Electromigration in aluminum, gold and silver thin films

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


4.3 Gold 45

4.3.1 Activation Energy for Electrotransport ... 45

4.3.2 Structural Differences in Gold Films .... 51


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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17

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

C£-P M-l

P•H&

spp •

•H ua rHp CNrHcd p

CD

p ecd •H

a•4-1 <d

o acn

CD 'w'

S•H4J •

Bco aPCO LO

H i

CD o> rH

X/-“N COo iH

LT)

•

pc; rH<

II'—

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II

T3CD

a • r>

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rH4-1

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§ II

X •r-)

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(D CJ> o•H CMP COcd corHCD

II

P4 Eh

<•

CD

HPCO•Hp4

T(°C)

425

375

325

3m

275

250

225

200

29

l>l—

Xv—

1

1

—

TdCD

<D rH4J cd

O CD

<d g•r—; s

cd

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gCO CD

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P. U GU

4-> G CO

1 a HCO GG 4-1 o•H a rGG (D

CD UG •HrH U'M oK2 cd 4-1

rOM

CO (\ 00 0) o<3*

CD

CM CM CM CM COfM)0

0

C

30

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

03

so3U0 o<D u

i—

I

0) ndcd

3 Nx: •H4-1 rH

cd

43 a4-1

•H o& 53

<D

60 •

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3 c42 0)

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33360•HpH

37

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

MCD

>r—

I

u•H cd

CO. CO

nd 0(U u G

i—

1 Ort m rC<D i

G o <TG r—

1

cd

XG Gcd CM O

•H• 4J

o i—

i *HCO

O) II O0 G,•H nd (U4J

• r\

Td

CO CM

3 0 a)

CD a 4J• 4-1

CD C cd

>LO 0)

X)\ X CD

Pd aCO o •

'W •V-I CD

vO CD MCD CD

W) II M JSG C CDcd *r) •H CD

rG rH OO • #\ « SU (D +J

0) 0 a nj

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1

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vO

(D

UG60•HP-i

T(°C)

300

275

250

225

200

175

150

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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61

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62

(/)

L.

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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

I

no&CO

c •«cc) CMn e+J OOS-i <4-1

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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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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„

AÂt= 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 îs 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_Â.

(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




'V'O

D . B . DoveProfessor of Materials Science

and Engineering

T certify that I have read this study and that in my opinion it




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

Documents

Electromigration in aluminum, gold and silver thin films