electromigration in aluminum, gold and silver thin films
TRANSCRIPT
ELECTROMIGRATION IN ALUMINUM, GOLD AND SILVER THIN FILMS
BY
HANS JOACHIM GEIER
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDAIN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1974
To my wife
To my daughter
To my parents
ACKNOWLEDGMENTS
The author expresses his grateful appreciation to Dr. R. E.
Hummel, his graduate advisor, for his genuine interest, guidance and
assistance throughout the course of this study. Acknowledgment is also
extended to Dr. R. T. DeHoff for helpful discussions, and to Dr. D. B.
Dove and Dr. R. Pepinsky for serving on the supervisory committee.
The author would also like to thank Dr. A. G. Guy and Dr. R. G.
Connell, Jr. for their assistance in the preparation of the final manu-
script; Mr. J. B. Andrews for his assistance in some aspects of the
experimental setup; and Dr. P. Thernquist for his guidance during the
initial part of the experiments.
The National Aeronautics and Space Administration (NASA)
provided the funding for this research under contract No. NGR 10-005-
080, for which the author is very grateful.
Thanks go also to the Conselho Nacional de Pesquisas , Rio de
Janeiro, Brazil, for the scholarship provided for the period between
September 1973 and June 1974.
The author wishes to convey his affectionate gratitude to his
wife and to his parents for their support and encouragement by
dedicating this work to them.
Special gratitude is expressed to his uncle and aunt. Dr. and
Mrs. Hans F. Gruene, for the numerous weekends spent together in Cocoa
Beach, which made the stay in the United States so much more enjoyable.
iii
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS iii
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT ix
I INTRODUCTION 1
II THEORY 5
2.1 Driving Forces in Electromigration 5
III EXPERIMENTAL PROCEDURE 10
3.1 Specimen Preparation 10
3.2 Measurement of the Ion VelocityDue to Electromigration 12
3.3 Resistance Measurements 15
3.4 Temperature Measurements 17
IV RESULTS AND DISCUSSION 23
4.1 Aluminum 23
4.1.1 General Remarks 23
4.1.2 Activation Energy for Electrotransportin Thin Aluminum Films 26
4.1.3 Temperature Range of Measurements 33
4.1.4 Velocity of the Moving Ions 33
4.2 Silver 38
4.2.1 Activation Energy for Electrotransportin Thin Silver Films 38
4.2.2 Temperature Range of Measurements 42
4.3 Gold 45
4.3.1 Activation Energy for Electrotransport ... 45
4.3.2 Structural Differences in Gold Films .... 51
4.3.3 Temperature Range of Measurements 54
iv
TABLE OF CONTENTS (Continued)
Page
IV (Continued)
4.3.4 Practical Consequences 57
4.3.5 Thermo transport 58
4.3.6 Direction of Electrotransport 58
APPENDIXES
A MICROGRAPH AND TABLES 66
B RESISTANCE MEASUREMENTS AS A TOOL FOR DETERMINING
ACTIVATION ENERGIES FOR ELECTROTRANSPORT 71
BIBLIOGRAPHY 8^
CURRICULUM VITAE 88
v
LIST OF TABLES
Table Page
3.1 Conditions for Vapor Deposition and Annealingof Thin Film Specimens 11
4.1 Activation Energies for Electrotransport inThin Aluminum Films 24
4.2 Experimental Data Obtained on Thin Aluminum FilmsSubjected to Electrotransport 37
4.3 Compilations of Activation Energies for Self-Diffusion in Silver and Our Data on Thin FilmElectrotransport 43
4.4 Activation Energies for Electrotransport inThin Gold Films 47
A4.1 Compilations on Experimental Data Taken on SeveralThin Aluminum Films 67
A4.2 Experimental Data Taken on Various Thin Silver FilmsSubjected to Electrotransport 68
A4.3 Experimental Data Taken on Various UnannealedGold Films 69
A4.3 Experimental Data Obtained on Several AnnealedGold Films 70
vi
LIST OF FIGURES
Figure Page
3.1a Deposition steps to produce an aluminum thin film
specimen with aluminum-gold thermocouple 13
3.1b Deposition steps to produce an aluminum thin film
specimen with aluminum-gold thermocouple 14
3.2 Circuit diagram used for the electromigration
experiments at constant temperatures 16
3.3 Specimen holder for resistance measurements 18
3.4 Calibration curves for aluminum and gold specimens
and silver specimens 21
3.5 Comparison of actual thin film specimen temperature
with resistometrically calculated film temperature . . 22
4.1 Relative change of resistance versus time of an aluminum
thin film 28
4.2 Arrhenius-type plot of data taken on thin aluminum films
subjected to a direct current 29
4.3 Activation energy for electrotransport in thin aluminum
films as a function of film temperature 30
4.4 Relative resistance change per 100 minutes determined
on aluminum films subjected to direct current at
various temperatures 34
4.5 Velocity of aluminum ions due to momentum exchange
with electrons 36
4.6 Relative resistance change versus time of an annealed
silver thin film 40
4.7 Arrhenius-type plot of data taken on thin silver
films (annealed) subjected to a direct current .... 41
4.8 The velocity of silver ions as a function of
film temperature 44
vii
LIST OF FIGURES (Continued)
4.9 Relative resistance change per 100 minutes determined for
silver films subjected to direct current at various46
4.10 Relative resistance change as a function of time for49
4.11 Arrhenius- type plot of measurements on annealed gold films50
4.12 Arrhenius- type plot of measurements taken on annealed
and unannealed gold films subjected to a direct current . 52
4.13 Average ion velocity in thin gold films subjected to
a direct current as a function of specimen temperature 53
4.14 Transmission electron micrographs of annealed and55
4.15 Relative resistance change per 100 minutes determined
on gold films subjected to direct current at various56
4.16 Relative resistance change of gold films during
electrotransport at two temperatures 60
4.17 Photomicrograph of thin gold film after electrotransport61
4.18 Relative resistance change of unannealed gold film
specimens during electrotransport 62
4.19 Photomicrograph of unannealed gold film after64
A4.1 Transmission electromicrograph of annealed silver66
B.l (a) Schematic shape of sample, (b) Schematic temper—
ature profile along sample 72
B. 2 Volume element of sample74
B . 3 Wedge-shaped reduction in cross sectional area 79
B. 4 Groove-type reduction in cross sectional area .82
viii
Abstract of Dissertation Presented to the Graduate Councilof the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
ELECTROMIGRATION IN ALUMINUM, GOLD AND SILVER THIN FILMS
By
Hans Joachim Geier
June, 1974
Chairman: Dr. R. E. HummelMajor Department: Metallurgical and Materials Science Engineering
The activation energy (Q) for electrotransport in thin al umi num,
silver and gold films was measured by a resistometric technique involv-
ing several individual resistance measurements along a stripe. The
activation energy for electrotransport in thin aluminum films was found
to be temperature dependent and to vary continuously between 0.45 eV
and 0.72 eV in a temperature range between 220°C and 360°C. For silver
films, two distinct temperature regions with different activation ener-
gies were found. Between 225°C and 280°C, Q is 0.95 eV which suggests
predominance of ion movement in the grain boundaries, whereas at temper-
atures between 160°C and 225°C, Q is 0.3 eV which suggests surface
dominated electrotransport. In gold films a uniform activation energy
of 0.98 eV was found in the entire temperature range (260°C-380°C)
.
New experimental results on the controversial issue upon the
direction of electrotransport in gold films are presented, which
suggests that the direction of ion movement in these films is
temperature dependent.
Thermotransport in gold films was found to be directed towards
the warm side of the stripe.
ix
I INTRODUCTION
Electromigration, electrodifusion and electrotransport are
terms used to describe the flow of matter in metallic conductors under
the influence of high electric currents. The mass transported under
the influence of the electric current is usually rather small. The
first known observation of electromigration in metals was made by
Gerardin [1] in 1861, who noticed that after electrolysis in the molten
state a sodium-mercury alloy would decompose water at one end only.
Electromigration depends directly on the diffusion coefficient
and is therefore highly temperature dependent. Since the diffusion
coefficient in solids is much smaller than in liquids, electromigration
in solids occurs at a much slower rate. As a consequence (although
experimental studies on both solid and liquid metals began to appear in
the literature in the 1920sJ it was not before the early 1930s that
experiments on electromigration in solid metals were done on a large
scale. The work of that period has been reviewed by Schwarz [2].
The phenomenon was at first believed to be due to coulombic interactions
between the moving ion and the electric field. However, later on it
was observed that the transport occurred in a direction opposite to that
expected from electrostatic ion-field interactions [3]. An explanation
for this problem had been proposed in 1914 [4] and was later confirmed
experimentally [5]. It was assumed that electromigration is caused by
scattering of the moving electrons with the ions, i.e., by momentum
1
2
transfer between electrons and ions. This ion-electron interaction is
sometimes referred to as "electron wind."
The most important theoretical and experimental investigations
in electromigration were reviewed by Verhoeven [6], Adda and Philibert
[7], Hehenkamp [8], Huntington [9,10], and Wever [11].
In the last twenty years numerous investigations on electro-
migration have been published and, recently, metallic thin films received
special attention because of their technological importance in the
development of semiconductor devices. The connecting metallic stripes
in the integrated circuits failed after short lifetimes because voids
developed due to electromigration. Because of the small dimensions of
microelectronic devices, very high current densities (of the order of
6 2 210 A/ cm ) are common in thin film stripes, as compared to 10 A/ cm
in bulk samples. As a consequence, an appreciable amount: of electro-
migration can be observed in thin films already at ambient temperatures.
The theory of mass transport developed by Huntington et al.
I iTip I
[12,13] and Penney [14] infers that a divergence in atomic flux is
necessary for a failure to occur. Some of the causes for such a diver-
gence are temperature gradients, grain size differences, grain boundary
triple points and changes in composition. In the absence of such gradi-
ents and inhomogeneities, the rate of mass transport is uniform along
the metallic film strip and no hole formation and failure is expected
to occur.
The first attempts made to explain the mechanisms of electro-
migration in thin films were to extrapolate to lower temperatures the
results obtained from investigations in bulk materials. However, it was
3
soon apparent that the electromigration in thin films may have a lower
activation energy. This was believed to be due to the rapid diffusion
of ions along grain boundaries or free surfaces.
Several investigations have been conducted with the main purpose
to increase the lifetime of metallic thin film stripes [15-34]. To date,
the most studied metal has been aluminum (due to highly favourable tech-
nological and economical aspects) and, to a lesser extent, also gold (due
to its higher electric conductivity and longer lifetime) . Most studies
were directed towards the determination of the lifetime of thin film
metallizations as a function of current density, composition, geometry
and temperature.
Various types of experimental techniques have been developed for
electromigration studies. The following techniques measure mass trans-
port and activation energies:
• measurement of the mean time to failure [16,18,28,29,31-33,35-37]
• direct observation of hole and hillock formation by electron
microscopy [34,38,39]
• studies of the concentration profile of solute elements by
microprobe analysis [22]
• resistometric techniques [21,27,40-43].
In order to obtain a semiquantitative measurement to use in the
matching of materials to conditions of temperature, current density,
composition and geometry, measurements of the activation energy for
electromigration in thin films were made. Most of these measurements
have been made on aluminum films. A compilation of these measurements,
as reported in the literature [16,18,28-31,35,38,40,44,45], can be found
4
in Section 4.2.1. The data which were obtained by using the above-
mentioned methods vary by a factor of four. Activation energy measure-
ments on silver films have not been reported yet.
The aim of this dissertation is to further elucidate the mechan-
isms of electromigration through the reliable determinations of activa-
tion energies in aluminum, gold and silver thin films.
II THEORY
2 . 1 Driving Forces In Electromigratlon
Electromigration is a current induced mass transport phenomenon
caused by two driving forces:
(1) a coulombic force exerted on the positively charged migrating
ion, and
(2) a friction force F^ resulting from the interaction between the
migrating ion and the charge carriers.
By applying an electrostatic field E to a particle with charge
Ze, a force F^ is exerted upon the particle. This force is
F = Z e E, (2.1)c
where Z is its valence and e the unit charge. Mass flow due to the
coulombic force is usually less than the mass flow resulting from the
frictional force. A small number of atoms (only those adjacent to
lattice defects) will be able to change their positions under the
influence of the coulombic force.
The force, F-, originating from the momentum transfer between
the ion and the flowing charge carriers can be estimated when the
number of collisions per unit time and the average momentum that every
charge carrier adds in the electric field between two collisions are
known [46]. The number of such collisions, v, per unit time is given by
5
6
v = n v a (2.2)
where n is the number of charge carriers per unit volume, v is the
average velocity of the charge carrier and a is the atomic scattering
cross section.
The average momentum added to each charge carrier during the
relaxation time t is equal to
a r. e E £Ap = e E x = —— (2.3)
where £ is the mean free path of the charge carriers and v is the aver-
age velocity of the charge carriers. The product of equation (2.2)
with equation (2.3) gives the magnitude of the friction force between
the moving atoms and charge carriers
,
Ff=vAp=eEn£o . (2.4)
lattice
Expressions for calculating resistivities due to perfect
PQ > an<^ defects p^, were calculated by Mott and Jones [47]
*m v
e
n e 2 £e
*
(2.5)
a( 2 . 6 )
*where m is the effective mass of the electrons, N, is the number of
d
defects per unit volume, n^ is the number of free electrons per unit
volume, and vg
is the average velocity of the electrons.
7
From equation (2.6)
2Pa ed e
m v N
,
e d
(2.7)
By substituting the a value in equation (2.4), the expression for F
becomes
P j n e 2
F = e E n £ ^. (2.8)
m v N
,
e d
With n^ - Z Nq , where N
qis the number of ions per unit volume,
equation (2.8) becomes
F = e E Z
N Pao d
N,
£ n ee
*m v
2 1
(2.9)
By comparing equation (2.9) with equation (2.5), the following expres-
sion for the friction force is derived,
N p aF = e E Z -2—
-
f N, P( 2 . 10 )
The expression for the total driving force responsible for the mass
flow is obtained by adding equations (2.1) and (2.10)
F = e E Z 1 +No
( 2 . 11 )
The exact expression for the total driving force present in pure metals
having both types of charge carriers (electrons and holes) [12] is
given by equation (2.12),
8
F = e E Z 1iVd2 N
dPo
( 2 . 12 )
The total force for electromigration is commonly expressed as
F = Z*e E, (2.13)
where Z*e gives the effective charge that the moving ion would have
in order to experience the same total force from pure electrostatick
consideration. The factor,, defines the sign of the friction
force caused by the charge carriers. Depending on the sign of the
effective mass of the charge carriers, two possible directions for
mass transport may result. These are:
(1) Hole conduction. The driving force acts in the same direction
as the coulombic force. As a consequence, the ions migrate
towards the cathode.
(2) Electron conduction. The effective valence Z* can be either
positive or negative, depending on whether the term,
,N p, *
. 1 o d m2 N p "U*T
’
is greater or less than zero. At some critical temperature
the direction of electromigration may reverse because of the
temperature dependence of the resistivities. Such a reversal
Pdwould result if the ratio, —
, varied so as to change the signP o
of the term.
The velocity of the migrating ions is proportional to the total
driving force exerted by the electric field. The relationship is given
by the expression.
9
v = yF, (2.14)
where y is the mobility. Mobility is related to the coefficient of
diffusion by the Nernst-Einstein equation,
Dy =
kT (2.15)
By relating equations (2.13), (2.14) and (2.15), the expression for
the velocity of the migrating ions becomes.
*Z e E „v = — — d •
kT(2.16)
With E = p j and D = Dq
exp (-Q/kT) , equation (2.16) becomes,
Z e p j Dv =
kT6XP
itf)’ (2.17)
where p is the specific resistivity of the metal and j is the current
density. A common form for equation (2.17) is,
*Z e p D _ ..
-iv o Q 1
In — = In — -,
• —,
J kT k T ’ (2.18)
where In (Z e p DQ)/kT is in general considered to be temperature
independent. (For more details, see Section 4.1.2.) The temperature
dependence of In v/j is primarily governed by the second term of
equation (2.18). By plotting In v/j versus 1/T, the activation energy
for electromigration, Q, can be obtained from the slope, Q/k.
Ill EXPERIMENTAL PROCEDURE
3.1 Specimen Preparation
In order to obtain reproduceable specimens, metal masks were
prepared which could be placed over the substrate before vapor deposi-
tion. Fabrication of these masks by a photo-etch technique has been
described elsewhere [43].
Glass microscope slides (1 mm x 25 mm x 38 mm) were used as
substrates. They were cleaned by immersing them for about 10 minutes
in acetone in an ultrasonic cleaner. Subsequently they were rinsed
thoroughly in water and placed for 15 minutes in a dilute MICRO labo-
ratory cleaning solution in the ultrasonic cleaner. After that, the
substrates were again rinsed thoroughly in running water and then
stored in pure alcohol. Shortly before the vapor deposition of the
stripes, the substrates were air dried and their surfaces polished with
cotton swabs. Subsequently, all cotton fibers were removed by a
stream of nitrogen gas.
The conditions under which the specimens were vapor deposited
and subsequently annealed are summarized in Table 3.1.
The specimen design used here was similar to the one described
by Breitling [27]. Because of the need to monitor the temperature of
the film during the experiments, thin film thermocouples were laid down
in an additional deposition step. The individual deposition steps
10
11
TABLE 3.1
CONDITIONS FOR VAPOR DEPOSITION AND ANNEALINGOF THIN FILM SPECIMENS
Deposition Vacuum Evapora-*
Annealing
Metal Purity
(%)
'
Rate
(A/s) (Torr)
tionSource
Temp
.
(°c)
Time
(hrs)
A1 99.999 14 IQ" 6 W
Filament400 4
Au 99.99 18 3 10~ 6 Mo or WBoat
350 20
Ag 99.99 40 2 10~ 6 MoBoat
300 4
*Annealing of specimens after deposition was done only wherespecified in Section IV.
12
required to produce aluminum specimens are shown in Figure 3.1. The
O
test strip and the electrode have thicknesses of about 1600 A and
2600 A, respectively. In addition, an aluminum-gold thermocouple is
deposited
.
3.2 Measurement of the Ion Velocity
Due to Electrotransport
Previous investigations [27,41,43] have shown that resistance
measurements in several areas along thin film stripes are a sensitive
tool to study electromigration. From the rate change of the resis-
tance (AR/At), the average velocity (v) of ions due to electrotransport
can be calculated by the equation.
where R is the resistance of a strip of length l. A rigorous deri-o
vation of equation (3.1) is given in Appendix B.
In applying equation (3.1) it is assumed that the resistance
change is solely due to the mass depletion in the stripe. This implies
that during an electromigration experiment the resistance does not
change due to stress relief, grain growth or other annealing effects.
We have verified repeatedly that heating our pre-annealed aluminum and
silver films by subjecting them to alternating currents does not change
the resistance of the stripe. (In gold, thermotransport causes a small
resistance change.) We can reasonably conclude, therefore, that the
entire resistance change which we observed is due to an electromigration-
induced change in mass.
13
(b)
Figure 3.1a Deposition steps to produce an aluminum thin filmspecimen with aluminum-gold thermocouple.(a) Gold deposition (1600 A)
(b) Aluminum deposition (1600 A)
14
(C)
600 A Au1 1600 A Al
2600A A!
Figure 3.1b Deposition steps to produce an aluminum thin filmspecimen with aluminum-gold thermocouple.(c) Second aluminum deposition (1000 A)(d) Final configuration of the specimenThe actual test stripe lies between the marks A and B.
15
Another increase in resistance could occur due to a rise
in temperature during the experiment. Therefore, attempts were made to
hold the temperature of the film constant during the entire experiment.
Details on this will be given below.
Equation (3.1) has to be modified when the mass depletion is
not uniform in the area under consideration which is, for example, the
case when voids are formed. Then the temperature and current density
vary locally. As a consequence, the resistance increases are no longer
linearly with time as our previous and the present investigations have
shown. Therefore, only the initial linear portion of the resistance
change was used for calculating the ion velocity. It can be shown that,
in this case, the above-mentioned modification to equation (3.1) gives
only a small contribution and can therefore be neglected.
One further point should be discussed here. The present and
previous investigations have shown that in thin films the ion movement
caused by a direct current occurs usually within grain boundaries.
In this case, the velocity calculated by equation (3.1) is the average
velocity of the ions in the grain boundaries and should not be compared
with velocities obtained by marker experiments used for volume electro-
transport.
3.3 Resistance Measurements
The resistance measurements were made similarly as described
by Breitling by using a K-3 type potentiometer. A complete circuit
diagram is shown in Figure 3.2.
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A specimen holder was used which provided stable electrical
contacts between the potential (and electrode) leads and the specimen.
Each of the contacts was independently spring loaded (see Fig. 3.3).
During the electromigration experiments, the temperature has
a tendency to increase gradually due to the resistance increase caused
by mass depletion. Further, a change in the temperature of the environ-
ment could also cause fluctuations. As mentioned above it is, however,
important to maintain a constant temperature of the specimens during
the entire test. This was done by adjusting the current appropriately
so that the signal from the thin film thermocouple remained unchanged.
If the current applied to a particular specimen is changed, its current
density is no longer a constant during the experiment. Therefore, a
coulombmeter was inserted into the circuit (see Fig. 3.2). The average
current was obtained by dividing the measured charge during one exper-
ment by the time the experiment was in progress. All resistance mea-
surements were conducted in air.
3.4 Temperature Measurements
Measuring the temperature of a thin metallic film has been
always a major problem. Yet, knowledge of the exact temperature is
imperative in all diffusion-related studies. The difficulty in obtain-
ing reliable temperature readings stems from the fact that these films
are very thin (characteristically a few 1000 Angstroms) and consequently
have a very low heat capacity. This excludes the use of conventional
thermocouples which act as a heat sink and therefore cool the film at
Figure 3.3 Specimen holder for resistance measurements.
19
the point of contact. As a consequence, the temperature is read too
low and, even worse, an additional temperature gradient is introduced
on the stripe.
Micropyrometers have been proposed for the measurement of the
surface temperature because no physical contact with the film is
required here. However, this technique has not been used much in thin
film electrotransport studies because of the low emissivity of metals
and the fact that the emissivity changes during an experiment due to
surface roughening (hole and hillock formation) and oxidation.
The most popular method for obtaining the temperature of a
thin film uses resistance measurements. Mostly, it is assumed that the
temperature distribution along the stripe is parabolic, an assumption
which is probably justified in those cases where the substrate belowi
a portion of the film is removed. In cases in which the film remains
on the substrate and potential leads are used, a linear temperature
distribution between the two center terminals is probably more adequate.
The calculation of the temperature of the film from resistance data
requires the knowledge of the temperature coefficient of resistance a.
The ot-values, used by various investigators vary somewhat depending on
whether they use the value for the bulk (which is probably not justified)
or measure a in a preliminary experiment.
Using the resistometric method, the temperature of a film can
only be determined during the initial phase of the experiment, because
the resistance changes during electrotransport due to void formation.
Therefore, if one wants to keep the temperature of a film constant dur-
ing an entire electrotransport experiment, other techniques have to be
used
.
20
In the present work, a thin film thermocouple was vapor-
deposited near the center portion of the stripe (see Section 3.1).
This thermocouple was electrically separated from the film by a cut
about 30 ym wide. The calibration of the thermocouple was achieved
by placing a very small metal chip on the stripe and observing its
melting with a microscope while the EMF was measured. The calibration
curve of the aluminum—gold and the aluminum-silver thermocouples taken
in this way is shown in Figure 3.4.
In order to obtain a clue on how temperature data obtained
resistometrically would compare to the actual temperature, resistance
measurements were taken at the moment the metal chips melted. For
calculating the temperature at the center portion of the stripe it
was assumed that the temperature distribution was linear between the
two center potential leads (see Fig. 3.1). In Figure 3.5 this compar-
ison is done for aluminum and two different a-values by using the
equation
R = R [1 + a(T - T )]X o X o
or
Tx
R1 + T
o_ o
where R and R are resistance values at the unknown temperature T andx o x
room temperature T ,respectively. It can be seen from Figure 3.4 that
the resistometrically obtained temperatures are smaller than the actual
temperature and that a = 4.0 [deg ] agrees better with the actual tem-
perature. A parabolic temperature distribution (which is not justified
for the present sample design) gives usually a higher maximum temper-
ature by a factor of approximately 1.5.
V
(mv)
21
f-
Figure
3.4
Calibration
curves
for
(a)
aluminum
and
gold
specimens
(aluminum-gold
vapor-
deposited
thermocouple),
and
(b)
silver
specimens
(aluminum-silver
vapor-
deposited
thermocouple)
.
22
Figure 3.5 Comparison of actual thin film specimen temperature (Tgp)
with resistometrically calculated film temperature (Tca ]_ c )
-3 -1 -3for a = 4.6x10 Degree [curve (a)], and a = 4.0x10
Degree ^ [curve (b)].
IV RESULTS AND DISCUSSION
4 . 1 Aluminum
4.1.1 General Remarks
The activation energy for electrotransport in thin aluminum films
has been extensively measured previously, mainly because of the great
interest of the electronics industry in aluminum metallizations for
microelectronic devices. The data reported so far in the literature
are compiled in Column 4 of Table 4.1. As can be seen there, the mea-
sured activation energies for thin film electrotransport in aluminum
varies between 0.3 eV and 1.14 eV, i.e., by a factor of four. (Some
investigators observed in glass-coated aluminum films an even higher
activation energy, 1.2 eV, which is identical with the activation
energy found in bulk specimens [14,48]. This observation was, however,
recently questioned [31].)
Three principal types of measurements have been employed so far
in these investigations:
1. The most common and probably the simplest measurement
records the time during which 50 per cent of a large number of identical
specimens fail when a direct current passes through them. This param-
eter is called "mean time to failure" (MTF) . The variation between the
results obtained by several investigators who have used this method is
greatest because of the statistical nature of this technique. A failure
23
24
TABLE 4.1
ACTIVATION ENERGIES FOR ELECTROTRANSPORT IN THIN ALUMINUM FILMS
Method ofInvestigation
Temperatureor
TemperatureRange (°C)
Method of
TemperatureMeasurement
ActivationEnergy
Q (eV)
GrainSize
Referenceand Year
109-260 Power dissi-
pation0.480.84
1.2 pm8 pm
Black [28,29]
(1969)
100 Radiometric 0.3- 1.14dependenton filmthickness
Spitzer andSchwartz [30]
(1969)
Mean timeto failure
(MTF)
140-300 Resistance 0.510. 73
2 pm8 pm
At tardo andRosenberg [31]
(1970)
75-380 Resistance 0.41 1 pm Satake [35]
(1973)
125-175 Temperatureof oil bath
0.5 - 0.
7
Ames, d'Heurleand Horstmann [16]
(1970)d'Heurle [18]
(1971)
Growth rateof voids ormass deple-tion (TEMor SEM)
180-350
360± 40
Resistance
Resistance
0.7 ± 0.2No Observedgrain sizeor filmthicknessdependenceof Q
0. 74±0. 08
0.5 pmto sev-eral
microns
Blech andMeieran [38]
(1969)
Berenbaum [44]
(1971)
230-550 Resis tance 0.7 1 pm Weise [45]
(1972)
Res is tome trie
60-150 Temperatureor oil bath
0.5-0.
6
Rosenberg andBerenbaum [40]
(1968)
100-200 Temperatureor oil bath
0.5-0.
6
Shine andd'Heurle [21]
(1971)
25
study of the type just mentioned comprises all phases of the destruc-
tion of a thin film stripe, including electrotransport alone at the
very beginning of an experiment as well as catastrophic failure near
the end. Shortly before a thin film opens, current density and temper-
ature vary considerably across the stripe and are certainly greatest
near voids. This nonuniformity probably leads to variations in the
time to failure.
It should be noted that the activation energies obtained by MTF
measurements have been found to be dependent on grain size and film
thickness, a dependence not confirmed by other techniques.
2. In another type of investigation the growth of voids is
measured by observations in a transmission electron microscope (TEM)
or scanning electron microscope (SEM) . From these measurements the
velocity of the moving ions can be easily deduced. From a number of
these measurements at various temperatures, the activation energy can
be calculated from the slope in an Arrhenius-type plot. The activa-
tion energy for thin film electrotransport in aluminum obtained by this
technique has been consistently found to be around 0.7 eV.
One reservation can be brought forward against this method.
The measurements cannot be started before identifiable voids have been
formed, i.e., only at a relatively late stage of the electrotransport
experiment. As mentioned above, the current density as well as the
temperature around voids is not identical with the macros copically
measured values. The differences could give rise to a systematic error.
A method free of this error is that used by Weise [45], who scans a
film in a SEM with an electron beam before and after it is "stressed"
26
for some time. Thus he is able to measure the total mass depletion in
the film before voids have been formed.
3. A third method employs resistance measurements while a film
is subjected to a direct current. This method assumes that the rate of
mass depletion is proportional to the rate of resistance increase.
As mentioned in Section III, the advantage of this technique is that the
mass depletion can be measured well before any voids are seen; conse-
quently, only electrotransport is probably being measured. The reported
activation energies obtained with the resistance technique are approx-
imately 0.1 to 0.2 eV smaller than those calculated from void growth
measurements. However, the experimental error limit of the activation
energies reported by previous investigators who have used the resisto-
metric technique was approximately 0.1 to 0.2 eV. This large error is
probably due to the way these resistance measurements were conducted,
involving cycling of the specimens between oil baths of different tem-
perature.
The above literature review on the activation energy of electro-
transport in thin aluminum films clearly demonstrates the need for more
investigations on this subject.
4.1.2 Activation Energy for Electrotransportin Thin Aluminum Films
O
Aluminum films which have an average thickness of 1600 A were
subjected to a direct current. Resistance measurements on different
areas along these stripes were performed as described in Section III.
During an individual measurement the center portion of the stripe was
held at constant temperature. A typical rate of resistance change of
27
an area close to the cathode (area II) is shown in Figure 4.1. In this
graph the resistance increases linearly during the first 250 minutes.
During this first time interval usually no voids can be visually
detected. It is therefore assumed that during this time no major dif-
ferences in the local current density or temperature distribution are
present. Therefore, the relative resistance increase in this region was
used for the calculation of the activation energy.
Resistance measurements were taken on nine similar aluminum
films at various temperatures and current densities. In Figure 4.2, an
Arrhenius-type plot of the results is shown. As discussed in Section II,
the slope of a line drawn through the data points equals Q/k (where Q is
the activation energy for electromigration and k is the Boltzmann con-
stant). It is significant that the data points in this plot form, not
a straight line, but a curve which is concave upward. This can be
interpreted to be due to one of the following reasons:
1. The activation energy Q varies in the given temperature
region. To explore this further, the activation energies calculated
from the data of Figure 4.2 were plotted versus the temperature
(Fig. 4.3). It can be seen from this graph that between 220 and 360°C,
Q increases from approximately 0.45 eV to 0.72 eV. These values are
well within the range of activation energies measured by previous inves-
tigators (see Table 4.1). Taking into account the fact that the tem-
peratures reported by most previous investigators must be regarded as
somewhat uncertain, the results presented in Table 4.1 suggest a lower
activation energy for lower temperatures and vice versa. Moreover,
Shine and d'Heurle infer from their MTF measurements a temperature
28
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Q (eV)
Figure 4.3 Activation energy for electrotransport in thinaluminum films as a function of film temperature.
31
dependence of the activation energy even though their experimental
uncertainties are of the same order of magnitude as their variation
of Q.
It has been pointed out by most previous investigators that an
activation energy in thin aluminum films of approximately 0.7 eV, i.e.,
about one-half of the activation energy for lattice diffusion (1.42 eV)
,
suggests a predominance of grain boundary migration compared to trans-
port in the volume. A low value for the activation energy at the
lower end of our temperature range indicates, on the other hand, that
contributions by surface diffusion should not be completely ruled out,
2. An alternative interpretation of the results presented in
Figure 4.2 is that the activation energy is dependent on the size of
the grains contained in the aluminum films. This grain-size dependence
of the activation energy was proposed by several investigators [28,29,
31], as shown in Table 4.1. These authors deduce from their MTF mea-
surements that large-grained films display a greater activation energy.
Bearing this in mind, it could be argued that if we measure at a rela-
tively high temperature, grain growth could occur in these particular
specimens and could be the cause for a higher activation energy. To
explore this idea further, some aluminum films were annealed prior to
current stressing at a temperature which was higher than the one which
was actually reached during the electrotransport experiment (4 hours at
400°C, in a argon atmosphere) . In addition, each specimen has usually
undergone a warm-up and stabilization period of approximately one hour
before resistance measurements are taken. The results of these studies
are included in Figure 4.2 (cross points). It can be clearly seen that
32
annealing (and possibly some grain growth) has no measurable effect on
the activation energy of aluminum films. The above-mentioned investi-
gation is of course not intended to settle the question of the grain
size dependence of the activation energy. (This can be done only by
repeating our investigations for coarse- and fine-grained films.) Our
results show, however, that in our case annealing is not the cause of
the observed increase of the activation energy with increasing temper-
ature .
°oZ*e p
3. It is commonly assumed that the term In — in
equation (2.18), i.e., the intercept in an Arrhenius-type diagram
(Fig. 4.2), is temperature independent. Since p varies in a small tem-
perature range linearly with temperature, the ratio p/T can be con-
sidered to be temperature independent. In order to investigate the
*possibility that In D0 Z
D
ln +kt
= lnZ*e p
TcT
varies with temperature, the function
was plotted with respect to the temperature
assuming a constant Q = 0.6 eV. It was found that this is a second
order function. In order to obtain a linear relationship between
Dq
Z and T (for example, a decrease of Z with temperature as observed
by several investigators for electrotransport in bulk aluminum [14,48]),
the activation energy can no longer be held constant but has to vary
with temperature. It is therefore concluded that the temperature depen-
dence of the activation energy for electrotransport in aluminum appears
to be real, as suggested above.
33
4.1.3 Temperature of Measurements
The temperature which a thin film stripe assumes during
electrotransport experiments is usually proportional to the joule-
heating in the specimen. It depends, among other factors, on the
resistivity (p) of the metal, the specimen dimensions, and the type of
substrate. The temperature range which is conveniently accessible in
aluminum films deposited on glass substrates can be deduced from
Figure 4.4 in which the resistance change per unit time is plotted
versus the specimen temperature. It can be seen from this graph that
at temperatures greater than about 360°C the resistance change per unit
time becomes fairly large. This factor causes the thin film stripe to
fail before data can be taken. Similarly, at temperatures much lower
than 220°C, the resistance change per unit time becomes so small that
meaningful results cannot be obtained in a reasonable amount of time.
A further extension of the useful temperature range could be achieved by
depositing the aluminum films on other substrates such as silicon wafers,
or by cooling or heating the specimens in a temperature bath. This,
however, would change the experimental conditions so that the results
would probably no longer be comparable with the data obtained by using
the present method.
4.1.4 Velocity of the Moving Ions
As mentioned in Section 4.1.2, electrotransport in thin aluminum
films is dominated by grain boundary diffusion. The resistance change
which is measured in these experiments is therefore predominantly caused
by loss of material in the grain boundaries. (The mass depletion along
34
CJ
h-
Figure
4.4
Relative
resistance
change
per
100
minutes
determined
on
aluminum
films
subjected
to
direct
current
at
various
temperatures.
The
resistance
changes
are
normalized
to
a
current
density
of
5x
10
5
A/
cm
2.
35
the grain boundaries can actually be observed by using the electron
microscope [44].) The mean velocity (v) of the moving ions obtained
from resistance measurements should therefore be related to the ion
velocity calculated from observations of the rate at which a grain
boundary opening proceeds. Our results support this suggestion.
The mean velocity (v) of the aluminum ions which drifted
through the grain boundary due to momentum exchange with the electrons
was calculated from the rate of resistance change, using equation (3.1).
Velocities obtained in this way on nine specimens at various temper-
atures are shown in Figure 4.5 and are compiled together with other
pertinent data in Table 4.2. (A more detailed Table A4.1 is given in
the Appendix.) Berenbaum [44], who measured the rate at which grain-
boundary opening proceeded, found at a stripe temperature of 360 ± 40°C
and a current density of 9.6 x 10 6 A/cm2 an ion velocity of 8.5 x 10~ 6
cm/sec. By normalizing this velocity and correcting for the current
density vector operating in the direction of the grain boundary, he
found vT/j to be 1 x 10“ 15 m 3 K/ (A sec). This value compares favourably
with our values in the corresponding temperature range as can be seen
from Table 4.2.
In electrotransport experiments, in which diffusion through the
lattice is predominant, a different type of velocity is usually defined.
In contrast to grain boundary diffusion, each ion in bulk diffusion can
be involved in the process of motion. Therefore, the velocity of ions
in lattice (v^) must be related to the whole volume of the specimen.
If a given velocity is averaged over the entire volume, the velocity is
much smaller than the same velocity averaged over the grain boundary
v
(cm/s)
36
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TABLE 4.2
EXPERIMENTAL DATA OBTAINED ON THIN ALUMINUM FILMSSUBJECTED TO ELECTROTRANSPORT
Temperature
(°c)
Thickness
d (cm)
CurrentDensity
j (A/ cm2 )
AverageVelocity
v(cm/sec)
v*T
j
(m 3K/A* sec)
218 1 . 18xl0-5 5.75x10 s 0.716xl0“ 7 6 . llxlO-1
7
239 1.52xl0“ 5 5.10x10 s 0.979xl0- 7 9 . 82xl0-1
7
242 1.55xl0“ 5 5.41x10 s 1.313x10-7 1.25xl0“ 16
271 1.70X10" 5 5.11x10 s 1.726x10-7 1.84xl0~ 16
302 1.70X10" 5 5.12x10 s 3.762x10-7 4.22X10- 16
317 1.5 xlO" 5 5.81x10 s 5.940x10-7 6.03xl0" 16
332 1 . 52xl0-5 5.94x10 s 6.871x10-7 7.00xl0~ 16
348 1.5 xlO- 5 6.00x10 s 10.3 xlO- 7 1.06xl0- ls
363 1.7 xlO" 5 5.28x10 s 14.16 xlO" 7 1.71xl0- ls
38
area. The proportionality factor is the ratio of the volume of the
grain boundaries to the total volume. Our studies, using quantitative
microscopy, have shown that for our specimens (which have an average
grain size of about 1 Pm), this ratio is approximately 1 x 10-3 . This
means that if a comparison is desired between a velocity, v , obtained
by bulk electro transport studies and one obtained by studies of the
mass reduction in grain boundaries, v , the latter value must be multi-St
plied by a factor of approximately 10-3 (depending on the grain size).
Not all studies of electrotransport in thin aluminum films
published so far have measured the mass reduction in grain boundaries.
Blech and Meieran [38], for example, observed the rate at which voids
grew and then calculated v^ by dividing the total volume of holes
formed per unit time by the entire cross-sectional area of the stripe.
Their ion velocities are therefore comparable to those found in bulk
electro transport and are about 3 orders of magnitude smaller than those
found by Berenbaum and us.
4.2 Silver
4.2.1 Activation Energy for Electrotransportin Thin Silver Films
To our knowledge, measurements of the activation energy for
electrotransport in thin silver films have not been reported in the
literature. These data are, however, of great interest, particularly
because of differences of opinion as to the type of diffusion which
occurs in thin film electro transport. Berenbaum and Rosenberg [49],
for example, infer from their in situ scanning electron microscopy
39
studies that the electromigration behavior of silver appears to be con-
trolled by surface diffusion. In contrast to this, Breitling and
Hummel [27] concluded from investigations in which they varied the
size of silver grains that electrotransport in these films is dominated
by diffusion in the grain boundaries. The following experiments were
designed to resolve this question.
Measurements of the velocity of silver ions caused by electro-
transport were carried out in as large a temperature range as possible
and in the same manner described in Section 4.1.2. The upper limit of
the temperature range (approximately 300 °C) was set by an extremely
rapid formation of voids which led to destruction of the films before
meaningful resistance data could be taken. On the other hand, at
temperatures below about 150 °C, the resistance change in a reasonable
length of time was found to be within the error limit of these exper-
iments, as discussed more fully below.
A set of characteristic resistance-changes (AR/Rq
) as a func-
tion of time, taken in three different portions along an annealed thin
silver film, is shown in Figure 4.6. As in our previous experiments on
silver films [27], the resistance change was largest in a region close
to the anode at all temperatures. From this fact it follows that ion
transport was always opposite to the direction of electron flow.
Figure 4.7 shows an Arrhenius- type plot of the data from
resistance measurements on silver films. It is interesting to note
that for two relatively distinct temperature regions, two lines of
different slope can be drawn through the data points, suggesting two
different activation energies. For the low temperature region
40
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41
Figure
4.7
Arrhenius-
type
plot
of
data
taken
on
thin
silver
films
(annealed)
subjected
to
a
direct
current.
42
(approximately 150°C to 215°C) an activation energy Q = 0.3 eV was
calculated, whereas at higher temperatures (215°C to 280°C) the Q
value was 0.95 eV.
Published information on the activation energies for self-
diffusion in silver, including grain boundary and surface diffusion,
are summarized in Table 4.3. Our Q values for electrotransport are
also included in this table. A comparison reveals that our measured
activation energy at "high" temperatures, 0.95 eV, compares favorably
with activation energies found by other investigators for grain bound-
ary diffusion. Similarly, the activation energy of 0.3 eV measured in
the present investigations at "low" temperatures compares well with
data found by others for surface controlled diffusion. This suggests
that at "low" temperatures electrotransport in thin silver films is
dominated by surface-controlled processes, whereas at higher temper-
atures grain-boundary effects become predominant. At temperatures even
higher than those used in the present study, volume electrotransport is
likely to take place. This suggestion is supported by the data obtained
by Kleinn [50] which yielded an activation energy of 1.9 eV.
4.2.2 Temperature Range of Measurements
In Figure 4.8 the velocity of silver ions during electrotrans-
port is plotted versus the temperature of the center portion of a thin
film stripe. It can be seen from this graph that for temperatures of
150°C or less, the ion velocity and particularly the change of this
velocity with temperature is small. This behavior illustrates the
existence of a lower limit of our temperature range in which meaningful
43
TABLE 4.3
COMPILATIONS OF ACTIVATION ENERGIES FOR SELF-DIFFUSION IN SILVERAND OUR DATA ON THIN FILM ELECTROTRANSPORT
VolumeDiffusion
Qv(eV)
GrainBoundaryDiffusion
Qb(eV)
SurfaceDiffusion
^s
(eV)
Reference and Year
1.95 0.88 — Tsitsiliano and Gertsriken(1958)
[51]
1.95 0.93 — Hoffman and Turnbull
(1951)
[52]
1.95 — — Patil and Huntington(1970)
[53]
1.91 — — Tomizuka and Sonder(1956)
[54]
— 0.78 — Love and Shewmon(1963)
[55]
— 0.85 — Turnbull and Hoffman(1954)
[56]
— 0.82 — Vardiman and Achter(1969)
[57]
— — 0.43 Nickerson and Parker(1950)
[58]
— — 0.35 Geguzin and Kovalev(1963)
[59]
— 0.95 0.30 Present paper (Thin filmelectro transport)
44
Figure
4.8
The
velocity
of
silver
ions
as
a
function
of
film
temperature.
45
resistance data can be taken. Similarly, the upper temperature limit
of our experiments can be deduced from Figure 4.9 in which the resis-
tance change per unit time is plotted versus the stripe temperature.
It can be seen that at temperatures greater than about 280°C the
resistance change per unit time becomes very large so that (as mentioned
above) the thin film stripe usually fails before meaningful data can
be taken. A detailed documentation of the experimental results can be
found in the Appendix, Table A4.2 and Figure A. 4.1.
4.3 Gold
4.3.1 Activation Energy for Electrotransport
Electromigration studies in thin gold films have recently
gained increased interest because metallizations in microelectronic
devices made out of this metal have a longer lifetime than those made
of aluminum. Few papers have been published so far in which the acti-
vation energy for electrotransport in gold films has been studied.
In most cases the MTF-method (see Section 4.1.1) has been used. In one
case the growth of voids has been measured in the electron microscope.
The procedure for fabricating the test stripes used for these studies
varied considerably among previous investigators. Electroplating,
sputtering or vapor deposition of the gold films on various substrates
with and without transition-metal underlayers were used. The activation
energy was observed to be in the range from 0.8 eV to 0.9 eV, i.e.,
approximately one-half of the activation energy for volume self-diffusion
(1.81 eV) [12,60]. The pertinent data from previous work are compiled
in Tab le 4.4.
46
Figure 4.9 Relative resistance change per 100 minutes determined forsilver films subjected to direct current at various tem-peratures. The resistance changes are normalized to
a current density of 6.8xl0 5 A/ cm 2.
ACTIVATION
ENERGIES
FOR
ELECTROTRANSPORT
IN
THIN
GOLD
FILMS
47
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48
The present studies of thin gold films were similar to those on
aluminum films (see Section 4.1.2). As before, the principal aim of
the investigation was to obtain an activation energy for ion movement
under the influence of an electric field.
In Figure 4.10 the resistance change in three different segments
of a gold film is plotted versus time. As described previously by
Breitling and Hummel [27,41], the resistance increase was largest at
the anode side of the stripe (segment IV). This behavior can be attri-
buted to void formation near the anode. If the temperature of the cen-
ter of the film is held constant, a relatively linear resistance increase
can be observed up to about 400 minutes. Comparable measurements were
taken on five gold films, using various current densities and temper-
atures (250-390°C) . The specimens were annealed at 350°C for about
20 hours in vacuum after vapor deposition.
In Figure 4.11 the results of these measurements are plotted in
an Arrhenius-type diagram. It is interesting to note that, in contrast
to the results for aluminum and silver films, the measured data fit
a straight line. This suggests a uniform activation energy in the tem-
perature range used for these investigations. The activation energy (Q)
obtained from the slope of Figure 4.11 was calculated to be 0.98 eV.
Our Q is thus slightly higher than the ones obtained by previous inves-
tigators but is still within the error limits of those authors, as can
be seen from Table 4.4. It is assumed that different specimen condi-
tions (underlayer, structure differences, etc.) are the cause of this
variation. This will be discussed in the following section.
49
Figure 4.10 Relative resistance change (AR/R0 ) as a function of time
for a gold thin film. T = 356° C; j = 6.3*10 5 A/ cm2;
d = 1.66xl0-5 cm. (Specimen 8A.)
50
T (°C)
Figure 4.11 Arrhenius- type plot of measurements on annealed goldfilms subjected to a direct current.
51
4.3.2 Structural Differences in Gold Films
In order to Investigate possible effects of annealing on the
activation energy for electrotransport in thin gold films, a batch of
specimens was used which was identical with those used for our previous
experiments except that they were not subjected to the annealing proce-
dure described above. The results obtained from these unannealed (ua)
films are compared in Figure 4.12 with those obtained from annealed (a)
films. As in annealed gold films, the experimental data plotted in an
Arrhenius- type diagram lie on a straight line. However, two distinct
differences between the two types of specimens can be seen in Figure 4.12.
Firstly, the slope and therefore the activation energy of electrotrans-
port is higher for the unannealed films. Calculations involving the data
of Figure 4.12 yield an activation energy for the unannealed specimens
of 1.1 eV (compared to 0.98 eV for the annealed films). Secondly, the
ratio v/j is distinctly smaller for the unannealed specimens. This
means that the velocity of the gold ions is smaller in these films.
The same conclusion can also be drawn from Figure 4.13 in which the
temperature dependence of the average ion velocity per unit current
density (v) is shown for the two kinds of films. It is interesting to
note that at lower temperatures v is about an order of magnitude smaller
for the unannealed films. However, at temperature close to the anneal-
ing temperature, the ion velocities become almost identical. It should
be noted here that in gold films the values of v cover 3 orders of magni-
tude in our useful temperature range, compared to about one order of
magnitude in aluminum films and one and one-half orders of magnitude in
silver films.
52
T (°C)
375 325 300 275 250 225 200
Figure 4.12 Arrhenius-type plot of measurements taken on annealed(a) and unannealed (ua) gold films subjected to adirect current.
53
v (cm/s)
Figure 4.13 Average ion velocity in thin gold films subjectedto a direct current as a function of specimentemperature; v is normalized to a current densityof 6.8 x 10 5 A/ cm2
; (a) annealed films; (ua)
unannealed films.
54
The greater activation energy and lower ion velocity in
unannealed gold films can be attributed to the following possible causes:
1. Unannealed films contain high stresses which may cause the
average ion to move more slowly. These stresses are also considered to
be the principal cause of the higher activation energy observed in
unannealed gold films
.
2. Annealing could cause grain growth. To investigate this
possibility further, transmission electron micrographs of an unannealed
and of an annealed film were taken. Figure 4.14 clearly shows that the
average grain size of the annealed films was about a factor of three
larger.
In aluminum films a possible grain-size dependence of the activa-
tion energy for electrotransport was reported in the literature (see
Table 4.1). It was suggested there that coarse-grained films usually
have a larger activation energy. Our observations on gold films show,
however, just the opposite behavior. The annealed, i.e., the coarse-
grained films, have a smaller activation energy. A possible grain size
dependence of the activation energy has therefore been excluded as an
explanation of our above-mentioned observation.
4.3.3 Temperature Range of Measurements
The useful temperature range for our experiments can be deduced
from Figure 4.15. By the same reasoning employed in previous sections,
the lowest temperature at which meaningful data could be taken in a
reasonable length of time was approximately 220°C and 250°C for the
unannealed and the annealed films, respectively. On the other hand,
55
Transmission electron micrographs of(a) annealed and (b) unannealed gold films.Average grain size: (a) 0.7 pm; (b) 0.2 ym.
Figure 4.14
56
^/lOO min
Figure 4.15 Relative resistance change per 100 minutes determinedon gold films subjected to direct current at varioustemperatures. The resistance change is normalized toa current density of 6.8 x 10 5 A/ cm2
. (a) annealed films;(ua) unannealed films.
57
at temperatures higher than 380°C and 390°C, respectively, the resis-
tance changed so rapidly that no reasonable data could be obtained.
Data supporting these conclusions are tabulated in the Appendix
(Tables A4.3 and A4.4).
4.3.4 Practical Consequences
The results presented here have practical significance for the
semiconductor industry. The lifetime (tf) of thin film metallizations
I
used in microelectronic devices is strongly dependent on the appropriate
activation energy for electromigration, as can be seen from the equation
[29,61],
tf
= A-jn
exp (^) ,
where A is a constant, j the current density, and n a positive number
lying between 1 and 3.
A higher activation energy for electrotransport means a longer
lifetime for the metallization. Among the metals investigated here,
gold has the highest activation energy (0.98 eV)
,
whereas silver has
the lowest (0.3 eV) in the temperature range used for device operation.
The activation energy of gold, and therefore the lifetime of metalliza-
tions made out of this metal, can be increased by introducing struc-
tural imperfections in the film. This can be done by omitting the
annealing step of the film, and by depositing the film at a temperature
as low as practicable.
58
4.3.5 Thermo transport
Thermotransport in bulk gold has mostly been observed to be
directed toward the hot side of the specimen (negative Q ) [62,63,64].
Only in one case has a positive Q been reported [65]. Since electro-
transport in gold films was found to be directed opposite to the direc-
tion observed in the bulk, a possible reversal of the thermotransport
was investigated.
Gold films were prepared and annealed as described above.
First, the resistance of the stripe was measured at room temperature.
Then the specimens were joule-heated to 320°C by subjecting them to an
alternating current. This procedure made sure that the temperature
profile along the stripe was similar to the one in our previous d.c.
experiments. After several hours the specimens were cooled carefully
to room temperature and the resistance was measured again. It was
observed that the resistance increased about 0.17 per cent per 100
minutes in areas II and IV, whereas at the center portion the increase in
resistance was 0.04 per cent per 100 minutes. These resistance changes
are about a factor of 20 smaller than those found for electrotransport
at a comparable temperature (see Fig. 4.15). We conclude from these
experiments that thermotransport in thin gold films is directed toward
the warm side as has been found for bulk gold.
4.3.6 Direction of Electrotransport
The actual direction of mass flow in gold films subjected to
a direct current is still controversial. Our previous observations
[27,41] and again the present investigations clearly indicate that
under our experimental conditions gold ions migrate against the
59
electron flow. Other authors [32-34,37,66], however, did not confirm
so far our observations . Because of this controversy we repeated our
experiments using a slightly modified technique. Contrary to our
earlier studies [27,41], we held the center portion of the film at
a constant temperature as described in Section III. Furthermore, in
some cases higher current densities and therefore higher temperatures
were used. Below, the results are presented and discussed.
In Figure 4.16 the familiar rate of resistance change is shown.
It can be seen there that as usual the initial increase in resistance
is largest in area IV, i.e., near the anode of the specimen. If the
experiment is conducted at constant temperature over a long period of
time, the resistance does not increase any further in area IV and fin-
ally becomes constant.
If the same specimen is subsequently subjected to a higher
current density and consequently to a higher temperature, the resistance
increases in area III (center) and at a later stage also in area II
(cathode), but to a lesser extent. The film finally fails in the center
portion as can be seen also from Figure 4.17.
In another experiment a gold film was immediately subjected to
a high current density. In this study, however, the temperature was not
held constant. Figure 4.18 shows that the largest initial resistance
increase occurs again in area IV (anode) . In the progress of this run
the temperature increases constantly because of the decrease in cross-
sectional area due to void formation. After a critical temperature has
been reached, the resistance becomes larger in the center portion and
60
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Figure
4.18
Relative
resistance
change
of
unannealed
gold
film
specimen
during
electrotransport.
The
temperature
was
not
held
constant;
j=
8x
10
s
A/
cm
;d=
1.2
x
10
-5
cm.
(Specimen
13-1.)
63
the stripe fails finally in this area, or slightly towards the cathode.
Figure 4.19 illustrates the two areas of void formation convincingly.
As above-mentioned observations suggest that temperature and
possibly other factors (such as grain size) have an influence upon the
direction of electrotransport in gold films. It is well known that at
higher temperatures volume electrotransport predominates. In this case,
ion migration with the electron flow was observed [48]. It is therefore
assumed that those investigators who did not observe migration of gold
ions against the electron flow were conducting their experiments at a
temperature at which volume electrotransport is predominant.
64
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APPENDIX
66
Transmission electron micrograph ofannealed silver film. Average grainsize: 0.8 pm.
Figure A4.1
TABLE
A4.1
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Ur*Inin
vO
SO
n *lO
m0<rm
In
ci
VO0*r|
mvO
T o *)
«* — i“
<x ^ « T
APPENDIX B
RESISTANCE MEASUREMENTS AS A TOOL FOR
DETERMINING ACTIVATION ENERGIES FOR ELECTROTRANSPORT
The purpose of this study is to discuss the possibility of
employing resistance measurements for determining an activation energy
(Q) for electrotransport in thin films. In order to obtain Q it is
necessary to measure, in a series of similar measurements, the average
velocity (v) of the ions while they are moving through the film due to
v
momentum exchange with the current carriers. If one then plots In .
(where j is the current density) versus the reciprocal temperature
(1/T) in an Arrhenius type diagram, the activation energy can be cal
culated in the usual way from the slope, as can be seen from the fol-
lowing equation:
1
T(B.l)
where D = pre-exponential diffusion constanto
p = resistivity
eZ* = effective charge
k = Boltzmann constant.
Suppose the resistance is measured by means of two potential
probes in a section with a length (A), approximately one-third of the
stripe length (Fig. Bla) . Because of Joule heating and the presence
of thicker electrodes which act as heat sinks, a nearly parabolic
71
72
Figure B.l. (a) Schematic shape of sample.
(b) Schematic temperature profile along sample.
73
temperature distribution along the entire stripe can be assumed
(Fig. B.lb). If the film is deposited on a substrate, the temperature
profile is likely flattened out at the center of the stripe.
Let us consider a volume element of length Z (Fig. B.2)
close to one of the electrodes (Sec. II, Fig. B. la). Let us further con-
sider the case in which the ions electromigrate from left to right.
The number of ions (n^) entering this volume through areaA^ in a time
interval (At); i.e., the flux (J^) is
Jl
=n„
A^At= C
1V1
(B.2)
where c^ is the concentration of atoms per cubic centimeter and v^
is the velocity of the ions in area 1. Similarly, an equation for the
ions leaving the volume element through area 2 can be written
n r
= = c„ v„ .
2 A2At 2 2
(B. 3)
The depletion of ions within the volume element is therefore (if
A1
A2
Ao )
n2
nl
J2
J1
" A AtC2V2 °1 V
1o
(B. 4)
or, by assuming the concentration of atoms in A^ and is alike
(i.e. , c2
= c^ = c)
,
AJ = irk = c(v2_v
i) •
(B . 5)
The mass (m) of the volume element equals the volume (V) times the
density (y), i.e..
Figure B.2. Volume element of sample.
75
nm = Y V = Y
~ (B. 6)
or
Am = y AV = yAn (B . 7)
Combining equations (B.5) and (B.7) provides
Am
YA At' V
2V1
'
o
(B .8)
Experiments have shown thnt the left-hand side of the volume
shown in Figure B.2 (area 1) is at a considerably lower temperature
than the right-hand side (see also Fig. B.lb). In addition, the thick-
ness of the electrode, i.e., the volume at left of A^^ is usually larger
so that the current density is lower there. As a consequence, only
a very small amount of ions is likely to enter the volume element through
Ax
,i.e., J
2»J
1,and therefore, v
2 »
equation (B.8) reads
_ AmV2 " yA At
o
With this notation.
(B. 9)
where v£
is the average velocity of the ions leaving the unit volume
through A2> Below, various approaches to determine v2
from resistance
measurements are discussed.
It has been shown that during the initial stage of an electro-
transport experiment, the resistance increases linearly with time.
This increase in resistance occurs usually in a well-defined area of
the stripe close to one of the electrodes. After the film has been
subjected to a direct current for a longer period, voids can usually
be detected in this area. The increase of the resistance (AR) in a
76
specific area can therefore be attributed to a depletion of mass (Am)
in this region. It could be argued that the resistance may also change
during an electrotransport experiment due to relief of stress, thermo-
transport, raise in temperature, or similar temperature—related pro
cesses. Our experiments on well-annealed films which have been sub-
jected to an alternating current (using an identical current density as
in the d.c. experiments) have shown, however, that in this case prac-
tically no resistance increase due to annealing takes place. In order
to prevent resistance increases due to a rise in temperature, the
temperature of the stripe has to be held constant during an entire
electrotransport experiment.
Let us consider now that after the experiment the cross-sectional
area (A(x)) of the film varies along the volume element of length Z.
In this case the resistance of the film is
rl dxR “ / » iw •
0
The original resistance was
(B . 10)
„ rZ dx pZRo
=/ P T =
A”u o n
(B.ll)
where A is the initial cross-sectional area. With ARo
one obtains the relative resistance change
1 f!L AA
R’-R ,o
AR 1 rZA0~A(X)
, _ I fiF = F J ~T7F— dx - —J
R Z J A(x)o °
A(x)dx
The relative change in resistance per mass change is
(B. 12)
F1 1 r«. AA ,
R - L dxo _ Z -*0 A(x)
y AA dxAm(B. 13)
77
where y is the density. Combining equations (B.9) and (B.13) yields
v2
£ AR
A At Ro o
f*q AA dx
f£ AA
L A(x)dx
(B.14)
B. 1. Uniform Reduction of Volume
of Stripe
We consider now the special case in which the mass depletion
is constant (i.e., uniform) along the stripe. In addition, the reduc-
tion of the area due to electrotransport shall be small, i.e.,
A(x) Aq
. Then, equation (B.14) reduces to
v2
AR _£_
R Ato
(B. 15)
Equation (B.15) probably assesses the situation quite well
during the initial stage of electrotransport. However, equation (B.15)
can most likely not be used at an advanced stage of the experiment in
which the resistance increases in a nonlinear way. This nonlinearity
is, among other effects, due to local variations in the mass distribution
(voids) and therefore due to local variations in temperature and current
density. Thus, equation (B.15) should be used only for the initial por-
tion of an electrotransport experiment in which the resistance increases
linearly with time and in which it can be assumed that the mass deple
tion is relatively uniform in a given segment of a sample. Equation (B.15)
provides a simple means of calculating the average velocity of the ions
electromigrating through area 2 by measuring the rate of relative resis-
tance change. By knowing the temperature of A2
»the activation energy
can be determined as described above.
78
B.2 Non-Uniform Reduction in
Cross-Sectional Area
In the foregoing section we assumed that the depletion of mass
due to electrotransport is uniform in a given section of a film.
However, as is shown by the following equation,
the maximum change in velocity and therefore the maximum change in mass
.. dT
takes place in a volume element in which the temperature gradient ^is largest. This has been confirmed also by experiments.
In Figure B.3, the mass depletion is sketched to be largest
close to an electrode and tapers off towards k^. In this case, the
resistance after an electrotransport experiment (R' ) varies along the
stripe; i.e., R' is a function of the varying cross-sectional area,
A(x) :
(B . 16)
(B . 17)
A(x) can be written according to Figure B.3
\ AA . * f
A(x) = — x + A .(B. 18)
Equation (B.18) inserted into (B.17) gives
Ao
(B . 19)
With
(B . 20)
79
<
Figure
B.3.
Wedge-shaped
reduction
in
cross-sectional
area.
80
one obtains
ARRo
R’-Ro
Ro
1 .CB.21)
In can be expanded in a series by using A' - Aq
- AA:
A
1 AA^2 A
2 '
o
(B . 22)
In equation (B.22) terms containing and larger order. terms are
Ao
neglected, which is only justified if AA << Aq
. This is true at
the initial stage of electrotransport. Inserting equation (B.22)
in (B. 21) yields
AR =1 AA (B. 23)
* R 2 Ao o
From Figure B.2 it can be seen that the change in mass (Am) is
proportional to the shaded wedge, i.e..
Am = XJL_^A.
(B. 24)
Inserting equations (B.23) and (B.24) into (B.9) provides
- _AR ft
v2 R At ’
o
i.e., equation (B.15). Without the series expansion of equation (B.22),
one obtains
v2 2At AR
1Ro
(B . 25)
81
A similar calculation which uses, contrary to Figure B.3, a double
wedge having its lowest point at the center of the volume element
(x =-|) leads essentially to the same result as above.
B. 3. Grain Boundary Grooving
Observations using the electron microscope have shown that in
thin films the mass depletion due to electrotransport occurs predom-
inantly along grain boundaries. Therefore, it is interesting to consider
the resistance change which is caused by a narrow groove in the stripe.
In Figure B.4, this groove is sketched to be perpendicular to the length
of the stripe. The film is thought to be divided into n segments
(length 6 = £/n) which have the initial area Aq
. One of these segments
is thought to contain a groove with an area A' (Fig. B.4). Before the
experiment, the mass of the stripe was
m = y SLA .
o o
After the experiment the mass is
m ' = Y A'
(B. 26)
(B.27)
Hence,
t Y& . .
Am — m —m — AAo n
(B . 28)
Similarly, the original and the final resistances can be written
to be
and
p£R =
Ao Ao
= _PL +RA'n A n
o
(B. 29)
(B . 30)
82
83
Therefore,
R 1 — RAR _ % = AA 1
R R A' n'
o o
Combining equations (B.9), (B.28), and (B.31) yields
- =AR Ai_
V2
" R At Ao o
(B.31)
(B. 32)
For a small depth of a groove (A’/Aq^ 1) equation (B.32) reduces to
the simple equation (B.15).
It is interesting to discuss the resistance change of
a groove as sketched in Figure B.4. Using the width of a grain bound-
ary 5 - 10-
7
cm and a specimen length of Z = 1 cm, n becomes approx-
imately 107
. Consider the case in which the groove has a depth about
one-half of the film thickness, i.e., AA = A'. Then equation (B.31)
provides that the relative resistance change AR/Rq
is about 10 ;
i.e., the relative resistance change of a narrow, perpendicular groove
is negligible. However, if n becomes smaller, or equivalently, <5
becomes larger (more or wider grooves), the relative resistance change
becomes appreciable.
B.4. Conclusions
The foregoing considerations have shown that for the initial
stage of an electrotransport experiment a relatively simple
equation (eqn. B.15) can be used to calculate an ion velocity from
resistance measurements. At a later stage of the electrotransport
experiment in which the rate of resistance change is no longer linear,
corrections to the simple equation (B.15) have to be applied, which are
depending on the failure model.
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CURRICULUM VITAE
1. Name : Hans Joachim Geier
2. Affiliation : Hans Joachim Geier (German diplomat)
Margareth Kratzig Geier (German)
3. Place and Date of Birth : Lisbon, PortugalAugust 31, 1943
4. Marital Status : Married to
Maria das Gracas La Rosa Geier (Brazilian)
5. Children : one daughterAndrea La Rosa Geier (American - Brazilian)
6. Nationality : Portuguese
7. Professional Titles:
1966 Metalurgical Engineer Universidade Federal do Rio Grande
do Sul, Porto Alegre - Brazil
1968 Nuclear Engineer (CNEN) Instituto Militar de Engenharia(IME) ,
Rio de Janeiro - Brazil
1970 Master of Science Instituto Tecnologico da Aeronautica(ITA) , Sao Jose dos Campos -
Sao Paulo - Brazil
1973 Master of Engineering University of FloridaGainesville - Florida - U.S.A.
1974 Doctor of Philosophy University of FloridaGainesville - Florida - U.S.A.
8. Pre-University Education :
In correct time sequence:
Lisbon (Portugal),Rio de Janeiro (Brazil)
,Recife (Brazil)
,
Montevideo (Uruguay) , Porto Alegre (Brazil)
.
75
76
9
.
Academic Formation :
1) Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
1962-1966 Metalurgical Engineering Program (5 years)1967 Introduction to Nuclear Engineering Program (1 year)
2) Instituto Militar de Engenharia (IME) , Rio de Janeiro, Brazil
1968 Nuclear Engineering Program (1 year)
3) Instituto Tecnologico da Aeronautica (ITA),Sao Paulo, Brazil
1969-
1970 Master of Science in Materials Science (18 months)
4) Southern Illinois University, Carbondale, Illinois, U.S.A.
1970-
1971 Molecular Science Program (9 months)
5) University of Florida, Gainesville, Florida, U.S.A.
1971-
1974 (2 years and 10 months)Master of Engineering in Met. & Mat. Sci. EngineeringDoctor of Philosophy in Met. & Mat. Sci. Engineering
10. Awards
:
1) Awarded in 1966 the gold medal "Medalha Maua" for highestachievement in the Metallurgical Engineering Program at the
Federal University of Rio Grande do Sul, concerning his fiveyears program.
2) Highest achievement on the "Introduction to Nuclear Engineering"Program (one-year program) offered by the Department of Physics
at the Federal University of Rio Grande do Sul, Porto Alegre,Brazil
.
3) Awarded a "Special Doctoral Assistantship" in April 1971 due to
high performance achieved as a graduate student and teachingassistant at Southern Illinois University.
11. Professional Activities :
1) Probationer at IPESUL S.A., Porto Alegre, Brazil (1966)
2) Probationer at ZIVI HERCULES S.A., Porto Alegre, Brazil (1966)
3) Metallurgical Engineer at ZIVI HERCULES S.A., Porto Alegre,Brazil (1966-1967)
4) Research Engineer at CENTRO TECNICO AEROESPACIAL (CTA)
,
Sao Paulo, BrazilMaterials Department, Division of Vacuum Metallurgy (1969-1970)
Division of Composite Materials5) Graduate Teaching Assistant at Southern Illinois University
(1970-1971)
6) Graduate Research Assistant at University of Florida (1971-1974)
<\o
77
12. Especialization Trips :
1) To Germany, in 1967, for purposes of especialization in heattreatment of metals.Sponsored by ZIVI HERCULES S.A.
Places visited: DEGUSSA FrankfurtINDUSTRIEOFENBAU HanauBOEHLER WERKE Dusseldorf
2) To U.S.A., in 1970, for purpose of especialization in MolecularScience.Place visited: Carbondale, Illinois
13. Scientific Work :
1) Monography "Uranium-Zirconium Alloys," CNEN-Rio de JaneiroBrazil (1968)
2) Paper "Consideracoes sobre a Mobilidade Ionica em SolidosMetalicos," METALURGIA, ABM (1971)
3) Author of the research project "High Density Graphite UsingBrazilian Natural Graphite," approved by the Institute of
Research and Development of the CENTRO TECNICO AEROESPACIAL,Sao Paulo, Brazil (1970).
4) Co-author of the project, "Vapor Phase Deposition of RefractoryMetals," approved by same Institution as Item 3 (1970).
14. Language Proficiency : in reading and conversation
German, Spanish, Portuguese, English
15. Metallurgical Societies :
Member of Alpha Sigma Mu, AIME, and ASM.
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
R. E. Hummed, ChairmanAssociate Professor of
Materials Science and Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
'V'O
D . B . DoveProfessor of Materials Science
and Engineering
T certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Professor of Physics andMaterials Science
This dissertation was submitted to the Graduate Faculty of the College
of Engineering and to the Graduate Council, and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
June, 1974tJxJl,
Dean, College of Engineering
Dean Graduate School