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Solid State Amorphization Reactions in thin Film Diffusion Couples
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Meng, Wen Jin
(1988)
Solid State Amorphization Reactions in thin Film Diffusion Couples.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/E13T-CN40.
Abstract
Metastable materials including amorphous materials have traditionally been synthesized from either the vapor or the liquid state. Very recently, it has been demonstrated that an amorphous alloy can be obtained by interdiffusion reactions in crystalline binary thin-film diffusion couples. This thesis focuses its study on the formation of amorphous alloys and the subsequent formation of crystalline compounds in thin-film diffusion couples. Both the thermodynamics and kinetics of amorphous phase formation have been examined. The evolution of these diffusion couples has been followed in some detail. Relevant factors governing the evolution of diffusion couples in general will be discussed.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Thin film diffusion couples, amorphous materials, thermodynamics and kinetics
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Johnson, William Lewis (advisor)
Bellan, Paul Murray (co-advisor)
Thesis Committee:
Johnson, William Lewis (chair)
McGill, Thomas C.
Corngold, Noel Robert
Fultz, Brent T.
Bellan, Paul Murray
Nicolet, Marc-Aurele
Defense Date:
7 January 1988
Non-Caltech Author Email:
wmeng1 (AT) lsu.edu
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Department of Energy (DOE)
UNSPECIFIED
NSF
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CaltechETD:etd-11022007-094005
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DOI:
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Solid State Amorphization Reactions In Thin Film Diffusion Couples

Thesis by
Wen Jin Meng

In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy

California Institute of Technology
Pasadena, California

1988
Submitted January 7, 1988

Wen Jin Meng

Ill

To my grandfather

Acknowledgements

My foremost gratitude goes to Professor W. L. Johnson. Bill’s keen
physical insights and vivid imaginations have provided much inspiration for the

work performed in this thesis. I have learned through Bill that good science, after

all, can be fun.

I have learned a great deal through interactions with many people.
Dr. K. M. Unruh’s expertise has helped me tremendously during the construction
of our sputter-deposition system. I am deeply indebted to Drs. C. W. Nieh and
C. Ahn for initiating me into the science, and often art, of electron microscopy.

Interactions with Dr. B. Fultz has been most fruitful, and my special thanks goes
to him for a critical reading of my thesis. Dr. E. J. Cotts taught me much of what

to do and what not to do.

I would like to thank the members of “the group”, past and present,
including Dr. D. V. Baxter, Dr. M. Atzmon, Dr. X. L. Yeh, Dr. Y. T. Cheng, Dr.
S. M. Anlage, P. Askenazy, P. Yvon, D. S. Lee, C. Krill, Zezhong Fu and Dr. H.

Fecht for making my years here a memorable experience.

I would like to thank C. Geremia and J. Ferrante for their help and
friendship. Without them, the memories of our group would be incomplete. Tech

nical assistance by C. Garland is gratefully acknowledged.

My love goes out to Mei. The many sleepless nights she shared with
me formed an inseparable part of this thesis. My love goes out to my familly, their
love has always been with me.

Financial support for this work has been provided by the Department

of Energy and the National Science Foundation.

Abstract

Metastable materials including amorphous materials have tradition
ally been synthesized from either the vapor or the liquid state. Very recently, it has
been demonstrated that an amorphous alloy can be obtained by interdiffusion reac

tions in crystalline binary thin-film diffusion couples. This thesis focuses its study

on the formation of amorphous alloys and the subsequent formation of crystalline
compounds in thin-film diffusion couples. Both the thermodynamics and kinetics of

amorphous phase formation have been examined. The evolution of these diffusion
couples has been followed in some detail. Relevant factors governing the evolution
of diffusion couples in general will be discussed.

Table of Contents

Acknowledgements

Abstract

List of Tables

viii

List of Figures

Chapter 1 Introduction

1.1 Diffusion in the Solid State

1.2 Interdiffusion and Reactions inThin Films

1.3 Metastable Phases

1.4 Solid State Amorphization

1.5 Introduction to the Thesis

1.6 References

Chapter 2 High Vacuum Sputter Deposition of Thin Films

2.1 Introduction to Sputter Deposition

2.2 Vacuum System

2.3 Sputter Deposition: Operationand Monitoring

2.4 Summary

2.5 References

Chapter 3 Solid-State Amorphization of Planar Binary Diffusion

Couples: Thermodynamics and Growth Kinetics

3.1 Equilibrium Phase Diagrams and Free Energy Diagrams

3.2 Planar Growth Kinetics of a Single Compound Interlayer

3.3 Growth of the Amorphous Interlayer:
X-ray and Resistivity Measurements

3.4 Differential Scanning Calorimetry

3.5 Summary

3.6 References

Chapter 4 Evolution of Planar Binary Diffusion Couples

Conclusion

100

4.1 Specimen Preparation

100

4.2 How Thick Can Amorphous Interlayers Grow

105

4.3 Is Nucleation Important

113

4.4 Models for Evolution of Diffusion Couples

121

4.5 Summary

127

4.6 References

129
130

viiï

List of Tables

Table 2.1 Residual gas content in the sputtering chamber as sampled by the resid
ual gas analyzer. Residual gas contents after introducing Ar into the chamber are
monitored both before and during sputtering of a pure Ti target at 6 mTorr of Ar.
Table 2.2 Low pressure properties of air. Particle density, n, mean-free path, λ;

particle flux on a surface, Γ. T = 22°C. Taken from Ref. 14.

List of Figures

Fig. 11 Schematic illustration of the Kirkendall effect. Taken from Ref. 15.
Fig. 1.2 Hypothetical free energy diagram and the associated phase diagram of a
binary system (A-B) with a positive enthalpy of mixing.
Fig. 1.3 Schematic Time-Temperature-Transformation (TTT) diagram for crystal

growth in an undercooled melt. Taken from Ref. 54.
Fig. 2.1 Schematic representation of the plasma during planar diode sputtering.
Taken from Ref. 11.

Fig. 2.2 Configuration of circular and rectangular planar magnetron sputtering
guns. Taken from Ref. 11.

Fig. 2.3 Vacuum system block diagram: (1) N? flush inlet valve; (2) pressure relief
valve; (3) gate valve; (4) throttle valve; (5) chamber vent valve; (6) piezoelectric

leak valve; (7) ion gauge; (8) chamber isolation/differential leak valve; (9) residual
gas analyzer; (10) ion gauge; (11) turbo-pump vent valve; (12) mechanical pump

isolation valve; (13) thermocouple gauge; (14) mechanical pump.

Fig. 2.4 Cryogenic pump regeneration history as monitored by the low temperature
sorption stage temperature during cooling.

Fig. 2.5 Typical cur rent-volt age characteristics of planar magnetron sputter guns
while sputtering Cu at 6 mTorr of Ar.

Fig. 2.6 Deposition rate of pure Cu at 9 mTorr of Ar vs. cathode current.
Fig. 2.7 X-ray small angle scattering from an Fe/'V multilayer with nominal com
position modulation wavelength of 40Â.
Fig. 3.1 Free energy functions of various phases and the A-B phase diagram derived

from them. Taken from Ref. 1.

Fig. 3.2 Schematic illustration of growth of a single compound interlayer in a planar

binary diffusion couple. Hypothetical free energy diagram and the concentration

profile.

Fig. 3.3 X-ray diffraction patterns of as- deposited (top) and reacted (bottom)

Ni/Zr multilayers (see text).
Fig. 3.4 Normalized Ni and Zr integrated Bragg peak intensities vs. f1∕2 at 250°C

and 315°C (see text).

Fig. 3.5 Shift of Zr Bragg peaks as a function of reaction time at 250°C.
Fig. 3.6 d-spacings of Ni (111), Zr (002), and Zr (100) Bragg peaks as a function

of reaction time at 250° C in reflection geometry. The insert shows the Zr (100)

d-spacing as a function of reaction time in both reflection (R) and transmission (T)
(see text).

Fig. 3.7 Resistance of a Ni/Zr multilayer (top) vs. reaction time at 225°C. Shown
also is the resistance of a pure Ni film (bottom) vs. time under identical experi
mental settings (see text).

Fig. 3.8 Schematic illustrations of various thermal analysis systems. Taken from

Ref. 21.
Fig. 3.9 Melting endotherm of pure Pb (4N+) at 10 K/min taken on a Perkin-

Elmer DSC-4.
Fig. 3.10 Apparent melting temperature of pure Pb (4N+) vs. DSC heating rate.
Fig. 3.11 Geometry of Ni/Zr multilayered diffusion couples.

Fig. 3.12 Measured heat flow rate as a function of temperature for a sputtered

Ni/Zr multilayer, Zjvï = lzr — 300Â, average stoichiometry Ni^Zr32Fig. 3.13 X-ray diffraction patterns for the thin film sample of Fig. 3.12, see text.

Fig. 3.14 Measured heat flow rate as a function of temperature for Ni/Zr multi
layers with varying individual layer thicknesses. Dotted curve, I = 300Â; dashed

curve, I = 450Â; solid curve, I — 1000Â.

Fig.

3.15 Heat-flow rate as a function of temperature normalized to the total

interfacial area of the respective Ni/Zr multilayers in Fig. 3.14.
Fig. 3.16 Heat-flow rate normalized by the total Ni/Zr interfacial area of mul

tilayers of various individual layer thicknesses and average compositions. Dotted
line, ∕jvi = 3OθΑ∕lzr = 450Â; dashed line, ljyl = 500⅛∕lzr = 800A; solid line,

= lzr — 1000A.
Fig. 3.17 Arrhenius plot for the determination of the activation energy and pre

exponential factor of the interdiffusion constant (see text).
Fig. 3.18 Heat-flow rate vs. temperature for sputtered Ni/Zr multilayers of two

different average compositions: (a) jfV⅛9Zr4l, (b) Ni^Zr^ (see text).
Fig. 3.19 Heat-flow rate vs. temperature of Ni/Zr multilayers with various Zr layer

thicknesses: (a) lzr = 800Â, (b) lzr = 45θA, (c) lzr — 24θΛ. Average composition
~ Art58^^42 fθr all three samples.
Fig. 4.1 Schematic of the morphology of bilayered elemental Ni/Zr diffusion couples

where one element (Ni or Zr) is sputtered polycrystals and the other (Zr or Ni)

consists of a mosaic of large single crystals on the order of 10 μm in size.
Fig. 4.2 XTEM bright-field micrograph of a Ni/Zr multilayered thin-film annealed

briefly around 150°C (see text).
Fig. 4.3 XTEM bright-field micrograph of a Ni/Zr multilayered thin-film annealed
at 320° C for 8 hours. Both amorphous and compound interlayers are clearly evident.

Amorphous interlayers are close to 1000Â in thickness.
Fig. 4.4 XTEM of a Ni/Zr diffusion couple reacted at 300°C: (a.) for 6 hours; (b)

for 18 hours. This diffusion couple is of the bilayered s-Ni/poly-Zr type (see Section

4.3).
Fig. 4.5 XTEM bright-field micrographs of a sputtered Ni/Zr multilayered thin-

Xll

film annealed at 360°C: (a) for 10 min; (b) for 45 min. Backgrowth of the compound
into the amorphous material at 45 min is clearly evident.

Fig. 4.6 Plot of the critical thickness of the amorphous NiZr interlayer vs. reaction
temperature.

Fig. 4.7 Reaction of a poly-Ni/s-Zr bilayer diffusion couple: (a) typical microstruc
ture of recrystallized Zr foil; (b) bright-field micrograph showing no reaction after

annealing at 300°C for 6 hours; (c) high-resolution micrograph of the poly-Ni/s-Zr
interface, showing the Ni (111) ande Zr (101) lattice fringes.
Fig. 4.8 Plane-view, bright-field micrograph showing a poly-Ni/s-Zr diffusion cou

ple after annealing at around 250°C for 4 hours. No reaction is observed at Zr grain

boundaries.
Fig. 4.9 XTEM bright-field micrograph of a s- Ni/poly-Zr bilayered diffusion couple

annealed at 300° for 6 hours. An amorphous NiZr interlayer around 1000Â thick
formed as a result of the reaction.
Fig.

4.10 Hypothetical concentration profile in a A-B diffusion couple during

parallel growth of two compound interlayers β and 7 (see text).

Chapter 1

Introduction

Thin films of solids were first obtained by either evaporation or cath
ode sputtering roughly around 1850[l,2]. Many more years passed during which
thin solid films remained a mere laboratory curiosity. Early studies were primarily
concerned with the physical mechanisms governing processes such as evaporation

from liquid and solid surfaces[3,4] or sputtering of the cathode material in a glow

discharge[5]. The science and technology of thin solid films have advanced together
with vacuum technology, which enabled the preparation of thin films of controlled
purity and microstructure. The use of thin films in magnetic or superconducting
devices[6] and, perhaps most importantly, in very large-scale intergrated circuits
(VLSI), and the technological demands associated with such usages, have been pri

marily responsible for the tremendus progress in both fields in the last thirty years.

This thesis focuses on the study of solid-state diffusive phase trans

formations in planar thin film diffusion couples. It will be demonstrated that, un
der suitable manipulation of thermodynamic and kinetic constraining factors, the

interdiffusion reaction between two crystalline elemental layers may result in the
formation of a metastable amorphous phase instead of equilibrium crystalline com
pounds. Through detailed examination of such solid-state interdiffusion reactions

that lead to the formation of metastable phases, new insights into the fundamen
tal processes governing solid-state diffusive phase transformations in thin films can

be gained. This chapter is organized as follows. In Section 1.1, a brief review of

some basic notions on diffusion in the solid state will be given. In Section 1.2, we
attempt to categorize the wealth of experimental results available on interdiffusion
reactions in thin film diffusion couples, some unifying features of such interdiffusion
reactions common to many systems will be delineated. In Section 1.3, we survey

our knowledge of metastable phases in general, with emphasis placed on the various
techniques for their synthesis. In Section 1.4, we give an introduction to solidstate amorphization reactions. Finally, in Section 1.5, some necessary background
information together with a brief introduction to this thesis will be given.

1.1 Diffusion in the Solid State

Diffusion in the solid state was first analyzed quantitatively by Fick[7].

By noting the similarity between mass transfer by diffusion and heat transfer by
conduction, Fick’s first law was formulated analogous to Fourier’s law of heat con
duction
J = -D

∂C

∂x ’

(1)

where if the concentration C denotes the number of atoms per cm3 and the current
J the number of atoms per cm2 per sec, then the diffusion constant D is given in the

units of cm2∕sec. Equation (l) relates the mass flux to the gradient in concentration
in one dimension. Combined with the condition for mass conservation, we arrive at

Fick’s second law

∂t

∂x’

∂x 7

(2)

In the special case when D is a constant, Equation (3) reduces to
∂C _ ^∂2C
∂t
∂x2 '

(3)

Many analytical and numerical solutions of Equation (3) subjected to different
boundary and initial conditions exist and solutions C(x,t) are compared with exper
imentally determined concentration profiles to extract the diffusion constant D[8].

Diffusion in the solid state is a complex problem. Various diffusion

constants can be defined according to different physical situations. Self-diffusion

refers to mass transport in homogeneous materials without the influence of a con
centration gradient. Experimentally, such situations are often realized by means of
radioactive tracer diffusion in an otherwise homogeneous material[9]. Self-diffusion
in pure metals is one of the most studied and best understood examples of diffusion
in the solid state[lθ]. One often models the process of diffusion by assuming that

the path followed by each atom during diffusion is adequately described as a ran
dom walk. Denote by Pτ(x) the normalized probability that an atom at the origin

at time zero will be at position x at time τ. Then given an initial concentration
profile C (x, 0) at time zero, the concentration profile at time τ will be obtained by

Expanding the left-hand side of Equation (4) in powers of τ and the right-hand side

in powers of X = x — x,, and noting that for a true random walk Pτ(x) = Pτ(-x),

we then obtain
∂C _ {x2) ∂2C
∂t
2τ ∂x2 ,

(5)

where
(x2) =

x2 Pτ(x)dx.

(θ)

Compareing Equation (5) to (3), we obtain

In an isotropic crystal, (x2} = {y2) = {z2) and (R2) = 3{x2). If a total of N jumps
takes place in time r, and each jump is of the same length r, then

(8)

(Λ2) = <(∑r,-)2> = JVr2∕,

where r2 = (r2) and f = 1 + 2((cos0i} + (cosög) ÷ ∙ ∙ ∙)∙ The average of the cosines

expresses the correlation between the angle of successive diffusive jumps. Note that
the total number of jumps N in time τ is τ times the jump frequency Γ; we can
thus rewrite Equation (7) as

£> = ^r2∕Γ.

(9)

It is important to inquire into the atomic mechanisms that lead to the diffusion.

In a pure element, atoms can diffuse interstitially without the assistance of any

particular type of defect. In this case, the diffusion process approximates a true
random walk and the correlation factor f is one. If a particular type of defect,
such as a vacancy in a crystal, is needed to assist a diffusive atomic jump, then
correlation effects will always arise[ll].

For diffusion by a single defect mechanism in a pure element, the

diffusive jump frequency Γ is simply the coordination number Z times a product
of the fractional defect concentration F and the defect jump frequency w. Simple
thermodynamics predicts that the equilibrium concentration of a particular defect i

is related to the enthalpy ΔU1∙ and excess entropy ΔS∕ of formation of this defect
by[!2]

exp[-

- Γ∆ff∕
kDT

(10)

The defect jump frequency w is usually calculated by means of Eyring’s reaction
rate theory as

MΓn - TΔSm
w — ι∕exp[- ___ I________ I
kcT

(H)

where v is the atomic vibration frequency and ΔH-n — TAS™ is the activation free
energy of migration via this particular defect[13]. Thus, an expression for the self
diffusion coefficient for diffusion by a particular defect mechanism i can be written
as

l^o z

rΔS∕ + ΔS"l1
kD

Δ∕√ + Δ∕∕ιm
kDT

D = - Zr~vfexp∖---- —,--------—exp------------------- —

(12)

The diffusion coefficient can therefore be expressed in an Arrhenius form
D = D0exp[-

KbT

(13)

When several defect mechanisms are contributing simultaneously to the diffusion

process, the diffusion coefficient is then composed of a sum of several terms with
similar form but with different activation energies. Because of the exponential de

pendence of the diffusion coefficient, one mechanism usually dominates the diffusion
process at a given temperature. For diffusion in pure metals, it is the general con

sensus that the dominant mechanism of diffusion is by monovacancies, although

higher order defects such as divacancies may have a minor contribution at higher
temperatures [ 10].

It is worth noting that the concept of self-diffusion applies not only

to pure elements, but also equally well to homogeneous binary or multicomponent
alloys, either with some components in dilution or all components in concentrated

proportions. An interesting example of this class of diffusion process in solids is

that of the solute diffusion in dilute binary alloys[l4]. By means of radioactive

tracer experiments, one can determine both the diffusion rate of solute at very low

concentration in the solvent and the solvent self-diffusion rate. For vacancy-assisted
diffusion, one generally finds that the solute impurity diffusion constant and the sol
vent self-diffus ion constant are similar in magnitude. For another class of solutes in

certain solvents, the impurity diffusion constant can be several orders of magnitude

higher than that of the solvent self-diffusion. Experimental evidence suggests that

a certain interstitial type of mechanism rather than the vacancy mechanism has to

be evoked in order to explain this kind of anomalous fast-diffusion behavior[l4].

The types of diffusion described above all refer to the random atomic
motion (defects may be required to assist this motion) in chemically homogeneous

materials. In contrast to heat flow where no motion of the medium is required, dif
fusion in chemically inhomogeneous materials may produce a motion of the medium
itself in addition to homogenization of the medium. For diffusion in binary alloys,

this situation can be readily visualized. Imagine a fictitious plane in a diffusion cou
ple across which both components interdiffuse. If the respective diffusion rates are

different, extra material will accumulate on the side of the slower diffusing compo
nent measured from the fictitious plane. This situation is schematically illustrated
in Fig. 1. From the reference frame of this plane, the whole diffusion couple partic

ipates in a translatory motion in the direction of the faster diffuser. Equivalently,
the fictitious plane is moving in the direction of the slower diffuser viewed in the
reference frame attached to one end of the diffusion couple. This is the Kirkendall
e0recf[l5].

In terms of an observer stationary with respect to one end of the

(a)

O 1
° 1

—1-

∕'

(b)

o 1
o 1
___ t

—X

(c)

Fig. 1.1 Schematic illustration of the Kirkendall effect. Taken from Ref. 15.

diffusion couple, the flux of A and B atoms across the fictitious plane is according

to the above discussion

dC--A H vrCa
A _— — Dn A —
∂x

(14.1)

Jb — -Dβ

D + vCb,

(14.2)

where v is the velocity of this plane. Combining Equation (14) with the condition
of mass conservation for both A and B atoms, we arrive at
∂(Ca + Cb)
∂ r
∂Ca
∂Cb
at
--äi^Dj~är~DB~äT+vi-CA+Cc'}]·

<15>

If we assume that the total density C = Ca + Cb remains a constant throughout
the diffusion process, then the quantity on the right-hand side of Equation (15)

must be a constant throughout the whole diffusion couple. This constant must be
zero since no mass transfer occurs at the end of the specimen. Thus, we must have

Ca + Cb

∖da-db∖9ca

(16)

∂x

Substituting Equation (16) into (14.1), we can then sidestep the problem of mass

flow and write the A or B atom flux solely in terms of the concentration gradient
of A or B atoms

JA(B)

-D>
Ca + Cb ^

Ca
Ca + Cb

Dd}

j^m

∂CA(B}

∂x

(17)

analogous to the original Fick’s formulation of diffusion expressed by Equation (l).

Diffusion process in binary alloys can thus be described either by the two intrinsic
diffusion constants Da and Db, or completely equivalently by a single interdiffusion
(or chemical diffusion) constant D plus the associated equation for the velocity of
mass flow (16). The interdiffusion constant D is related to the two intrinsic diffusion

constants by

D = NbDa + NaDb,

(18)

where Να and Np are the respective atomic compositions Ca/C and Ce∕C. It is
the interdiffusion constant that is determined in ordinary experiments.

In binary alloy systems, the general thermodynamic equilibrium con
dition is that the chemical potential for both components be constant throughout.
Thus, in the spirit of irreversible thermodynamics, we expect that it is the gradi

ent of chemical potential rather than that of concentration which constitutes the
driving force for diffusion and produces mass currents[16]. If we assume that va

cancies are in overall equilibrium, and further, that the cross correlations between

the individual components are negligible (i.e., the chemical potential gradient for
component B produces negligible current of component A), we can then write the

respective atomic fluxes as

CaMaa^,—

911a

(19.1)

Jd = -CbMdb-^,
ox

(19.2)

Ja =

Λf

where Maa and Meb are the mobilities of the individual components A and B[17].
Writing the gradient of chemical potential in terms of the gradient of concentration,

we arrive at Darken’s expression for the intrinsic diffusion coeficients

J>a

9μΑ
Maa
∂1∙πNa

(20.1)

∂μn M∏b ■
∂lnNβ

(20.2)

1.2 Interdiffusion and Reactions in Thin Films

10
Although interdiffusion in multilayered metal-metal thin films was ob

served by Dumond et al. as early as 1940[l8], a full-scale attack on the problem of

diffusion and reactions in thin films began only with large-scale applications of thin
films in integrated circuits[ 19]. Understanding interdiffusion and the formation of

new phases at temperatures well below the elemental melting points is often imper
ative to assure satisfactory performance of circuit elements, as is evidenced by the

problem of contact failure when a AuAl2 compound forms at Al/Au junctions[20].

Advances in experimental techniques adequate to deal with variation of materials
properties on the length scale of a few hundred angstroms, most noticeably the

extensive usage of ion beam analysis techniques for probing composition profiles in
thin films, and the use of transmission electron microscopy for characterizing the
existence of various phases and their microstructures, have contributed enormously

to the understanding of reactions in thin films[21,22]. A wealth of experimental
results on the interdiffusion and reaction of binary diffusion couples now exists[23].

The simplest case of metal-metal interdiffusion occurring in a binary
diffusion couple consists of single crystals of the individual components, which in

terdiffuse to form a continuous solid solution. The extrinsic diffusion mechanisms
are well- known. For example, the rate of interdiffusion at low temperatures in a

single crystal diffusion couple can be drastically different from that in a polycrys
talline diffusion couple. In Ag-Au system, it has been demonstrated that diffusion

via defects, e.g., grain boundaries, can be dominant at low temperatures[24]. In

cases where interdiffusion leads to the formation of an intermetallic compound, the
much faster diffusion via crystal defects, compared with diffusion in the bulk, may
lead to irregular grain growth and island formation. Examples of such behavior

11
have been reported in the systems Al-Ni and Al- Hf[25,26]. Thus, the interdiffusion

and reaction process may depend strongly on the morphology of the original diffu
sion couple. Reaction of metals with silicon has been extensively studied owing their

importance in VLSI technology[27]. In contrast to metal-metal thin films, interdiffu
sion and reaction in metal-silicon systems generally begins with either single crystal

or amorphous silicon. Although the bonding of metals and silicon is completely
different, striking simplicities exhibit themselves in reaction of both bimetallic and

metal-silicon thin films. In many systems, reaction of the two pure elements leads

to a well-defined planar compound interlayer so that the growth process can be
treated as one-dimensional.

Growth of any compound in a binary diffusion couple involves trans

port of one or of both types of atoms to one or both compound/element interphase

interfaces and a subsequent reaction at these interfaces to form additional com
pound. Both diffusion across the compound layer and interfacial reaction kinetics

can be rate-limiting. In the limit where the compound interlayer is extremely thin,

the transport of atoms across it by diffusion will take little time and the rate
limiting step in compound formation is expected to be the interfacial reaction. In

this case, the reaction is termed interface-controlled. If, on the other hand, the
compound interlayer is very thick, the interdiffusion process will be rate-limiting

and the reaction is termed diffusion-controlled.

The binary phase diagram will typically predict several compounds
in a binary system, and according to early theories based on diffusion controlled

growth of compound layers, all compounds that appear in the phase diagram should

appear simultaneously in an actual interdiffusion experiment[28]. Experimentally,
however, the evolution of a diffusion couple consisting of two pure elements proceeds

in a dramatically different way. For both metal-metal or metal-silicon systems, it
is generally observed that only one compound forms and grows initially. The for

mation of the second compound does not occur until a certain critical thickness of
the first compound interlayer has been reached. Examples of such behavior include

Al-Au and Ni-Si[29,30]. The eventual outcome of such interdiffusion experiments

agrees with that predicted by the equilibrium phase diagram, satisfying the ther
modynamic equilibrium requirement. However, the process of reaching equlibrium

seems to be one where compounds form sequentially instead of simultaneously.

In the course of compound formation in a diffusion couple, the process
of interdiffusion is often dominated by the movement of one element, the so-called
dominant moving species. Attempts to identify the dominant moving species in a
binary diffusion couple date back to work by Kirkendall around 1940. An inert

wire was embedded at the interface of a bulk diffusion couple; the dominant moving
species was identified according to the direction of movement of the wire[31]. As
discussed in Section 1.1, the role of the inert marker, in this case the inert wire, is to
mark out the “fictitious plane.” Modern marker experiments in thin films generally

employ an extremely thin (~ 10Â) layer (or, in fact, isolated islands) of inert and

immobile atoms, ideally buried inside the compound layer to avoid dragging of the
marker by the original element/compound interface[27]. Most marker experiments

in thin films have been carried out on metal-silicon systems where the motion of
the marker, prepared either by evaporation or ion implantation, is detected by
Rutherford backscattering spectrometry[27],

13
Although there is an abundance of experimental information about

interdiffusion and reaction in thin films, to date, certain fundamental questions in
this field remain unanswered. One of the most prominent problems is the prediction
of the particular phase that forms first in a diffusion couple consisting of two pure

elements. Walser and Bene have formulated a rule predicting the first phase in the
case of reacting metals with silicon. The argument is heuristic in that it presup

poses that a thin glassy interlayer forms at the metal/silicon interface during or post
preparation, and the first silicide to nucleate upon annealing of the diffusion couple
is basically the crystallization product from the glassy membrane[32]. Although

this rule accounts, with some success, for the body of existing data on silicide for

mation, exceptions to this rule do exist. Gosele and Tu have shown that, contrary

to early theories that assume diffusion-controlled growth of compound phases, the
diffusional flux through a particular compound phase does not go to infinity in the

limit of small compound interlayer thickness because of the presence of interfaces.
Thus, it is possible that even though all compound phases could nucleate at the
original elemental interface, some would not grow initially because of unfavorable
interfacial kinetic parameters for growth[33]. Their theory predicts that the first
phase to form is the one with the highest interface mobility. The parameters in

this theory, being phenomenological, can be obtained from a combination of experi
ments, at least in principle, although to the author’s knowledge, there have been no

systematic experiments to test the validity of this theory. At present, there exists
no satisfactory rule that predicts the first phase or accounts for the sequence of

phase formation in general, including the successive phases.

1.3 Metastable Phases

14
Man’s experience with metastable materials stems from his everyday
life. Substances ranging from ordinary window glass to diamonds all belong to

the class of material we call metastable, which by definition could have their free
energy lowered by transforming into different phases. The transformation of some

metastable materials into thermodynamic equlibrium states can be an extremely

slow process, as exemplified by the common belief that diamonds exist “forever.”
On the other hand, at the extremities of metastability lies another class of material

which we call unstable. How to distinguish between metastability and instability,
and how to establish a measure of metastability are amongst the most fundamental
questions relating to nonequilibrium materials.

Consider a homogeneous binary solid solution of A and B with its
Gibbs free energy versus composition shown schematically in Fig. 2. A simple

example of such behavior can be obtained in a model system of regular solution

with a positive interaction parameter[34]. It is apparent that any homogeneous
solution with composition Na ranging between Na and Nβ is not in equilibrium

since its free energy can be lowered by separating into a mixture of two components

a and β. However, inside this nonequilibrium region, solutions with compositions
7Vu < Na < Na> or Nβ' < Na < Nβ are qualitatively different from solutions with

compositions Na< < Na < Np<. Composition fluctuations in the latter region, how
ever small, result in a decrease in the free energy. Small fluctuations in composition

in the former region cause the free energy to increase, and a decrease in free energy
is obtained only for a sufficiently large concentration fluctuation. The difference

in these two types of phase regions is a manifestation of the different curvature of
the free energy of the solid solution with respect to its composition. The transition

Atomic Percent A (Na)

Fig. 1.2 Hypothetical free energy diagram and the associated phase diagram of a
binary system (A-B) with a positive enthalpy of mixing.

points between these different regions are marked by a' and β,, where the second

derivative of the free energy with respect to composition is zero. The loci of Na∣ and
Np' as a function of temperature defines the spinodal curve in the corresponding

phase diagram[34].

Thermal fluctuations are responsible for the eventual transformation

of the nonequilibrium solid solution into its equilibrium counterpart. The nature of
these fluctuations can be separated into two categories[35]. One is an infinitesimal

composition fluctuation spread over a large volume; the other one is a large fluctu

ation localized in a very small volume within which the material resembles that of

a different phase. The nature of a long wavelength composition fluctuation can be
examined as follows. In general, one expects that the total free energy G of a solid

solution is dependent not only on the composition, but also on the composition
variation[36]. If we assume that this variation is small, then the total free energy
can be expanded in terms of the composition gradient

G = f {G0(Na) + K(VNa)2}

(22)

where Go is the free energy per unit-volume and depends only on the local com
position. The second term in the integrand expresses the dependence of the total
free energy on spatial composition variation to lowest order[36]. The change in the

total free energy of the system, initially homogeneous with composition N°a when

subjected to a sinusoidal fluctuation

Na = N⅛ + Acosβx,

(23)

can then be calculated from Equation (22) by expanding Go in powers of Na — N⅛.

The result is
δG=^[^ + W2],

(24)

where V is the total volume and K the positive gradient energy coefficient[37j. The
second-order partial derivative of the free energy with respect to composition is
evaluated at N⅛. Thus, if <92G0∕∂N^ is positive, then the total free energy of the
system will be raised by composition fluctuations at all wavelengths. On the other

hand, if ∂2G0∣∂N^ is negative, then a lowering of the total free energy will be
obtained by all composition fluctuations with a wavelength larger than a critical

value λc, where
λc

8⅛ 11
3.
V 7wT 1

(25)

regardless of the amplitude of fluctuation. Such spinodal decomposition can continu
ously lower the total free energy of the system via rather long wavelength concentra

tion fluctuations. The limit of metastability in a binary solid solution is defined by
the spinodal curve. The requirement for chemical stability in binary solid solutions
∂2G0

∂N2

(26)

is but one of a set of general criteria for thermodynamic stability against various

types of fluctuations. A particular material is unstable against certain fluctuations

if the corresponding Gibb’s stability criterion is violated[38].

In the case of localized fluctuations, the small region can be regarded

as a nucleus of another phase and the well-known theory of nucleation describes
such processes[39]. If we assume that we can describe the separation between a

nucleus and the original matrix by an interface and associate with this interface an
interfacial energy σ, then the interfacial energy dominates when the nucleus is small

18
so its surface-to- volume ratio high. The total change of free energy when a nucleus
is formed (the nucleus is assumed to be spherical with radius r for simplicity) is

given by the sum of a volume and a interface term

ΔG = 4πr2σ -)—7τr3ΔG0,

(27)

where ΔG0 is the change in volume free energy associated with the transformation.
In order for the nucleus to grow, we must have

critical free energy ΔG* or the activation energy for nucleation
ΔG*

16π σ3
3 (ΔG0)2

(28)

A finite energy barrier to such nucleation events therefore exists as long as the in

terfacial energy between the nucleus and the matrix is positive. Assuming that this

is the case, we see that the solid solution depicted in Fig. 2 with its composition in

side the two phase a and β coexistence region is truely metastable and not unstable
against such localized fluctuations regardless of whether it is within the spinodal,
in the sense that a finite energy barrier has to be overcome before the nucleus can
grow. The instability of any solid solution with composition inside the spinodal
region stems from the fact that its free energy can be continuously lowered by long

wave length composition fluctuations where no well-defined interface exists. Since
the activation energy for nucleation is critically dependent on the interfacial energy,
oftentimes nucleation of one particular phase occurs because of its lower interfacial

energy with the parent phase despite the fact that another phase may have still
lower free energy. One example of such sequential precipitation of metastable and
finally stable phases in supersaturated solid solutions is the case of Al-Cu[40]. The
fact that many metastable phases, once formed, seem to be highly stable is due to

the slow nucleation of the equilibrium phases. Since atomic mobility is dependent on

19
temperature exponentially, at low enough temperatures, even when the nucleation

centers are present, negligible growth of these nuclei will result. Thus, the degree
of metastability of a particular phase, i.e., its resistance against transformation to

phases lower in free energy, is a combination of effects due to nucleation and growth.

Synthesis of metastable phases can be achieved by condensation of va

por on a substrate in the so-called vapor-quenching technique, pioneered by Buckel

and Hilsch[4l]. In this case, the vapor is converted into a solid, atom by atom,
upon arrival at the substrate. This condensation process can be dictated to take
place at any desired temperature, e.g., at cryogenic temperatures. In particular,

since any two elements are completely soluble in the vapor phase, one might hope

to obtain homogeneous solid solutions in systems with essentially no solid solubil

ity. A wide variety of materials including alkali halides, heavy metal halides, pure

metals, binary alloys and pseudobinary admixtures of different types of salts have
been evaporated onto substrates with temperatures ranging from room tempera
ture down to liquid helium temperature[42]. During early investigations, particular

emphasis was on the conditions under which an amorphous substance could be

obtained. It was discovered that pure metals and pure salts only rarely became

amorphous even when evaporated onto liquid-helium temperature substrates. Ex
ceptional cases such as pure Bi or pure Ga can be made amorphous by condensing

onto liquid-helium temperature substrates but transform into the crystalline state

below 20K[42]. Later, many works showed that by vapor quenching suitable binary
and multicomponent alloys of a wide variety of metals, concentrated amorphous
alloys could be obtained that do not transform to the crystalline state up to well
above room temperature[43,44]. Among such studies, the early work of Mader et

al. has demonstrated some important features[45]. By coevaporation of pure Cu

and pure Ag with control of individual evaporation rates onto amorphous substrates
held at liquid nitrogen temperature, they were able to produce concentrated amor

phous alloys with 35-65% Ag content, while evaporation of dilute alloys resulted
in a metastable single phase f.c.c. solid solution. It is now generally believed that

there exists a continuous range of composition in many binary alloy systems within

which an amorphous phase can be obtained by vapor quenching[47]. In the case of
Ag-Cu, if the substrate was kept at 200K instead of 80K, a solid solution rather than

the amorphous phase was obtained at all compositions[45]. The latter fact led the
above authors to conclude that the crystalline structure will be reached if some sur

face diffusion is permitted during vapor deposition. Such competition between the

atomic arrival rate, in vapor quenching determined by the evaporation rate, and the
rate of nucleation and growth of various phases, metastable or stable, constitutes

a main theme in the synthesis of metastable materials. Early works suggest that

atomic size mismatch between the two components is important and an amorphous
alloy will be obtained if the atomic size difference is greater than 10%[46]. Recently,

the effect of atomic size mismatch of the two elements on the glass- forming range

in the binary alloy was reexamined by Egami et al.[48]. It is argued on the basis

of elasticity theory that, when atomic size mismatch is sufficiently large, a critical
concentration exists in the crystalline solid solution beyond which the solid solu
tion is rendered topologically unstable by the atomic level stresses that arise from

atomic size mismatch. This theoretically predicted critical concentration is used
with good success to correlate with experimentally obtained glass forming range in

vapor deposited binary thin films[47]. When two elements with virtually the same

size, such as Fe and Cu, are codeposited onto a substrate, a metastable crystalline
phase always results instead of an amorphous alloy[49].

Intense research effort on the synthesis of new metastable alloys, in
cluding amorphous alloys, from the liquid state was launched after the demonstra
tion by Duwez et al., that a metastable extension of solid solubility in the system

Cu-Ag was possible by rapidly cooling a binary liquid of Cu and Ag[50]. Shortly
afterward, a metastable crystalline phase of Ag-Ge was obtained by such a liquid

quenching technique[5l], and then an amorphous alloy of Au-Si was also obtained
for the first time by quenching from the liquid state[52]. Preparation of amorphous
alloy by liquid quenching is unique in that, if formation of crystalline phases can
be avoided, the undercooled liquid will eventually go through a kinetic freezing or

glass transition at a temperature 3j,[53]. Below the glass transition temperature,

the undercooled liquid is no longer able to sample all available atomic configurations

and the amorphous solid so obtained is said to retain a single frozen-in topological

configuration of the liquid state. To achieve the amorphous state, fast cooling of
the liquid is necessary in the undercooled regime down to T,j. According to classical

nucleation theory, the rate of crystallization from the undercooled melt reaches a
maximum at a specific temperature Γn, below the melting temperature[54], as shown
schematically in Fig. 3. Therefore, if the liquid can be cooled from above the melt

point to well below Tn in time less than that required to nucleate crystalline phases,

the undercooled liquid will reach Γσ without crystal formation, thus forming a glass.
Again, it is the competition between two kinetic processes, cooling of the liquid on
one hand, and nucleation and growth of the crystalline phases on the other, which

determines whether or not an amorphous alloy will be formed. Experimentally, fast
cooling of the liquid is achieved by jetting a stream of liquid against a cold metal
substrate. The resultant geometric configuration of the quenched specimen is nec

essarily a thin ribbon or foil so that heat can be conducted away effectively during

quenching. Variations of such cooling schemes give rise to techniques referred to as

TEMPE RATURE

Fig. 1.3 Schematic Time-Temperature-Transformation (TTT) diagram for crystal
growth in an undercooled melt. Taken from Ref. 54.

the gun technique, the piston and anvil and the melt spinning techniques, etc.

The cooling rate achieved in such experiments ranges from 105 to 108 K∕sec[55].
The term glass is traditionally associated with an amorphous solid obtained by

cooling from the liquid state. In what follows, we will use the terms amorphous
solid and glass without distinction. From the above discussion, we expect that by

varying the cooling rate and depending on the specific alloy system, a wide variety
of phases in addition to amorphous phases can be formed directly from the liquid
state. Experimentally, supersaturated binary solid solutions in systems such as Cu-

Ag, Cu-Rh, Pt-Ag, over 60 binary non-equilibrium crystalline phases and a large
number of binary and ternary amorphous phases have all been obtained by rapid
quenching from the melt[55]. Large- scale production of liquid quenched alloys is

now yielding commercially important materials for a number of applications[56].

1.4 Solid State Amorphization

The first example of synthesis of an amorphous alloy from the solid

state by Yeh et al. involved reaction of hydrogen gas with a metastable crystalline
ZrsRh alloy[57]. It was quickly realized that certain thermodynamic and kinetic

conditions are satisfied in such a reaction. Thermodynamically, the final amorphous
Zr3RhHx hydrid has considerably lower free energy than that of the initial state.
Kinetically, the time scale for the system to reach the thermodynamic equilibrium
state, which is a chemically segregated state of pure Rh plus ZrJT2, is much longer

than that of reaching a chemically homogeneous metastable state, the amorphous

state, by hydrogen diffusion[58]. These two conditions, one thermodynamic and
one kinetic, were used as guide lines to search for other systems that may exhibit

24
similar solid state, amorphization behavior. Subsequently, Schwarz and Johnson
showed that multilayered diffusion couples consisting of crystalline La and Au indi

vidual layers can be transformed into an amorphous La-Au alloy by isothermal heat

treatment at low enough temperatures[59]. Although the amorphous La-Au alloy is
expected to have a large negative heat of mixing and thus furnishes the thermody

namic driving force for this reaction, the kinetic condition of the disparity between
the time scales for reaching the amorphous state and the equilibrium crystalline

state was originally justified in terms the anomalous solute diffusion of Au in the

La matrix. It was later pointed out that fast diffusion of Au in the amorphous state
also occurs but can be a few orders of magnitude slower than the corresponding
solute diffusion in crystalline La[60]. The curious correlation between fast impurity

diffusion in the crystalline matrix and substantial mobility of the fast diffuser in
the amorphous alloy remains without a fundamental explanation at present. Pre

sumably it is associated with the atomic size difference between Au and La. The
synthesis of an amorphous alloy in diffusion couples consisting of crystalline ele
mental starting layers is accomplished solely by reaction in the solid state without

the necessity of gaseous hydrogen acting as the fast-diffusing element. This method
thus opens up a new route for synthesizing metastable amorphous materials. To

date, solid state amorphization has been observed in numerous metal-metal systems
including early-late transition metal, noble-rare earth metal systems, etc.[61]. More
recently, a number of metal-silicon systems have been observed to form amorphous

silicides by solid state reaction, including Rh-Si, Ti- Si, and Ni-Si[62,63,64]. Thus,

the glassy membrane originally hypothesized by Walser and Bene[32] has taken on
a new significance. It is to be emphasized that production of metastable phases by

interdiffusion reaction in the solid state is not limited to that of amorphous phases.
Experiments stimulated by the discovery that amorphous alloys can be produced

25
by reactions in the solid state have thus far shown that many metastable alloys,

crystalline or non-crystalline, can be obtained via the same route under suitable
conditions. Most recent examples include the formation of the Al-Μη quasi- crys

talline phase in elemental Al/Μη diffusion couples and metastable bcc solid solution

and subsequently the A15 phase in Nb-Al systems[65,66,67].

1.5 Introduction to the Thesis

This thesis will focus on the study of interdiffusion and reaction in pla

nar thin film diffusion couples of pure Ni and Zr. As will be exemplified through-out

this thesis, the ability of synthesizing planar thin film diffusion couples with high
purity and well-characterized geometry and well-defined interfaces is crucial for be
ing able to address and answer some key problems in such a study. In Chapter 2,

we will describe the high vacuum sputter deposition system we have constructed
for fabrication of thin-film diffusion couples used in this research. Formation of an

amorphous NiZr alloy in vapor deposited polycrystalline Ni/Zr thin film diffusion

couples was first demonstrated by Clemens et al.[68] and constitutes one of the ear
liest examples of solid state amorphization reactions in metal-metal systems. The
process of interdiffusion and reaction in Ni/Zr diffusion couples is subsequently stud

ied as a prototype case of solid-state reactions by many others, using a wide variety

of experimental techniques. The use of the Rutherford backscattering spectrometry

(RBS) technique has elucidated some important aspects of the growth kinetics of
the amorphous NiZr interlayer. Barbour has shown, using RBS, that the growing

amorphous NiZr interlayer possesses a linear concentration profile with constant in
terfacial compositions determined by equilibrium conditions[69], Cheng et al. have

shown, using a marker technique together with RBS measurements, that Ni is the

dominant moving species in the formation of amorphous NiZr in Ni/Zr diffusion
couples during solid-state reaction[70]. The choice of Ni-Zr system was originally

guided by the fact that a large negative heat of mixing exists in this system and
Ni is known to be a fast diffuser in crystalline Zr[71,72]. In Chapter 3, we will

describe our study of the growth kinetics and thermodynamics of amorphous NiZr
formation in sputter-deposited polycrystalline Ni/Zr multilayered diffusion couples.

With a combination of experimental techniques such as x-ray diffraction, differen
tial scanning calorimetry, and resistivity measurements, the process of amorphous

phase formation can be studied in some detail. We have directly measured the heat

of mixing of amorphous NiZr alloys via calorimetric methods and confirmed that
it constitutes the major thermodynamic driving force toward amorphization in this

system[73,74]. The growth kinetics of the amorphous NiZr has also been measured.
We have shown that, although substantial atomic transport through the amorphous

NiZr occurs during reaction, the measured diffusion constant is still orders of mag
nitude below that of Ni impurity diffusion through crystalline Zr[74,75]. Vredenberg

et al. have shown that, in contrast to the results obtained using vapor-deposited

polycrystalline Ni/Zr diffusion couples, the use of a single crystal of Zr in a bilayered
polycrystalline-Ni/single crystal-Zr diffusion couple prohibits the formation of the

amorphous NiZr alloy[76]. Using the RBS technique, they showed that no reaction
occurred in such a polycrystalline-Ni/single crystal-Zr diffusion couple at elevated

temperatures for extended periods of time. Thus these authors concluded that the
use of single crystal Zr creates a nucleation barrier against amorphous phase for

mation. In a related study, Pampus et al. have shown that the use of single crystal
Ni in contact with polycrystalline Zr does not pose such a nucleation barrier for

the amorphous NiZr formation[77]. We have since fabricated bilayered diffusion

27
couples of Ni and Zr in our vacuum deposition system where one layer consists of

a mosaic of large single crystals with typical grain sizes in the 10 μ,m range. In

addition to creating the above-mentioned polycrystal/single crystal interfaces, our

sample configuration allows further examination of the role of grain boundaries on
the reaction process[78]. In Chapter 4, the reaction process of such Ni/Zr diffusion
couples is examined together with sputter- deposited polycrystalline Ni/Zr diffusion

couples by the technique of transmission electron microscopy. Emphasis is placed

not only on the process of amorphous phase formation but also on the observation
of the formation of the Ni-Zr compound phase succeeding that of the amorphous
phase[79]. Such a study provides a concrete example of the phase-sequencing be

havior observed in many thin film diffusion couples. We will attempt to ellucidate
the key ingredients for understanding the evolution of diffusion couples in general.

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71. A. R. Miedema, R. Boom, F. R. De Boer, J. Less Common Met. 41,
283 (1975).

72. G. M. Hood, R. J. Schultz, Acta Met. 22, 459 (1974).
73. E. J. Cotts, W. J. Meng, W. L. Johnson, Phys. Rev. Lett. 57, 2295
(1986).

74. W. J. Meng, E. J. Cotts, W. L. Johnson, Mater. Res. Soc. Symp.
Proc. Vol. 77, 223 (1987).

75. K. M. Unruh, W. J. Meng, W. L. Johnson, Mater. Res. Soc. Symp.
Proc. Vol. 37, 551 (1985).

76. A. M. Vredenberg, J. F. M. Westendorp, F. W. Saris, N. M. van der
Pers, Th. H. de Keijser, J. Mater. Res. 1, 774 (1986).

77. K. Pampus, K. Samwer, J. Bottiger, Europhys. Lett. 3, 581 (1987).
78. W. J. Meng, C. W. Nieh, E. Ma, B. Fultz, W. L. Johnson, in Pro

ceedings of the Sixth International Conference on Rapidly Quenched
Metals, Montreal, August 3-7, 1987.

79. W. J. Meng, C. W. Nieh, W. L. Johnson, Appl. Phys. Lett. 51, 1693
(1987).

34
Chapter 2

High Vacuum Sputter Deposition of Thin Films

Techniques for fabrication of thin solid films include thermal evapora
tion, electron beam evaporation and various sputter deposition methods[l]. Ther
mal evaporation of some pure elements, e.g., refractory metals, by resistive heating

can be rather difficult, and it has been increasingly replaced by the method of elec
tron beam evaporation. Electron beam (e-beam) evaporation occurs in vacuum
without the need of a carrier gas and is thus compatible with ultra-high-vacuum

(UHV) requirements. For this reason, it has been extensively used in vapor-phase
synthesis of thin films where the UHV condition is required, such as in Molecu

lar Beam Epitaxial (MBE) growth of semiconductor devices[2]. However, control

and stabilization of the e-beam evaporation rate is difficult and real time feed

back control is often necessary to ensure stability of deposition. Furthermore, since
the constituents present in a binary liquid usually differ in their vapor pressures,
the composition of the vapor and consequently that of the condensed thin binary

film is often different from the composition of the binary alloy used as the evap
oration source. Thus, compound thin films are usually prepared by simultaneous

co-evaporation of elemental constituents from separate sources with individual rate
control, making the overall process quite complex. We have chosen, in this project,
to utilize instead the technique of planar magnetron sputter deposition for the

preparation of thin-film diffusion couples. This chapter serves as an introduction to
the sputter-deposition technique itself as well as a more detailed account of some
specific features particular to the sputter-deposition system contructed for use in

this research.

2.1 Introduction to Sputter Deposition

Sputtering refers to the erosion of solid surfaces under particle bom

bardment^]. In particular, energetic ions are slowed when impinging onto solid
surfaces and deposit energy into the solid, some near-surface atoms are ejected as

a result of this energy deposition. In addition, many other effects are created by
incoming ions such as radiation damage and ion-beam mixing if the initial solid
is inhomogeneous[4]. Although observation of cathode erosion in discharge tubes

has been observed over one hundred years ago, reliable experimental information
on sputtering was obtained mainly during the last thirty years because of the ad
vances in particle accelerators and high-vacuum technology. The sputtering process

is largely characterized by the sputtering yield Y, defined as the average number

of solid atoms ejected per incident particle. For bombardment of metal targets by
noble gas ions in the 100 eV to 1 KeV range, Y usually ranges from 10~2 to 10[5].

Energetic ions incident upon a solid dissipate their energy by elastic

collisions with the target atoms and by the creation of electronic excitations. Binary
collisions between incident ions and target atoms can displace the target atoms, and
these primary recoil target atoms undergo further collisions with more target atoms

to generate higher order recoils, thus generating a collision cascade. Some of the

recoil target atoms may reach the surface and may be ejected if they are energetic

enough to overcome the surface binding forces. The theory of collision cascade

sputtering is most developed in the linear cascade region where it is assumed that

the spatial density of moving atoms is small, and binary collisions happen mainly

between one moving atom and another at rest. In this case, the sputtering yield Y
is given by the expression[6]

0.042Fd(E,Θ,x)
®’I) =-------- NU<,--------

where E and Θ are the energy of the incident ion and the incidence angle with
respect to the target surface normal respectively; N and Uo are the target density

and average surface binding energy and x is the distance between the atom ejection

surface and the entrance point of the ion, for backsputtering x = 0. Fe>(E,Θ,x) is
the depth distribution of ion energy deposition in the target, the energy dependence
of which follows that of the nuclear stopping power when inelastic energy loss to

electronic processes can be neglected[6].

Fabrication of thin films by sputter deposition utilizes the sputterejected target atoms as the deposition source. Direct ion beam bombardment of

target surfaces can be used, giving rise to the ion beam deposition technique[7]. The
majority of the sputtering-deposition techniques, however, use plasma discharge in

various configurations to provide the ion source. Thus, some carrier gas is neces

sary for the various glow-discharge sputtering techniques. Noble gases are usually
used as the carrier gas because of their chemical inertness, although chemically
active gases can also be deliberately introduced if compound thin films between
the pure elements and these gases are desired, leading to the technique of reactive
sputtering[8}.

When two conducting electrodes are placed in a low-pressure gas and

subjected to a DC bias, electrons in the gas drift towards the anode. The presence

of electrons in a neutral gas can be due to spontaneous ionization, ionization by
cosmic rays, etc. During their course from the cathode to the anode, these electrons

will further ionize the neutral gas atoms, provided that the external bias exceeds
the ionization potential. In addition to these extra electrons, positive ions so gen
erated drift toward the cathode and upon strike generate secondary electrons. The
situation is schematically shown in Fig. 1. The total current is controlled by the
combined effect of electron ionization and secondary electron generation at the cath
ode by positive ions. If we suppose that a fixed number Io of primary electrons are

generated per unit time, further that a and 7 denote the number of ions produced
per unit length of electron travel and the number of secondary electrons generated
per incident ion onto the cathode, then the total current I is given approximately
by[9]

e∙'d
° 1 — '^y e'jr'i ’
where d is the anode cathode separation distance. As the external bias is increased,
both a and η increase[9], and the total current predicted by Equation (2) tends to

infinity when ^e,ld approaches unity. Equation (2) is no longer valid under such
conditions and a breakdown is said to have occurred in the gas. Physically, the
number of secondary electrons generated at the cathode is sufficient to maintain

the discharge and a self-sustained glow discharge is obtained. Positive ions strike
the cathode surface in a self-sustained glow discharge and cause sputtering of the
cathode material.

This is usually referred to as the planar diode sputtering∖8}.

Ionization efficiency of a planar diode plasma discharge is low, and relatively high
bias (few kilovolts) and high gas pressures (100 mTorr or higher) are required to

CATHODE DARK
SPACE (CDSI
ION INDUCED
SECONDARY EMISSION

SPUTTERED ATOMS
NEGATIVE GLOW

PRIMARY
ELECTRONS

LOST IONS

ELECTRON INDUCED
SECONDARY EMISSION
ANODE SHEATH

SUBSTRATES

Fig. 2.1 Schematic representation of the plasma during planar diode sputtering.
Taken from Ref. 11.

39
maintain the glow discharge. In order to sputter at lower gas pressures and external

bias, various methods have been used to increase the ionization efficiency. The

triode sputtering technique supplies the plasma region with additional electrons by
introducing another electrode, which emits electrons thermionically[8]. Instead of

providing more electrons, a more frequently used method to increase ionization
efficiency utilizes an added magnetic field to influence the motion of the electrons
so that they execute helical instead of straight paths, thus making more ionizing

collisions before reaching the anode. Since the electrons drift in the direction of

E × B in the presence of both an electric and a magnetic field [10], axially symmetric

magnetic fields are often used such as to allow the E × B drift current to close
on themselves, resulting in various magnetron sputtering arrangements[ll]. Both

the circular and rectangular planar magnetron configurations are shown in Fig. 2.
Planar magnetron sputtering is the most frequently used research technique bacause
of the simplicity of target construction. The sputtering system we have constructed

consists of two circular planar magnetron sputter guns housed in a vacuum chamber

capable of reaching a base pressure below 4 × 10^^9 Torr. As will be demonstrated,
very clean deposition conditions can be achieved with such a setup. In what follows,
analysis of each component of this sputter deposition system will be given.

2.2 Vacuum System

A block diagram of the vacuum system is given in Fig. 3. The whole

vacuum chamber (Perkin-Elmer Inc.) is metal-sealed with the exception of the top
flange, which can either be sealed by a Viton O-ring or a Cu wire-seal. The major

pumping system consists of an eight-inch intake cryogenic pump, with two

CATHODE

POLE PIECE

PERMANENT
MAGNETS

Fig. 2.2 Configuration of circular and rectangular planar magnetron sputtering
guns. Taken from Ref. 11.

RGA √2)

Vacuum
Chamber

IG —θ
Turbomoleculer
Pump

t⅛—©

Fig. 2.3 Vacuum system block diagram: (l) N2 flush inlet valve; (2) pressure relief

valve; (3) gate valve; (4) throttle valve; (5) chamber vent valve; (6) piezoelectric
leak valve; (7) ion gauge; (8) chamber isolation/differential leak valve; (9) residual

gas analyzer; (10) ion gauge; (11) turbo-pump vent valve; (12) mechanical pump

isolation valve; (13) thermocouple gauge; (14) mechanical pump.

cryopanels maintained at 77K and 15K, respectively (air-pumping speed 1500
liters/second, Perkin-Elmer Inc.). The cryogenic pump is assisted by an indepen

dent turbomolecular pump (air-pumping speed 150 liters/second, Leybold-Heraeus

Inc.) backed up by a mechanical pump (Edwards High Vacuum Inc.). This pump
ing scheme eliminates oil backstreaming from the mechanical pump into the main

chamber. During regeneration, the cryogenic pump is isolated from the main cham
ber by a gate valve and purged by purified N? gas through the pressure relief
valve until the cryopanels reach room temperature. The whole cryopump system
is then pumped by the turbomolecular pump through the chamber to ~ 10~5 Torr
to achieve thorough desorption of adsorbed molecules on the cryosorption surface.

The cryogenic pump system is re-isolated by the gate valve and cooled down; a

typical cooling process as monitored by the second cryopanel temperature is shown
in Fig. 4. Baking of the main chamber is crucial for obtaining the lowest ultimate
base pressure[l2]. Baking temperature when all metal seals of the main chamber
including the top flange are in place can be as high as 250°C. In actual operation,

the chamber surface temperature can be made to range from 100 to 150oC with
electrical heating tape when all metal seals are in place. A base pressure below
4 × 10~9 Torr can be reached in this case. When the top flange is sealed with a Vi
ton O-ring, the baking temperature near the top flange should be maintained lower

than 100°C and a base pressure of 1 to 4 × 10-s Torr can be routinely achieved
in this case with a total of 24 to 30 hours of pumping time. Ar is used as the

carrier gas for sputtering. During the actual deposition process, the main chamber
is backfilled with Ar to pressures ranging from 5 x 10-4 to 1.5 x 10^^2 Torr. The

resultant gas throughput would overload the cryogenic pump, and a throttle valve
has to be placed in between the main chamber and the cryopump system to cut

down the gas flow. We have designed and built a magnetically coupled butterfly

Fig. 2.4 Cryogenic pump regeneration history as monitored by the low temperature

sorption stage temperature during cooling.

valve that cuts down the gas throughput during sputtering to an acceptable value
when set to the closed position and offers no reduction in conductance from the
chamber to the cryopump when placed in the fully open position. In order to achieve

a stable deposition during sputtering, the Ar pressure has to be stabilized. The Ar

pressure stabilization scheme we have chosen uses a hot cathode ionization gauge,
which is able to operate at pressures below 10-2 Torr to monitor the Ar pressure
while a piezoelectric leak valve interfaced to the ion gauge controller allows more

or less Ar into the main chamber according to the ion gauge reading (this whole
pressure control package manufactured by Perkin-Elmer Inc.). The Ar pressure in

the main chamber can be so maintained to ±0.2 mTorr. An rf quadrupole mass

spectrometer[13] is used to analyze the gas content in the main chamber. Both
the residual gas content when the chamber has reached its base pressure and the

impurity content during sputtering when Ar is introduced into the main chamber
can be analyzed.

Since the upper pressure limit for the mass spectrometer to

function is 1 × 10~5 Torr, a differential pumping scheme is needed to reduce the

pressure in the spectrometer chamber in order to sample the impurity content in

the main chamber during sputtering. This is accomplished by the introduction of
a multipurpose valve between the main chamber and the spectrometer chamber.
This valve has three positions, fully closed to isolate the mass spectrometer and

the turbo pump from the main chamber; fully open to allow sampling of the main
chamber at its base pressure; and the differential leak position to allow sampling

of the main chamber (upper limit of the main chamber total pressure ~ 40 mTorr)
during sputtering (the quadrupole mass spectrometer along with all accessories for

differential pumping manufactured by Inficon Inc.). The main chamber gas content

is reduced in proportion in the spectrometer chamber as long as the conductance
between the turbo pump and the spectrometer chamber is throttled down[l3], thus

achieving a reliable monitor of the sputter deposition process.

2.3 Sputter Deposition: Operation and Monitoring

Sputter depositions were carried out from two planar magnetron sput
ter guns installed in the vacuum system (US Gun Inc.). Conducting materials to

be sputtered such as metals or alloys are placed on top of the sputter guns biased
negatively with respect to the substrate platform, which is grounded. These two

guns were biased externally from two DC power supplies (l.7 kilowatt, Sputtered
Films Inc.). Typical Ar pressures in the sputtering chamber are 3 to 15 mTorr.
Typical voltage-current characteristics of both sputtering sources are shown in Fig.

5. The maximum power input into the sputtering sources is limited by the effec

tiveness of the target cooling, which, because of the poor thermal link between the
water-cooled gun top and the actual target is limited to below 500 watts. The min

imum currents and voltages required to maintain a stable plasma discharge range

from 0.05 to 0.1 amperes and 50 to 100 volts, which increases with decreasing Ar
pressure, although very little material is sputtered at this lower limit, and actual

depositions are always carried out at much higher power. Since the E × B electron

drift current is shaped like a ring over the target in a circular planar magnetron gun,

the plasma density over the target surface is consequently nonuniform. Sputtered
material originates from the regions of high plasma density and the sputter erosion

of the target also posseses a ring shape. Thickness distribution of the resultant thin
film condensed on the substrate agrees with calculated results, assuming a super

position of cosine emission from the whole erosion area[3]. The substrate platform

is placed 12 to 15 centimeters away from the targets. This distance is found to be

Fig. 2.5 Typical current-voltage characteristics of planar magnetron sputter guns
while sputtering Cu at 6 mTorr of Ar.

a good compromise between reasonable deposition rates and minimal influence of

the cathode plasma region on the condensing film such as substrate heating during

deposition. The actual deposition rates are measured in real time by two separate
quartz crystal oscillators (Inficon Inc.), each mounted directly on top of the sub
strate overlooking the sputter guns through a hole in the substrate. Calibration
of the crystal oscillators is necessary since their positions do not coincide with the

actual substrates. The calibration can be accomplished by several methods such
as Rutherford backscattering spectrometry, direct massing of a deposited film, or a

direct measurement of the film thickness (in the range of a few thousand angstroms)
by means of a mechanical stylus. Results from calibrations via these different meth
ods can be used to check their consistency. In using the backscattering method, the

actual film thickness (~ 500 Â) is measured directly and compared to the registered
value from the thickness monitor. Direct massing of the film (thickness ~ lμm) de

posited on a prescribed area of a substrate can also be used to determine the actual

film thickness. Both methods have been used for the calibration of our crystal os
cillators with consistent results obtained. Over a 5- centimeter distance from the
center of the sputter guns, the film thickness has been found not to vary by more

than 5%. The sputtering yield for most metals is effectively a constant in the usual
gun operating range; thus, the target erosion rate or the deposition rate is pro

portional to the cathode current, as shown in Fig. 6. The deposition rate versus

power is consequently nonlinear. Multilayered thin film diffusion couples consisting
of alternating layers of two pure elements are made by simultaneously sputtering

two elemental targets from two separate sputter guns while alternating the sample

substrate over each individual sputter gun. Fig. 7. shows the result of x-ray small
angle scattering from the artificial composition modulations of an Fe/V multilayer

fabricated in our deposition system with nominal individual elemental layer thick-

D e p o s it io n R a te ( A /s e c )

Cathode Current (amp)

Fig. 2.6 Deposition rate of pure Cu at 9 mTorr of Ar vs. cathode current.

INTENSITY (Arbi tra ry Units)

Fig. 2.7 X-ray small angle scattering from an Fe/V multilayer with nominal com
position modulation wavelength of 40Â.

nesses of 20 Â as determined by the crystal oscillators after calibration, in excellent
agreement with the measured modulation wavelength from x-ray diffraction of 42Â,

indicating the ability of our sputtering system for synthesizing very accurately tai

lored compositionally modulated thin films. The absence of higher order diffraction
satellites in Fig. 7, however, signals some interfacial roughness or interlayer mixing
between the elemental layers of Fe and V.

Impurity incorporation into the sputter-deposited thin films is of ma
jor concern.

It is the common impression that sputter- depostion is a “dirty”

process. However, the precise meaning of “dirty” requires a more careful analysis.
The introduction of Ar carrier gas into the main chamber during sputtering intro

duces along with it reactive gas impurities such as O2 and H^. In order to keep
the impurity level in the Ar gas to a minimum, ultrahigh purity (99.999 + %) Ar is
made to pass through a pure Ti metal sponge heated to and maintained at 800° C

(Centorr Inc.) before entering the main chamber. Table 1 shows typical main cham
ber residual gas contents as measured by the mass spectrometer when the system

has reached its base pressure. Table 1 shows also the typical residual gas contents
in the main chamber during sputtering deposition at an Ar pressure of 6 mTorr.

It is to be emphasized that the residual gas contents in the main chamber during
sputtering is obtained by converting the sampled gas contents in the differentially
pumped spectrometer chamber without subtracting the background contribution

(i.e., the residual gas content measured when the system is at its base pressure).
Thus, the impurity gas level so measured represents an upper limit to the actual
gas content in the main chamber during sputtering. The results indicate that while

the Ar pressure during sputtering is in the mTorr range, the partial pressures of the

51
TABLE 2.1 Sputtering chamber residual gas content.

Background

(Torr)

with Ar (Torr)

(sputtering Ti) (Torr)

h2o

2 × IO“8

6 × 10^g

4 × 10-7

2 × 10^9

3 × 10^e

1 × 10~7

7 × 10-1°

4 × 10^θ

3 × KT 7

7 X 10"10

unreadable

2 × 10"1°

6 × IO“3

6 × 10"3

Table 2.1 Residual gas content in the sputtering chamber as sampled by the resid

ual gas analyzer. Residual gas contents after introducing Ar into the chamber are
monitored both before and during sputtering of a pure Ti target at 6 mTorr of Ar.

TABLE 2.2 Low pressure properties of air.
Pressure

(Torr)

(m'^3)

(m)

(m2∕sec)

760

2.5 × 1025

6.5 X 10~8

2.8 X 1027

7.5 × 10~3

2.5 X 102θ

6.6 X 10~3

2.8 X 1022

7.5 × 10~θ

2.5 X 10i7

6.64

2.8 X 1019

7.5 X 10~8

2.5 X 1015

664

2.8 X 1017

7.5 × 10^1°

2.5 X 1013

6.6 X 104

2.8 X 1015

Table 2.2 Particle density, n; mean-free path, λ; particle flux on a surface, Γ.

T = 22°C. Taken from Ref. 14.

predominant impurity gases such as //2, (¾, and Nq. are generally in the 10-c Tonrange or below. Table 2 lists the mean-free path and expected number of molecules

incident upon unit-area per unit-time calculated for air at room temperature[l4].
At a pressure of 10^^3 Ton, the incident molecules upon the condensing film surface
amount to about one thousand monolayers per second (assuming one monolayer

amounts to ~ 1015 molecules per square centimeter). Thus, our first conclusion is

that carrier gas incoporation into the resulting thin film is an unavoidable side effect
inherent to all glow- discharge sputtering technique. The actual Ar incoporation is

usually in the 1% level or lower due to the chemical inertness of Ar, hence the low
sticking probability[15]. At a pressure of 10~g Torr, the incident molecules upon
the condensing film still amount to about one monolayer per second. Thus, at first

sight, contamination of the condensing thin films by reactive gas impurities in the
lθ-o rporr level would reach 10 to 50% (assuming a sticking coefficient of unity) with

typical deposition rate of pure metals ranges from one to five monolayers per second
(3 to 15 Â/sec). However, the rate of incidence of the reactive impurity gases onto

the substrate surface is greatly reduced by the presence of the Ar gas. Since the
mean-free path of gas molecules is inversely proportional to pressure, assuming equal

scattering cross sections for all gas species in the main chamber, the rate of impurity
gas i incident upon the substrate is, roughly speaking, reduced in the presence of

Ar by a factor of P;/P,4r where Pi and P24r are the partial pressures of gas i and

Ar, respectively. Thus, the effective impurity level during sputtering as measured
by the rate of impurity gas incident onto the substrate can be as low as 10-° Torr!
Such impurity levels rival those found in conventional e-beam evaporation, although

it is still inferior to techniques such as semiconductor or metal MBE depositions.

2.4 Summary

It has been only until relatively recently that synthesis of thin films
by sputter deposition has become competitive with the more established vapor

deposition techniques such as the various evaporation techniques. The principal
shortcoming, which is the commonly perceived “dirtiness” associated with sputter
deposition, has been increasingly overcome by better vacuum practice and better
gas-handling capabilities. The inherent easier control and versatility of the sputter

deposition technique will probably warrant more usage and further developement
of this technique. We hope the succesful construction of our rather simple sputter

deposition system will serve as one such example.

2.5 References

1. Handbook of Thin Film Technology, edited by L. I. Maissel and R.

Glang (McGraw-Hill, New York, 1970).

2. Molecular Beam Epitaxy, edited by B. R. Pamplin (Pergamon Press,
Oxford, 1980).

3. G. K. Wehner and G. S. Anderson, in Handbook of Thin Film Tech
nology, edited by L. I. Maissel and R. Glang, Ch. 3 (McGraw-Hill,

New York, 1970).
4. P. D. Townsend, J. C. Kelly, and N. E. W. Hartley, Ion Implantation,

Sputtering and Their Applications (Academic Press, London, 1976).
5. H. H. Anderson and H. L. Bay, in Sputtering by Particle Bombardment
I, edited by R. Behrisch, Ch. 4 (Springer- Verlag, Berlin, 1981).

6. P. Sigmund, Ch. 2, ibid.
7. J. M. E. Harper, in Thin Film Processes, edited by J. L. Vossen and
W. Kern, Ch. 2.5 (Academic Press, Orlando, 1978).

8. J. L. Vossen and J. J. Cuomo, Ch. 2.1, ibid.

9. L. Maissel, in Handbook of Thin Film Technology, edited by L. I.
Maissel and R. Glang, Ch. 4 (McGraw-Hill, New York, 1970).

10. F. F. Chen, Introduction to Plasma Physics and Controlled Fusion,
Ch. 2 (Plenum Press, New York, 1974).
11. R. K. Waits, in Thin Film Processes, edited by J. L. Vossen and W.

Kern, Ch. 2.4 (Academic Press, Orlando, 1978).

12. J. F. O’Hanlon, A User’s Guide to Vacuum Technology, Ch. 6 (Wiley,
New York, 1980).

13. J. F. O’Hanlon, Ch. 4, ibid.
14. J. F. O’Hanlon, Ch. 2, ibid.

15. H. F. Winters, E. Kay, J. Appl. Phys. 38, 3928 (1967)

57
Chapter 3

Solid-State Amorphization of Planar Binary Diffusion Couples: Ther

modynamics and Growth Kinetics

A bilayer or multilayer planar, binary, thin film diffusion couple con

sisting of two pure elements is, by construction, not in thermodynamic equilibrium.
The overall free energy of the system can be decreased by interdiffusion of the

pure elements until the system consists of a single equilibrium crystalline phase
or a combination of such phases according to equilibrium thermodynamics. The
process of reaching the global thermodynamic equilibrium, however, often involves
intermediate steps where metastable phases, because of their competitive kinetics,

are produced. The present chapter concentrates on the thermodynamics and ki

netics of the formation of amorphous NiZr alloys by solid- state interdiffusion of

sputter-deposited polycrystalline binary diffusion couples consisting of pure Ni and

Zr.

3.1 Equilibrium phase diagrams and free energy diagrams

Equilibrium thermodynamic information for a binary system are sum
marized in the corresponding equilibrium binary phase diagram[l]. The final state

reached by a binary diffusion couple consisting of two pure elements is always given

by the equlibrium phase diagram. In a binary system where multiple compounds
exist, the phase diagram does not, however, predict the sequence of formation of

these various compounds. A binary phase diagram can be derived if the dependence

of the free energies of the terminal solid solutions and various compounds on tem

perature and composition is known. A schematic example is given in Fig. 1, where
the derived phase diagram contains a congruently melting compound together with

two terminal solid solutions. Strictly speaking, free energy functions are defined

only for equilibrium phases. However, oftentimes free energies can also be defined
for various metastable phases[2]. A knowledge of the free energy functions of all
phases, stable or metastable, determines whether the formation of a particular phase

is thermodynamically possible. Thermodynamic data of pure elements are available
from which the free energies of pure elements can be calculated[3]. Experimentally

determined equilibrium phase diagrams together with some thermodynamic mod
eling are often used to determine the free energy functions of equilibrium phases[4].

Amorphous alloys are usually modeled as an extension of the liquid state down to

the undercooled regime. Various extrapolation schemes are used to estimate the
free energy of an amorphous alloy[5]. Direct measurement of thermodynamic data

on metastable alloys including amorphous alloys is at best scarce.

3.2 Planar Growth Kinetics of a Single Compound Interlayer

Growth of a particular phase is partially characterized by the mor
phology, i.e., whether the growth is three-dimensional (spherelike), two-dimensional

(island growth) or one-dimensional (layered growth). Phase formation in planar bi
nary elemental diffusion couples often proceeds by planar one-dimensional growth
starting at the original elemental interface[6]. In this case, analysis of the growth

kinetics of a particular compound is equivalent to knowing the compound interlayer

«/>

(∕,)

‘br

(ο

(Ο

(ΖΊ

Fig. 3.1 Free energy functions of various phases and the A-B phase diagram derived

from them. Taken from Ref. 1.

thickness as a function of time. Several general models of planar growth kinetics
exist in the literature[7,8,9]. In our treatment below, we present a steady-state
single compound layer growth model, which follows in essence the treatment due
to Gosele and Tu[9]. This model, although simplified, offers the essential physical

picture necessary to understand such growth processes.

It is assumed that compound β forms and grows between two sat
urated phases a and ^∕ (e.g., the two saturated terminal solid solutions).

The

hypothetical free energy diagram together with the schematic concentration pro
file through the diffusion couple is shown in Fig. 2. The a∕β and β/^ interfaces

move because of interdiffusion and the thickness of the β phase grows with time.
In general, a set of coupled differential equations are needed to solve this mov
ing boundary diffusion problem[l0]. Analytical solutions can be obtained with the

following simplifying assumptions. The steady-state assumption approximates the

concentration profile in the β layer at any instant as the steady-state concentration

profile with the moving a∕β and β∕^ boundaries fixed in their positions at that
instant[ll]. Thus, the A atom diffusional flux should be a constant through the β

compound layer. The steady-state approximation therefore dictates that

~ ∂Ca

Dβ------ — constant,
∂x

(1)

where Dp is the interdiffusion constant through the β compound layer. If we fur

ther assume that the variation of this interdiffusion constant with concentration

in the β concentration range can be neglected, then Equation (l) is equivalent to
the condition that the concentration profile through the β layer is linear. Such a
condition is implied in the concentration profile depicted in Fig. 2 and the A atom

Fig. 3.2 Schematic illustration of growth of a single compound interlayer in a planar
binary diffusion couple. Hypothetical free energy diagram and the concentration

profile.

62
diffusional flux through the β interlayer can be written in this case as
jJPa

-bβ

— Cβa

Xβ

(2)

The interface motion is assumed to be driven by diffusional fluxes into and leaving
this interface. For the two interfaces depicted in Fig. 2, we have
= ',∙*C ~ ⅛∙<

(3'1)

(Ci,1-ς-')⅛⅛=⅛-⅛,

(3.2)

(cf1'i! -

where all concentrations and fluxes refer to those of the A atom. J,tp and Jβ,,
denote the flux from the a side into the a∕β interface and the flux into the β phase
from the a∕β interface, respectively; similar interpretations hold for the fluxes Jzj-y

and Jrιβ. Since we have assumed that the terminal phases a and q, are saturated

(i.e., with constant compositions determined by the equilibrium conditions), Jltβ
and J-1β are consequently zero. The steady-state condition can be used to further
simplify the situation since under this assumption
Jp∣ι

J'∕j^∣

Jβ j

(4)

where Ja is given by Equation (2). Thus, Equation (3) can be rewritten as
(c∙S-‰)⅞i = -⅛

(5∙1)

(‰-ς∙⅞)¾1 = ^∙

<5∙2)

The condition of interface quasi-equilibrium is implicitly assumed; i.e., the deviation
from thermodynamic equlibrium at the interfaces is assumed to be small enough to
justify a linear response of the interfaces to the degree of deviation from equilibrium.

Specifically, the notion of interfacial reaction barrier is introduced to relate the

A atom flux at the interfaces to the interface concentration deviations from the
equilibrium values
jpa = κpa(Cβ1
iχ - Cβn)

(6.1)

^pffCp^ ~ Cβlι^,

(θ∙2)

Jpi

where κpit and κ,βΊ are the mobilities for the two interfaces in the diffusion couple.
Combining Equations (6) with (4) and (2), it can easily be derived that
J∕ = ΔCβ,Dp

Xp + Dp∣Kβπ

(7)

where ΔCβ1 = Cβ,[1 — Cß^ is the equilibrium concentration difference accross the
β compound layer, and κeβ^ is the effective interfacial reaction barrier for the β
compound layer given by

= l∕κ,pa + 1/κ,ρΊ. Since xp = χΡί — xap, Equation

(5) can then be used to give the desired growth kinetics
dip
dt=G^’

(8)

where Gp is a constant determined by the concentrations of the three phases in
volved^]. It is clear from Equation (7) that there exists a characteristic length

Xp = Dp∣Kβi in the growth of the β compound interlayer such that the β inter

layer thickness is proportional either to time t, or to the square root of time f1∕2,
depending on whether the interlayer thickness is substantially below or above this
characteristic length; i.e.,

⅛=Gj,∆ς∕'⅛", ⅛≪⅛

(9.1)

⅛ = Gi,ΔC"'⅛,

(9.2)

» ⅛.

Experimental determination of the growth kinetics of a single compound layer most
often involves the determination of the compound interlayer thickness as a function

64
of annealing time. The interdiffusion constant or the interfacial barrier constant can
then be extracted from experimental data using kinetic models such as Equation

(9). Such a phenomenological description of the interdiffusion process may break
down in the limit of very small interlayer thicknesses[l2].

3.3 Growth of the amorphous interlayer: X-ray and Resistivity Measure

ments

X-ray diffraction is commonly used to detect the presence of various
solid phases. We have used x-ray diffraction in the Bragg-Brentano geometry to fol

low the process of amorphous phase formation in Ni-Zr system[13]. Samples studied
in this work were prepared by a dc magnetron sputtering technique described pre-

viouslyfl4]. Each sample contained a total of about 25 layers with individual layer
thicknesses around 500Â. Samples were prepared on both glass and Be substrates.
Sample heat treatments were carried out in a flowing He gas furnace. A liquid

nitrogen trap and a Ti gettering furnace for He assured minimal oxygen contami

nation. Similar results were also obtained when the annealing was carried out in a
vacuum furnace with pressure kept below 5 × 10~7 Torr. The x-ray measurements

were performed on a Philips vertical diffractometer using Cu Ka radiation.

The x-ray diffraction pattern of an as-deposited Ni/Zr multilayer is
shown at the top of Fig. 3. This sample was prepared under an Ar sputtering
pressure of 15 mTorr. It is clear that the Ni and Zr layers are both highly textured
with the film growth normal to close-packed planes, i.e., (002) in Zr and (ill) in

Fig. 3.3 X-ray diffraction patterns of as- deposited (top) and reacted (bottom)

Ni/Zr multilayers (see text).

Ni. This texturing effect is commonly observed in sputtered-deposited thin films[l5].

The bottom half of Fig. 3 shows the result of a four-hour anneal at 315°C. It can

be seen that the sharp Bragg peaks of the as-deposited films have been greatly

reduced in intensity and a broad band has appeared indicating the presence of an
amorphous phase. It should be noted that the initially very strong a—Zr (002) peak
has essentially disappeared, while the initially weaker a—Zr (100) peak has become

the dominant Zr peak. While the as- deposited films are smooth and flat, the
reacted films often buckle from the substrate. This effect will be discussed later. A
rough measure of the growth kinetics of the amorphous NiZr alloy can be obtained

by a detailed examination of the x-ray diffraction data. We have focussed on one
set of identically prepared films. Because the amorphous NiZr alloy is the only
new phase observed throughout the annealing process, its growth can be monitored

by the consumption of elemental Ni and Zr, which in turn is proportional to the
decrease in the Ni and Zr integrated x-ray Bragg peak intensities, assuming that

no change in film texture occurs during the course of annealing[ 16]. The results
of these measurements are shown in Fig. 4 for two films, one annealed at 250°C

and the other at 315°C. In both cases the total Bragg peak intensities of Ni and
Zr have been normalized to their initial as-deposited values. The slight increase
in the Ni total peak intensities following the first 30- minute anneal at 250° C is
most likely due to recrystallization of some Ni crystallites. There is no evidence
for further recrystallization during subsequent anneals. At both temperatures an
initial decrease in the Ni and Zr total peak intensities is followed by a region of less

rapid decrease. In addition, the 250°C annealing data exhibit a break in the peak
intensity curve between these two regions. This break is the result of a smaller total

scattering area due to the buckling of the film from the substrate. A similar effect is

not observed in the case of the 3150C anneal because the film buckling has already

NORMALIZED INTENS ITY

Fig. 3.4 Normalized Ni and Zr integrated Bragg peak intensities vs. t1∕2 at 250°C

and 3150C (see text).

occurred during the first 30-minute annealing period. The fact that the consumption
rate of the crystalline Ni and Zr follows a Z1∕2 time dependence, as evidenced in

Fig. 4, implies a diffusion rather than an interface-limited growth process of the
amorphous phase. The rate of consumption of the elemental materials can be related

to the interdiffusion constant of the amorphous phase Dam∙ Based on the respective

slopes of the data shown in Fig. 4, we estimate Dam(250°C) = 2 × 10-10m2∕sec

and jD,,,n,(315°C,) = 4 × 10~i8m2∕sec before the buckling of the film occurred. The
activation energy for this interdiffusion constant is thus estimated to be 1.2eV. Ni
is a fast diffuser in crystalline a—Zr[17]. It is important to note that our estimated

interdiffusion constant is at least two orders of magnitude less than that of Ni tracer
diffusion in a—Zr extrapolated to the reaction temperature[l7]. Corresponding to
the decrease in the Ni and Zr integrated peak intensities shown in Fig. 4, there is
also a shift in the Bragg peak positions from their as-deposited values, which can

be seen clearly in Fig. 5. The measured shift in d-spacings as a function of time

is displayed in Fig. 6. The d-spacings measured in reflection correspond to lattice

planes parallel to the sample surface. Both the Zr (100) and (002) lines exhibit a

rapid initial increase in their d-spacings, followed by a decrease. The Ni (111) line
position, on the other hand, remains essentially unchanged throughout the entire

annealing period. The dilation of the Zr unit cell in a direction perpendicular to the
film surface can arise because of an in-plane compressive stress at the Zr/amorphous

interfaces. Such an interpretation will require a contraction of in-plane Zr lattice

spacings and can be verified by transmission x-ray measurements. We have chosen
to use Be substrates for this purpose due to their low x-ray absorption. The results

of these measurements are shown in the insert of Fig. 6. It can be seen that the Zr

cell dilation perpendicular to the sample surface is accompanied by a contraction
parallel to the film surface. The effect of amorphous interlayer growth is therefore

20 (deg)
Fig. 3.5 Shift of Zr Bragg peaks as a function of reaction time at 250°C.

TIME (min)

Fig. 3.6 d-spacings of Ni (111), Zr (002), and Zr (100) Bragg peaks as a function
of reaction time at 250oC in reflection geometry. The insert shows the Zr (100)

d-spacing as a function of reaction time in both reflection (R) and transmission (T)
(see text).

seen to result in a compressive stress on the unreacted Zr layers. It should also

be noted that even though the amorphous layer also stresses the Ni layers, little

relative strain results because of the substantially greater bulk modulus of Ni[l8].
It is this building up of in-plane compressive stress that eventually results in the

buckling of the film from the substrate. The slower rate of consumption of the

elemental Ni and Zr after the film buckles away from the substrate, as shown in
Fig. 4, may be a result of the relief of this in-plane stress.

The changing resistivity during growth of the amorphous NiZr inter

layer can also be used to monitor the growth kinetics. It can shown that, under
the assumption that secondary effects such as recrystallization are negligible, the
reduced conductivity of a Ni/Zr bilayer or multilayer diffusion couple, the average
composition of which equals that of the growing amorphous interlayer, is related

directly to the growth of the amorphous interlayer by

<Ψ) -<7(°) =
—σ(0)

Un(⅛)
÷ fzr (θ) ’

where σ(∕) and σ(0) denote the conductivity at time t and the intitial conductivity,
Z∕√,(0), ^Zr(θ)5 and lam(t) are the initial Ni and Zr individual layer thickness and

the amorphous interlayer thickness, respectively. A term on the order of the ra
tio of conductivities for the amorphous phase and the elements has been neglected

because of the substantially higher resistivity of the amorphous phase. Resistiv
ity measurements were carried out with a standard four-point probe method[19] in
real time as the amorphization reaction is in progress. A typical resistance-versustime curve taken during reaction of a Ni/Zr multilayer at a furnace temperature

of 225°C is shown in Fig. 7. The reduced conductivity exhibits linear dependence
on the square root of time at long times, in agreement with a diffusion-controlled

RESISTANCE (Ar bitr ary Units)

TIME (min)

Fig. 3.7 Resistance of a Ni/Zr multilayer (top) vs. reaction time at 2250C. Shown
also is the resistance of a pure Ni film (bottom) vs. time under identical experi
mental settings (see text).

73
growth of the amorphous interlayer[20]. Shown also in Fig. 7 is the measured
resistance versus time for a pure Ni film prepared in the same way as the Ni/Zr

multilayer on the same type of substrate. The initial increase in the resistance of the
pure Ni film is due to the sample temperature equilibration, the time constant of
which is about 10 minutes. The measured resistance curve of the Ni/Zr multilayer

displays a kink as a result of the changing temperature in the early stage of the
reaction. Thus, any attempt to extract the early stage growth kinetics of the amor

phous interlayer is rendered unreliable by the effect of changing temperature during

measurement[20]. Our result does, however, indicate that the diffusion-controlled

growth of the amorphous interlayer sets in rather early.

3.4 Differential Scanning Calorimetry

Phase transformations such as the melting of a solid to a liquid or
transition from one solid phase to another are first order, and such transformations

are accompanied by the absorption or release of heat. The effects of this heat ab

sorption or release are experimentally detected by various calorimetric techniques,
which are used in turn to elucidate the original process of phase transformation

in the sample. Two major high-temperature calorimetric techniques are differen
tial thermal analysis (DTA) and differential scanning calorimetry (DSC). Although

some contemporary DSC instruments are capable of performing calorimetric work

down to liquid nitrogen temperature, commercially available thermal analysis in
struments are used most often in the temperature range from room temperature

up to 1500oC. Fig. 8(a) and 8(b) show schematic illustrations of a DTA system.
A furnace block contains two symmetrically located and identical chambers, each

S∣ng⅛ neat source

(b!,Boersmo'DTû

(o) C∣oss∣cαi DTû

Fig. 3.8 Schematic illustrations of various thermal analysis systems. Taken from

Ref. 21.

containing an identical temperature detection device. The sample to be investi
gated is placed in one chamber, and a thermally inert reference material (such as
AIq,Oq) with similar heat capacity as the sample is placed in the other chamber.

Both chambers are then heated in an identical manner by the furnace at a constant
heating rate, and the temperature difference between the sample and reference ma
terial is detected by the temperature detection devices located in each chamber and

recorded as a function of furnace temperature. Endothermic or exothermic reac

tions occurring in the sample are manifested as a negative or positive temperature

difference although quantitative evaluation of the total heat evolution is difficult,
since instrumental factors have to be taken into account[21].

Fig. 8(c) shows a schematic of a DSC system. A sample and reference
material are placed in two separate furnaces each equipped with its own tempera
ture detection-device and heater. An average electronic control loop controls both
the temperature of the sample and the reference material to follow a predetermined

thermal history, and an additional control loop adjusts the power inputs to remove
any detected temperature difference between the sample and the reference material.

The sample temperature is thus always kept the same as the reference temperature
and a signal proportional to the power difference between power input into the sam

ple and reference material is recorded as a function of temperature. The recorded

signal at any instant is proportional to the instantaneous rate of heat absorbed or
released by the sample in the limit of small thermal resistance between the sample

and the furnace[21]. Thus, the DSC technique is well suited for the study of kinetics
of phase transformations, since it is capable of subjecting samples to be investigated

to a precisely controlled thermal history as well as of monitoring the rate of reac

76
tion by directly measuring the rate of heat evolution from the sample. Calibration
of temperature (abscissa) and energy (ordinate) on a DSC instrument is usually
accomplished by observing melting of high-purity metals[22]. Fig. 9 shows the

melting endotherm of pure lead. A flat lead sheet (99.99%+) was encapsulated in

between two Al pans that are hermetically sealed together. The melting endotherm
rises linearly on the leading edge because of the finite thermal resistance between

the sample pan and furnace[2l]. Melting points of several pure metals (e.g., In, Sn,
Pb) can be determined and the instrument adjusted so that the measured melting

points do not differ from tabulated values by more than ±20C in the temperature
range 50 — 600°C. Since the apparent transition temperature is slightly dependent
on the heating rate, as shown in Fig. 10, the final adjustments are made at the

heat rate used for real measurements. The energy calibration constant can also be

obtained from such melting endotherms, since the total heat release associated with

the melting endotherm should be the heat of fusion which for pure metals is known
very accurately. After determination of the calibration constant, the ordinate is

read directly in units of millicalories per second.

We have utilized differential scanning calorimetry to monitor the solid-

state amorphization reaction in multilayered thin-film diffusion couples of elemental

Ni and Zr. DSC measurements were carried out on a Perkin-Elmer DSC-4 interfaced
to an Apple HE computer for data collection. Ni/Zr multilayered thin films were

fabricated consisting of alternating layers of elemental Ni and Zr with every Ni (Zr)

layer being the same thickness. The total number of Ni and Zr layers is equal. A
schematic of the geometry of such multilayered diffusion couples is shown in Fig.

11. The average atomic composition of the multilayer Ni., NiZr.rzr is determined by

TEMPERATURE (K)

Fig. 3.9 Melting endotherm of pure Pb (4N+) at 10 K/min taken on a PerkinElmer DSC-4.

Trans ition Temp eratur e (K)

Heating Rate (kZmin)

Fig. 3.10 Apparent melting temperature of pure Pb (4N+) vs. DSC heating rate

Fig. 3.11 Geometry of Ni/Zr multilayered diffusion couples.

the ratio of the individual Ni and Zr layer thicknesses lpu and l∑r. For the geometry
shown in Fig. 11, we have
X∑r∣XNi = (

I Zr P Zr
Mzr

^NiPNi

)∕(

(10.1)

(10.2)
where p and M refer to the densities and molar masses of the pure Zr and Ni,

respectively. Equation (10) can be simplified to
XNi ~ l + 0.47‰‰)∙

The very top and bottom two layers of such Ni/Zr multilayers are always made of

Zr. The thickness of the top and bottom Zr layers should be one-half of a full Zr
layer to insure the symmetry of the whole diffusion couple. In practice, the extra

half-thickness layers of Zr on both the top and the bottom of the samples serve as
protective caps against oxidation[23]. Multilayered thin films were deposited onto

cleaved NaCl substrates. After deposition, samples were immersed in distilled wa
ter, and the Ni/Zr films floated off the substrate. They were captured and rinsed in
ethanol. These freestanding films were dried and immediately hermetically sealed

in aluminum pans by cold welding in an inert gas atmosphere (Ar or He) with a

minimal volume of gas sealed in each sample pan. The sample configuration, a

flat metal sample in intimate contact with a flat metal pan, is optimal for DSC
measurements. Actual measurements were carried out at a constant heating rate of

10K∕min in the temperature range 320 to 870K with sealed Au pans as reference.
Sample scans were followed immediately by a second scan of identical thermal his
tory. If we assume that all phase transformations were completed at the end of the

first scan, then the DSC signal from these two consecutive scans can be summarized

81
as follows:

sisnal(l) = ^- + (C-(l)~C')R + d

(12.1)

signal(2) = (Cfö) ~ C')R + d,

(12.2)

where dHfdt denotes the rate of heat release due to the phase transformation
undergone by the sample, Cζ denotes the heat capacity of the reference material

and Cj',(l) and C,f"(2) denotes the heat capacity of the sample before and after the
phase transformation. R is the heating rate and d denotes any instrumental drifts.

Thus, the difference spectrum between these two spectra

signal(l — 2) =

÷ ΔCj',J2

(13)

eliminates instrumental drift and better elucidates phase transformations undergone
by the sample. All subsequent DSC data shown are, in fact, such difference spectra
where no attempt was made to compensate for changes in the heat capacity of

the sample upon transformation. After a DSC run, the cold-welded flanges of the

sample pan were cut off and the samples were removed for x-ray diffraction study.
A Norelco x-ray diffractometer with Ni- filtered Cu Ka radiation was used for
obtaining x-ray diffraction patterns of the materials.

The rate of heat release upon amorphization of a Ni/Zr multilayer,
as well as upon crystallization, is displayed in Fig. 12. This DSC scan was con
ducted at 10K∕min with a 5.06 milligram sample consisting of 45 Ni and 45 Zr

layers each; all layers were 300Â in thickness. The scan reveals two separate re

actions: the first reaction (centered at temperature T = 580K), which we identify
with the amorphization of the original crystalline multilayers and the second reac
tion (centered at temperature T = 830K), which we identify with the subsequent

Fig. 3.12 Measured heat flow rate as a function of temperature for a sputtered
Ni/Zr multilayer, lNi = l∑r = 300Ä, average stoichiometry NiG3Zr32.

crystallization of the amorphous phase. An x-ray diffraction pattern of the as- de
posited sample (a control sample from the same deposition) is shown in Fig. 13(a).
Fig. 13(b) shows the diffraction pattern for a sample heated up to 670K and then

cooled quickly to room temperature. Finally, Fig. 13(c) shows the diffraction pat

tern for a sample heated up to 870K and then cooled quickly to room temperature.

Diffraction of the as-deposited sample reveals Bragg peaks corresponding to ele
mental Ni and Zr. After the sample has been heated to 670K at 10K∕min, the

elemental peaks have vanished and a broad diffuse maximum characteristic of an
amorphous phase centered at 2θ = 41.4° has appeared, with a secondary maximum
visible at a higher angle. The residual (002) reflection of Zr corresponds to the

thicker external Zr layers on the sample, which we do not expect to react fully[23].
By examining the correlation between the position of the first diffraction maxima
of various liquid-quenched amorphous NiZr alloys and their compositions[24], we
interpolate the average composition of the amorphous NiZr alloy formed during

this in situ reaction to be 68 ± 2 atomic percent Ni. This agrees with the nom

inal average composition of the as-deposited multilayer, which is Ni^Zr^· The

nearly constant heat-flow rate observed at temperatures in the range up to 350K
and the range near 720K is interpreted as corresponding to the rate of reaction
being zero. The growth rate of the amorphous interlayers first becomes observable
at T ~ 370K and finally falls to zero at T ~ 720K. At the latter temperature,

the amorphization process is apparently completed. The total heat release of the

crystalline- to- amorphous transformation seen in Fig. 12 can be calculated via

integration between these two temperatures. We find for this sample a heat re
lease upon amorphization of 510 J∕g, or 35 kJ/mole. The peak observed at 830K,
corresponding to crystallization of the already formed amorphous material, falls be

tween the previously measured crystallization temperatures (with the same heating

2 0 (deg)

Fig. 3.13 X-ray diffraction patterns for the thin film sample of Fig. 3.12, see text.

rate of 10K∕min) of liquid quenched amorphous Nic,7Zr33 and 7VtG8.8∙Zr3i.2[25].

The integrated enthalpy release for this crystallization peak is 4.2 ± 0.2 kJ/mole,
which compares well with an enthalpy release of 3.9 kJ/mole previously observed
for liquid-quenched JVtG7Zr33[25]. This is viewed as further evidence that upon

heating of the Ni/Zr multilayer to 670K at 10K∕min, a completed solid-state amorphization reaction to a relatively homogeneous amorphous state has occurred. We
have further examined these solid-state amorphization reactions in Ni/Zr multi

layered samples of varying individual layer thicknesses. In Fig. 14, one observes

that the basic shape of the DSC scans is repeated for multilayers with individual
layer thicknesses of 300, 450, and 1000Â , respectively. For the samples with in
creasing individual layer thickness, the maximum rate of heat release is observed to
occur at higher temperatures. Nevertheless, the total amount of heat release per

mole, obtained upon integration of a DSC curve, remains constant, independent of
the individual layer thicknesses in a multilayered sample. The enthalpy release of
the amorphization transformation displayed in Figs. 12 and 14 should correspond

closely to that of the formation enthalpy of the amorphous phase. Evaluation of the

reaction product by use of x-ray and DSC analysis indicates an amorphous alloy

with a high degree of homogeneity, similar to that obtained in liquid- quenched
samples. X-ray analysis of the initial, multilayered sample indicates that it is com

posed of polycrystalline layers of pure elements, although there may be some initial

intermixing at the original Ni/Zr interfaces during film deposition[26]. We note
that examination of samples with thicker individual layers showred no marked de

pendence of the measured enthalpy release on layer thickness, an indication that

any prior intermixing does not significantly influence the measured heat of forma
tion within the precision of the measurement. Internal stresses are also known to
accompany the formation of amorphous interlayers in these multilayered diffusion

Fig. 3.14 Measured heat flow rate as a function of temperature for Ni/Zr multi

layers with varying individual layer thicknesses. Dotted curve, I — 300À; dashed
curve, I — 450Â; solid curve, I = 1000Â.

87
couples (see Section 3.3), but any resultant strain energy should be 1 to 2 orders of

magnitude less than the relevant chemical energy[27]. We therefore conclude that
the present measurement yields an accurate determination of the heat of formation
of the amorphous phase. Including the experimental precision, we thus arrive at 35±

5 kJ/mole for the heat of formation of amorphous NiG8Zr33 alloy from the elemental
metals. Our measurement is slightly lower compared with previous measurements
via dissociation calorimetry on liquid-quenched amorphous NiZr alloys of similar

concentrations[28]. The heat of mixing for amorphous NiG3Zr33 alloy reported by
these authors is 45 kJ/mole.

From the data shown above, we see that the heat release from the

amorphization reaction and crystallization can be separated. The rate of heat re
lease upon amorphization of a planar multilayered sample is directly related to

the amorphous interlayer growth kinetics. Growth of amorphous NiZr interlay
ers has been observed to be planar.

Previous RBS measurements showed that

the growing amorphous interlayer possesses a linear concentration profile and con

stant interfacial concentrations fixed by thermodynamic equilibrium conditions[29].
The average concentration of the growing amorphous interlayer remains constant
in time[29]. Therefore, a proportionality exists between the measured heat release
rate dH∕dt and the rate of amorphous interlayer growth dX∕dt, where X is the

interlayer thickness. An approximate relationship can be written as

M(c)

' j dt

(14)

where A is the total Ni/Zr interfacial area of the original multilayers, p(c), M(c),

and H{c) are the density, molar mass, and enthalpy of formation of amorphous NiZr

alloy at the average concentration c of the growing amorphous interlayer. The total

Ni/Zr interfacial area is given by

2M
l∙NiPNi + lZrPZr ’

where pχt∙ and p%r are densities of pure Ni and Zr, and M is the mass of the mul
tilayered sample. Therefore, the rate of heat release normalized by the total Ni/Zr

interfacial area of the sample is a direct reflection of the growth kinetics involved.

The data shown in Fig. 14 between 320K and 720K are redrawn in Fig. 15 after
normalizing each curve by the total interfacial area of the corresponding Ni/Zr mul
tilayer. All normalized DSC curves show qualitatively the same form, indicating

that the growth law is independent of layer thicknesses. Fig. 16 shows a set of such
normalized data taken from samples of different average compositions (i.e., differ

ent Ni-to-Zr layer thickness ratios). All data again show similar growth behavior

with increasing temperature up to the point where deviations are caused by the ex
haustion of the supply of one or both elemental components. This implies that the

average composition of the amorphous interlayer formed is the same, independent
of the starting elemental layer thicknesses up to the point where the supply of one

or both of the elements is consumed. If the growth of the amorphous interlayer is
diffusion-limited, according to Section 3.2, an average interdiffusion constant Dam

of the amorphous alloy can then be directly related to the growth velocity dX/dt
by

^ = G,,mΔC-⅛,

(16)

where ΔC∕∕,, is the equilibrium concentration difference across the growing amor

phous interlayer, G,ιm. is a constant of order unity and A' is the thickness of the

amorphous interlayer. If the interdiffusion process is assumed to be thermally acti
vated with a single activation energy Q', i.e., D,1,n = D0exp(Q, ∕ kβT), then

in(X^) = ∕n(G.....ΔC-',,Do) -

(U)

Fig.

3.15 Heat-flow rate as a function of temperature normalized to the total

interfacial area of the respective Ni/Zr multilayers in Fig. 3.14.

Fig. 3.16 Heat-flow rate normalized by the total Ni/Zr interfacial area of mul
tilayers of various individual layer thicknesses and average compositions. Dotted

line, Ifji — 300⅛∕lzr = 450A; dashed line, ∕^t∙ = 5OθΛ∕lzr = 800Â; solid line,
— lzr — 1000√4.

Analysis of typical DSC scan accordingly is plotted in Fig. 17 with H(c) assumed
to be 40kJ∕mole in the analysis. A linear fit to the data shown in Fig. 17 yields
both the activation energy Q' and the pre-exponential factor Do for interdiffusion

through the amorphous NiZr interlayer. The activation energy Q' is determined

to be 1.05eV, and Do = 4 × 10-9m2∕sec if ΔC,^'∕n is taken to be 0.21 [29], and
Gam to be 1.0[9]. Both the activation energy and pre-exponential factor for in

terdiffusion through the amorphous NiZr interlayer so determined agree well with
previous measurements[30], demonstrating that the interdiffusion process through
the amorphous NiZr interlayer is indeed diffusion- controlled. The advantage of

such DSC measurement on the growth kinetics lies in the capability of precisely

controlled thermal history and continuous measurement over a large temperature
interval (~ 100K); such features can not be easily reproduced by other commonly

used techniques such as Rutherford backscatterng measurements. Linearity of such
plots persists to rather early stages of the amorphization reaction, in agreement

with the previous suggestion that the amorphous interlayer growth switches from

interface to diffusion-controlled fairly early on in the reaction.

A DSC measurement yields information not only on the amorphiza

tion of the original crystalline Ni/Zr multilayers, but also on the subsequent homog
enization and crystallization of the amorphous phase. Depending on the average

concentration of the multilayer, the formation of the amorphous phase exhausts
either the supply of one element first or both elements at the same time. Any

subsequent compositional homogenization processes compete with the crystalliza

tion of the amorphous reaction product. Since the crystallization temperature of
amorphous NiZr alloys has been reported to have a strong dependence on composi-

(39S∕ 2^ )

(⅜ p∕ χp χ) u

Fig. 3.17 Arrhenius plot for the determination of the activation energy and pre
exponential factor of the interdiffusion constant (see text).

93
tion[25], the subsequent crystallization of the amorphous phase should consequently
be a sensitive function of its degree of compositional homogeneity. Shown in Fig.

18 are the DSC data obtained by reacting two Ni/Zr multilayers, both with indi
vidual Zr layer thicknesses of 450Â. However, the individual Ni layer thickness of

one sample is 300Â with its corresponding DSC scan shown in Fig. 18(a). The

average concentration of this sample is 7Vf59Zr4l. The individual Ni layer thick
ness of the other sample is 450Â with its corresponding DSC scan shown in Fig.
18(b). The average concentration of this sample is Ni^Zr^· Amorphization of

these two samples proceeds similarly, as is evident from Fig. 18, although there are
significant differences between their crystallization behaviors. In the reaction of a

sample of average stoichiometry jViG8zfr32 as shown in Fig. 18(b), the amorphiza
tion process is essentially complete by T ~ 700K. Crystallization of the amorphous
phase manifests itself in a single exothermic peak at T ~ 830K. Both the temper

ature and enthalpy of crystallization agree with previous DSC measurements on
liquid- quenched amorphous Λγig7∙^γ33 alloy[25]. This suggests that the amorphous
reaction product is relatively homogeneous when crystallization occurred. On the
contrary, in the reaction of an average Ni5ς>Zr4l sample as shown in Fig. 18(a),

the process of crystallization starts at T ~ 700K, and heat is continuously released

until T ~ 830K. A homogeneous liquid- quenched amorphous 7VtcoZr4o alloy is
observed to crystallize at 750K in a single step[25]. Therefore, the data indicate

that crystallization in this case occurred when the amorphous reaction product is

still compositionally inhomogeneous. Fig. 19 shows a set of DSC data from sam

ples with average compositions near Ni^Zri2 but with different individual layer
thicknesses. This average composition corresponds to the case where both elemen
tal Ni and Zr layers will be consumed by the amorphous phase simultaneously[29].

The DSC scans in Fig. 19(a), 19(b), and 19(c) were obtained from samples with

Fig. 3.18 Heat-flow rate vs. temperature for sputtered Ni/Zr multilayers of two

different average compositions: (a) TV⅛9Zr4χ, (b) NiG8Zr32 (see text).

Fig. 3.19 Heat-flow rate vs. temperature of Ni/Zr multilayers with various Zr layer

thicknesses: (a) l∑r — 8OθΛ, (b) l∑r = 450A, (c) l∑r — 240A. Average composition

~ 7V⅛8^r42 fθr all three samples.

96
individual Zr layer thicknesses of 800, 450, and 240Â , respectively. Similar crystal
lization behavior is observed in all data shown in Fig. 19, indicating in all cases that

crystallization occurred before the composition homogenization of the amorphous

interlayer is complete. Data shown in Fig. 19 suggest that composition homog
enization within the amorphous interlayer is a very slow process. This serves as

a warning against too loosely regarding measured total heat release during amor-

phization as the heat of mixing for the amorphous phase, since it is clear from the
above discussion that obtaining a homogeneous amorphous phase can be difficult

at certain compositions. Integration of the DSC scan shown in Fig. 19(c) from
330K to 670K yields a total heat release of 38kJ∕mole. Since the reaction product
at 670K is still inhomogeneous, this value can be regarded only as a lower bound

for the enthalpy of mixing of an amorphous Nir,c,Zrii alloy.

3.5 Summary

It has been shown in this chapter that the process of formation of

amorphous alloys in thin film diffusion couples, both the growth kinetics and ther
modynamics, can be studied in some detail by a combination of x-ray, resistivity,

and thermal measurement techniques. The growth of an amorphous NiZr interlayer
has been determined to be diffusion-controlled. The lowering of free energy upon
amorphization is demonstrated to be chemical in nature, arising mainly from a large

negative heat of the mixing of the elements to form the amorphous phase.

97
3.6 References

1. P. Haasen, Physical Metallurgy, Ch. 5 (Cambridge University Press,

London, 1978).

2. W. L. Johnson, Prog. Mater. Sei. 30, 81 (1986).
3. CRC Handbook of Chemistry and Physics, edited by R. C. Weast,

section D-43 (CRC press, Florida, 1986).

4. L. Kaufman and H. Bernstein, Computer Calculation of Phase Dia

grams (Academic Press, 1970).
5. D. Turnbull, J. Chem. Phys. 20, 411 (1952); J. D. Hoffman, J. Chem.
Phys. 29, 1192 (1958); C. V. Thompson, F. Spaepen, Acta Met. 27,

1855 (1979); H. B. Singh, A. Holz, Solid State Comm. 45, 985 (1983).

6. Thin Films-Interdiffusion and Reactions, edited by J. M. Poate, K.
N. Tu, and J. W. Mayer (Wiley-Interscience, New York, 1978).
7. G. V. Kidson, J. Nucl. Mater. 3, 21 (1961).

8. B. E. Deal, A. S. Grove, J. Appl. Phys. 36, 3770 (1965).
9. U. Gosele, K. N. Tu, J. Appl. Phys. 53, 3252 (1982).
10. B. P. Dolgin, Ph.D. thesis (California Institute of Technology,

Pasadena, California, 1985).
11. J. Crank, The Mathematics of Diffusion (Oxford University Press,

London, 1975).
12. F. M. d’Heurle, P. Gas, J. Mater. Res. 1, 205 (1986).

13. H. P. Klug and L. E. Alexander, X-ray Diffraction Procedures (Wiley,
New York, 1974).
14. A. P. Thakoor, S. K. Khanna, R. M. Williams, R. F. Landel, J. Vac.

98
Sei. Tech. Al, 520 (1983).

15. K. L. Chopra, Thin Film Phenomena, Ch. 4 (McGraw-Hill, New
York, 1969).

16. A. Guinier, X-ray Diffraction (W. H. Freeman and Company, San
Francisco, 1963).

17. G. M. Hood, R. J. Schultz, Phil. Mag. 26, 329 (1972).
18. C. Kittel, Solid State Physics (Wiley, New York, 1976).
19. L. B. Valdes, Proc. I. R. E. 42, 420 (1954).
20. W. J. Meng, K. M. Unruh, W. L. Johnson, unpublished.
21. A. P. Gray, in Proc. Amer. Chem. Soc. Symp. Analytical Calorime
try, edited by R. S. Porter and J. F. Johnson (Plenum Press, New
York, 1968) p.209.

22. E. S. Watson, M. J. O’Neill, J. Justin, N. Brenner, Anal. Chem. 36,
1233 (1964).

23. M. Van Rossum, M. A. Nicolet, W. L. Johnson, Phys. Rev. B 29,
5498 (1984).

24. K. H. J. Buschow, N. M. Beekmans, Phys. Rev. B 19, 3843 (1979).
25. Z. Altounian, Tu Guo-hua, J. O. Strom-Olsen, J. Appl. Phys. 54,
3111 (1983).

26. B. M. Clemens, Phys. Rev. B 33, 7615 (1986).

27. M. Atzmon, Ph.D. thesis (California Institute of Technology,
Pasadena, California, 1986).

28. M. P. Henaff, C. Colinet, A. Pasturel, K. H. J. Buschow, J. Appl.
Phys. 56, 307 (1984).

29. J. C. Barbour, Phys. Rev. Lett. 55, 2872 (1985).
30. H. Hahn, R. S. Averback, S. J. Rothman, Phys. Rev. B 33, 8825

99
(1986).

100
Chapter 4

Evolution of Planar Binary Diffusion Couples

We have shown in Chapter 3 that the growth of an amorphous phase

as well as the stability of the amorphous interlayer formed can be studied in some

detail by a combination of structural and thermal measurements. In this chapter,
we use primarily the technique of transmission electron microscopy (TEM) to fur
ther examine the process of amorphous phase formation in planar binary diffusion
couples. Again, we have concentrated our efforts on the Ni-Zr system. Emphasis of

this study will be placed on ellucidating key factors that limit the initial formation
of the amorphous NiZr as well as those that limit the extent of amorphous NiZr

formation. Specifically, we will show that a critical thickness of amorphous NiZr

interlayer exists beyond which growth of the amorphous phase is replaced by forma
tion of a Ni-Zr intermetallic compound. It will also be shown that formation of the

amorphous NiZr is critically dependent on the nature of the initial Ni/Zr interface
present. Our results suggest that nucleation plays an important role in controlling
the phase formation sequence in Ni/Zr diffusion couples.

4.1 Specimen Preparation

In addition to sputter-deposited Ni/Zr multilayers where both elemen
tal Ni and Zr layers are polycrystalline with typical grain sizes of a few hundred

angstroms, we have also fabricated bilayer diffusion couples of Ni and Zr where one

101

element (Ni or Zr) consists of a mosaic of large single crystals with typical grain
sizes on the order of 5-20 μm. Since we are dealing with metal-metal diffusion cou
ples, these large, single crystal mosaics are obtained by recrystallizing commercially

available metal foils (Zr foil 25μm, t3N8; Ni foil 100μm, t3N+) in vacuum at high
temperatures.

A special heating stage was constructed for this purpose. Two cop

per pipes were welded to a Confiât vacuum flange through a ceramic-to-metal

feedthrough (Ceramaseal Inc.), which isolates the flange from the copper pipes

electrically. The two copper pipes are joined by another ceramic-to-metal sealed
tube (Ceramaseal Inc.), which electrically isolates them from each other. A metal

foil with two ends clamped on a hollow copper block connected with each copper
pipe forms the only electrical link between the two. By passing current through the

terminals outside the vacuum and also water through the copper pipe, the metal
foil can be heated to above 1000°C, while the rest of the assembly stays close to

room temperature by water cooling. The temperature of the metal foil (at high

temperatures, > 700°C) can be measured by an optical pyrometer. A pure metal
foil (Zr or Ni) is first rolled between two stainless steel sheaths to a thickness of

around 5 μπι; this rolled foil is cleaned in acetone and ethanol and immediately
loaded into the vacuum system. Surface cleaning as well as recrystallization is ac
complished by current heating the foil to around 800oC for a period of 2 - 12 hours.

Such modest mechanical deformation of the initial foil along with subsequent high

temperature heat treatment for an extended peroid is ideal for growth of large sin
gle crystals[l]. The base pressure in the chamber during recrystallization is kept

below 3 × 10-8 Torr with oxygen, nitrogen and hydrogen partial pressures of less

102

than 2 × 10~9 Torr as sampled continuously by the residual gas analyzer. At such

residual gas levels, the impingement rate of reactive gases onto the surface of the
metal foil amounts to about one monolayer per hour; thus, negligible foil surface

contamination results from the impurity gas background in the vacuum chamber.
The oxygen in the original surface oxide layer will diffuse into the metal foil at such
a high temperature, resulting in negligible oxygen contamination of the metal foil

surface after high-temperature recrystallization. The metal foil (Zr or Ni) can be

cooled to room temperature within a few seconds and a second layer of pure metal

(Ni or Zr) is immediately sputtered onto this fresh foil without breaking the vac

uum, creating a bilayer diffusion couple between one polycrystalline metal (denoted
poly-Ni or poly-Zr) and another metal in the form of large single crystal mosaics

(denoted s-Zr or s-Ni). A schematic of the resultant morphology of such a bilayered
diffusion couple is shown in Fig. 1. It is to be noted that the concentration of
defects in a single crystal mosaic such as the density of dislocations is drastically

reduced by the high temperature heat treatment; the subsequent reaction may be
influenced as a result.

Specimens were examined both in plane-view and in cross-section with

a Philips EM 430 transmission electron microscope operated at 300 kV. Crosssectional specimens of sputtered Ni/Zr multilayers were made from multilayers sput
ter deposited onto oxidized silicon wafers. After deposition and heat treatment, the

silicon wafer together with the deposited multilayer was cut by a diamond scribe to
squares approximately 3mm × 3mm. Two such squares were bonded together w,ith

the multilayers face to face by epoxy (M-Bond 610 Adhesive, Vishay Intertechnol
ogy Inc.). Cross-sectional specimens of bilayered polycrystal/single crystal diffu-

103

(Zr)Ni thin film

(Ni)Zr bulk

Fig. 4.1 Schematic of the morphology of bilayered elemental Ni/Zr diffusion couples
where one element (Ni or Zr) is sputtered polycrystals and the other (Zr or Ni)

consists of a mosaic of large single crystals on the order of 10 μm in size.

104
sion couples were prepared similarly. After deposition and heat treatment, the free

standing metal foil was again cut to 3 × 3 mm squares, and two blank Si wafers (3 × 3
mm squares) were used to sandwich two such metal foils face to face for protection.

Constant pressure is applied to such an assembly by a special clamping device during

the epoxy curing. Curing of the epoxy takes about one to two hours at around
100° C. The curing temperature is low enough to avoid interdiffusion in the curing

stage. After curing, the specimen is mounted vertically onto a flat platform by
crystal bond and polished mechanically (600 grade SiCpaper) to a thickness around
100 μτn. This mounting necessarily heats the specimen to the melting temperature

of the crystal bond, which is greater than 100° C. The specimen temperature during

such mounting is usually kept under 150oC, and brief heating to this temperature

does not induce great change in the sample. In certain cases, a limited amount
of interdiffusion is observed at the original interface of the diffusion couple. The

polished surface is then smoothed by a final polishing with 1 μm diamond paste.
A 3 mm Cu ring is then glued onto the smoothed side of the specimen by fast

setting epoxy for integrity of the specimen and ease of handling. This specimen is
then mechanically polished from the other side by a rotating wheel (the Dimpler,

VCR Inc.) with 1 or 0.3 μm diamond pastes applied. The specimen is so polished
to a thickness of less than 5 μτn and finally ion-milled in the center region by

Ar ion bombardment (ion mill, VCR Inc.) until it is electron-transparent. Typical

pressure in the sample chamber during ion milling ranges between 1 to 8 × 10-5Torr.
Typical ion gun settings are 5kV and 1mA. The sample stage is usually cooled to
liquid nitrogen temperature during ion milling. However, no significant differences

between samples milled at liquid nitrogen temperature or at room temperature
have been observed. Some multilayers were deposited onto NaCl substrates and
can be examined directly in plane-view by floating the deposited multilayer off the

105
substrate in de-ionized water and capturing the foils on Cu TEM grid.

4.2 How Thick Can Amorphous Interlayers Grow?

In Chapter 3, the enthalpy of mixing of pure Ni and pure Zr upon
formation of amorphous NiZr alloys of various concentrations has been directly

measured. In the relevant composition range, the heat of mixing of the amorphous
phase averages about 30 kJ/mole. A large thermodynamic driving force thus exists

for the reaction
pure — Ni + pure — Zr —> amorphous — NiZr.

The rate at which the amorphous NiZr alloy forms, however, diminishes with reac
tion time as i⅛~1∕2" since the amorphous interlayer growth is diffusion-controlled.
It is thus appropriate to ask whether an amorphous interlayer, once formed, can

grow to arbitrary thickness, given a sufficient supply of both elemental materials

and sufficient time.

To answer this question, we have examined Ni/Zr diffusion couples
heat-treated under various conditions by cross-sectional transmission electron mi

croscopy (XTEM). Fig. 2 shows a XTEM bright-held micrograph of a sputterdeposited multilayered Ni/Zr diffusion couple. The specimen has not been subjected

to heat treatment except during sample preparation, which amounts to a brief heat
treatment around 150°C. The as-deposited microstructure of both the pure Ni and

the pure Zr layers as well as the amorphous NiZr interlayers originating at each
Ni/Zr interface, which formed as a result of heating during the sample preparation

106

Fig. 4.2 XTEM bright-field micrograph of a Ni/Zr multilayered thin-film annealed
briefly around 150°C (see text).

107

process, are clearly evident. This multilayer consists of three Zr and two Ni layers,
individual Zr and Ni layer thicknesses are 2500Â and 1700Â, respectively. The Zr

layers are made up of columnar Zr grains around 200Â in diameter, and many of
those grains extend across an entire whole Zr layer. The Ni layers are made up of a
multitude of Ni grains that are not as uniform in size, but range typically from 200

to 500Â. The initially formed amorphous NiZr interlayers are about 50Â thick and

are very uniform laterally, a point deserving further discussion later. From Fig. 2

we see that the first phase in such polycrystalline Ni/Zr diffusion couples is indeed
the amorphous phase.

Fig. 3 shows a XTEM bright-field micrograph of a Ni/Zr multilayer
from the same deposition annealed at 320°C for 8 hours. A section of the original
sample is shown in the micrograph. In addition to the amorphous NiZr interlay

ers, which are now about 1000Â in thickness, one additional compound interlayer
about 1000Â in thickness can be seen to have formed between every amorphous

interlayer and its adjacent remaining Zr layer. Microdiffraction information from

the compound layer shows that the compound is orthorombic equiatomic NiZr. En
ergy dispersive x- ray analysis (EDX) was performed. The standardless method

for thin specimens[2] was used to calculate the atomic compositions from collected
x-ray characteristic line intensities. EDX analysis on this cross-sectional specimen

indicates that the average composition of the amorphous layers is about Ni6c,Zr4∩,
whereas that of the compound layers is close to ΛT5,∣Zr,5∩. Thus, the compound

NiZr is the second phase during evolution of polycrystalline Ni/Zr diffusion couples,

which succeeds the amorphous phase.

108

Fig. 4.3 XTEM bright-field micrograph of a Ni/Zr multilayered thin-film annealed
at 320°C for 8 hours. Both amorphous and compound interlayers are clearly evident.

Amorphous interlayers are close to 1000Â in thickness.

109
It is of interest to know in more detail how this compound formed.

One possible scenario would be that the amorphous interlayer actually grew to a

thickness of about 2000Â and the compound subsequently crystallized from the
already formed amorphous material. Fig. 4 shows two XTEM bright field micro
graphs of another Ni/Zr diffusion couple annealed at 300° C for 6 and 18 hours,

respectively. At the end of 6 hours, the amorphous interlayer has grown to about

1000À in thickness. Additional annealing to 18 hours resulted in the formation of
the NiZr compound instead of further growth of the amorphous NiZr interlayer, in

agreement with other measurements[3]. It is worth noting that, according to Fig.
4, the extent of back growth of the compound into the amorphous material already

formed is very little at 300°C; this has been commonly observed in many areas
of the specimen. Thus, the hypothesis that the compound interlayer formed by
crystallization of the already formed amorphous interlayer is invalidated by these
results. Fig. 5 shows two XTEM bright-field micrographs of a Ni/Zr diffusion

couple reacted at 360°C for 10 and 45 minutes, respectively. The amorphous NiZr
interlayer grew to a thickness of about 850Â in 10 minutes. Further annealing to
45 minutes resulted in the formation of the compound NiZr, starting at the amor

phous NiZr/Zr interface, and the compound grew backward at the expense of the
amorphous material, in contrast to the result shown in Fig. 4 obtained for heat
treatment at 300°C. It should be noted that in this case the backward growth of

the compound into the already formed amorphous material is much faster than the
forward growth of the compound into the pure Zr.

The following scenario is suggested based upon the above observa
tions. The compound NiZr forms at the moving amorphous NiZr/Zr interface after

110

Fig. 4.4 XTEM of a Ni/Zr diffusion couple reacted at 300°C: (a) for 6 hours; (b)
for 18 hours. This diffusion couple is of the bilayered s-Ni/poly-Zr type (see Section

4.3).

Ill

Fig. 4.5 XTEM bright-field micrographs of a sputtered Ni/Zr multilayered thin-

film annealed at 360°C: (a) for 10 min; (b) for 45 min. Backgrowth of the compound

into the amorphous material at 45 min is clearly evident.

112

the amorphous interlayer reaches a certain thickness. Formation of this compound
creates two additional interfaces, namely, the compound/amorphous interface and

the compound/Zr interface. The compound/amorphous interface is relatively im
mobile at low temperatures (< 320oC) but mobile at high temperatures (> 360oC).

The composition of the amorphous NiZr alloy at the the original amorphous/Zr in
terface is close to TV⅛o^r5θ as determined by previous RBS measurement^], also in
agreement with our EDX analysis. The local situation at the amorphous/compound

interface is thus rather analogous to that found during polymorphic crystallization
of an amorphous Ni^Zr^o alloy to the orthorombic NiZr compound[5]. The fact

that the amorphous/compound interface goes from being relatively immobile to mo

bile in a temperature interval of 40 to 60 degrees signifies a rather high activation
energy for moving this interface, in agreement with previous crystallization studies,

which showed an activation energy around 2.5 eV for crystallization of amorphous

ΛT50Zr50 alloy[6]. The compound/Zr interface is mobile even at 300oC, but its mo

tion is limited by the diffusional transport of Ni through the amorphous interlayer

plus the compound interlayer and can thus be rather slow. Since the compound NiZr
is lower in free energy than the amorphous NiZr alloy, the amorphous/compound

interface can not move into the compound phase. The growth of the amorphous
NiZr interlayer is limited by the formation of the compound NiZr. Once the com

pound NiZr forms at the amorphous/Zr interface, the growth of the amorphous
interlayer will cease. Thus, a maximum thickness exists for growth of the amor

phous NiZr interlayer. This would not be the case if the second compound phase
formed instead at the Ni/amorphous interface; it would then be possible for the

amorphous interlayer to grow simultaneously with the compound phase by growing
into the pure Zr layer.

113
We have measured the maximum thickness of amorphous NiZr inter

layers as a function of isothermal annealing temperature by direct cross-sectional
observation; the result is displayed in Fig. 6 in an Arrhenius form. The temperature

dependence of this maximum thickness is quite weak, the apparent activation energy
of which is only 0.1 eV by linear regression of the observed data. The maximum
thickness an amorphous NiZr interlayer can grow is about 1000Â.

4.3 Is Nucleation Important?

In sputter-deposited polycrystalline Ni/Zr diffusion couples, the ob

servation of lateral uniformness of the amorphous NiZr interlayer during its early
stage of growth is important (see Fig. 2). Formation of the amorphous phase re
quires nucleation. The fact that an amorphous interlayer around 50Â in thickness
is laterally uniform suggests that nucleation centers for the amorphous phase exist
in abundance at the original Ni/Zr interface, since islandlike amorphous clusters
would probably be found in the early growth stage if very few nucleation centers

were present. It is natural to connect such observations to the well-known Walser

and Bene conjecture, which effectively states that a glass interlayer always exists
first in an elemental diffusion couple prior to the appearance of any intermetallic

compound, which can essentially be viewed as the crystallization product of this
glass interlayer[7]. This glass interlayer can be a result of either the particular vapor

deposition process or the interdiffusion at very small distances. Our observations on

sputtered polycrystalline Ni/Zr diffusion couples seem to support such a conjecture.

Fig. 4.6 Plot of the critical thickness of the amorphous NiZr interlayer vs. reaction
temperature.

Thick ness (A)

In (X om)(Λ)

114

115

The present experiment aims at clarifying whether an interfacial glass
interlayer is always present by creating interfaces of polycrystalline Ni with single

crystal Zr or vice versa and by observing the evolution of such interfaces under heat
treatment. Fig. 7(a) shows a XTEM bright field micrograph of Zr foil recrystallized
at about 800° C. Resulting individual Zr grains are as thick as the foil with grain
boundaries running through the entire foil. Little additional grain growth results

from further heating beyond this point. The recrystallized Zr foil has a strong
(002) texture with the c-axis perpendicular to the foil, the same as the sputtered

polycrystalline Zr. A diffusion couple between sputtered polycrystalline Ni and

recrystallized Zr foil is fabricated as described in Section 4.1. Shown in Fig. 7(b)
is a XTEM bright-field micrograph of such a diffusion couple annealed at 300° C
for 6 hours. Although reaction at this temperature for the above duration would
have produced a fairly thick amorphous NiZr interlayer in polycrystalline sputtered

diffusion couples, it is evident from this micrograph that no reaction is initiated at

this interface between polycrystalline Ni (poly-Ni) and single crystalline Zr (s-Zr).
A more detailed examination is shown in Fig. 7(c), which shows a high-resolution

lattice image XTEM micrograph of the poly-Ni/s-Zr interface of a similarly reacted
specimen. The specimen was tilted so that the poly-Ni/s-Zr interface was parallel
to the electron beam direction. Lattice fringes of pure Ni and pure Zr extend to and

meet at this interface, showing that the interface was originally atomically sharp

and remained sharp after prolonged heat treatment with no indication of other

phases, amorphous or crystalline, present. The apparent inertness of such a Ni/Zr

interface when single crystal Zr is used is in agreement with previous RBS analysis
on the same type of poly- Ni/s-Zr diffusion couples[8].

lie

Fig. 4.7 Reaction of a poly-Ni/s-Zr bilayer diffusion couple: (a) typical microstruc
ture of recrystallized Zr foil; (b) bright-field micrograph showing no reaction after

annealing at 300°C for 6 hours; (c) high-resolution micrograph of the poly-Ni/s-Zr
interface, showing the Ni (111) ande Zr (101) lattice fringes.

117

Our result indicates the existence of a nucleation barrier for amor

phous phase formation when polycrystalline Ni is placed in contact with a Zr single

crystal at 300°C. Thus, the formation of an amorphous NiZr alloy in sputtered poly
crystalline Ni/Zr diffusion couples must be due to the presence of nucleation centers
at the original poly-Ni/poly-Zr interface, which are absent when polycrystalline Zr

is replaced by Zr single crystal. Grain boundaries are known to catalyze many
precipitation reactions. The Zr grain boundaries may provide the neccessary nucle

ation centers for the amorphous phase. Since grain boundaries are indeed present in
our recrystallized Zr foil, their influence on the formation of the amorphous phase
is pursued. Fig. 8 shows in plane-view a bright-field micrograph of the same polyNi/s-Zr diffusion couple after annealing. One can see the Zr grains few microns

to tens of microns in size as well as the few hundred angstrom Ni polycrystals on

top of them. Some Ni grains are over one thousand angstroms in size because of
grain growth during heat treatment. Electron diffraction revealed no sign of new
phase formation. This micrograph shows that these remaining low-energy Zr grain
boundaries do not catalyze the formation of the amorphous phase. To examine

the influence of Ni grain boundaries at the Ni/Zr interface on the reaction process,

we have similarly fabricated s-Ni/poly-Zr diffusion couples, where Ni consists of a
mosaic of single crystals, again as described in Section 4.1. Fig. 9 shows a XTEM

bright-field micrograph of a s-Ni/poly-Zr diffusion couple annealed at 300°C for 6

hours. No nucleation barrier seems to exist in this case and, as the result of this
reaction, the amorphous NiZr interlayer has been grown to around 1000Â in thick

ness^]. This shows that the absence of Ni grain boundaries at the Ni/Zr interface in
such s-Ni/poly-Zr diffusion couples is immaterial for forming the amorphous phase.

118

Fig. 4.8 Plane-view, bright-field micrograph showing a poly-Ni/s-Zr diffusion cou
ple after annealing at around 250oC for 4 hours. No reaction is observed at Zr grain

boundaries.

119

Fig. 4.9 XTEM bright-field micrograph of a s- Ni/poly-Zr bilayered diffusion couple

annealed at 300° for 6 hours. An amorphous NiZr interlayer around 1000Â thick
formed as a result of the reaction.

120

In addition, the behavior of such s-Ni/poly-Zr diffusion couples should
also be contrasted with that of sputter-deposited polycrystalline Ni/Zr diffusion cou

ples. Ni has been shown to be the dominant moving species during amorphization

of Ni/Zr diffusion couples[10]. The predominant movement of Ni atoms across the
Ni/amorphous interface into the amorphous interlayer is expected to generate ex

cess vacancies on the Ni side of the Ni/amorphous interface. These vacancies may

condense and form voids. We have observed large voids in the elemental Ni layers

in sputter-deposited polycrystalline Ni/Zr diffusion couples after reaction (e.g., an
nealing at 320°C for 8 hours), in agreement with previously reported work[2]. One
needs to keep in mind that existing voids may be enlarged by the ion milling pro
cess. However, the existence of voids exclusively on the Ni side confirms that Ni is

the dominant moving species during interdiffusion of Ni and Zr. One notice that no

void exists in the poly-Ni layer during the early stage of amorphous NiZr formation
(see Fig. 2); thus, we speculate that void formation in the Ni layer by condensation

of excess vacancies takes place only after a certain vacancy concentration level is
reached. In Ni/Zr diffusion couples where Ni consists of a single crystal (see Fig.

9), no voids are observed anywhere in the Ni layer. We suggest that condensation of

vacancies into voids in the Ni layer requires the presence of certain void nucleation

sites. Apparently, Ni grain boundaries serve as such sites. With such sites absent
when a single crystal of Ni is used, the vacancies diffuse into the Ni layer and eventu
ally annihilate at the nearest sink. In our case of a bilayered s-Ni/poly-Zr diffusion

couple, this nearest vacancy sink is apparently the Ni free surface. In addition,
the same maximum thickness of amorphous NiZr interlayer was observed at 300oC,

using either sputtered polycrystalline Ni/Zr multilayers or s-Ni/poly-Zr diffusion

couple, suggesting that the presence of voids does not influence the formation of
the compound NiZr in any significant way.

121
The phase formation behavior of Ni/Zr diffusion couples of the
polycrystalline/single-crystalline type is essentially asymmetric, and we are led to

believe that the formation of amorphous NiZr alloy in sputtered Ni/Zr diffusion
couples is controlled by the presence of high-energy Zr grain boundaries that act as

nucleation centers for the amorphous phase.

4.4 Models for Evolution of Diffusion Couples

The behavior of sequential phase formation in planar diffusion couples
is experimentally demonstrated in the above sections for Ni/Zr diffusion couples.

The first formation of an amorphous phase in this system indicates the need to
include metastable phases in a complete description of diffusion couple evolution.
Any theoretical attempt to describe the evolution of diffusion couples must face the

problem of predicting the first phase, the critical thickness of the first phase prior
to formation of the second phase, etc. Because of the complexity of the problem,
experimental determination of a complete set of parameters that appear in any

model is hard if not impossible. Thus, various phenomenological models are most
often used to rationalize the general behavior of many systems instead of giving

concrete predictions regarding any one system. In what follows, we will briefly

present one model by Gosele and Tu, which rationalizes the phase sequencing in

planar diffusion couples by focusing entirely on the relevant, one-dimensional growth

kinetics[ll]. We will also suggest a simple, phenomenological model that focuses on
the nucleation kinetics[l2]. Relevance of these models to experimental observations
will be discussed.

122

The Gosele and Tu model sidesteps the question of nucleation by

assuming that two compound interlayers β and 7 exist at the beginning together

with the two pure elements (saturated terminal solutions a and 0). The hypothetical
concentration profile is shown in Fig. 10, and correspondence is easily made to the
case of growth of a single compound interlayer, as shown in Section 3.2. Steady-state

approximation is again used to simplify the problem so that analytical solutions are
possible. One key assumption in this model is that the motion of every interface is
assumed to be driven by diffusional fluxes into and out of this interface, and every

interface is free to move in both directions depending on the relevant fluxes. A
simple derivation completely parallel to the one given in Section 3.2 gives

dxp
= Gf>J* -- Gcjf
dt

(1.1)

dx~j
= c,7 - Gt. jfi.
dt

(1.2)

where Jfi and J^ are the A atom fluxes through the β and 7 compound interlayers,
given respectively by

ΔC"1Dp

δc*wι

xp + Dp ∕ cJI

x-1 + Dι∕kι^

(2-1)

(2∙2)

where the equilibrium concentration differences, interdiffusion constants and effec
tive interfacial reaction barriers refer to those of the /? or 7 compound layers by
their respective subscripts. The constants Gp, G~t and G,. account for the change

in concentration at the interfaces and they depend only on concentration of the

respective compounds. Thus, the ratios of these constants, specifically ri = G,.∣Gp
and r2 ≡ G'^∕G'f., are time-independent. It can be proved that r1 < r2. The ratio of
A atom fluxes through the β and 7 compound interlayers r ≡ Jft ∕J^ is, however,

123

Fig.

4.10 Hypothetical concentration profile in a A-B diffusion couple during

parallel growth of two compound interlayers β and 7 (see text).

124

time-dependent. From Equation (1), we see the condition for the growth of β and
q is r > ri and r < r2, respectively. A variety of growth behaviors can in principle

be generated from this model, given suitable combination of parameters. Let us

consider the following scenario. Let the two compound β and q interlayers be
very thin initially, such that transport across both layers are interface-controlled.
This situation might simulate the very early stage of evolution of a binary diffusion

couple when two compounds nucleated simultaneously. The flux ratio in this case

can be obtained from Equation (2), r = ΔC'lβ∕ΔC'βκ↑lii. If r falls in between
rl and r2, then both interlayers will grow. However, if the mobility of q interfaces

are much higher than that of the β interfaces such that k,pι^ » κ,e^, then the flux

ratio will be less than r1 and the q interlayer will grow but the β interlayer will
shrink. Thus, this model predicts that the first phase appearing in a binary diffusion
couple is the one with the highest interface mobility. Eventually, the growth of the

q interlayer will become diffusion-controlled. In this case, the flux ratio will be
given by r = (ΔC^'iκ^∕ΔC'^'iZλγ)x.7, and it will be dependent on the thickness of

the q interlayer. Suppose that r initially lies below r1j then as the q compound
interlayer grows thicker, the flux ratio will increase and will eventually reach τq,

allowing the β compound to grow. The critical thickness of the q compound in
this model is thus given by x°rιt — r1(ΔC^'i∕ΔC^'i)(J97∕∕c^^). Thus, given suitable
choice of parameters, this model is suggestive of some general features found during

the evolution of many diffusion couples.

How pertinent is this model when applied to the particular case of

Ni-Zr system which we have investigated experimentally in some detail? We have
to qualify first that no experimental data for the interface mobility parameters exist

125
for either the amorphous or the compound phase. One may justify the first appear
ance of the amorphous NiZr alloy in sputtered Ni/Zr diffusion couples by assuming

a higher interface mobility for the amorphous phase than for the compound, since
it may be argued that less topological arrangement at the interface is required to

form the amorphous phase than the compound. However, this hardly explains the
observed asymmetric phase formation behavior when single crystals of either Ni

or Zr are placed in contact with the other element, which is polycrytalline (see
Section 4.2). Since a higher interface mobility for the amorphous phase, according
to this model, would seem to predict that the amorphous phase would form first
in both cases regardless of which side is a single crystal. Thus, the sensitivity of

phase formation to the initial state of the interface as indicated by our experiments

seems to suggest the need for considering nucleation kinetics in addition to growth

kinetics. Furthermore, our observation that, at 360oC, the compound NiZr forms at
the amorphous/Zr interface after the amorphous NiZr interlayer grows to a certain

thickness and then grows back at the expense of the amorphous material, provides
strong evidence that the formation of the compound NiZr is rate-limited by nucle
ation. With a mobile compound/amorphous interface, it would be impossible for

the amorphous interlayer to grow to any thickness if the compound were to exist
at the initial interface. Therefore, we believe that our experiments suggest that, at

least in the Ni-Zr system, the kinetics of nucleation has to be considered in order to
understand the formation of both the first and the second phase. In what follows,
we present a simple phenomenological model based on the premise of interfacial het

erogeneous nucleation, and we show how the evolution of Ni/Zr diffusion couples
can be understood in this context[l2].

126
Growth of an amorphous NiZr phase in Ni/Zr diffusion couples oc

curs at rather low temperatures ( ~ 300° C ). The collective atomic rearrangements
required for crystallization within the already formed amorphous interlayer do not
occur until much higher temperatures are reached. The transition from growth

of an amorphous phase to a compound phase occurs heterogeneously at the mov
ing amorphous/Zr interface, as suggested by experiments outlined in the previous

sections. Formation of any Ni-Zr compound phase at the amorphous/Zr interface
requires formation of a heterogeneous nucleus. Assuming this to be the rate-limiting
step in compound formation, we can analyze this transition from the growth of an

amorphous phase to a compound. Since the growth of the amorphous interlayer
is one- dimensional, the relevant dimension of this compound critical nucleus is its

thickness in the growth direction, denoted by L. Denote further the velocity of the
amorphous/Zr interface during growth of the amorphous interlayer as Vj,nt. These
parameters define a natural time scale Tint required for the necessary atomic rear
rangements taking place at the amorphous/Zr interface to form a Ni-Zr compound

nucleus
Tint = -^-∙
^int

(3)

In time τint, the amorphous interlayer would advance a distance of L, leaving behind
the interface an immobile glassy atomic comfiguration. The competing time scale
rnuc for nucleating the Ni-Zr compound at the amorphous/Zr interface can be taken

as the inverse of the heterogeneous nucleation rate I. According to the classical
steady-state nucleation theory, this nucleation rate I is given by

I = Kvexp(-^-^^),

(4)

where K is a dimensionless constant, i∕ is an attempt frequency, Q is an activation
energy for atomic transport in the interface region, and ΔGi is the heterogeneous

127
nucleation barrier[l3]. The condition for the continued growth of the amorphous

interlayer can be stated simply as an inequality between these two time scales

(5)
where the equality denotes the critical condition when the formation of the par

ticular compound becomes possible. Equation (5) dictates a lower critical amorphous/Zr interface velocity L∣τnuc below which the growth of the amorphous phase

cannot be sustained against nucleation of the intermetallic compound. Equation (5)
originates from general considerations of the two competing kinetics of amorphous
phase growth and compound nucleation. Since the growth of the amorphous inter

layer is diffusion-controlled, the amorphous/Zr interface velocity can be related to

the thickness of the amorphous interlayer xam by
Vint — K

t Dam

(6)

where Kt is a dimensionless constant and Dam = D0exp(-Q,∕kBT) is the interdiffusivity through the amorphous interlayer. An explicit expression limiting the
thickness of the growing amorphous interlayer can be reached in this case
%am ≤(

K'Do
LKu

)exp(

(AG* + Q) - Q,
kBT

(7)

where the equality yields our prediction for the amorphous interlayer critical thick

ness Xam. It is to be emphasized that Equation (7) is obtained under the assump
tion that the diffusion constant is time-independent up to the transition between

amorphous phase growth and compound nucleation.

4.5 Summary

128

We have monitored the formation of amorphous alloys and the subse
quent formation of crystalline compound phases in planar thin-film diffusion couples

by the technique of plane-view and cross-sectional transmission electron microscopy.
Direct microstructural observations provided valuable detailed information that is

not available from other techniques such as x-ray diffraction, backscattering spec
trometry, or thermal analysis. These experimental observations suggest that, in ad
dition to thermodynamic considerations, it is the combined nucleation and growth

kinetics that determines the evolution of a thin-film diffusion couple.

129

4.6 References

1. R. W. Cahn, in Physical Metallurgy, edited by R. W. Cahn and
P. Haasen, Ch. 25 (North-Holland Physics Publishing, Amsterdam,

1983).

2. L. Reimer, Transmission Electron Microscopy, Ch.

9 (Springer-

Verlag, Berlin, 1984).

3. S. B. Newcomb, K. N. Tu, Appl. Phys. Lett. 48, 1436 (1986).
4. J. C. Barbour, Phys. Rev. Lett. 55, 2872 (1985).
5. U. Koster and U. Herold, in Glassy Metals I, edited by H. J. Gun-

therodt and H. Beck, Ch. 10 (Springer-Verlag, Berlin, 1981).
6. Z. Althounian, Tu Guo-hua, J. O. Strom-Olsen, J. Appl. Phys. 54,
3111 (1983).

7. R. M. Walser, R. W. Bene, Appl. Phys. Lett. 28, 624 (1976).
8. A. M. Vredenberg, J. F. M. Westendorp, F. W. Saris, N. M. van der

Pers, Th. H. de Keijser, J. Mater. Res. 1, 774 (1986).
9. K. Pampus, K. Samwer, J. Bottiger, Europhys. Lett. 3, 581 (1987).

10. Y. T. Cheng, W. L. Johnson, M.-A. Nicolet, Appl. Phys. Lett. 47,
800 (1985).

11. U. Gosele, K. N. Tu, J. Appl. Phys. 53, 3252 (1982).
12. W. J. Meng, C. W. Nieh, W. L. Johnson, Appl. Phys. Lett. 51, 1693
(1987).
13. J. W. Christian, The Theory of Transformations in Metals and Alloys

(Pergamon Press, Oxford, 1975).

130

Conclusion

It has been almost five years since the publication of the first paper
on solid-state amorphization reactions by Schwarz and Johnson. Since then, the

synthesis of metastable materials, including amorphous materials, from the solid

state has gained wide attention. We have concentrated our efforts on the experi
mental study of the solid state reaction processes in Ni-Zr thin-film diffusion couples
in this thesis. It is our approach to obtain as much understanding as possible by

attacking this problem from a variety of angles using a variety of experimental tech
niques. Among the issues to be investigated, the study of the growth kinetics of

the amorphous interlayer is a relatively easy task and results obtained from various
independent studies, including our own, are consistent. We have demonstrated that

the dominant thermodynamic driving force for the amorphization reaction in Ni-Zr

system arises from a large negative heat of mixing between the two elements. Our
results are in agreement with other available thermodynamic data. Studies on both

problems mentioned above are fairly complete at present and a general consensus

exists on the conclusions derived. We have also demonstrated that the nucleation

of the amorphous phase is sensitively dependent on the nature of the interfaces
present. However, the study of nucleation of various phase, stable or metastable,

at interphase interfaces, with or without heterogeneities such as grain boundaries

or dislocations, of which our investigation serves as but one example, is only at
its beginning. Well-designed experiments carried out with exquisite techniques are
desperately needed in order to further our understanding on this subject.