were using much smaller current densities
in our experiments than usual in metallic interconnections and lower than in the previously mentioned studies of EM by STM [10–12] where they
were in the 104–106 A/cm2 range.
3. Results and discussion
Fig. 1 shows a typical 1×1 mm2 scan of the
surface of a gold film in a three-dimensional view.
The surface of the gold films grown by evaporation
on glass is very rough (a mountain-like landscape)
[16–18]. Fig. 1 shows that the surface is formed
by the typical granular structure with mountainlike structures on the surface. The height and
lateral extensions of these structures have values
Fig. 1. Aspect of the surface of a gold film recently prepared.
It is formed by very rough grains.
504
M. Aguilar et al. / Surface Science 409 (1998) 501–511
that are statistically distributed. The origin is the
growth of islands that spreads until a liquid-like
coalescence happens. This liquid-like coalescence
of gold on glass is a well-known phenomenon
[17,18]. The consequence is a weak correlation
between surface structures, i.e. a wide-ranging
statistical distribution of the surface irregularities
that produce a fractal surface. We have made a
fractal analysis of the surface by frequency methods [19] and we have obtained that, in fact, the
surface is fractal with D about 2.05. In our case,
the average grain size is about 0.1 mm (1000 Å)
diameter, whereas the average height is 60 Å (from
the lowest points around the grain). It is also clear
that the grains have an important roughness.
Surface rearrangements that can change the
appearance and topography – and, in particular,
the roughness – can occur with time after film
preparation. In fact, the stability of the gold thin
film surface is a matter of discussion [20–22]. For
this reason, we previously made a study of the
dynamic phenomena occurring in the surface of
our samples when the current is not flowing
through the film. The results are reported elsewhere
[13], but we have to remember here that we found
that surface roughness decreases exponentially
with time up to a limiting value that is reached in
a matter of a few hours. Thus, the EM studies
were always made several hours after sample preparation. In these conditions, the tunnelling current
and the images were very stable.
A DC bias was applied so that an 1 A current
is flowing through the film. The current density
was about 0.25×104 A/cm2. Because the current
density was small, a few days would be required
to observe damage [4]. This implied a small
electrotransport value. We thought that this low
current might not produce any observable phenomena taking into account the results of the STM
study on gold wires [12]. In fact, in the case of
the wires, no appreciable change in surface morphology was observed until a current density of
5×106 A/cm2 was applied. However, as a result
of the applied current, we observed by STM a
large movement of matter in the film surface that
resulted in a strong rearrangement and modification of all the surface structures in a matter of
minutes.
In particular, we observed by STM two different
effects: (i) a strong drift both in the horizontal
and vertical directions, that was a result of the
sample heating by the Joule effect; and (ii) a large
movement of matter in the film surface that produced a strong rearrangement and modification of
all the surface structures in a matter of minutes.
From the thermal movement, we calculated the
temperature increase of the film using the thermal
expansion coefficient of gold. This kind of estimation had a very large error, since it depends on the
relative position of the STM tip and the actual
thermal expansion coefficient of the film. However,
it can give an estimation of the order of magnitude.
We observed that when 1 A current (current density of 0.25×104 A/cm2) is applied for 1 min, it
produces a thermal shift in the surface structures
of 0.74 mm, as shown in Fig. 2. Since the coefficient
for thermal linear expansion of glass is about
3.2×10−6/°C and for gold is a=14.2×10−6/°C
(at 25°C ), then only the expansion of gold film is
applicable. Thus, from DL=L aDT we obtain that
o
DT will be about 5°C. We confirm this value by
measuring the increase of film temperature by
using a small mass thermocouple. Although this
kind of measurement has also a large error, we
can give an upper limit for the temperature increase
of 10°C. This result is consistent with the study
of Ag thin film with a current density of
5×104 A/cm2 where the temperature increase was
4°C [11] and in Au wires where the temperature
increase was about 70°C for a current density of
5×106 A/cm2 [12]. We obtained a similar increase
of temperature than in silver film with a current
density about 20 times smaller. The reason for this
is probably the poor adherence of gold to glass
that decreases the heat transmission to the
substrate.
The driving force F resulting from thermal
t
gradients VT in a sample at temperature T is
described [23] by the equation
VT
F =−Q*
,
t
T
where Q* is the heat of transport and equals the
energy flow per unit mass transported minus the
intrinsic heat of solution. Experimental values for
M. Aguilar et al. / Surface Science 409 (1998) 501–511
505
Fig. 2. Thermal drift due to the current flowing through the film: (a) surface before current is applied; (b) after 1 min of current flow
j=0.25×104 A/cm2). The white arrows mark a given surface structure that has shifted the relative position in the image due to
thermal dilatation of the film. Image size 2×2 mm.
Q* in the literature are inconsistent for most
metals, but we can be sure that it should be lower
than 0.1 eV and that VT will be in our case
certainly lower than 0.1 K/min. Thus, F will be
t
lower than 0.03 eV/m.
We can now compare with the electromigration
force. EM is due to the electrical driving force and
it is usually described by the expression
F =Z*eE=Z*erj,
em
where E is the electrostatic field, r is the resistivity
of the metal, j is the local current density and Z*
is the effective charge number [2]. Substituting in
this equation the resistivity of gold (2.35 mV-cm)
and giving an approximate value for Z* of −8 [2]
we obtain that, for a current density of
0.25×104 A/cm2, F will be about 3 eV/m. That
em
is about 100 times larger than the driving forces
resulting from thermal gradients. In other words,
in our experiments, driving forces are predominantly of electrical nature. As final argument, in
the previous studies by STM of electromigration,
where the current density is larger than in our
case, the thermal effects were ruled out.
The energy necessary to increase the temperature
this amount (5°C ) can be estimated from the
equation
DQ=mC DT=rVC DT,
p
p
where r is the gold density (19.32 g/cm3), C the
p
gold heat capacity (0.031 cal/g°C ) and V the film
volume. The result is DQ=4.089×10−3 J. Since
this energy is applied to the film in a time of 60 s,
then the power will be 6.8×10−5 W.
On the other hand, we can estimate the resistance of the gold film from the gold resistivity
and the film shape. The result obtained is
R=5.8×10−3 V. Since the electric power is
W=I 2R, then W=5.8×10−3 W, i.e. about 100
times larger than the power estimated from the
thermal drift.
The difference in estimated powers probably has
three different causes: (i) power lost by thermal
conductivity to the substrate (its temperature
increases a few degrees) and also by radiation and
convection; (ii) the error in the determination of
the current density and/or the dilatation; (iii) the
error in using the thermal linear expansion coefficients, heat capacity and density of gold for the
thin films. Most of the electrical power is lost
because of the large surface/volume ratio in the
thin film and the relatively large contact area with
the substrate. In fact, it is well known that most
of the heat is dissipated to the substrate: that is
why thin films can withstand such high current
densities. The result obtained is very important
when a comparison is made with the actual connections used in VLSI devices. In these cases, the
surface/volume ratio is much smaller than in our
case and then larger temperature increases will
happen because the power loss will be smaller.
506
M. Aguilar et al. / Surface Science 409 (1998) 501–511
Thus, in the migration process an additional
component should be taken into account: the stress
field produced by the different thermal expansion
coefficients of the film and the substrate
(14×10−6/°C and 3.2×10−6/°C, respectively). In
fact, during the heating of the film by Joule effect,
most of the power is dissipated by thermal conduction to the substrate. The differential expansion of
film and substrate will produce a bending of the
film that will yield a stress gradient that could
produce important movements of matter. The
stress is probably insignificant at 0.1 A because we
have not observed significant topographical
changes and shifts of structures in the STM images.
However, the thermal shift shown in Fig. 2 for a
1 A current implies an important mechanical stress
that could cause a great increase in relaxation rates
of the grain structure.
In order to be able to obtain sequences of images
that will keep some similarities, we have reduced
the current by an order of magnitude. Thus, we
are able to see the movements of matter in the
surface by using the STM. Fig. 3 shows four
images of the surface taken with a time interval of
10 min when a 0.1 A current (current density of
0.25×103 A/cm2) is flowing. By carefully observing
Fig. 3, both splitting and fusion of the surface
grains can be seen in the images. Fig. 4 shows the
variation of a profile in a given position with
elapsed time to help identify the changes. We
calculate the maximum difference in height among
all the points in a profile, R , and the rootp−v
mean-squared roughness (standard deviation of
the height data) or rms-r
S
rms-r=
N
∑ (z −z: )2
n
n=1
,
N−1
where z: is the mean z height and N the number of
points in the profile. Since rms-r contains squared
terms, large deviations from the average z height
are weighted heavily. We obtained rms-r and
R
as a function of the time elapsed for the
p−v
profiles shown in Fig. 4. The result is presented in
Table 1. It is clear the surface flattens with time
while the current is flowing (a decrease in roughness in 35 min between 25% and 36% depending
on the method to measure roughness). Since the
Fig. 3. STM topographic image of the surface after a current of 0.1 A ( j=0.25×103 A/cm2) has flow through it for: (a) 80; (b) 95;
(c) 105; and (d) 115 min. The white arrows in the images show the approximate position of the profiles shown in Fig. 4 (there are
shifts from image to image because of the STM thermal drift).
M. Aguilar et al. / Surface Science 409 (1998) 501–511
Fig. 4. Profiles corresponding to the same position in the surface, but at different times. The profiles are of 437 nm long and
obtained following the diagonal lines whose ends are marked
in images of Fig. 3 with white arrows. The position of the arrows
indicate the image change due to the thermal drift. The profiles
show the topographic evolution of the surface with a 0.1 A
current flow for: (a) 80; (b) 90; (c) 95; (d ) 105; (e) 110; and
(f ) 115 min.
variation in roughness over a profile is not statistically significant, we also obtained the variation of
rms-r over a surface (in DIN4768 norm with values
in nm/mm2) – instead of a profile – and the result
is the same (see last column in Table 1): a flattening
of the surface (the rms-r value decreases 26%
in 35 min).
Because we have observed large movements in
the film surface, we studied the crystallinity of the
surface by grazing incidence X-ray diffraction [14]
507
to find out which kinds of gold microcrystals are
formed in the surface. Thus, we could obtain some
insight into what happens with the gold surface
microcrystals as a result of the rearrangement due
to the surface migration. First, we obtained the
whole diffractogram for a well-stabilised sample.
The result is reported elsewhere [13], but for the
present study the important point is the peak
corresponding to the (111) reflection plane. In
fact, it is (compared with the standard ) higher
than expected indicating that we have a (111)
textured gold. This result agrees with the work of
Golan and co-workers [24] who arrive at the same
conclusion from electron diffraction measurements
of gold films grown on glass. Thus, the granular
structure is apparent in the STM images that
corresponds to actual microcrystals rounded by
small scale grain boundary grooving that is due to
the rounding out produced by random atom deposition during growth that yields the fractal character
of the surface. This last component produces a
broad and small intensity band of an amorphous
nature that we observed in the X-ray diffractogram
with a grazing incidence (0.2°).
To see the surface contribution, we obtained the
diffractogram under grazing incidence [14] with
very small angles. Gold surfaces tend to absorb
impurities when exposed to ambient conditions.
These can give rise to amorphous mounds in low
angle X-ray scattering. We have looked for these
mounds in the spectrum and we concluded that
they are not present in our samples, neither at the
Table 1
Statistical data obtained from the line profiles. Values of the maximum difference in height among all the points, R , the rootp−v
mean-squared roughness (standard deviation of the height data), rms-r, the average roughness, ave.-r, in nanometers for the profiles
shown in Fig. 4. Column marked DIN4768 (nm/mm2) shows the values of rms-r obtained averaging over the surface from which the
profile was obtained. The period of 0.1 A current application is also shown. The last row shows the % decrease of the roughness
measured by the four different methods in the time interval of 35 min
Profile
R
a
b
c
d
e
f
Decrease (%)
27.5
23.6
22.9
23.8
21.5
20.6
25
p−v
(nm)
rms-r (nm)
ave.-r (nm)
DIN4768 (nm/mm2)
Time (min)
7.8
7.1
6.9
5.8
5.7
5.3
32
7.3
6.6
6.4
5.1
5.0
4.7
36
178
165
160
150
147
132
26
80
90
95
105
110
115
35 min
508
M. Aguilar et al. / Surface Science 409 (1998) 501–511
beginning of the experiment nor at the end (after
days of current flowing). Fig. 5 shows the result
at different angles of the (111) diffraction peak. It
is very clear in the figure that, as the angle decreases
(i.e. as the surface contribution increases), the
position shifts and the half-width increases. The
broadening means that the microcrystals in the
surface are smaller than in the bulk and/or with
higher crystallographic defect density. On the other
hand, a shift in the peak position means, in general,
that the microcrystals are under uniform strain
[25]. Thus, the irregular shape of the peak means
that the strain is not uniform. This result is not
surprising. In fact, since the gold is rapidly deposited and at a low substrate temperature, it will
certainly grow strained microcrystals having a
large number of dislocations or facets. The shape
at 20° incidence angle reveals the presence of the
peak corresponding to the gold standard. Thus,
the microcrystals in the surface are under large
mechanical strain, whereas in the bulk a large
number of microcrystals are strain free. The shape
of the broad peak at 0.2° incidence angle (i.e.
corresponding to the surface) changes with time
during the hours of surface rearrangement [13].
However, the peak always has a broad and irregular shape without the peak corresponding to the
gold standard.
To study the implication of the large movements
of matter on the grain crystallinity we obtained
the temporal evolution of the X-ray diffractogram
whilst the current was flowing through the sample.
Fig. 5. XRD spectrum showing (111) peak at different angles
of incidence.
We found that the peak corresponding to microcrystals with strain moves and changes in shape.
In particular, we measured the temporal evolution
of the (111) peak of the X-ray diffractogram under
grazing incidence. Fig. 6 shows this evolution for
two different orientations (at angles of 0.5° and
1°). We found that the broad (111) diffraction
position shift towards the gold standards with
elapsed time indicating that the surface strains
formed during film growth disappeared as a result
of the migration of gold atoms. As we discussed
previously, the reason could be thermally-induced
electromigration and/or mechanical stress, but not
thermal diffusion because the temperature increase
is only about 5°C.
The inset in Fig. 6 shows the temporal evolution
of the intensity of the (111) reflection correspond-
Fig. 6. Evolution of the gold standard (111) diffraction peak
shape at grazing incidence with time when 0.25×104 A/cm2 current density is flowing through the film. The X-ray incidence
angle was: (a) 0.5°; and (b) 1°. The inset shows the evolution
of the gold standard (111) diffraction peak intensity with the
time that a 0.25×104 A/cm2 current density is flowing through
the film.
M. Aguilar et al. / Surface Science 409 (1998) 501–511
ing to the gold standard up to about 1 week of
the current being applied.
Fig. 6b shows the diffractograms for 1° incidence
angle. Comparison with Fig. 6a shows that the
conversion from stressed microcrystals towards the
standard is less important. Since in Fig. 6b the
contribution of the surface is less important than
in Fig. 6a, these results indicate that the observed
migration of gold atoms is more important in the
surface. These results ruled out mechanical stress
as the origin of the migration, since in that case
the large differences between surface and bulk
would not occur. On the other hand, the results
are in agreement with the suggestions of Levine
et al. [11]. In fact, they hypothesised that the most
likely mechanism of EM is current-driven surface
diffusion in which the relatively unstable atoms at
the grain boundary–surface intersection are perturbed out of their positions and preferentially
migrate in the direction of the electron flux [11].
Our X-ray results illustrate that their hypothesis is
quite probably correct. Thus, regardless of the
migration process, the result is that in the surface
it produces the elimination of the surface strains
formed during film growth. This result agrees also
with the calculations of Schreiber [26 ] on the
activation energy of the different diffusion mechanisms acting in polycrystalline material and that
could account for electromigration. He obtained
an activation energy of 1.4 eV for diffusion in the
bulk, 0.45 eV in grain boundaries and 0.28 eV in
the surface. Thus, clearly the effect of electromigration should be observed predominantly in the
surface and in the grain boundaries. This is exactly
what we are observing by STM and grazing incidence X-ray.
Large microcrystals without strain are formed
as a result of the gold atoms’ migration by the
effect of the electrical current. In fact, in Fig. 6a is
also clear that the half-width of the peak corresponding to the gold standard decreases with time.
This means that the average size of the strain-free
microcrystals increases with time when the 1 A
current is applied and/or that the crystallographic
defect density decreases with time. This process is
probably owing to an electromigration phenomenon and not random thermal diffusion since
the temperature increase is lower than 10°C.
509
Mechanical stress due to the differential thermal
dilatation coefficients should be also ruled out, as
mentioned above, because of the large difference
in intensity of the peak at the gold standard
between surface and bulk. Moreover, the shape of
the diffractogram changes very little in periods up
to 3 weeks when no current is applied [13].
It is timely to point out here that the temporal
evolution shown in Fig. 5 changes from sample to
sample. In fact, it can be much faster or slower,
and the shape of the diffractogram corresponding
to the as-grown sample can also vary. However,
evolution towards the gold standard always occurs.
Fig. 7 shows that the surface topography has
changed drastically after about 2 weeks of 1 A
current flow. The surface is formed now by grains
without fine structure, that is, they are smoother
than those initially ( Fig. 1).
The sample was no longer able to withstand a
current flowing through it after about 2 weeks of
application of the 1 A current and failure occurs.
In fact, the sample is no longer able to withstand
a current through it: if a voltage is applied then,
the current starts to flow, but goes down to zero
immediately and suddenly. Conductivity was eliminated. We repeated this experiment several times
and the film always initially allows the current to
flow, but conductivity is eliminated after a fraction
of a second. This behaviour implies that when the
current is switched off the film resistance recovers
partially. This implies the existence of grain boundary’s diffusion, as shown in experiments of EM
induced resistance changes in Al lines [27].
Fig. 7. Surface topography of a gold film that has withstood
0.25×104 A/cm2 current density for 2 weeks. The main characteristic is that it is formed by very smooth grains.
510
M. Aguilar et al. / Surface Science 409 (1998) 501–511
Probably, the formation of large microcrystals and
the elimination of very small crystals between the
crystalline grains as well as the small amorphous
part in the surface (that accounts for the fractal
behaviour) induce the formation of holes or voids
between the microcrystal. Then, the application of
a current produces a dilatation of the film because
of the Joule effect. The dilatation induces the
separation of the huge microcrystals increasing the
resistance. The large Joule effect in the microcrystal
boundaries produces further enlargements of the
resistance, and, as result, the current flow stops.
This must be the origin of the final failure of the
electrical connections in the VLSI devices.
When the current stops, the sample cooled down
and the relaxation of the mechanical stress allows
partial recovery of the resistance. Results of recovery of electrical resistance in Al films by reducing
temperatures have been observed and explained as
due to relief of the mechanical stress and microstructural changes by bulk diffusion involving the
co-operative motion of large groups of atoms [28].
As mentioned above, at high current density a
stress field is produced by the different thermal
expansion coefficients of the film and the substrate
(because most of the power is dissipated by thermal
conduction to the substrate). Thus, the stresses
and subsequent relaxation could produce mechanical damage, as observed in aluminium films [29].
Also, the stress field at high current densities could
explain the persistence in the diffractogram, at the
region near the gold standard, of the broad and
irregular peak corresponding to microcrystals
under strain. Moreover, because small crystallites
are formed – creating low-energy facets in large
grains and relieving intergranular strains – then
the adherence to the substrate decreases. The result
of this process will be two-fold: (i) the ‘‘de-percolation’’ will lead to the formation of high-resistance
necks that will fail, as observed; and (ii) the film
can bend more easily in regions where the adhesion
to the substrate is lost, which in turn will produce
a large dislocation flow to accommodate strain. In
particular, it is well known that gold on glass
presents structural instabilities and poor adhesion
to the substrate that makes it a problematic system
to study the EM process [30]. Thus, in the final
stages of the EM process, before the final failure,
the stress gradient will become important.
4. Conclusions
The conclusion of the study is that the electrical
current induces a rearrangement of the gold film
surface by electromigration from strained microcrystals. The movement of surface matter induces
the formation of large microcrystal with a lattice
constant corresponding to the gold standard. In
the process of de-percolation, large voids between
the microcrystals are formed and the adherence
to the substrate decreases. As a result, large strains
appear due to the overheating of the film and the
differential linear dilatation constants of film and
substrate. Failure is the result.
Acknowledgements
This work was supported by grants given by the
institution CONACYT-SEP (Mexico), project
numbers 4483A and 2362P. Appreciation is also
given to the DGICYT-MEC (Spain) and
CONACYT for partial support to the stay of
M.A. in CINVESTAV-Merida. The authors thank
the technical assistance of E. Corona, O. Ceh and
A. Escobedo.
References
[1] P.S. Ho, T. Kwok, Rep. Prog. Phys. 52 (1989) 301.
[2] A. Scorzoni, B. Neri, C. Caprile, F. Fantini, Mater. Sci.
Rep. 7 (1991) 143.
[3] D.W. Malone, R.E. Hummel, Critical Rev. Solid State
Mater. Sci. 22 (1997) 199.
[4] R.E. Jones Jr., M.L. Basehore, Appl. Phys. Lett. 50
(1987) 725.
[5] A. Blech, E.S. Meieran, Appl. Phys. Lett. 11 (1967) 263.
[6 ] L. Berenbaum, R. Rosenberg, Thin Solid Films 4 (1969)
187.
[7] G. Binnig, H. Rohrer, Helv. Phys. Acta 55 (1982) 726.
[8] C.J. Chen, Introduction to Scanning Tunneling Microscopy, Oxford University Press, Oxford, 1993.
[9] J.A. Stroscio, W.J. Kaiser (Eds.), Methods of Experimental Physics. Scanning Tunneling Microscopy, Vol. 27,
Academic Press, New York, 1993.
M. Aguilar et al. / Surface Science 409 (1998) 501–511
[10] L.E. Levine, G. Reis, D.A. Smith, J. Appl. Phys. 74
(1993) 5476.
[11] L.E. Levine, G. Reis, D.A. Smith, Phys. Rev. B 48
(1993) 858.
[12] M. Paniccia, P. Flinn, R. Reifenberger, J. Appl. Phys. 73
(1993) 8189.
[13] M. Aguilar, A.I. Oliva, P. Quintana, J.L. Peña, Surf. Sci.
380 (1997) 91.
[14] S. Battaglia, Appl. Surf. Sci. 93 (1996) 349.
[15] K. Dagge, W. Frank, A. Seeger, H. Stoll, Appl. Phys. Lett.
68 (1996) 1198.
[16 ] J. Vancea, G. Reiss, F. Schneider, K. Bauer, H. Hoffmann,
Surf. Sci. 218 (1989) 108.
[17] H. Hoffmann, J. Vancea, Thin Solid Films 85 (1981) 147.
[18] S. Norman, T. Anderson, G. Peto, S. Somogyi, Thin Solid
Films 77 (1981) 359.
[19] M. Aguilar, E. Anguiano, M. Pancorbo, J. Microsc. 172
(1993) 233.
[20] R.C. Jacklevic, L. Elie, Phys. Rev. Lett. 60 (1988) 120.
511
[21] H. Wang, J. Jing, H.T. Chu, P.N. Henriksen, J. Vac. Sci.
Technol. B 11 (1993) 2000.
[22] C.J. Roberts, B. Hoffmann-Millack, W.S. Steer, Surf. Sci.
224 (1989) 1.
[23] H.B. Huntington, Thin Solid Films 25 (1975) 265.
[24] Y. Golan, L. Margulis, I. Rubinstein, Surf. Sci. 264
(1992) 312.
[25] B.D. Cullity, Elements of X-ray Diffraction, AddisonWesley, Reading, MA, 1978.
[26 ] H.U. Schreiber, Solid State Electron 24 (1981) 583.
[27] J.R. Kraayeveld, A.H. Verbruggen, A.W.-J. Willemsen, S.
Radelaar, Appl. Phys. Lett. 67 (1995) 1226.
[28] S. Ohfuji, M. Tsukada, J. Appl. Phys. 78 (1995) 3769.
[29] R. Venkatraman, P.R. Besser, J.G. Bravman, S. Brennan,
J. Mater. Res. 9 (1995) 328.
[30] F.M. d’Heurle, P.S. Ho, Electromigration in thin solid
films, In: J.M. Poate, K.N. Tu, J.W. Mayer, Thin Films
Interdiffusion and Reactions, Wiley, New York, 1978,
pp. 243–303.