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3 1293 01570 7908

ii" 1Illillllllllllllllllllllllll'llllllilllllillI r

This is to certify that the

dissertation entitled

"Structure and Magnetism in Cobalt/X, Fe/Si,

and Fe/[FeSi] Multﬂayers"

presented by

Michael Ray Franklin

has been accepted towards fulﬁllment
of the requirements for

Ph. D. degree in PhYSiCS

(MM/7% («4/

Ma jorr professor

Date July 22. 1997

M5 U is an Afﬁrmative Action/Equal Opportunity Institution 0-12771

STRUCTURE AND MAGNETISM IN Co/X,
Fe/Si, AND F e/ {FeSi} MULTILAYERS

by

Michael Ray Franklin

A DISSERTATION

submitted to
Michigan State University
in partial ﬁilﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1997

 

ABSTRACT

STRUCTURE AND MAGNETISM IN Co/X,
Fe/Si, AND Fe/{FeSi} MULTILAYERS

by

Michael R. Franklin

Previous studies have shown that magnetic behavior in multilayers formed by
repeating a bilayer unit comprised of a ferromagnetic layer and a non-magnetic spacer
layer can be affected by small structural differences. For example, a macroscopic
property such as giant magnetoresistance (GMR) is believed to depend signiﬁcantly upon
interfacial roughness. In this study, several complimentary structural probes were used to
carefully characterize the structure of several sputtered multilayer systems-Co/Ag,
Co/Cu, Co/Mo, Fe/Si, and Fe/{FeSi}.

X-ray diffraction (XRD) studies were used to examine the long-range structural
order of the multilayers perpendicular to the plane of the layers. Transmission electron
diffraction (TED) studies were used to probe the long-range order parallel to the layer
plane. X-ray Absorption Fine Structure (XAF S) studies were used to determine the

average local structural environment of the ferromagnetic atoms.

For the Co/X systems, a simple correlation between crystal structure and saturation

 

Michael Ray Franklin

magnetization is discovered for the Co/Mo system. For the F e/X systems, direct evidence
of an Fe-silicide is found for the {FeSi} spacer layer but not for the Si spacer layer.
Additionally, differences were observed in the magnetic behavior between the Fe in the

nominally pure Fe layer and the Fe contained in the {FeSi} spacer layers.

in memory of Dr. Carl L. F oiles

iv

ACKNOWLEDGEMENTS

I wish to thank Dr. Carl F oiles for his invaluable guidance and support during this
project. He was more than just a research advisor; he was also a good friend.

I also wish to thank Dr. Jerry Cowen for several enlightening conversations about
magnetism and Dr. Peter Schroeder for his ﬁnal review of this dissertation.

Thank you to all the faculty, staff, and graduate students in the Physics Department
at MSU. So many have helped me more than they know. Special thanks are given to
Reza Loloee and Vivion Shull for their many hours spent helping me with this project.
Special thanks to Paul Holody for our many discussions of physics. Also, special thanks
to Dr. Jules Kovacs and especially Stephanie Holland for helping me with those
administrative headaches.

Also, ll must thank my parents for the many years of selﬂess support and wise
instruction they have given me. I could never have reached this point without them.

Many thanks are also given to my wife Kathy for her sacriﬁces of time as well as for
her never-ending support.

Most of all, I wish to thank God for giving me such a wonderful opportunity. I
pledge to use this blessing to serve my fellow man.

Finally, I wish to thank the Department of Physics and Astronomy and the Center

for Fundamental Materials Research for their ﬁnancial support during my time at MSU.

 

TABLE OF CONTENTS

1. INTRODUCTION ................................................................................................. 1
2. SAMPLE FABRICATION ................................................................................... 3
2.1 Sputtering Process ......................................................................................... 3
2.2 Sputtering System Description ..................................................................... 5
2.3 System Preparation and Cleanliness ............................................................ 7
2.4 Typical Operating Procedures and Conditions .......................................... 7

3. X-RAY DIFFRACTION ..................................................................................... 10
3.1 Introduction ................................................................................................. 10
3.2 Bragg's Law ................................................................................................. 11
3.3 Powder Diffractometry ............................................................................... 13
3.3.1 Diffraction Patterns ............................................................................. 14

3.3.2 The Rigaku Rotating-Anode Powder Diffractometer ......................... 19

3.4 Typical Measurements ................................................................................ 24
3.5 Analysis ......................................................................................................... 24
3.5.1 Determination of Planar Spacings ...................................................... 24

3.5.2 Determination of Bilayer Spacing ...................................................... 25

3.5.3 Determination of Coherence Length (Scherrer's Equation) ................ 27

vi

4. TRANSMISSION ELECTRON DIFFRACTION ............................................ 31

4.1 Introduction ................................................................................................. 31
4.2 Bragg's Law Modification .......................................................................... 33
4.3 Diffraction Patterns ..................................................................................... 34
4.3.1 The Ewald Sphere ............................................................................... 34
4.3.2 Single Crystal and Polycrystalline Diffraction Patterns ..................... 35
4.3.3 Textured Diffraction Patterns ............................................................. 35

4.4 Transmission Electron Microscopy ........................................................... 38
4.4.1 Conventional TEM ............................................................................. 38
4.4.2 Image and Diffraction Pattern Formation ........................................... 41
4.4.3 VG HBSOl FESTEM .......................................................................... 46

4.5 Sample Preparation and Typical Settings of the FESTEM ..................... 49
4.6 Analysis ......................................................................................................... 50
4.6.1 Structural Determination .................................................................... 50
4.6.2 Compound Identiﬁcation .................................................................... 51

5. X-RAY ABSORPTION FINE STRUCTURE ................................................... 54
5.1 Theory ........................................................................................................... 54
5.1.1 Physical Origin ................................................................................... 55
5.1.2 The XAF S Equation ........................................................................... 55

5.2 Experimental Procedures ............................................................................ 57
5.2.1 The Synchrotron ................................................................................. 58
5.2.2 XAF S Measurement Techniques ........................................................ 59

vii

5.3 MacXAFS Analysis ...................................................................................... 62

 

5.3.1 Data Conversion (Raw -—) XMU Files) .............................................. 65

5.3.2 Normalization and Background Removal (XMU —> CH1 Files) ........ 65

5.3.3 Fourier Transform (CHI —) RSP Files) .............................................. 68

5.3.4 Inverse Fourier Transform (RSP —> ENV Files) ................................ 69

5.3.5 Least-squares Fit ................................................................................. 70

6. CO/X MULTILAYERS ...................................................................................... 72
6.1 Introduction ................................................................................................. 72
6.2 Co/Ag ...... - ...... - -- - ...... - -- 73
6.3 Co/Cu ............................................................................................................ 74
6.3.1 Sample Fabrication ............................................................................. 76

6.3.2 XAF S Results ..................................................................................... 76

6.3.3 XRD and AXRD Results .................................................................... 80

6.4 Co/Mo ........................................................................................................... 86
6.4.1 Samples Fabricated ............................................................................. 88

6.4.2 Magnetic Studies ................................................................................ 88

6.4.3 XRD Results ....................................................................................... 91

6.4.4 TED Results ........................................................................................ 94

6.4.5 XAF S Results ..................................................................................... 94

7. FE/SI AND FE/{FESI} MULTILAYERS ....................................................... 104
7.1 Introduction ............................................................................................... 104

viii

7.2 Samples Fabricated ................................................................................... 107

7.3 Magnetic Studies ........................................................................................ 107
7.4 XRD Results ............................................................................................... 110
7.4.1 Low-angle XRD ................................................................................ 110
7.4.2 Higher-angle XRD ............................................................................ 112

7.5 TED Results ............................................................................................... 115
7.6 XAFS Results ............................................................................................. 119
8. SUMMARY AND CONCLUSIONS ................................................................ 122
8.1 Co/Cu Multilayers ..................................................................................... 122
8.2 Co/Mo Multilayers ..................................................................................... 122
8.3 Fe/Si and Fe/{FeSi} Multilayers ............................................................... 123
8.4 Future Investigations ................................................................................. 124
8.4.1 Co/X Multilayers .............................................................................. 124
8.4.2 Fe/Si and Fe/{FeSi} Multilayers ...................................................... 125

ix

Table 2-1:
Table 6-1:

Table 6-2:

Table 6-3:

Table 6-4:

Table 7-1:

Table 7-2:

LIST OF TABLES

Deposition rates for various targets. .................................................................. 8

Saturation magnetization and ﬁtted EXAF S results.5 N values are estimated
to be accurate to within i 15%. GMR values are current-in-plane data at 5K
from PA. Schroeder—the percent change is relative to the resistance at or
near magnetic saturation. ................................................................................ 74

EXAFS results for Co/Cu samples. The upper portion of the table contains
results for the sputtered samples of the present study. The lower portion of
the table summarizes the results reported by Pizzini, et al. for evaporated
samples.15 Since Pizzini, et a1. ﬁxed the coordination number N at 12, the
data analysis for the present study treated N both as a ﬁxed parameter and as
a variable to be ﬁt. .......................................................................................... 78

Summary of d-spacings from XRD and AXRD data. I<> denotes the dominant
line; 1' denotes the satellite located just below the dominant line while F
denotes the satellite just above it. A is the measured value of the bilayer
spacing. The * indicates unusually large intensities and the ** indicates the
sample with a 60A Fe buffer and a 50A Cu cap. (The buffer is the ﬁrst layer
sputtered; the cap is the last). The procedure for calculating positions is
described in the text. ....................................................................................... 82

XRD structural results for Co/Mo multilayers. <D> denotes a single line
interpreted as a composite line composed of the Mo<110> line and 3 Co line.
The relative error for these d-spacings is $0.003 A. The * denotes a broad,
weak line which is more likely an indication of the nearest neighbor distances
in an amorphous sample. ................................................................................ 93

Magnetic properties of Fe/{FeSi} multilayers as a function of spacer layer
thickness. The M5,. data were obtained with the DC SQUID, and the Hsat and
Mr/Msat data, with the AC SQUID. ............................................................... 108

TED Bragg lines observed in Fe/Si samples. The lines are identiﬁed by their
Miller indices. Y indicates that the line is observed, and N that it is not. ...1 17

Figure 2-1:
Figure 2—2:

Figure 3-1:

Figure 3-2:
Figure 3-3:

Figure 3-4:

Figure 3-5:
Figure 3-6:

Figure 3-7:

Figure 3-8:
Figure 4-1:

Figure 4-2:

Figure 4-3:

Figure 4-4:
Figure 4-5:
Figure 4-6:

Figure 4-7:

Figure 4-8:

LIST OF FIGURES

Schematic diagram of the sputtering process. .................................................. 4
Sputtering system schematic (courtesy of P. Holody) ...................................... 4
X-rays diffracted from atomic planes. ............................................................ 12
Diffractometer layout. .................................................................................... 14
XRD diffraction pattern for Co/Mo (14.4A/1 1.2A). ...................................... 15
Harmonics for Co/Mo (14.4A/11.2A) shown in Figure 3-3. ......................... 17
The average Bragg line and its satellites for Co/Mo (14.4A/1 1.2A). ............ 17
Schematic diagram of the Rigaku rotating-anode powder diffractometer. ....20
Typical A1 sample holder used in XRD. ........................................................ 22
Focusing geometry for (a) small incident angle and (b) large incident angle.24
Transmission geometry in TED (after von Heimendahl). .............................. 32
The Ewald sphere construction in a) XRD and in b) TED ............................. 34
Portion of the reciprocal lattice for a (001) ﬁbre-textured bcc ﬁlm (after Tang
and Thomas). .................................................................................................. 36
STEM imaging mode (after Watt). ................................................................ 39
Schematic of the primary components of a typical conventional TEM. ........ 40
The objective aperture blocks the diffracted rays thus providing contrast in the
TEM image. .................................................................................................... 42
Schematic of (a) BF - and (b) DF-imaging. Io = primary beam, It = transmitted
beam, Is = weakly scattered beam, and Id = diffracted beam. ......................... 42

Image formation in a conventional TEM. The rays for the diffracted beams
are blocked beyond the plane of the objective aperture but are included here

for illustration (after Crimp). .......................................................................... 44
Figure 4-9: Diffraction pattern formation in a conventional TEM (after Crimp). ............ 45
Figure 4-10: Schematic diagram of the primary components used in TED for the VG
I-IBSOI FESTEM. ........................................................................................... 47
Figure 5-1: Schematic diagram of a Lytle detector. .......................................................... 61

xi

Figure 5-2:
Figure 5-3:
Figure 5-4:
Figure 6-1:

Figure 6-2:

Figure 6-3:

Figure 6-4:
Figure 6-5:
Figure 6-6:

Figure 6—7:

Figure 6-8:
Figure 6-9:

Raw data from a ﬂuorescence measurement of a 2000A sputtered Co ﬁlm. .63
CHI data for the same 2000A sputtered Co ﬁlm shown in Figure 5-2. ......... 63
RDF for the same 2000A sputtered Co ﬁlm shown in Figure 5-2. ................ 64

Normalized saturation magnetization vs. nominal Co layer thickness for
Co/Mo multilayers with tMo = tCo- In addition to data from the present study,
the data of Wang, et a1.20 and Sato19 are presented. ........................................ 89

Field dependence of the normalized magnetization for the a) 14ML/14ML and
b) 2ML/8ML Co/Mo multilayers on A1203 substrates. The diamagnetic
contribution of the substrate is ﬁt with a straight line to determine the y-
intercept thus providing the saturation magnetization of the multilayers. ...... 90

Comparison of the higher-angle XRD data for the 5ML/5ML, 10ML/10ML,
and 28ML/14ML Co/Mo multilayers. ............................................................ 92

TED line scan for Co/Mo (5 ML/SML). ........................................................ 95
TEM image of Co/Mo (7 ML/SML). The nominal magniﬁcation is 50 K. ..95

TED line scans from different regions of the same Co/Mo (7ML/5ML)
sample illustrating the varying degree of crystallinity. ................................... 96

a) TED line scan for Co/Mo (7ML/7ML) and b) TED line scan for Co/Mo
(IOML/IOML) ................................................................................................. 97

Combined raw data from 5 ﬂuorescence scans of the 7ML/7ML multilayer.98

Comparison of the CHI and RSP data for the 5ML/5ML and 7ML/7ML
samples clearly shows the transition from an amorphous to a crystalline

structure. ......................................................................................................... 99

Figure 6-10: Saturation magnetization and number of nearest neighbors as a function of

Figure 6-1 1

Figure 7-1:

nominal Co layer thickness. The solid data points are for samples of equal
layer thickness. The unfilled data points are for the 28ML/14ML and
2ML/8ML multilayers. ................................................................................. 100

: Comparison of the CH] and RSP data for the Co standard and all of the
Co/Mo multilayers included in the XAF S study ........................................... 101

Field dependence of the magnetization normalized to the volume of the
nominally pure Fe layers for the a) {Fe2ASi2A} X 4 and b) {Fe2ASi2A} X 7
spacer layer samples on A1203 substrates. These AC SQUID data give
slightly larger saturation magnetizations than the DC SQUID data (see Table
7-1). ............................................................................................................... 109

Figure 7-2: Measured bilayer spacing as a function of nominal Si layer thickness for F e/Si

multilayers. The solid line indicates nominal bilayer spacings. .................. 111

xii

Figure 7-3:

Figure 7-4:

Figure 7-5:

Figure 7-6:

Figure 7-7:

Coherence length vs. nominal Si layer thickness for both Fe/Si and F e/ {F eSi}
multilayers on A1203 substrates. The horizontal line indicates a constant
value .............................................................................................................. 1 1 1

a) Planar spacing as a function of spacer layer thickness for the F e/Si samples
and b) a comparison of the higher-angle XRD data for the tgi = 10A and ts, =
20A multilayers ............................................................................................. 113

a) Planar spacing as a function of spacer layer thickness for the Fe/{FeSi}
samples and b) a comparison of the higher-angle XRD data for the
{FeZASiZA} X 3, X 6, and X 10 multilayers. .............................................. 114

TED line scans for Fe/Si samples with nominal Si layer thicknesses of a) 12A
and b) 30A. ................................................................................................... 116

TED line scan for the {Fe2ASi2A} X 10 spacer layer sample with the two
non-bcc lines indicated by the arrows. .......................................................... 118

xiii

CHAPTER 1
INTRODUCTION

Magnetic coupling in artiﬁcially-layered metallic systems known as multilayers is a
current topic of debate. Since many of these systems have potentially important
technological applications, the nature of the coupling mechanism needs to be thoroughly
understood.

Speciﬁcally, certain multilayers formed from the repeating of a bilayer unit comprised
of a magnetic layer and a non-magnetic spacer layer show oscillations between
ferromagnetic and antiferromagnetic coupling which accompanies giant magnetoresistance
(GMR) effects. One hypothesis for the coupling mechanism is an RKKY-type coupling
which is mediated through the spacer layer. The period of such a mechanism should be
dependent on the Fermi surface of the spacer material; however, current experimental
results show that the observed period is very insensitive to the speciﬁc metal used as a
spacer. This result along with some other observations has led many investigators to claim
that small structural changes may greatly affect the coupling mechanism.

As a result of such claims, a very careful structural characterization of several systems
including Co/Ag, Co/Cu, and Co/Mo has been performed. These different metallic spacer
layers provide a variety of crystal structures. In addition, Fe/Si which has a non-metallic
spacer has been studied for comparison to the other systems. The study of Fe/{FeSi} was
included in an attempt to understand the Fe/ Si system better.

Several types of structural characterizations have been done. Standard x-ray

diffraction (XRD) has been used for a direct probe of the structure perpendicular to the

plane of the layers, and transmission electron diffraction (TED) has been used as a
complementary in-plane probe. Both of these methods have provided average information
about each multilayer sample as a whole; however, these probes alone fail to provide a
complete picture of the interfacial structure.

For additional information, X—ray Absorption Fine Structure (XAF S) measurements
have been used to determine the average local environment about the magnetic atoms to
provide information about the interfacial regions. Correlations between the coordination
number as measured relative to a standard and saturation magnetizations have been
observed which support the idea that the detailed structure does indeed affect the magnetic
behavior of these systems.

Any conclusions drawn about the actual structure of the multilayers are model
dependent; therefore, several different probes which provide complimentary information
about the structure of the multilayers were chosen. Only in this way could the number of
possible models be signiﬁcantly reduced since a satisfactory model must be consistent
with the results of every probe used.

Since the reasons for researching the above systems differ, they are discussed
individually in each introductory section prior to the experimental ﬁndings. Fairly
detailed descriptions of each structural probe are also presented at a level hopefully
requiring little knowledge beyond that obtained at the undergraduate physics level.

Finally, the results of the experiments are given along with the conclusions drawn.

CHAPTER 2
SAMPLE FABRICATION

All sputtered samples were made at Michigan State University using a dc-magnetron
sputtering system and were subsequently stored in a vacuum dessicator at approximately
0.1 torr to limit surface oxidation. Several different substrates were used including
crystalline silicon and sapphire for XRD, magnetic, and synchrotron studies as well as
sodium or potassium chloride substrates for TED studies. No deﬁnitive evidence was
found that the choice of substrate had any signiﬁcant effect on the multilayer structure.

In the remainder of this chapter, a detailed description of the sputtering system and its
operation will be given. Other sources for descriptions of the sputtering system which
include some excellent detailed drawings are the dissertations by P. Holodyl and ML.

Wilson.2

2.1 Sputtering Process

Sputtering is a method of deposition in which ionized gas atoms collide with the
material to be deposited—the target or source—causing the ejection of individual atoms
which then accumulate on a substrate. This process is shown schematically in Figure 2-1.
During sputtering, electrons are thermally activated and then accelerated to ionize the gas
(usually Ar) which is sufﬁciently conﬁned to create a plasma. The gas ions are then
accelerated toward the target by holding it at a large negative potential. Upon collision
with the source material, the ions transfer their kinetic energy to individual target atoms
causing them to be ejected in all directions above the plane of the source because the

incoming ions have undergone multiple collisions and consequently come in from all

3

a
6;) G?
. <94

‘

    

Figure 2-1: Schematic diagram of the sputtering process.

stepping motor

substrate holder

atmosphere

 

UI-IV shaft

SPAMA plate
\

 

Chimney _ Chimney
with hole ' without
hole
- - .
, sputtermg
gun

 

 

 

 

 

 

 

 

Figure 2-2: Sputtering system schematic (courtesy of P. Holody’).

directions. A substrate is properly positioned to collect the target atoms. By controlling the
time the substrate is positioned above a target and by monitoring the rate of accumulation
on the substrate, the thickness of a given target material is speciﬁed. Moreover, by
positioning the substrate over different targets for alternating set periods of time, artiﬁcially-

layered metallic systems are created.

2.2 Sputtering System Description

The dc-magnetron sputtering system shown in Figure 2-2 is housed in a stainless steel
cylinder. At the bottom are four L. M. Simard "Tri-Mag" triode guns which as measured
from the target center are placed 14 cm from the cylinder center and spaced 90° apart.
Since all of the samples made consisted of a repeated bilayer, only two guns were required.
Each gun assembly includes a ﬁlament and anode to provide the necessary accelerating
electrons to ionize the sputtering gas. The gas used was always ultra-high purity Ar
(99.999%) which is passed through a LNz cold trap, then a gas puriﬁer, and ﬁnally forced
through several small closely-spaced openings at the gun base. The target material is
mounted on a Cu base which is subsequently attached to a Cu block containing circulating
water to remove the tremendous heat buildup caused by the sputtering process. Both the
base and the source are held at potentials of -400 to -600 V to accelerate the Ar+ ions. A
grounded aluminum ring surrounds the target to limit the ejection of atoms from other areas.
At the very top of the gun, a magnetic shield is positioned such that in combination with the
two magnets at either end of the gun, a magnetic ﬁeld is created to conﬁne the Ar+ ions and
create a plasma just above the target.

The guns are covered by a manually—controlled rotating chimney assembly wrapped in

aluminum foil for ease of cleaning. Each gun requires two chimneys. The ﬁrst is
completely covered with foil to help prevent contamination when the shutter (described in
the following paragraph) which is normally protecting the sample must be opened for a
brief period prior to sample fabrication. The second is rotated into position once the sample
is actually ready to be made. It has a small opening approximately 5 cm in diameter to limit
system contamination.

Above the chimney assembly lies the computer-controlled SPAMA (Substrate
Positioning And Masking Apparatus) plate. Eight sample holders are mounted on it—each
of which contains two sample substrates. The sample holders consist of two openings
which are ﬂared out at the bottom to be smaller than the substrates. Also, a small Cu block
is placed above the substrates under a slight amount of pressure and connected to the
SPAMA plate for temperature control. The SPAMA plate itself is cooled using high-
pressure N2 gas cooled by LNz. Underneath each holder are manually-rotated shutters
which help prevent contamination of the samples either before or after manufacture. They
may have either one or two openings. Those with two are used when the same sample is
desired on two different substrates so that they may be made simultaneously. In addition to
the sample holders, two quartz ﬁlm thickness monitors have openings on the SPAMA plate.
These measure the resonant frequency of the quartz disk which decreases as mass is added
to it. Given information about the density and acoustic impedance of the target, this change
in the resonant ﬁequency can then be used to calculate the ﬁlm thickness accumulated over
a given time interval, i.e., the deposition rate. It is measured for each target prior to,
periodically during, and after each run so that accurate values may be entered into a

computer which is programmed to rotate the SPAMA plate back and forth between targets

holding the substrates in place over each target for the appropriate time interval.
Conﬁgurations other than that depicted in the preceding are also possible. These are

described in detail elsewhere.4

2.3 System Preparation and Cleanliness

First, all of the parts mounted on the SPAMA plate were removed. Then the aluminum
gun casings, target rings, and those parts mounted underneath the plate and consequently
exposed to the target beam (the parts on the top of the SPAMA plate were not cleaned) were
placed in a bath consisting of 3 parts HNO3 acid (70% soln.) /1 part H20, rinsed in water,
and scrubbed with a wire brush. The SPAMA plate was also chemically etched with the
acid solution afterward but not immersed in it. When this procedure was not sufficient for
cleaning, it was repeated or a small amount of HF acid added for those parts made of
stainless steel. After rinsing with water, all of these parts except the SPAMA plate were
cleaned ultrasonically ﬁrst using acetone and then ethyl alcohol. The plate itself was too
large for this procedure and consequently was only rinsed with these chemicals.
Additionally, the Si and A1203 substrates were treated using this ultrasonic cleaning method
while the salt substrates were cleaved just before insertion into the sample holders.

Assembly of the system was performed while wearing cotton and/or latex gloves.

2.4 Typical Operating Procedures and Conditions

The vacuum chamber was initially pumped down using an Edwards E2M-18
mechanical pump with a molecular sieve trap to limit oil backstreaming and further
evacuated using a CTI Cryo-Torr 8 cryopump. Additionally, the system was typically baked

overnight for approximately 16 hours at 60°C enabling base pressures on the order of 10'8

torr to be achieved as measured using a Dycor M100 Quadrupole residual gas analyzer.
During a run, the Ar required for plasma formation was admitted to the system at a
pressure of 2.5 mtorr. The substrate temperatures were monitored using two thermocouples
in thermal contact with two of the substrates and were typically maintained between -5 0°C
and -20°C. Only one shutter was open at a given time, and the covered chimneys remained
closed over all of the targets until just prior to deposition. They were then opened during
deposition and closed again immediately afterward. Deposition rates were generally chosen
to be the maximum values possible without losing the Ar plasma or shorting out the target.
These values varied depending upon the source material. Table 2-1 shows the range of
deposition rates associated with each target. The typical time to fabricate one sample was
15 minutes with the exception of the F e/ {F eSi} samples so run times were kept to a
minimum—usually about 2 hours. In the F e/ {F eSi} case, sample times were approximately

30 minutes each, and these runs lasted 3-4 hours.

Table 2-1: Deposition rates for various targets.

 

 

 

 

 

 

Deposition

Rate

Target (A/s)
Co 3.4-9.0
Cu 3.4-14
Fe 4.0-6.6

Mo 7.9

Si 2.4-4.3

 

 

 

 

 

‘P. Holody, Ph.D. dissertation, Michigan State University (1996).
2ML. Wilson, Ph.D. dissertation, Michigan State University (1994).

3P. Holody, ibid.

4J.M. Slaughter, W.P. Pratt, Jr., and RA. Schroeder, Rev. Sci. Instrum. 60 (1), 127
(1989).

CHAPTER 3
X-RAY DIFFRACTION

3.1 Introduction

X-ray diffraction (XRD) results from the scattering of x-rays by electrons in atoms.
When atoms are arranged periodically on a lattice, deﬁnite phase relationships exist
between the scattered rays. This scattering occurs in all directions, but in most directions
destructive interference occurs between the scattered rays coming from different atomic
sites. Only in a select few directions does constructive interference occur—this
reinforcement of scattered rays is known as diffraction. The solid state physics texts by

2 contain brief introductory descriptions of

Myers1 and also by Ashcroft and Mermin
crystallography and XRD while Cullity’s classic text3 is a more in-depth reference.

The manner in which x-rays are diffracted is unique to a given crystal structure. So
analysis of a resulting diffraction pattern whether recorded on photographic ﬁlm or
electronically with detectors will reveal structural information for a particular sample. If
a sample consists of a single crystal or a random distribution of one type of crystal
structure, then the structure of that sample can be uniquely determined. Complications
may arise for systems consisting of more than one crystal structure—multilayers are often
such systems.

There are many different methods for observing how x-rays are diffracted from a
particular sample, and the resulting diffraction pattern is determined not only by the

crystal structure of the sample but also by how the diffraction pattern is recorded. The

method chosen depends upon the characteristics of the sample and upon what information

10

11

is to be determined. For example, the back-reﬂection Laue method can be used to
determine the orientation of a single crystal, the rotating-crystal method can be used to
determine the unknown structure of a single crystal, and the Debye-Scherrer or powder
method can be used to determine the unknown structure of a polycrystalline sample or a
powder of single crystals. All of these techniques record the diffracted x-rays on
photographic ﬁlm with single crystal patterns appearing as spots and polycrystalline
patterns appearing as rings or portions of rings depending upon the ﬁlm size. The use of
ﬁlm allows quick measurements but limits the accuracy of measured intensities. Other
methods such as the use of a powder diffractometer utilize some type of counter to more
accurately determine intensities. In the remainder of this chapter, a discussion of Bragg's
Law, a description of powder diffractometry, and the analysis of typical multilayer
diffraction patterns will be given. In this chapter, it is assumed that the reader has a basic
understanding of crystallography including Miller indices and the reciprocal lattice. If

not, the previously mentioned texts should be consulted.

3.2 Bragg's Law

The atoms of any sample can be envisioned as lying on a set of atomic planes as in
Figure 3-1. In this diagram, the incident x-rays strike the set of planes at an angle 6. Due
to conservation of energy and momentum requirements, the diffracted x-rays must
"reﬂect" from the sample at an angle 0 such that the scattering angle is 20. The terms
"reﬂect" and "reﬂection" are often used in reference to x-rays diffracted from atomic
planes even though no reﬂections actually take place.

Using basic trigonometry, it is easy to determine the "Bragg condition" which is the

12

 

 

 

 

m 9 9 a
v v i
9 9
d.
A C
B ll 29

Figure 3-1: X-rays diffracted from atomic planes.

condition for diffraction to occur. The path difference for the two rays shown in Figure
3-1 is given by the length of the two line segments ﬂ and If which equals 2d'sin0.

The necessary requirement for constructive interference is that this path difference equals

an integral number of wavelengths. The result is the well-known Bragg equation:
2d'sin9 = nl (Eqn. 3-1)

where d' is the interplanar separation typically referred to as the "d-spacing", 9 is the
angle between the incident x-ray and the sample, A is the wavelength of the radiation, and
n is the order of reﬂection which can take on any integral value. Typically, this equation
is written with d = d'/n such that all reﬂections can be considered as ﬁrst order. In other
words, an nth order reﬂection from the (hkl) planes of spacing d' can be regarded as a ﬁrst
order reﬂection from the (nh nk n1) planes of spacing d, either real or ﬁctitious, such that

the result is the more familiar form of the Bragg equation:

13

2d sine = A (Eqn. 3-2)

Though Bragg's Law speciﬁes the conditions for diffraction to occur, it does not
provide any information regarding the amplitude of the diffracted beams from a given set
of planes. The amplitude depends upon the crystal structure, so that certain families of
planes have zero amplitude diffracted beams referred to as forbidden lines. (The reader
should consult one of the texts mentioned in the introduction about the structure factor if
unfamiliar with this result). The non-zero ones are referred to as the allowed lines or
peaks for that crystal structure and are unique to it; therefore, a sample's structure can be
determined by identifying the allowed lines. For example, the ﬁrst 5 allowed lines of a
body-centered cubic (bcc) structure, (110), (200), (211), (220), and (310), and the ﬁrst 5
allowed lines of a face-centered cubic (fcc) structure, (111), (200), (220), (311), and (222)
provide a distinction between the two structures. Also, a useful resource in identifying

structures from their observed lines is the Powder Diffraction File.4

3.3 Powder Diffractometry

A powder diffractometer consists essentially of an x-ray source, a sample mount, a
detector, and some slits. For the standard 0-29 reﬂection geometry shown in Figure 3-2,
the x-ray source remains ﬁxed while the sample and the detector are rotated
synchronously during a scan such that the detector moves through twice the angle that the
sample moves through. The incoming x-rays are incident at an angle 9 with the sample
plane and the detector is located at 29; consequently, diﬂraction occurs for those planes

which are nearly coincident with the sample plane.

14

 

 

detector

Figure 3-2: Diffractometer layout.

3.3.1 Diffraction Patterns

A diffraction pattern recorded by a powder diffractometer is typically displayed as
the number of counts/second (N) vs. the scattering angle (29). It varies ﬁ'om large
regions in 29 where N is very small and fairly constant due to background radiation to
much smaller regions where peaks (commonly called Bragg lines or peaks) are observed
in N which result from diffraction by the sample. In the remainder of this section, the
diffraction patterns associated with a single crystal, a polycrystalline sample, and a
multilayer are discussed.

If a single crystal were placed in a powder diffractometer, most likely nothing would
be seen in the diffraction pattern since the likelihood that any set of planes would be

properly aligned to satisfy the Bragg condition would be small. In a polycrystalline or a

15

 

 

 

     

2 _ I I r I I I f T I f I r I r I I I d
103 E ave. Bragg line J
A * I
U) “ .1
3:: 3 “ i
t: 2 r . . 1
=5 102 i harmonics satellrtes _?
g : :

V 3 _ 2nd order effects
3? 2 r 1
'c'Z T :
I: 101 g .2

0 : I
E * ll . ‘
ﬂ 3 a l ‘ ‘ _,
2 r u ' l ' ‘ i
t ‘ , j ”’ I :
100 r ‘ ' ' g
l L L I l l A J n M 1 1 I 1 4 1 i I

 

 

 

50 6O 70 80 90 100110
29 (deg)

O 10 20 3O 40

Figure 3-3: XRD diffraction pattern for Co/Mo (14.4A/11.2A).

powdered single crystal sample in which all possible planar orientations are contained in
one sample, all allowed Bragg lines corresponding to the crystal structure will be
observed up to the limit of 29 allowed by the diffractometer which is typically around
135°. If the crystals contained in the sample were inﬁnitely large and the diffractometer
ideal, these lines would be spikes with no width. Departures from these conditions cause
these spikes to be broadened. The explanation for this broadening is given in section
3.5.3.

However, an XRD pattern for a typical sputtered multilayer such as that shown in
Figure 3-3 does not contain all of the allowed Bragg lines. Instead, it has only one Bragg
line (sometimes also a weaker second order line—for example, both the (110) and the
(220) lines might be observed for a bcc structure) which can be identiﬁed as belonging to

the two constituent components making up the bilayer unit if the layers are thin enough

l6

and if the components have comparable d-spacings for their densest set of planes. These
planes are usually the planes with the greatest density of atoms corresponding to the ﬁrst
allowed line for cubic systems. In such a case, the Bragg line will typically be a weighted
average of the two d-spacings which depends on the relative atom concentrations;
otherwise, 2 Bragg lines may be observed—one for each component. This result is
consistent with the presence of ﬁbre texture.

When a sample possesses ﬁbre texture, then only one family of planes (a set of
symmetrically equivalent planes) is oriented parallel to the substrate; consequently, only
lines associated with those planes can be observed in the standard 9-29 geometry. Of
course, these planes are not perfectly parallel to the sample plane, but if the vast majority
of planes which lie nearly parallel to the sample plane belong to this family, then the
sample is said to possess strong ﬁbre texture. This result is expected since it is well
known that sputtered metallic atoms typically align themselves such that only the densest
set of planes lie parallel to the substrate.

In addition to the appearance of the above-mentioned lines corresponding to the d-
spacing of the individual components, additional lines are found in the diffraction pattern.
These lines result from the repeating bilayer unit of the multilayers and manifest
themselves in two different ways.

First, at low angles, lines are observed which are referred to as harmonics (see
Figure 3-4). These lines obey Bragg's Law which is usually rewritten in this slightly

modiﬁed form:

2Asin9 = ml (Eqn. 3-3)

l7

 

 

 

 

 

I I * I I n I F r T ‘
4 ._ q
3~ .
27 1
A » .
i3 ' .
a 102 E harmonics E
:3 E 3
‘5 4t *
r-t 3 ~ .
3 2 1
r: ’ ‘4
OF! 101 : 1
CD : :
C I. .
2 ,~ -
.5 3 — .
2 1
100 : j
'- l I l L I I L l T

O 2 4 6 8 10 12 14

29 (deg)

Figure 3-4: Harmonics for Co/Mo (14.4A/11.2A) shown in Figure 3-3.

 

     

 

 

 

 

2 > I I I . I ' I ' T I I I I I I ' I j
103 E ave. Bragg line :
A E satellite 3
t: 2 r i
:3 t , .
. 102 L satellrte :
.D . :
g ” satellrte I
v 3 :
5‘ 2 r 1
'53 f ‘.
t: 101 5 a
O : 2
u _ -
t: - -
1-1 3 a _
2 r 1
100 -

34 36 38 40 42 44 46 48 50 52

29 (deg)

Figure 3-5: The average Bragg line and its satellites for Co/Mo (14.4A/11.2A).

18

where A is the bilayer spacing (sometimes referred to as the compositional modulation
wavelength), the m is now included so the observed lines will be denoted as lst order,
2nd order, etc., and the remaining quantities are the same as before. Typically, 2-6 of
these peaks are seen before their intensities sufﬁciently decrease from varying average
bilayer spacings, thickness ﬂuctuations within layers, etc., to the point that they are no
longer observable.

Second, additional lines referred to as satellites are seen near the Bragg peaks as
shown in Figure 3-5. These satellites can be associated with both the ﬁrst and second
order peaks. To fully understand why satellites occur only near the Bragg lines, it is
necessary to examine the diffraction pattern for an idealized multilayer consisting of 2
alternating crystalline regions repeated for a large number of cycles described perfectly by
a step model, i.e., no thickness ﬂuctuations or interdiffusion. The intensity of such a

multilayer is given by the following:5

 

 

2
sinnanvl 2(sinrtﬂnada Mo]2 2[sinitt’nbdb /do]

sin‘rwda /d0 b sinnt’db /d0
(Eqn. 34)

 

sinnt’nada /d0)(sinrt€nb MOJ}

2ff 2
+ a ”05“ “i sinttrt1,/ti0 ksinntdb/d,

where Z is deﬁned by the momentum transferq = 2m / d , N is the number of times the
bilayer unit is repeated (the number of cycles), 11a and 11b are the number of atomic planes
of material a and b respectively, da and db are the planar spacings, n = na+ nb ,
ndo = nada+ nbdb , and fa and fb are the atomic scattering factors.

The frequency of the ﬁrst term listed in parentheses is obviously much larger than

19

the second term in the curly brackets. So this ﬁrst term is a rapidly oscillating function,
and the second term is an envelope function governing the intensity of the ﬁrst term. For
relatively small 113 and nb, this envelope function consists of a single peak centered
around the value of the average lattice spacing. As the individual layers become thicker,
however, it becomes a bimodal distribution peaked around (1, and db. (Notice that this
equation explains the presence of the one or two Bragg peaks mentioned previously on p.
15 where ﬁbre texture is ﬁrst discussed). The intensities of these satellites will be

symmetric about the Bragg peaks only if both d3: db and 11,: nb.

3.3.2 The Rigaku Rotating-Anode Powder Diffractometer

In the following paragraphs, the components of the Rigaku rotating-anode system
used in this study will be discussed in detail. Its overall layout including the various slits
is shown in Figure 3-6. Finally, the reason why this basic geometrical setup is chosen
will then be explained.

Housed in a tube, the x-ray source consists of a metallic target—the anode—and a
source of electrons which are accelerated toward the anode. X-rays are generated both by
the deceleration of the electrons which generates x-rays with a continuous spectrum of
energies as well as by the ejection of inner core electrons which creates x-rays of speciﬁc
energies. This last process occurs during the atom's transition from an excited state back
to its ground state when it emits photons with energies related to differences in the energy
levels of the atom. This radiation is characteristic of the target material and is used for
XRD because it has a much greater intensity than the continuous spectrum.

The most intense of these characteristic emissions is the Kor emission which occurs

’ sample t

~ ~ 4?-
L_..

I SOLII'CC

 

Soller slits ’

E/

RS
monochromator

RSm

‘ detector

Figure 3-6: Schematic diagram of the Rigaku rotating-anode powder diffractometer.

21

when an electron moves from the L level to the K level where K and L respectively
denote the lowest two electron energy levels. The Kor emission is separated out from the
total emission spectrum since the determination of d-spacings requires a monochromatic
source of x-rays, but the Kort and the Kong radiation is not resolved, so the effective
unresolved wavelength for a Cu target is 1.5418A.6

In order to increase the intensity of the characteristic x-rays, the tube current is
increased which increases the number of electrons striking the target; however, since
most of the electron energy is converted into heat, the maximum current is limited by the
maximum amount of heat which can be dissipated. One method for dissipating this heat
is to rotate the target which serves as the anode of the tube—this is known as a rotating
anode. In this manner, greater intensities can be generated. The Rigaku system uses a Cu
rotating-anode.

The type of source used in the Rigaku system is known as a line source. It emits an
x-ray beam in the shape of a narrow rectangle which is diverging both vertically
(perpendicular to the diffractometer plane) and horizontally. Consequently, slits are used
to collimate the beam, i.e., to make the x-rays parallel, which is required for proper
focusing of the x-rays. The slits marked DS and SS are thin vertical divergence slits
which collimate the beam horizontally and should be the same size. Typically, the
smallest slits available (1/6°) were used for DS and SS to improve resolution although
with some loss in intensity. Though a given Bragg peak position is unaffected by these
slits, they do determine the inherent minimum width of the peaks. Since the peak widths
are used to determine the coherence lengths of the samples, the slits were chosen to

minimize these instrumental broadening effects. The Soller slit assemblies which consist

22

     

Front Back Side

Figure 3—7: Typical Al sample holder used in XRD.

of thin metal plates parallel to the plane of the diffractometer collimate the beam
vertically.

After leaving the source, the x-rays pass through a Soller slit assembly and the DS
slit and emerge to strike the sample. The sample is held in place by an Al sample holder
which is fastened by a clip against a ﬂat metal plate. In this manner, the sample is
secured in place at the center of the diffractometer circle which has its origin at the
sample center and has a radius deﬁned by the source-to—sample distance (this distance
must also equal the sample-to-RS slit distance). The sample holders use either a rigid
stainless steel clip or a spring-like Cu clip to hold each sample in place. The holder
shown in Figure 3-7 uses a stainless steel clip. The clip presses the sample against four
protruding "feet" which were machined to within a tolerance of i0.025 mm each and
made so that their back surfaces just coincide with the front surface of the holder.
Oftentimes, several Al lines from the holder were observed in the XRD scans. Since
these lines very closely matched the expected d-spacings for Al, the x-rays are clearly

striking the main body of the sample holder which lies in the same plane as the sample. If

23

the x-rays were being diffracted from the feet which lie signiﬁcantly in front of the plane,
the observed d-spacings would be smaller than expected. As long as the same sample
holder was used for each sample in a run, then these lines can serve as an internal
consistency check.

Any diﬂiacting x-rays are then reﬂected from the sample and pass through the SS
slit, then a second Soller slit assembly, and another divergence slit marked RS for
"receiving slit". The x-rays then strike a graphite monochromator which consists of a
single crystal oriented such that the Cu Ka radiation satisﬁes the Bragg condition and is
"reﬂected" into the monochromator receiving slit (RSm), i.e., the monochromator selects
the desired wavelength along with its harmonics. After passing through RSm, the x-rays
enter the detector. It consists of a scintillating NaI crystal which converts the x-rays into
visible light before entering a photomultiplier tube.

As shown in Figure 3-8, the source (S) and the focal point (F) both lie on the
diﬁractometer circle with the ﬂat sample located at the center (0). This particular
geometry is known as the Bragg-Brentano geometry and is chosen to maximize the
intensity of the detected diffracted beam. The dashed line in both ﬁgures indicates the
focusing circle. As long as S, F, and 0 lie on this circle as shown, then from simple
geometrical considerations,7 all x-rays leaving the source and striking the sample will be
focused at point F. In order to be perfectly focused, the sample would need to have the
same radius of curvature as that of the focusing circle; however, this requirement cannot
be reasonably satisﬁed since the radius of the focusing circle varies with incident angle 9.
As a result, some broadening of the diffracted beam does occur though this can be limited

by a narrow incident beam.

24

focusing
circle

 

\ diffractometer
circle

(a) (b)

Figure 3-8: Focusing geometry for (a) small incident angle and (b) large incident angle.

3.4 Typical Measurements

For each sample, a relatively quick scan was performed over a very large range of
29—at least well beyond the 2nd order peak of the ﬁrst allowed line. These scans
typically covered 6°/min in 29 with a step size of 006°. After this initial investigation,
slower scans were performed in the regions of interest—typically the low-angle
harmonics, the average Bragg line along with its associated satellites at ﬁrst and second
order, and any undetermined lines. Depending on the strength of these lines, the scans

typically covered O.25°-1.25°/min with a step size of 0.02°-0.03°.

3.5 Analysis

3.5.1 Determination of Planar Spacings

The d-spacing of a given x-ray line was determined using software to place a cursor
at the peak center. The value of 29, the d-spacing, and the intensity were printed out on

the diffraction pattern corresponding to this position. This seemingly inaccurate

25

determination of the d-spacing actually introduced an exceedingly small error. To justify
this statement, the peaks of four F e/ {FeSi} samples were ﬁt using a Gaussian distribution
along with an additional constant parameter for the undetermined background.
Comparison between these values for the d-spacings and those determined by
"eyeballing" the peak center showed a maximum Ad = 0.0006A. From these
comparisons, it seems quite conservative to estimate a maximum error of Ad < 0.001A
introduced by this method of measurement for well-defmed, symmetrically-shaped peaks.
By comparing the measured d-spacings with those listed in the Powder Diffraction Files,
the lines were identiﬁed.

Another source of error is deviation of the sample position from the center of the
diffractometer circle; however, no relative error is introduced as long as the same sample
holder is used for samples in a given run. Since correlations between the structure and
the exhibited magnetic properties are desired, only relative differences are important.
Thus no attempts were made to calibrate the d-spacings using a standard, although the
previously mentioned Al lines from the sample holders were used as a check for self-

consistency.

3.5.2 Determination of Bilayer Spacing

The bilayer spacing may be determined by ﬁtting either the harmonics or the
satellites positions as described in the remainder of this section. For calculation of the
bilayer spacing using harmonics, the earlier statement of Bragg's Law is incorrect. At
small angles, the index of refraction should be included. Not doing so can introduce

errors in A as large as 3% though this percentage amounts to less than one monolayer in

26

the multilayers studied. The modiﬁed version of Bragg's Law8 is written as:

 

5
2A(1- sin2 9) sin9 = m (Eqn. 3-5)

where 5 is deﬁned by the index of refraction n=1-5. For x—rays, n<1 by a small amount
which is typically 5z10'5 for most metals. The corresponding value of 9 for the mth order
harmonic was determined using the method described in the previous section. The
remaining symbols have the same meaning as in Eqn. 3-3.

Unfortunately, a ﬁt of data taken with the Rigaku system cannot determine both A
and 8 as free parameters. At low angles, the displacement of the sample from the exact
center of the diffractometer circle prevents an accurate determination of 5; consequently,
5 was calculated theoretically and a linear least-squares ﬁt used to determine A. For an

alloy, 8 = cﬁa + (1 — c)25b where a and b are the individual components and c is the

alloy

volume fraction of material a.9

This treatment seems justiﬁable since this expression

should be reasonably close to the actual value assuming that the amount of compounds

formed at the interfaces is relatively small compared to the remainder of the bilayer unit.
The determination of the bilayer spacing using the satellite positions is

accomplished by using the following equation which is derived by combining Equations

3-2 and 3-3:
m = — (Eqn. 3-6)

where m is the order of the satellite with planar spacing d. A linear least-squares ﬁt was

27

used to determine A even though the order of each satellite was not determined since A
depends solely on the slope of the described ﬁt.

In spite of the less complicated ﬁtting procedure, the typically smaller number of
satellites makes the determination of A using satellite positions less reliable than using
harmonic positions. As a result, unless stated otherwise, all bilayer spacings listed herein

were determined using harmonics.

3.5.3 Determination of Coherence Length (Scherrer's Equation)

The structural coherence length is the average crystallite size in a particular
direction. For a standard 9-29 scan, the average dimension measured is the one
perpendicular to the plane of the layers. It can be obtained from the following
relationship between the breadth of a line and the average crystallite size originally
derived by Scherrer:

_ Kl
_ LcosG

 

B (Eqn. 3-7)

where 7t and 9 have the same deﬁnitions as before, [3 is some measure of the Bragg peak
width (often, simply referred to as the linewidth), L is the crystallite size, and K is a
constant approximately equal to unity and determined by assumptions about crystallite
shapes and the precise deﬁnitions of L and B. In this treatment, B will be deﬁned as the
linewidth at FWHM in radians from the diffraction pattern on the 29 scale. For K taken
to be unity, L is the volume-averaged crystallite dimension perpendicular to the reﬂecting
planes. For a complete description of the treatment given by Stokes and Wilson

eliminating the assumptions about crystallite shape and Gaussian symmetry made by

28

Scherrer, see the XRD text by Klug and Alexander—an encyclopedic reference for XRD
by polycrystalline and amorphous materials.10

Line broadening can result from at least two other sources. First, an inherent
minimum instrumental broadening occurs which is mainly a function of the width of the
divergence slits DS and SS as well as the Bragg angle 9. For DS=SS=l/6°, the
instrumental linewidth B varies from 005° for 29 = 10° to 0.1 1° for 29 = 120°.H Clearly,
the measured linewidth must be larger than this instrumental linewidth to have any
chance of determining a coherence length; therefore, the smallest divergence slits
available were used since the intensity loss did not prevent observation of the lines.
Second, non-uniform strain can cause the broadening of Bragg lines. While uniform
strain leads to the displacement of a Bragg line from its non-strained position since the
average d-spacing is different, non-uniform strain produces several closely spaced peaks
which cannot be resolved thus creating one broadened peak. This effect along with others
not discussed here such as the presence of faults must also be considered when
determining coherence lengths. Thus, L is really an "effective" coherence length and not
actually a crystallite dimension though this designation will not be used anywhere else in
the text. However, the large changes observed in L for the Fe/Si system are attributed to
an actual change in the coherence length since the other broadening effects would not be
expected to change so dramatically.

The coherence length L was calculated from Scherrer's equation using the measured
value of B determined graphically directly from the diffraction pattern. Again, this might
seem to introduce large errors, but they are actually quite small. For the same Fe/{FeSi}

samples and ﬁtting procedure mentioned in Section 3.5.1, B was calculated and compared

29

with the results obtained from a graphical analysis. It was found that AB was never larger
than 0.05° which results in a 9% error in L.

In summary, conventional 9-29 XRD diffraction patterns contain lines associated
with the repeated bilayer unit and only one or two lines associated with the structure of
the individual components of the multilayer which is indicative of ﬁbre texture. As a
result, it provides information concerning the long-range order of the multilayers
perpendicular to the plane of the layers, but it is insufﬁcient to determine the in-plane and
interfacial structures of the multilayers. Alternative structural probes must therefore be

used.

 

IH.P. Myers, Introductory Solid State Physics, (Taylor & Francis, Philadelphia, 1991).

2Neil W. Ashcroft and N. David Mermin, Solid State Physics, (Saunders College,
Philadelphia, 1976).

3B.D. Cullity, Elements of X-ray Diffraction, (Addison-Wesley, Reading, Massachusetts,
1956)

4Powder Diffraction File: Inorganic, formerly published by the American Society for
Testing and Materials (ASTM) and presently published by the JCPDS (Joint Committee
on Powder Diffraction Standards)—International Centre for Diffraction Data in
Swarthmore, PA is a compilation of diffraction data from various sources consisting of
many volumes. New ones are added as data for new materials are acquired.

5Leroy L. Chang and BC. Giessen, Synthetic Modulated Structures, (Academic Press,
New York, 1985), p. 49.

6This value is the weighted mean of the Kort and Kong wavelengths with Kort being
weighted twice that of Kong as is customarily done since the ratio of the intensities is 2:1.

713.13. Cullity, ibid., pp.156-7.
8Klug and Alexander, ibid., p.101

9P.F. Micelli, Appl. Phys. Lett. 48, 24 (1986).

3O

 

10Harold P. Klug and Leroy E. Alexander, X-ray Diffraction Procedures for
Polycrystalline and Amorphous Materials, (John Wiley & Sons, New York, 1974), pp.

689-90.
”ML. Wilson, Ph.D. dissertation, Michigan State University (1994), p. 20.

CHAPTER 4
TRANSMISSION ELECTRON DIFFRACTION

4.1 Introduction

In many ways, transmission electron diffraction (TED) is similar to XRD. Electrons
are scattered by atomic nuclei much the same as x-rays are scattered by electrons. This
scattering of electrons leads to diffraction which obeys Bragg's Law and to the same
extinction laws, i.e., the allowed lines for a given structure observed in TED are the same
as those in XRD. Also, the diffraction patterns are quite similar with single crystal
patterns consisting of spots and polycrystalline patterns consisting of rings, but there are
important differences as well.

Because the interaction between electrons and atomic nuclei is much stronger than
those between x-rays and electrons, diffraction intensities in TED are 106-107 times
stronger than those observed in XRD, penetration depths in TED are approximately 100
times lessl, and double diffraction can lead to the presence of forbidden lines in TED
diffraction patterns except in the foe and bcc systems. (Double diffraction occurs in these
systems as well, but a diffracted beam which is diffracted again can create only other
allowed lines in these systems). A typical beam cross section used in TED is also smaller
by a factor of 106-107 than a typical one used in XRD, so the affected sample volume is
about 109 times smaller in TED.l But perhaps the most signiﬁcant difference between
TED and XRD results from the fact that electron wavelengths are approximately 100
times shorter than x-ray wavelengths. Consequently, the Bragg angle is limited to

approximately 0-2°, and the reﬂecting lattice planes are very nearly parallel to the primary

31

32

+ Primary beam

 

 

 

 

   
 

 

if ‘ Wit 7 - Sample
1‘ ”a .. ,,,,,, ,,
/
Diffracted // % Transmitted
beam \ beam
1K4 L

 

 

Screen

 

 

_J’_4

R

-71—

Figure 4-1: Transmission geometry in TED (after von Heimendahlz).

beam as shown in Figure 4-1. Since diffraction is limited to these planes, then the
structural information provided by TED is parallel to the sample plane making it a good
complement to the perpendicular structural information gained from conventional XRD.
In the remainder of this chapter, the modiﬁcations made to Bragg's Law, instrumentation,
sample preparation, diffraction patterns, and subsequent analysis will be discussed. If the
reader would like additional information about transmission electron microscopy in
general or about TED in particular, several texts can provide that information. The text
by Wyatt3 provides a good overview of the practical aspects of electron microscopy (EM)
and an easily understood, yet thorough presentation of the concepts involved in
transmission electron microscopy (TEM). Additional texts in increasing order of
completeness and difﬁculty in understanding are those by von Heimendahl4, Thomas and

Goringes, and Hirsch, et al.6 The latter is considered to be the classic text on TEM.

33

4.2 Bragg's Law Modiﬁcation

As mentioned in the introduction, the de Broglie wavelength of electrons is much
smaller than the wavelength of x—rays generated by a Cu target. For example, electrons
with an energy of 100 keV have a wavelength of 3.704 pm which is about two orders of
magnitude smaller than Cu K.ll x-rays. It follows that 7t/2d <<1 since d-spacings are on
the order of A. From Bragg's Law (2dsin9 = 2.), sin9 = M2d<<1; therefore, 9 is always
quite small. From Figure 4-1 in which the transmission geometry is shown, it follows
that tan29 = M (R and L are deﬁned below). This result combined with the small angle
approximation (sin9 z 9 and 0039 z 1) leads to the modiﬁed version of Bragg's Law used

in TED:
Rd = AL (Eqn. 4-1)

where R is the distance between the diffracted spot and the transmitted (undeviated) beam
as measured on a screen or photographic ﬁlm, (1 is the planar spacing, it is the electron
wavelength, and L is the camera length, i.e., the distance between the screen or ﬁlm and
the sample. If there are lenses between the sample and the screen, L is not an actual
physical distance but the equivalent distance if the same size diffraction pattern resulted
with no intervening lenses. The product AL is often referred to as the "diffraction" or
"camera constant" and must be determined using a suitable standard if accurate

measurements of the d-spacings are to be made.

34

Ak

 

 

 

Figure 4-2: The Ewald sphere construction in a) XRD and in b) TED.

4.3 Diffraction Patterns

The best method for understanding diffraction pattems is to use the Ewald sphere
construction and the reciprocal lattice. In TED, this particular method is made simpler
than in XRD because the shortness of the electron wavelengths make the sphere nearly
planar on scales comparable to those of the reciprocal lattice. In this section, the
relationship of the Ewald sphere to the diffraction patterns for single crystals,

polycrystalline samples, and textured samples including multilayers will be discussed.

4.3.1 The Ewald Sphere

In Figure 4-2, the construction of the Ewald sphere in reciprocal space is shown.
The incident x-rays have wave vector k, and the diffracted rays have wave vector k'. The
Ewald sphere has radius k = 27t/}t and its orientation is that of k relative to the origin 0
which is some reciprocal lattice point. The allowed difﬁacted rays are those

corresponding to the reciprocal lattice points which lie on the sphere. Since the electron

35

wavelength it is so small, the radius of the Ewald sphere is quite large relative to the
reciprocal lattice; consequently, it may be regarded as a planar section through the
reciprocal lattice. The resulting diffraction pattern then is just the intersection of this

plane with the reciprocal lattice.

4.3.2 Single Crystal and Polycrystalline Diffraction Patterns

The reciprocal lattice of a single crystal is just another lattice. For example, the
reciprocal lattice of a bcc structure is an fcc lattice and vice versa. As a result, the
intersection of a plane through the reciprocal lattice, and hence the diffraction pattern,
consists of spots. On the other hand, a polycrystalline sample has a random distribution
of orientations; therefore, its reciprocal lattice is a set of concentric spheres generated by
moving the associated single crystal reciprocal lattice through all possible orientations
about the origin. Consideration of only one rel-point7 constrained to move about the
origin at a constant distance for all possible orientations reveals that the rel-point would
trace out the surface of a sphere. All of the rel-points taken together would trace out a set
of concentric spheres. Consequently, the diffraction pattern of a polycrystalline sample
consists of rings since the intersection of a plane with the reciprocal lattice forms rings.
As previously mentioned in the XRD chapter, however, the sputtered multilayers

examined in this study are not polycrystalline—they have texture.

4.3.3 Textured Diffraction Patterns

There are two types of texture important for multilayers: ﬁbre and orientational. As
previously mentioned in the XRD chapter, ﬁbre texture refers to the alignment of one

family of planes parallel to the plane of the layers. If a sample has ﬁbre texture only, then

36

hu+kv+lw = [001]

 

Figure 4-3: Portion of the reciprocal lattice for a (001) ﬁbre-textured bcc ﬁlm (after Tang
and Thomass).

its grains are randomly oriented about the ﬁbre axis. If in addition, orientational texture
is present, then the grains can possess only certain allowed orientations about the ﬁbre
axis. In this section, the expected diffraction patterns for such samples and their
relevance to multilayers will be discussed. For additional details about this subject, the
reader should consult Vainshtein9 or lReimer.IO

For a sample of perfect crystallites with perfect ﬁbre texture, the reciprocal lattice
consists of stacked concentric rings—the orientation of a rel-point is now constrained by
a constant distance from the ﬁbre axis as well as a constant distance from the origin as
shown in Figure 4-3. For the case where the beam axis is normal to the plane of the

layers in a multilayer, i.e., the beam lies along the ﬁbre axis, the resulting diffraction

pattern will not contain all of the rings because the Ewald sphere intersects only those

37

rings in the zeroth layer. For example, in a perfectly [1 lO]-textured ﬁlm, the 310, 321,
and 420 rings will not be observed.

For a sample of perfect crystal structure and perfect ﬁbre and orientational texture,
these concentric rings of the reciprocal lattice become several spots situated around the
ring since only certain allowed orientations are present. The spacing and number of spots
exhibit the symmetry of the orientational texture. For a beam of normal incidence, the
diffraction pattern would consist of only these spots which lie on the rings of the zeroth
layer.

For the multilayers examined in this study, all of the rings allowed by Bragg's Law
were observed just as in a polycrystalline sample. Does this indicate a lack of both types
of texture? No, since most ﬁlms do not exhibit perfect ﬁbre texture, the ﬁbre axis is
distributed through some angle. Also, some small number of grains are probably
randomly oriented, so the reciprocal lattice consists of concentric spherical belts and
concentric spheres. So for an incident beam parallel to the normal of such a ﬁlm, the
resulting diffraction pattern will contain all of the rings observed for a random
distribution.7 Likewise, most samples do not exhibit perfect orientational texture. The
grains are distributed through some angle so the spots become arcs along the ring in the
reciprocal lattice. The arc lengths are indicative of the strength of the orientational
texture. The resulting diffraction pattern for a multilayer using a normally incident beam

will consist of arcs of the rings observed in a random distribution.

38

4.4 Transmission Electron Microscopy

The use of acronyms in electron microscopy is confusing at best. Two of the main
modes of Operation in transmission electron microscopy have acronyms which refer to
particular instruments—the transmission electron microscope (TEM) and the scanning
transmission electron microscope (STEM). Unfortunately, several different instruments
can be referred to using the same acronym. For example, STEM may describe a
dedicated scanning electron microscope being operated in a transmissive mode, a
dedicated transmission electron microscope being operated in a scanning mode, or a
dedicated scanning transmission electron microscope. To avoid such ambiguities here,
the use of TEM and STEM will be used primarily to refer to the two different modes of
operation described in the following paragraph.

In TEM mode, the beam cross section that reaches the sample (referred to as the
probe size) has a diameter on the order of a few um, illuminates all of the region of
interest simultaneously, and is very nearly parallel to the optical axis of the instrument
column in the sample plane when operated in an imaging mode. By contrast, in STEM
mode, the probe size is on the order of nm, and the beam scans back and forth across the
much larger region of interest much like an electron gun scans across a television screen
or a computer monitor. Just as in TEM mode, however, the beam is parallel to the optic

axis in the specimen plane for the entire scan region as depicted in Figure 4-4.ll

4.4.1 Conventional TEM

In this section, the primary components of a conventional TEM (see Figure 4-5)

necessary for its use in TEM mode are described in descending order of their positions in

39

 

 

 

Scan coils

Pre-ﬁeld of
the objective

 

 

\/ Specimen
/ \ p ane

Post-ﬁeld of
the objective

 

 

Figure 4-4: STEM imaging mode (after Watt”).

40

l
Filament —I:VJ Wehnelt cylinder

I

|

I — Condenser aperture
l

I
: Double condenser lens
I
|
I

——>

— <—— Sample

_ — — — T — — — — Objective lens plane

 

m
m

I
l
|
l
|
I
|
l
l
l
I
_ — — — T — — — — Projection lens plane
i
l
l
l
|

 

Screen

Figure 4-5: Schematic of the primary components of a typical conventional TEM.

41

the instrument column. These components must be well-aligned each time the
microscope is used to minimize electron optical aberrations which are the same as those
for visible light. Starting at the top of the column, the electron gun consists of a cathode
ﬁlament (typically a hairpin), a Wehnelt cylinder, and an anode. The cathode ﬁlament is
held at a large negative voltage and heated to emit electrons via thermionic emission.
The Wehnelt cylinder is held at a slightly more negative voltage and helps to focus the
electrons. A large potential drop between the grounded anode and the cathode accelerates
the electrons. The condenser aperture collimates the electron beam, and the double
condenser lens system demagniﬁes the beam onto the sample. The objective lens focuses
the sample image. The objective aperture lies in the back focal plane of the objective lens
and blocks out the diffracted rays to provide contrast when viewing the specimen. The
SAD (selected area diffraction) aperture lies in the image plane of the objective lens and
stops diffracted rays coming from outside the region of interest during diffraction, i.e., it
"selects" the area of the sample contributing to the diffraction pattern. As this method of
TED is typically the one used in most electron diffraction experiments, the procedure
itself is often referred to as SAD. The intermediate lens focuses either the sample image
or the diffraction pattern which is then magniﬁed by the projection lenses onto either a

ﬂuorescent screen or photographic ﬁlm.

4.4.2 Image and Diffraction Pattern Formation

In this section, the formation of images and diffraction patterns in a conventional
TEM operated in TEM mode will be discussed. Though the details of the processes may

vary from one instrument to another, the basic concepts remain the same.

42

Object plane of the

objective lens Sample

Objective lens plane - — _ _ -

 

Back focal plane

of the objective lens - _ — _ — Objective aperture

Object plane of the
intermediate lens

 

__________ a_—— ——-——— Intermediatelensplane

Figure 4—6: The objective aperture blocks the diffracted rays thus providing contrast in
the TEM image.

 

    

 

 

\ Objective /

/v I aperture

Figure 4-7: Schematic of (a) BF- and (b) DF-imaging. I0 = primary beam, 1, =
transmitted beam, Is = weakly scattered beam, and Id = diffracted beam.

43

Images obtain their contrast from the scattering of electrons in the sample. Though
inelastic scattering may provide some weak contrast, the real contrast mechanism is
diffraction. By inserting a small enough objective aperture, the diffracted beams are
blocked from detection as in Figure 4-6. Consequently, regions that meet the Bragg
condition appear darker than other regions. This difference results in differing contrast
for crystallites and for differently oriented regions within a given crystallite such as a
dislocation. This method of imaging in which the transmitted and weakly scattered
electrons create the ﬁnal image is known as bright-ﬁeld (BF) imaging. In dark-ﬁeld (DF)
imaging, the incoming beam is tilted as shown in Figure 4-7 so that only one diffracted
beam is used to form the image. In either case, the ﬁnal image is that formed in the
image plane of the objective lens. In a conventional TEM, this is accomplished by
making the object plane of the intermediate lens lie coincident with the image plane of
the objective lens as shown in Figure 4-8. By tracing all of the diffracted beams and the
transmitted beam coming from the same spot on the specimen to their ﬁnal destination, it
is clear that the ﬁnal image is of the sample and not the diffraction pattern.

In order to view the diffraction pattern, the ﬁnal image must be that of the image
formed in the back focal plane of the objective lens. The SAD aperture is inserted and
aligned such that the region of interest (R01) is imaged—only this region of the specimen
will contribute to the diffraction pattern. The ROI size is given by D/M where D is the
diameter of the SAD aperture and M is the magniﬁcation of the objective lens. So for D
= 40pm and a typical value of M = 40, the ROI size would be 1m. Below this size,
electrons from outside the ROI would contribute to the diffraction pattern due to spherical

aberration of the objective lens. Upon switching to diffraction mode in a conventional

Object plane of the
objective lens

Objective lens plane

Back focal plane
of the objective lens

Image plane of the
objective lens

Object plane of the
projector lens

Projector lens plane

Image plane of the
projector lens

44

 

 

 

 

 

 

 

 

 

Sample

Objective aperture

Object plane of the
intermediate lens

Intermediate lens plane

Image plane of the
intermediate lens

Figure 4-8: Image formation in a conventional TEM. The rays for the diffracted beams
are blocked beyond the plane of the objective aperture but are included here for
illustration (after Crimp”).

Object plane of the
objective lens

Objective lens plane -

Back focal plane
of the objective lens

Image plane of the
objective lens

Object plane of the
projector lens

Projector lens plane

Image plane of the
projector lens

45

 

 

 

 

 

 

Sample

Object plane of the
intermediate lens

SAD aperture

Intermediate lens plane

Image plane of the
intermediate lens

Figure 4-9: Diffraction pattern formation in a conventional TEM (after Crimp”).

46

TEM, the object plane of the intermediate lens is made coincident with the back focal
plane of the objective lens so the ﬁnal image is that of the diffraction pattern as shown in
Figure 4-9. By tracing all of the beams diffracted in the same direction from the three
spots at the specimen which combine to make one spot on the ﬁnal image, it is obvious
that the ﬁnal image is that of the diffraction pattern. Also, the objective aperture should
be removed during operation in diffraction mode to observe all of the diffraction pattern

possible.

4.4.3 VG HB501 FESTEM

The VG HB501 FESTEM is a dedicated ﬁeld-emission scanning transmission
electron microscope manufactured by VG Instruments and is the EM used in this study.
The term "ﬁeld-emission" refers to the type of cathode used by the FESTEM in which the
electrons are extracted by a strong electric ﬁeld instead of by thermionic emission. A
ﬁeld-emission gun forms a brighter and smaller probe, but it can only be used in ultra-
high vacuum (UHV) on the order of lO'Htorr which greatly increases the cost and
maintenance of the instrument.

In the remainder of this section, only the primary components of the FESTEM
necessary for imaging and for observing diffraction patterns are discussed; however, the
FESTEM includes several other components used in other modes of operation. As shown
in the schematic diagram of Figure 4-10, the entire column is upside down relative to a
conventional TEM. This design allows the sample stage to be mounted rigidly on top of
the objective lens to provide greater mechanical and thermal stability required for high

magniﬁcation and simpliﬁes detector mounting.15

47

 

BF detector

I

 

 

 

 

Collector aperture

 

 

Annular DF
detector
Sample
— — — — —L — — — — Objective lens plane
I I
__ _ <— ROA

— <— SAD aperture

Scanning coils

EIZ

I

I

I

I

I

I

I

I

Optic |
axis l
I

I

l

I

I

I

I

I

 

Double condenser lens

— VOA

I‘A_I Field-emission gun
I
I

Figure 4-10: Schematic diagram of the primary components used in TED for the VG
HB501 FESTEM.

48

Starting with the ﬁeld-emission electron gun at the bottom of the column and
working upward, the gun is followed by the virtual objective aperture (VOA). It is used
instead of the real objective aperture (ROA) during certain operations of the microscope
to prevent detection of unwanted x-rays when the x-ray detector, which is very close to
the RCA, is in use. As in the TEM, the double condenser lens system controls the
demagniﬁcation of the source. It is followed by the scanning coils which scan the beam
back and forth across the sample. The SAD aperture, the RCA (corresponding to the
objective aperture in the TEM), and the objective lens serve basically the same purposes
here as in the TEM. The specimen is situated very near the center of the objective lens.

The detection of the electrons is performed quite differently compared to the TEM.
The diffracted electrons are collected by the annular dark-ﬁeld detector consisting of a
scintillator, a light guide (since the detector is not mounted along the column axis), and a
photomultiplier (PM) tube. This detector collects the electrons scattered into an annular
cone in the approximate half angle range 0.04 rad to 0.2 rad16—-—these are the angles at the
specimen before the beam is compressed by the post specimen ﬁeld of the objective lens.
A hole through the scintillator and light guide allows the transmitted and weakly scattered
electrons to pass through the annular dark-ﬁeld detector, then the collector aperture, and
ﬁnally into the bright ﬁeld detector which also consists of a scintillator and PM tube. The
signals ﬁom these detectors may be viewed on two oscilloscope screens so that a BF and
a pseudo-DF image of the sample can be viewed simultaneously. The BF image is
formed in the same manner as it is in a conventional TEM; however, since all of the
diffracted beams are used to form the "DF image" instead of only one, it is referred to as a

pseudo-DF image.

49

Since the electrons are detected electronically, the diffraction patterns can be
displayed on an oscilloscope screen in several different ways. One of the most useful is
to scan across the rings of the diffraction pattern in a line to display an intensity proﬁle of
the rings. Since this type of display looks very similar to an XRD diffraction pattern
recorded by a diffractometer, often the allowed rings will be termed allowed lines. Also,
a display on one of the two viewing screens can be imaged on a third screen and recorded

using an instant black-and-white Polaroid camera.

4.5 Sample Preparation and Typical Settings of the FESTEM

The samples used for TED had to be sputtered thinner than those used for the other
studies. Typical total thicknesses were chosen to be near 500A to limit the effects of
chromatic aberration. For larger thicknesses, the energy lost by the diffracted electrons
becomes large enough to result in serious focusing errors, and for still greater thicknesses,
the sample simply becomes opaque to electrons.

Either NaCl or KCl were chosen as substrates for the sputtered samples since they
dissolve in water unlike the Si and A1203 substrates. For a given sample, the salt
substrate was cleaved to the required size (around 2-4 mmz) using a new razor blade for
each sample run, and the multilayer was ﬂoated off the substrate in distilled water onto a
Cu grid mesh. The grids used were 3mm in diameter, about 15pm thick, and had 200
lines to the inch in both directions of the square mesh.17 They had a shiny ﬁnish on one
side and a matte ﬁnish on the other. The sample was always placed on the matte side to
aid the electrostatic attraction between the sample and the grid. Of course, the sample has

to be viewed between the grid bars since the grids are opaque to electrons.

50

The VG HB501 FESTEM was operated at 100 kV using the cold stage for the Fe/Si
and Fe/{FeSi} samples which kept them at approximately -140°C when not interacting
with the beam to minimize interdiffusion.‘8 At least 3 different regions of the sample
were investigated to verify that the samples were homogeneous. A region was selected,
the column aligned, and the diffraction patterns recorded at two different camera
lengths—typically 0.5m and 1.0m. Typical aperture sizes used were 300 um for the VOA
aperture, 100 pm for the SAD aperture, and 50 um for the collector aperture. Since the

RCA aperture was not used during TED measurements, its size is unimportant.

4.6 Analysis

4.6.1 Structural Determination

In the multilayer TED patterns, typically many lines were observed allowing an
unambiguous determination of the average structure of the bilayer unit or at least one of
the component layers—in the Co/X multilayers, no lines uniquely associated with Co
were observed with the VG HB501 FESTEM. Unlike XRD, the d-spacings cannot be
determined unless a calibration standard is used to determine the diffraction constant XL.
In a conventional TEM, AL can be measured accurately once for a given setting and thus
be determined for all samples. Only one calibration is required since each sample region
can be placed at the exact same height in the microscope by using a eucentric stage to
hold the sample. Such a stage can be tilted while observing the R01 and changing the
height of the specimen. When the sample image movement is minimized, then the R01
coincides with the tilt axis and is placed at a speciﬁc height in the column. The other

requirement for making only one calibration is that the high voltage transformers are

51

quite stable so the electron wavelength does not change. Unfortunately the VG H3501
does not have a eucentric stage; therefore, a calibration involving simultaneous
examination of both the sample and a suitable standard would have to be performed for
every measurement if it were desired to determine d-spacings accurately. Structural
identiﬁcation can be done without such a calibration since AL is constant for a given ROI.
Consequently, the ratio of one ring radius to another is independent of XL, and the
allowed lines may be determined. This method is known as the method of ratios.

In examining the modiﬁed Bragg equation, Rd = AL, it is clear that the ring radii are
inversely pr0portional to the d-spacings; consequently, Rl/R2 = d2/d1 independent of the
diffraction constant. The actual procedure consists of measuring the ring radii and
calculating the ratios of each ring radius to the ﬁrst ring of signiﬁcant intensity (the
dominant line) which is almost always the ﬁrst allowed line of the given structure.
Comparison of these ratios to the predicted values for the various structure types allows

identiﬁcation of the structure to be made.

4.6.2 Compound Identiﬁcation

On occasion, additional lines may be observed which do not correspond to any ratios
for the determined structure. Ifthe structure is not fcc or bcc, then double diffraction may
have led to the presence of forbidden lines; otherwise, compounds may have formed at
the interfaces from the constituent components resulting in additional Bragg lines. In
either case, some assumptions must be made about the d-spacing of the dominant line.

In determining the possibility of a forbidden line, the expected d-spacing should be

determined by using the relationship between planar spacings, lattice constants, and

52

Miller indices for a given structure. The expected ring ratio can then be calculated as in
the preceding section and compared to the actual value.

In determining the possibility of compound formation, the Powder Diffraction File
may be consulted to ﬁnd possible equilibrium compounds that may be formed from the
constituent materials. The ring ratios for the listed d-spacings can be found as before and
compared to the actual values. Since typically in this study only one or two additional
lines were ever observed, the strongest statement that may be made is that the line(s) are

consistent with the presence of certain compounds.

 

lManfred von Heimendahl, Electron Microscopy of Materials: An Introduction,
(Academic Press, San Diego, 1980), p. 96.

2Manfred von Heimendahl, ibid.

3Ian M. Watt, The Principles and Practice of Electron Microscopy, (Cambridge
University Press, New York, 1985).

4Manfred von Heimendahl, ibid.

5 Thomas and Goringe, Transmission Electron Microscoy of Materials, (J. Wiley & Sons,
New York, 1979).

6Hirsch, Howie, Nicholson, Pashley, and Whelan, Electron Microscopy of Thin Crystals,
(Krieger Publishing, 1977).

7Quantities such as points or planes associated with the reciprocal lattice are denoted by
"rel".

81.. Tang and Gareth Thomas, J. Appl. Phys. 74 (s), 5025 (1993).
9Vainshtein, Structure Analysis by Electron Diﬂraction (Pergamon, New York, 1964).

10Ludwig Reimer, Transmission Electron Microscopy: Physics of Image Formation and
Microanalysis, (Springer-Verlag, Berlin, 1984).

”Ian M. Watt, ibid., p. 71.

12Ian M. Watt, ibid.

53

 

13 M. A. Crimp, course notes, Michigan State University (1994).
14M. A. Crimp, ibid.

l5Ian M. Watt, ibid., p. 75.

l6VG HBSOl operation manual.

17Ian M. Watt, ibid., p. 82.

18Ludwig Reimer, ibid., p. 440.

CHAPTER 5
X-RAY ABSORPTION FINE STRUCTURE

5.1 Theory

X-ray Absorption Fine Structure (XAF S) refers to the oscillations in the x-ray
absorption in a material which occur beyond a given absorption edge as a function of the
incident photon energy. The deﬁning equation for this absorption in a transmission

experiment is
Izloe’”x (Eqn.5-1)

where 10 and I are the intensities of the incident and transmitted x-ray beams respectively,
p. is the absorption coefﬁcient, and x is the sample thickness.

A marked increase in the absorption occurs at an absorption edge where the
incoming x-ray energy just matches the binding energy of a core electron. If the atom
containing this electron is isolated, then the absorption decreases monotonically;
however, if it is surrounded by other atoms, ﬁne structure variations in the absorption
occur known as XAF S.

Until recently, these oscillations were divided into two different regions. In the
region approximately 40-1000 eV above the edge where weak single scattering
dominates, the resulting oscillations were referred to as EXAF S (Extended X-Ray
Absorption Fine Structure). In this region, the Born approximation is valid, i.e., the
assumption that the wave states of the ejected photoelectron are plane waves does not

cause signiﬁcant error—the next section will describe this process in greater detail.

54

55

Before this EXAFS region, strong multiple scattering dominates since the photoelectron
is ejected with little kinetic energy. This much smaller region is the XANES (X-Ray
Absorption Near Edge Structure) region. Here the Born approximation introduces
unacceptable error, and until recently, made analysis quite difﬁcult. Now that
improvements in calculating the XANES region theoretically have been made, it is

becoming more customary to combine the two regions into one—the XAF S region.

5.1.1 Physical Origin1

The probability that a photon will be absorbed by a core electron depends upon the
initial and ﬁnal states of that electron. The initial state is just the wavefunction of an
electron in the core of the atom. For an isolated atom, the ﬁnal state of the ejected
photoelectron is represented by an outgoing spherical wave leaving the absorbing atom.
If there are surrounding atoms, then the ﬁnal state is represented by a sum of this
outgoing wave and all the backseattered waves from these neighboring atoms. It is the
interference between these waves that give rise to the oscillations in the absorption
coefficient. Proper analysis of these oscillations provides structural information about the

local environment (within ~ 6A) around a particular type of atom.

5.1.2 The XAFS Equation

The following equation is valid for an unoriented sample incorporating Gaussian

disorder and many-body effects.2

x (k) = Z-gz—Sﬂkmat) exp( — 218s?) exp[— 2(Ri — Amt] sin[2kRi + 5i(k)] (Eqn. 5-2)

1 1

56

The term sin[2kRi + 6,(k)]/(k2R2) is the functional form of the outgoing spherical

wave with an amplitude of F1 (k) = mti (2k)/21r hzk where
k = wave number of the outgoing spherical wave,
m = electron mass,
ti(2k) = factor proportional to the backward scattering amplitude of the
outgoing wave which is characteristic of the backseattering atom,
N, = number of atoms of the type "i" in a given shell, and
R, = average distance from the center of the ith shell.
The term S3 (k) is the amplitude reduction factor associated with the relaxation of

the wavefunctions of the "passive" electrons, i.e., those electrons which were not ejected.

Pi>

electron in the central atom and p,’ is the relaxed state of the ith passive electron. The

2
where p, is the wave function of the ith passive

 

 

It is determined by SE) = MI<PI

reason for the relaxation is that the ejection of the active electron upon absorption by the
central atom causes the passive electrons to see a different potential. This new potential
is approximately the same as that for the atom with Z increased by one. As a result, the
remaining electrons are more attracted to the nucleus which "pulls" the wavefunctions in
closer thus relaxing them to a lower energy.

The term exp (-2kzoi2) is the Debye-Waller like term where o, is the rms deviation
for the average distance to the central atom for the ith shell (Ri)——it will hereafter be
referred to simply as the Debye-Waller factor. It is required because not all of the atoms
in a given shell are equidistant from the central atom due to thermal vibrations and
structural disorder. Writing the term in this manner assumes that the disorder is relatively
small and has a Gaussian distribution about Ri. One very important distinction between

this factor and the Debye-Waller factor in XRD is that in XRD, this deviation is about the

57

lattice site for each atom. In EXAF S, this deviation is a relative one between the
absorbing and backscattering atoms; consequently, it is a measure of disorder only along

the bond direction.
The term exp[— 2(R, — A) / A] is a modiﬁed mean-ﬂee path correction. In order for

interference to take place, two waves must be coherent; therefore, the lifetime of the
excited photoelectron state is important. Both the lifetime of the hole in the excited atom

as well as that of the ejected photoelectron determine the lifetime of the excited state.
Phenomenologically, a mean free path term exp[— 2Ri /?t] can be used to take this into

account. This term can be used to take many energy loss mechanisms into account. By
including both Sf, (k) and t(2k) in the XAFS equation, however, the mean free path

contribution needs to be reduced so it includes only the additional energy loss factors.
These losses will correspond to only a fraction of the interatomic distance; consequently,
the A term is added.

At ﬁrst glance, Equation 5-2 seems not to have incorporated the Born approximation
(sometimes referred to as the small-atom approximation in XAF S references) since the
functional form sin[2kRi + 5,(k)]/(k2R2) is that of a spherical wave. However, this
approximation really has been included in the dependence of ti(2k) and 8i(k) on k only

and not on both k and R,.

5.2 Experimental Procedures

XAF S experiments are typically carried out using synchrotron radiation. This
source of x-rays has a ﬂux of 1012-1016 photons/s/mrad/mA which improves the signal-to-

noise ratio by a factor of 103-106 over that of more conventional sources.3 In addition, the

58

energy resolution of synchrotron radiation is superior to that of conventional sources. For
dilute samples such as the multilayers studied here, these improvements are absolutely

necessary.

5.2.1 The Synchrotron

A synchrotron is a high energy circular accelerator used to accelerate electrons to
relativistic speeds. Classically, all accelerated charges radiate energy, and in the
relativistic limit, the angular distribution of the intensity is reduced from that of the
classical dipole distribution to a narrow cone along the instantaneous direction of motion.
From the microwave to the hard x-ray region, a continuous spectrum of strongly polarized
radiation is generated with the radiation emitted in the orbital plane of the electrons being
100% polarized with the electric ﬁeld parallel to the orbital plane. Above and below this
plane, the radiation is elliptically polarized with the degree depending upon the elevation
angle.

The radiation is emitted in pulses of about 10'8-10'93 duration at an approximate rate
of 106-107 pulses/s.4 The storage ring containing the electrons are interfaced with
numerous user stations by individual beamlines which are placed tangent to and all
around this ring thus enabling many users to use the facility at the same time. In this
study, all XAF S experiments were performed on the X23A2 beamline at the National
Synchrotron Light Source (N SLS) at Brookhaven National Laboratory.

A monochromator is used by each beamline to select a particular beam energy. Both
a good energy resolution and the absence of harmonics are desirable. The presence of

harmonics are part of a general class of effects which appear to depend upon thickness.

59

On X23A2, a double Si <311> crystal monochromator is used which has a resolution of
better than 2 eV near 6.5 keV. One reason for the choice of two crystals is that by
detuning them, the ﬁmdamental to harmonic ratio is improved. Direct tests were

performed to check for the presence of harmonics in every experiment.

5.2.2 XAF S Measurement Techniques

Several different techniques may be used to measure the XAF S. Either x-ray or
electron detection may be used. The direct measurement of the transmitted x-rays is the
most straightforward technique. In it, the intensity of the x-rays incident upon the sample
(10) and through the sample (I) are measured—the absorption is then given by ux = ln(Io/I)
from Equation 5-1. Other measurement techniques monitor processes that are
proportional to the absorption including x-ray ﬂuorescence and Auger electron emission.
In ﬂuorescence measurements, the intensity of the ﬂuorescent x-rays (If) is measured
along with 10. These ﬂuorescent x-rays are generated when electrons from higher shells
ﬁll the hole left behind by the ejected photoelectron resulting in a characteristic photon
emission. Auger electron detection is one of several electron detection methods including
total electron yield. Auger electrons are emitted when the emitted ﬂuorescent photon
described above is absorbed by another electron in the same atom causing its ejection—
this ejected electron is an Auger electron. The choice of these techniques for a XAF S
measurement depends upon the sample being examined.

In this study, the ﬂuorescence technique was chosen over transmission for the
following reasons. One, the samples would require either sputtering onto transparent

substrates such as kapton tape or removal from their A1203 or Si substrates. Two, for the

6O

thickness range of samples studied here, the systematic error corrections from thickness
effects are negligible for ﬂuorescence measurements but not for transmission
measurements. These "thickness effects" occur whenever a portion of the incident beam
is not attenuated by the sample in the same manner as the remaining incident beam—this
discrepancy can result from anything such as pinholes in the sample to disparate energies
in the beam (harmonics)—the "leakage" becomes a greater portion of the total signal as
the sample thickness increases. As a result the absorption signal appears to depend upon
the sample thickness resulting in systematic errors in the measured absorption.5

The reason for choosing ﬂuorescence over electron detection is not as obvious. For
those elements with Z < 30 including Fe, Co, and Cu studied here, the Auger channel for
K-edges dominates the ﬂuorescence channel;6 however, the origination of the Auger
electrons is limited to within approximately 30A of the surface.7 Perhaps as a result of
this surface limitation, attempted electron-yield measurements had a very poor signal-to-
noise ratio, so the ﬂuorescence technique was chosen.

In ﬂuorescence, the measured signal u'(E) is proportional to the absorption as shown

in the following equation8 for thick samples:

 

' If p.(E)sin9
11 (E) =- ~ . .
I uT(E)/sm9+uT(Ef)/srncp

0

(Eqn. 5-3)

where 9 is the entrance angle of the incident x-rays, (p is the exit angle of the ﬂuorescent
x-rays, 11r(E) is the total absorption coefficient at energy E, Ef is the ﬂuorescent energy,
and the equation is integrated over the angles (p subtended by the detector.

In the studies performed here, an in-house Lytle detector9 operating in ﬂuorescence

 

l 11, I

- — <— Soller slits
ﬁlter /

 

ionization chamber

Figure 5-1: Schematic diagram of a Lytle detector.

mode was used. A schematic diagram of this detector is shown in Figure 5-1. The
incident beam (10) enters one end through a slit and strikes the sample. The transmitted
beam (I) then exits the detector at the opposite end where another detector may be
positioned if it is desired to measure the transmission signal. The majority of the
ﬂuorescent x-rays emerge from the sample at a 45° angle as shown in the diagram. The
x-rays then pass through a ﬁlter selected such that the elemental composition is typically
one less in atomic number than that of the absorbing atom, e.g., Mn is used as the ﬁlter
for Co. The ﬁlter reduces the intensity of x-rays with energies above the absorption edge
energy. After passing through a set of Soller slits, the ﬂuorescent x-rays then enter the
ionization chamber which is typically ﬁlled with ﬂowing Argon to enhance the ionization
process. Concerns about the presence of harmonics were sometimes handled by using
static air in this chamber causing the detected harmonic to ﬁmdamental ratio to decrease
since the air is not as absorbing as the Ar. The Io detector had either static air or a

mixture of N2 and He ﬂowing through it. Though a rough rule of thumb for determining

62

the gas mixture used in this detector is to decrease the intensity of the primary beam by
10%, ultimately, the choice is made by empirically determining what provides the best

signal-to-noise ratio.

5.3 MacXAFS Analysis

All analysis of XAF S data was limited to the EXAF S region and was performed
using MacXAF S v. 2.0 or v. 3.6 both of which are based on the University of Washington
EXAFS analysis package written by Bruce Bunker. Subsequent generations of this
software have been written with many different contributors, and the package has been
ported to several different machine formats. The MacIntosh format modiﬁcations used in
this study were made by Charles Bouldin of the National Institute of Standards (NIST)
and Lars Furenlid of the NSLS. This software package enables the user to perform all the
required steps of an analysis.

First, the raw data is converted into the format required by MacXAF S. An example
of the raw data from a ﬂuorescence measurement of a 2000A sputtered Co ﬁlm is given
in Figure 5-2. Second, the data are normalized to the step height so that samples with
different total numbers of absorbing atoms—different thicknesses in this study—may be
directly compared, and an appropriate background is subtracted to isolate the EXAFS
oscillations. At this point, the data has the form of Equation 5-2 which is x(k). An
example of this CHI data is shown in Figure 5-3. Since R, is different for each shell, the
EXAFS corresponding to different coordination shells oscillate at different frequencies.
As a result, the third step consists of Fourier transforming these oscillations in k-space

into a more physically meaningful form—the radial distribution function (RDF). The

63

 

XMU

 

 

__,J

O r _
. 1 .

1 1114 t l r 11 Iml I I‘LLMLLI

7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7
Energy (keV)

 

 

 

Figure 5-2: Raw data from a ﬂuorescence measurement of 3 2000A sputtered Co ﬁlm.

 

0.10 . . - T . I . . . , , ,
0.08 L «I
0.06 2 . l
0.04 L I L

1

0.02 -

0.00 . AVAVAVAX
.._\/ III

A

CHI

 

l

 

 

 

 

I-
-0.04 I
-0.06 a

 

 

2 4 6 8 10 12 14 16
k (5.")

h—
>—

 

-0.08

Figure 5-3: CHI data for the same 2000A sputtered Co ﬁlm shown in Figure 5-2.

64

 

4O ' I ' l I I T l ' l I f f I

RSP

 

 

 

l r l l L A l 1 l .1 l 1 l

 

R (A)
Figure 5-4: RDF for the same 2000A sputtered Co ﬁlm shown in Figure 5-2.

RDF for the 2000A sputtered Co ﬁlm is shown in Figure 5-4. The RDF consists of peaks
which may or may not be resolved corresponding to the various shells surrounding the
central atom. Integration of this function provides the number of atoms contained within
the limits of integration. Unfortunately, this analysis does not provide the actual RDF.
Since the phase shift 5,(k) of each backscattered wave is not constant but has a k-
dependence, the Fourier transform of x(k) results in a pseudo-RDF. Additional
discrepancies between the Fourier transform and the actual RDF result ﬁom the ﬁnite
range of integration as well as an improper background subtraction. Consequently, the
pseudo-RDF cannot be analyzed directly to obtain the coordination number for each shell.
Instead, a peak in the RDF is backtransforrned to isolate the contribution of that
coordination shell, and a non-linear least squares ﬁt using the Levenberg/Marquardt

search strategy is made to an appropriate experimental standard. In this manner, the

65

coordination number (N), the interatomic distance (R), and the Debye-Waller factor (0)
are determined for the given shell(s). The standard and the sample must be treated in the
exact same manner when performing the data analysis to obtain meaningful results.
MacXAFS v. 3.6 uses an interactive graphical interface which allows the user to treat the
sample and the experimental standard exactly the same more easily than previous
versions. The user invokes this interface by selecting the graph/hand icon located near
the center of the given XMU, CHI, RSP, or ENV display. In the following sections, the

speciﬁc details of each step are discussed.

5.3.1 Data Conversion (Raw —> XMU Files)

First, the raw data is converted into a format readable by MacXAFS—an XMU ﬁle.
Several beamline formats are included in MacXAFS v. 3.6; however, any data format can
be deﬁned by the user. Once this conversion is complete, the background is removed

creating a CHI ﬁle.

5.3.2 Normalization and Background Removal (XMU —-) CHI Files)

Prior to subtracting the background, any single point glitches which exist in the
region to be examined are removed since they may affect what background is subtracted.
Though MacXAFS includes a method for the removal of wider multiple point glitches,
they should be dealt with during the course of the experiment. Oftentimes, such glitches
are caused by the underlying sample substrate, so if the sample is rotated, they will
disappear or move allowing acceptable regions of different scans to be combined. In any
case, the glitches must be removed since Fourier transformations are performed later

causing signiﬁcant broadening of the glitches.

66

Ideally, the CHI data would be normalized according to x(E) = [u(E) - I1(,(E)]/p0
where u is the absorption coefﬁcient and no is the bare atom absorption. Unfortunately,
no cannot be measured independently nor determined theoretically near an absorption
edge; therefore, the following normalization is used:

= ME) - ME)
ME.)

 

x(E) (Eqn- 5-4)

where u(Eo) is the value of p at the absorption edge, i.e., the step height, and pb(E) is a
suitable background since the actual background cannot be measured. The data are
normalized to the step height since different samples have different total numbers of
absorbing atoms.

Since the actual background cannot be removed, a suitable background consisting of
a linear ﬁt to the pre-edge region and a cubic spline ﬁt for the remaining data is used.
The user must be careful to insure that the cubic spline does not follow the EXAFS
oscillations. This background removal is satisfactory as long as both the experimental
standard and the sample have similar backgrounds subtracted. The remainder of this
section discusses the speciﬁcs of this procedure.

Using Interactive Data Plot (IDP), the various scans for a given sample are
simultaneously displayed to determine if each background should be subtracted
separately. Though the article by Vaarkamp, et a1.10 suggests that backgrounds should
always be removed separately for each scan to average out statistical errors during the
subtraction process, no statistically meaningful differences in the parameters obtained

from the analysis were observed in this study unless the scans had visibly different

67

backgrounds. Dissirnilar backgrounds sometimes occur when the gas mixture in
detection chambers has not yet come to equilibrium.

If the backgrounds do not need to be removed separately, then the XMU ﬁles
created after the data conversion are combined using FMERGE which averages the data
from all the scans included in the merge. Since the statistics are better for this combined
data, the background removal may actually be superior to those performed separately.

In determining the pre-edge background subtraction, two points, EFl and EF2, are
chosen to give the best linear ﬁt to the pre-edge. Obviously, as large a range as possible
is selected while avoiding substrate and monochromator glitches. In determining the
cubic spline portion of the background, the fewest number of knots (zero crossings)
which allow for a suitable subtraction are used. The best ﬁrst attempt is one knot with an
unspeciﬁed position. Also, the data should be weighted more heavily toward the high k-
range since low-k data tend to be less reliable than high-k data.11 Typically, a ﬁt weight
of three is used for most metals.

The range of data selected includes a minimum energy no less than 20 eV above the
edge and preferably higher. The maximum energy is determined by the signal-to-noise
ratio or by the presence of glitches either of which could signiﬁcantly alter the subtracted
background.

Finally, an easily observable feature of the edge step is chosen to specify the edge
energy—consistency is much more important than choosing an exactly correct value.
This choice is determined by selecting the zoom option which displays the derivative of
the step so the point of inﬂection is easily seen. The edge step is selected such that its

bottom is a good average of the EFI and EF2 points. The top of the step is then chosen

68

such that the background is approximately midway between the extrema of the
oscillations. The selected background can be previewed visually before actually
removing it by selecting the "poly-ﬁt" button after the parameters have been chosen.

Once the background is removed, Tekplot is used to examine its derivative. If it
seems to follow the oscillations of the raw data at all, then the parameters must be

adjusted and the process repeated until this is no longer the case.

5.3.3 Fourier Transform (CI-II —> RSP Files)

If the backgrounds were removed separately for each individual scan, then these
CHI ﬁles are merged. Now only one CHI ﬁle exists to be Fourier transformed. Since the
CHI data extend over a ﬁnite range of k, the Fourier transform introduces Fourier ﬁltering
errors; therefore, the width of this range must be the same for all samples and standards
so the errors will be the same for all. To reduce the effects of this Fourier ﬁltering, the
minimum and maximum k-values are chosen at zeroes in the CHI data. Once this k-range
window is set, it can be moved without changing its size. The largest k-range possible is
selected though it is more important to determine a zero accurately than to increase the
size of the k-range. Again, the k-weighting chosen will probably be three; however, the
CHI data should verify this choice. The value of the k-weighting is chosen such that the
weighted CHI plot (k"x(k) vs. k) is closest to having equal amplitude over the entire
range. This check can be made by selecting Wgt'd Chi Plot in the Plot Options during the
background removal.

Further reductions in Fourier ﬁltering errors are made through the use of a Hanning

function or window W(k). By combining the data with W(k), the data are not as sharply

69

truncated as they would be with a step function thus minimizing the introduction of
spurious peaks into the pseudo-RDF. Though this method minimizes truncation ripple, it
does cause some peak broadening. The values of dkl and dk2 determine the width of this

Hanning window which is deﬁned by the following:

 

 

W(k) = sinzIn(:(_d:3m)I kmin < k < (kmin +dk1)
=1 (kmin +dk1)<k<(kmax—dk2)
_ 2 ”(k-(kmax Tde»
—cos I 2(dk2) I (kmax —dk2)<k<kmax

(Eqn. 5-5)

In this study, values of dkl = dk2 = 0.5 A'1 were typically used and produced satisfactory

results.

5.3.4 Inverse Fourier Transform (RSP —> ENV Files)

After obtaining the pseudo-RDF, a given peak is backtransformed to isolate the
contribution of a speciﬁc coordination shell. In this study, only the nearest neighbor
(NN) peak was backtransformed except in the case of Fe where the ﬁrst two shells are
simultaneously backtransformed since the two peaks in the pseudo-RDF are unresolved—
these two peaks are unresolved for all bcc structures. The NN peak is typically the easiest
to analyze since multiple scattering and the k-dependence of the electron mean-free path
are minimized for it. Just as in the case of Fourier transforming, all samples to be
compared along with the standard must use the same backtransform range. Once the
window has been set for the ﬁrst sample, it can be moved without changing its width. In

choosing the backtransform range, it is absolutely imperative to include all of the peak—

70

even the tails. In a comparison of Fourier ﬁltered and unﬁltered spectra created using
FEFF--a theoretical XAF S modeling software program which does not use the Born
approximation making it the best generator of theoretical XAF S data currently available,

1.12 determined that omitting even a small portion of the main peak results

Vaarkamp, et a
in relatively large errors. Comparisons made in this study show that the coordination
number obtained through the ﬁtting procedure decreases signiﬁcantly as the
backtransform range is decreased even though both the standard and the sample are

backtransformed over the same range width.

5.3.5 Least-squares Fit

Once the contribution to x(k) by the ﬁrst shell has been isolated, i.e., the
backtransform has been completed, several parameters are varied to obtain the best
agreement between the standard and the sample. The maximum number of parameters 11
which may be ﬁt are determined by n = 2AkAR/7t where Ak is the momentum space range
and AR is the real space range of the ﬁrst shell.13 The coordination number N, the
nearest-neighbor distance R, and the Debye-Waller factor 6 (denoted by SS in
MacXAFS) are typically varied in the ﬁtting procedure. The data ﬁtting weight is usually
three since the high-k data are more reliable. Typically, o is set to zero for the standard
since it is unknown; therefore, the value obtained for the sample is a relative one. Also,
as a general rule of thumb, AR z 0.01-0.02A and AN/N z 15-20%. Finally, the goodness

of ﬁt parameter <x2> should be signiﬁcantly less than one.

71

 

lB.K. Teo and DC. Joy, EXAFS Spectroscopy: Techniques and Applications, (Plenum
Press, New York, 1981), pp. 13-17.

2D.C. Koningsberger and R. Prins, X-Ray Absorption: Principles, Applications,
Techniques of EXAFS, SEXAFS, and XANES, (John Wiley & Sons, New York, 1988), p.
45.

313.x. Teo and DC. Joy, ibid., p. 36.

4DC. Koningsberger and R. Prins, ibid., p. 127.
51bid., p. 108.

°Ibid., p. 455.

7Ibid., p. 93.

81bid., p. 92.

9F.W. Lytle, R. Greegor, D. Sandstrom, E. Margues, J. Wong, C. Spiro, G. Huffman, and
F. Huggins, Nucl. Instr. Meth. A226, 542 (1984).

10M. Vaarkamp, I. Dring, R.J. Oldman, E.A. Stern, and DC. Koningsberger, Phys. Rev.
B 50(11), 7872 (1994).

llD.C. Koningsberger, ibid., p. 232.
12M.Vaar1tamp, ibid., p. 7874.

l3F.W. Lytle, D.E. Sayers, and EA. Stern, Physica B 158, 701 (1989).

CHAPTER 6
CO/X MULTILAYERS

6.1 Introduction

Metallic multilayers formed by alternating layers of ferromagnetic metals with
layers of non-ferromagnetic metals exhibit a number of striking macroscopic magnetic
properties. A loss of ferromagnetisml or a rapid large increase in the magnetoresistance2
as the layers become thinner are two distinctly different examples of such properties. The
latter behavior is known as giant magnetoresistance (GMR). Although the macroscopic
properties are commonly reported as a function of layer thickness, two XAF S studies of
Cu/F e multilayers illustrate the inadequacy of attempting to understand these macroscopic
properties without better structural information. Pizzini, et a1. studied samples having
15A Fe layers with a variety of Cu layer thicknesses.3 Their XAFS data indicated a
structural transition occurred as the Cu layer thickness varied. Below 3 layer thickness of
10A the Cu layers were bcc and as the layer thickness increased a transition to a fcc
structure occurred. Not surprisingly, an increase in local disorder was observed in the
thickness regime between the limiting bee and fcc structures. This thickness regime was
correlated with changes observed in the GMR. Cheng, et al. studied a series of Cu/Fe
samples for which the Cu layer thickness was dominant.4 Their XAF S data identiﬁed a
structural transition in the Fe layer that was correlated with the observed loss of
magnetism in their samples.

Many Co/X systems show similar behaviors in their macroscopic magnetic

properties but obtaining reliable structural information can be more difficult.

72

73

Complications arise because of the difficulty in distinguishing between hop and fcc
structure for thin Co layers. In this chapter, three Co/X systems will be discussed—
Co/Ag, Co/Cu, and Co/Mo. For thin Co layers, both Co/Ag and Co/Cu exhibit GMR,
while Co/Mo displays a loss of ferromagnetism. Aside from these interesting magnetic
properties, these systems provide three interesting cases for comparison. The fcc
structures of Ag and Cu are very similar to the hcp structure of Co; however, Ag (d<111> =
2.359A) has a rather large lattice mismatch with C0 (d<002> = 2.03 5A) while the mismatch
of Cu (d<||]> = 2.087A) with Co is small. On the other hand, Mo has a bee structure
which is quite different from that of Co. In this chapter, the results of an earlier study of
Co/Ag will be summarized, and the results of the other two Co/X systems will be

presented in detail.

6.2 Co/Ag

In this section, the results of an earlier publications are summarized for comparison
with the other two Co/X systems. In this study, most of the samples had a 35A Ag layer
and a C0 layer varying in thickness from 6-35A. The XRD data were consistent with a
strong <111> texture and good layering. All of the samples except one had a saturation
magnetization that was 85% or more of the measured saturation for a 5000A Co ﬁlm.
This Co ﬁlm's magnetization was 1390 emu/cm3 which is within 4% of the value for bulk
Co. No clear dependence upon layer thickness was observed. In the XAF S portion of the
study, the Co 35A/Ag 35A sample was used as the standard, and R, N, and (I2 were
determined for the remaining samples. The results of these ﬁts along with the

magnetization data are presented in Table 6-1. The only signiﬁcant change is in the

74

Table 6-1: Saturation magnetization and ﬁtted EXAFS results.5 N values are estimated
to be accurate to within i 15%. GMR values are current-in-plane data at 5K from PA.
Schroederé—the percent change is relative to the resistance at or near magnetic
saturation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample M53, GMR
Co A/Ag A N R(A) 62(A'2) <x2> (103 emu/cm3) (%)
Pure Co 12 2.502 1.446
35/35 12 2.502 0 1.28 14
20/35 10.8 2.50 -0.0006 0.137 1.41 20
16/35 10.3 2.51 -0.0004 0.100 1.08 22
12/35 9.7 2.50 0.0007 0.194 1.25 24
6/35 8.4 2.49 0.0009 0.053 1.33 32
6/6 7.9 2.50 0.0008 0.007 1.26 ~l
4/ 12 Poor Fit 1.18 >20
4/15 Poor Fit 1.20 60
4/25 No data 1.35 40

 

 

 

 

 

 

coordination number which varies from 7.9-12 and gives a simple scaling with Co
thickness. Since for this same thickness range, both the GMR and the manner in which
the magnetization approached saturation changed dramatically, the ﬁnal conclusion was
that no simple correlations between the local structure and the magnetic behavior of these

multilayers exist.

6.3 Co/Cu

Cu/Co multilayers exhibit GMR7'8 and have been the subject of a number of
structural studies. Lamelas, et al. used RHEED complemented by demanding in-plane
XRD studies and found that the Co in Cu/Co prepared by molecular beam epitaxy (MBE)

was stabilized in a fcc structure for Co layer thicknesses up to 20A and that interfacial

75

coherence persisted up to 40A of Co.9 Despite the poor x-ray contrast between Cu and
Co, they were able to identify an expansion of > 1% in the Co lattice. Several early NMR
studies claim the Co in Cu/Co has a mixture of fcc and hcp environments, and the
proportions of the two structures appear to depend upon the method of sample
preparation.‘0" "'2 These studies do agree that the Cu/Co interfaces in both MBE and DC
sputtered samples with each layer thickness below 40A can be abrupt. The scale for
interfaces is monolayers (ML) and the value is one to a few. More recent NMR studies of
Cu/Col‘l"l4 introduce some additional preparation parameters but do not alter the
conclusion that thin Cu/Co samples prepared by DC sputtering and MBE can have abrupt
interfaces.

XAFS can provide valuable structural information about the local environment.
Pizzini, et a1. did XAFS studies on 5 thin, evaporated Cu/Co samples and concluded that
the atomic layer spacings perpendicular to the layers remained that of bulk Cu and Co,
but in the layers, Cu contracted and Co expanded.15 Unfortunately, the contrast between
Co and Cu scattering functions was too weak to allow identiﬁcation of the fraction of Co
and Cu scatterers in the ﬁrst shells surrounding each element. In this section, the XAF S
results for DC sputtered Cu/Co samples are presented. These results are complemented
by AXRD data where AXRD denotes XRD studies in which the x-ray energy has been
tuned just below the Co K edge and thus the anomalous dispersion enhances the x-ray

contrast between Cu and Co.

 

76

6.3.1 Sample Fabrication

The samples were prepared using the previously described sputtering system. The
substrates were 1 cm squares cut from a Si wafer. The total thickness of each sample was
typically 60 to 70 times the basic bilayer unit. XAF S studies were done on a series of Co
15A/ Cu xA samples where x = 9, 16, 25, and 35. This series was chosen for three
reasons: (i) this set of samples has layer dimensions near extrema of anti-ferromagnetic
and ferromagnetic couplings, (ii) bilayer and individual layer thicknesses are consistent
with NMR reports of sharp interfaces, and (iii) the two samples with smaller x values
have thicknesses comparable to the evaporated samples studied by Pizzini, et al.15 A
survey AXRD study of Co/X samples included the Co 15A/ Cu 9 and 16A samples, a Co

15A] Cu 9.5A with buffer layers, and a C0 4A/ Cu 25A sample.

6.3.2 XAF S Results

XAF S studies were done on line X23A2 at NSLS described in section 5.2. Data for
the Cu and Co K edges were taken using a Lytle detector operating in a ﬂuorescence
mode. The samples were mounted at 45 degrees to the beam and px = 3 ﬁlters were
placed before the Soller slits. A Ni ﬁlter was used for Cu data, and a Mn ﬁlter was used
for Co data. The incoming beam was monitored by an ionization detector ﬁlled with
static air rather than a more absorbing mixture to reduce complications from harmonic
contributions. A XAF S scan of Co for a Co/Ag sample directly conﬁrmed the lack of
harmonic contamination; there was no evidence of the Ag K edge which would be
produced by a third harmonic. This gas selection did not compromise sensitivity. The

same Co/Ag sample had been part of an earlier Co/Ag study on the harmonic free line

 

77

X23B where the Lytle detector16 was ﬁlled with ﬂowing Ar. Analysis of the present Co
data relative to a pure Co standard gave results identical to those of the earlier study. All
the present data were taken at room temperature. Typically 5 scans were performed for
most samples, and 7-9 scans were done for those samples with weaker signals. Results
from different scans were combined during the analysis using MacXAFS v. 2.0. Data
from pure Co and Cu foils were used as the standards in this analysis. Since comparison
of the present XAF S results for DC sputtered samples with the earlier results for
evaporated samples was a major goal of this experiment, the XAFS results will be
presented in a manner permitting direct comparison to those results.

The oscillations for Cu typically extended to a zero crossing near 11.5A'l and
occasionally further, but the oscillations for Co generally became noisy above a zero
crossing near 10A". As long as the same momentum range was used for both the
standard and unknown in forming the Fourier transforms used to isolate the ﬁrst shells,
the results from ﬁtting the ﬁrst shell back transforms were independent of the actual
momentum range used. Given this independence, the Cu and Co data were ﬁt over
comparable momentum ranges. Table 6-2 presents the detailed XAF S results under two
different constraints. First, the number of nearest neighbors were varied, and second, the
coordination number was fixed at 12. The latter condition was used by Pizzini, et a1.15
and was supported by their model calculation which indicated that nearest neighbor Cu
and Co atoms were indistinguishable. Paralleling their analysis, the present study used
experimental data for pure Cu to ﬁt Cu data and experimental data for pure Co to ﬁt Co
data. Despite the somewhat more limited momentum range, the quantity 2AkAR/7t is

nearly 5 and thus ﬁtting 2 or 3 parameters is valid.

78

Table 6-2: EXAF S results for Co/Cu samples. The upper portion of the table contains
results for the sputtered samples of the present study. The lower portion of the table
summarizes the results reported by Pizzini, et al. for evaporated samples.IS Since Pizzini,
et a]. ﬁxed the coordination number N at 12, the data analysis for the present study treated
N both as a ﬁxed parameter and as a variable to be ﬁt.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample Cu Data Co Data
Co A/Cu A N R (A) 02 (A'Z) <x2> N R (A) 62 (A‘z) <X2>
15/9 11.16 2.551 0.0005 0.085 1 1.61 2.513 0.0009 0.005
=12 2.551 0.0010 0.134 =12 2.512 0.0011 0.019
15/16 12.75 2.551 0.0009 0.213 12.39 2.512 0.0013 0.029
=12 2.551 0.0005 0.253 =12 2.512 0.0011 0.042
15/25 10.90 2.553 0.0000 0.167 N/A N/A N/A N/A
=12 2.553 0.0006 0.258 N/A N/A N/A N/A
15/35 1 1.58 2.557 0.0003 0.035 11.69 2.512 0.0007 0.006
=12 2.557 0.0006 0.048 =12 2.512 0.0009 0.015
Pizzini, et a1.15
in-plane =12 2.54 |02|< N/A =12 2.52 0.0003 N/A
0.0005 to
0.0023
out-of-plane =12 2.55 0.0000 N/A =12 2.50 0.0008 N/A
to to
0.0005 , 0.0023

 

 

 

79

Since the samples were mounted at 45° to the beam, the differences that Pizzini, et
al.15 found for in-plane versus out-of-plane nearest neighbor distances R cannot be
conﬁrmed. However, this 45° mounting makes their cosine squared polarization factor
equal 0.5, and thus agreement exists if the distances determined here are the simple
average of their distances. Here Co R = 2.51A and is the average of the in-plane R =
2.52A and out-of-plane 2.50A values found by Pizzini, et al. The Cu R values found in
this experiment appear to show a pattern, but appropriate error limits for the R values
must be established before any interpretation. These errors are believed to be better than
the often quoted generic i0.02A based upon several factors. First, increasing the

momentum range used in analyzing Cu data by nearly 25% on several samples changed
the distances by a maximum of 0.002A. Second, with N = 12 and 02 ﬁxed at its

optimum value, a systematic variation of R caused the goodness of ﬁt parameter < x2 > to
increase an order of magnitude for a change of i0.006A. Consequently, the NN distance
results are good to better than i0.01A, and the reader is permitted to do the necessary
rounding of values. Returning to the pattern of R values for Cu, R for the thickest Cu
layer is essentially the 2.556A of bulk Cu while the two thinner Cu layers have a value
nearer the average of this bulk value and the 2.54A in-plane value found by Pizzini, et
al.15 for samples of comparable thickness. Thus, in the thickness regime where the
samples of the present study and the evaporated samples of Pizzini, et al. are comparable,
the observed R values are consistent. Outside this thickness regime, R for the thicker Cu
layers approaches that of pure Cu for the multilayers studied here.

The results for disorder in the layers are also consistent with the Pizzini, et al.‘5

 

80

ﬁnding that Co layers are more disordered than Cu layers. First, there is the qualitative
ﬁnding about the data momentum ranges noted earlier. The C0 oscillations typically
become noisy above lOA'l while Cu oscillations continue to 11.5A'l or greater. Both the
Cu and Co standards give well-deﬁned oscillations to nearly 14A’1. Second, there is
quantitative agreement in the 02 values. Whether the number of nearest neighbors is

varied or ﬁxed at 12, 0'2 values obtained are similar to theirs.

6.3.3 XRD and AXRD Results

XRD data were obtained using two different sources. Initial conﬁrmation of
layering was obtained from low angle XRD data taken with the Rigaku system. AXRD
data were obtained at NSLS beamline X6B using two wavelengths. The wavelengths
were calibrated using absorption of standard foils and their reproducibilities were tested
by determining the location of the <400> line from the Si substrates. The reproducibility
of the Co edge setting was 0.03% or better for the present data.

AXRD data provide a valuable check upon XAFS results that indicate altered R
values. All the Co/Cur samples show an average dominant Bragg line that is consistent
with a fee structure having <111> ﬁbre texture and a lattice spacing similar to Cu. This
line's location should be independent of the in-plane changes in R and should vary
systematically with the differences in Co layer thickness relative to Cu layer thickness.
Denoting the location of this dominant line in terms of an atomic layer distance <D>
produces a quantity independent of x-ray wavelength. The results from both the present
study and that of Pizzini, et al.15 are consistent with a linear dependence of <D> upon the

relative amount of Cu in the bilayer unit though the slopes from the two studies differ.

81

Despite this difference, the basic agreement for the two sets of Cu/Co samples is good.
The agreement for F WHM values of the average Bragg line from the two studies is not as
good. Pizzini, et al. ﬁnd values of 0.l9°-0.23° while those of the present study for the
more comparable x-ray wavelength have values of 0.25°-0.36°. However, even 0.36°
gives a coherence length over 10 bilayer units long which suggests that the samples are of
good quality.

Table 6-3 summarizes the results associated with line positions found in the AXRD

study. I<> denotes the average Bragg line while I‘ and 1+ denote satellites occurring at

smaller and larger 29 values, respectively. The calculated values given in the table were
obtained using a simple step function model for the interfaces. Deviations from this
simple model typically have pronounced effects upon line intensities and only minor
effects upon line locations.l7 Values of the anomalous scattering corrections used in the
calculation were obtained from the f-prime routine in the General Structure Analysis
System (GSAS) program.‘8 Bulk parameters were used for planar spacings normal to the
plane of the layers, and a change in <111> planar atomic density was used to obtain the
values for in—plane distortions consistent with the XAF S results of Pizzini, et al.15 The
effects of variations in resetting the x-ray beam energy were determined by doing the
model calculations for a range of energies. Neither the planar density changes nor the
0.03% variation in resetting the beam energy thus changing the wavelength produced
signiﬁcant changes in the calculated locations of the lines. Experimental 29 values
marked with an * have unusually large intensities and may be associated with the

presence of more than a single satellite line. Experimental values for the bilayer distance

 

82

Table 6-3: Summary of d-spacings from XRD and AXRD data. 10 denotes the dominant
line; 1' denotes the satellite located just below the dominant line while I+ denotes the
satellite just above it. A is the measured value of the bilayer spacing. The * indicates
unusually large intensities and the ** indicates the sample with a 60A Fe buffer and a
50A Cu cap. (The buffer is the ﬁrst layer sputtered; the cap is the last). The procedure
for calculating positions is described in the text.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

@ 7.0 keV @ 7.689 keV
Co A/Cu A Rigaku Calculated Exp. Calculated Exp.
data 29 29 29 29
15/9 I 46.30 46.28 41.91 41.88
10 50.97 50.72 46.12 45.89
F 55.72 55.08 50.51 ---
extra lines 59.7? 43.33,53.63
25.1 A (A) 25.5305
15/9.5** I 46.40 46.12 42.02 41.74
10 50.96 50.77 46.12 45.90
1+ 55.88 --- 50.37 49.72*
extra lines 47.85?
23.8 A (A) 26.33213
15/16 I 47.18 47.08 42.77 42.68
10 50.82 50.62 45.98 45.80
I+ 54.52 54.19 49.38 --
‘ extra lines
31.9 A (A) 31.6:03
4/25 I 46.70 --- 42.30 42.16
10 50.38 50.32 45.60 45.53
1+ 54.41 5505* 49.20 4969*
extra lines 58.84 53.14
29.1 A (A)

 

 

 

83

A are also given in Table 6-3. Low angle XRD data using the Rigaku powder
diffractometer produced only two lines; thus, no error estimates are available.
Experimental values for A from the higher angle data, with an error estimate, are given
when three line locations are available.

Results in Table 6-3 for the three 15A Co samples at the lower energy form a regular

pattern. Experimental 29 results are systematically smaller than predicted with 29 for 10

being about 02° below its predicted value. This difference is within the combined error
associated with beam wavelength error and sample alignment error. For the two samples
having three lines, the A values determined from higher and low angle data agree within
experimental error. Moreover, these experimental values differ from the nominal values

by less than one monolayer. Suggestive features of this pattern also appear in the data at

higher energy. The lack of 1+ lines except for the one suspect apparent I+ line, suspect
based upon intensity considerations as indicated by the *, prevents full completion of the
pattern.

AXRD results for the 4A Co sample are quite different. Only one satellite line is
observed unambiguously, I" at the higher energy. Both the strong intensity of an

apparent I+ line, and the fact that it is the only line in Table 6-3 whose experimental

location is greater than its predicted value make its identiﬁcation suspect. A strong extra

line is observed at both energies. Converting the locations of the apparent 1+ line and the
extra line into d-spacings reveals that the former is within 0.01A of the value for the bulk
hcp <101> Co line while the latter is within 0.01A of the value for a bulk fcc <200> Cu

line. At both energies the d-spacing associated with the 10 line is within 0.005A of the

 

84

value for the bulk Cu <111> line. These higher angle results strongly suggest that this
sample might be more correctly described as being a mixture of fee Cu and hcp Co.

Any attempt to upgrade this suggestion of a Cu and Co mixture to a conclusion must
address several conﬂicting considerations. From a practical perspective, a 2 ML Co layer
must be all interface, and from a fundamental perspective there are not enough Co ML's
to establish a fcc structure. Starting with the latter point and arguing that the Co layer has
a basic hcp structure with Cu impurities might support the appearance of a hop line.
However, actual separation of this structure from Cu, even with the addition of thickness
ﬂuctuations that increase local sizes to several times the 2ML's, would be associated with
a serious line broadening that would render the line unobservable. Moreover, this
structural model ignores the fact that low angle data conﬁrm some form of layering.
Since the small fraction of Co ML's in the bilayer unit would cause the Cu <111> line and
a composite <1 1 l> line to be nearly identical, using the position of this single line to
distinguish between pure Cu and a multilayer is not reliable. Identifying the observed
<111> Bragg line as such a composite line leads to structural coherence over 7 or more
bilayers thus eliminating any line broadening concerns.

A strong <200> Bragg line is also observed for the 4A Co sample. This line's

presence indicates the sample's <1 1 1> ﬁbre texture is weaker and raises another possible
source for the unusual strength of the apparent 1+ line. A layered structure would produce
satellites on a composite <200> line. Given the nominal bilayer distance of 29A, the 1‘

satellite on the <200> line would be located within 0.2 degrees of the I+ satellite on the

<111> line. Moreover, a general pattern of satellite intensities discussed in the following

85

paragraph suggests that falsely identifying a <200> I“ satellite as a <111> I+ satellite
would lead to an increased intensity at the higher beam energy. Such an increase is
observed.

Following is a reprisal of the signiﬁcance of line locations for structural
characterization of the XAFS samples. First, layering is conﬁrmed and bilayer distances
determined from low and higher angle data agree within experimental error. One datum
questioning this simple result is related to an unusually strong line at 49.72° for the
buffered/capped sample at higher beam energy. However, given the empirical presence

of a strong line at 49.69° for the Co 4A/Cu 25A sample at this same beam energy and the

usually strong intensity of this questionable datum, a simple I+ identiﬁcation is suspect.
Second, the Co ISA/Cu 9A sample has a weak extra line located near the position
expected for a <200> line. The stronger <200> line observed for the Co 4A/Cu 25A
sample provides a "standard" for this weak extra line. It is unclear whether the observed
shift from the "standard" location is associated with a composite Cu and Co <200> line or
simply the difﬁculty in correctly locating such a weak line. In either case, the very
weakness of this line in the XAF S sample is direct conﬁrmation of a strong <111> ﬁbre
texture that typically accompanies good layered structure in sputtered Co/Cu samples.

In principle, a comparison of the satellite intensities obtained from the simple model
calculation with the experimental intensities could provide an additional structural test.
The calculated intensities can be viewed as an upper limit for actual results since
deviations from an abrupt step interface typically decrease satellite intensities. Using the
distortions suggested by Pizzini, et al.” produce calculated intensity changes of less than

i20% relative to the undistorted samples. A double normalization of the satellite

86

intensities, ﬁrst to the beam intensity to remove beam-decay effects and second to the I<>

intensity to remove any orientational texture effects leads to the following remarks. First,

the simple model correctly predicts general intensity trends. It predicts that I' intensities

increase by a factor of 2.3 to 2.9 as the beam energy is increased from 7 to 7.69 keV. The
observed increase factors are between 1.7 and 2.1. The model predicts I+ intensities will
be less than those of I“ at the lower energy and will decrease by an additional factor of
2.5 or more at the higher energy. The I+ intensities are smaller at the lower energy and no

l+ lines are unambiguously observed at the higher energy. Second, all observed satellite
intensities are near the upper limit values predicted by the simple step model. This result
is consistent with the inferences of sharp interfaces which arise from NMR studieswm
Third, lines marked by an * in Table 6-3 have intensities that are at least 300% greater
than the values predicted by the simple model. Such large intensity discrepancies contrast

sharply with the general consistency of calculated and experimental results and ﬁrrther

support the alternate identiﬁcation of these lines.

6.4 Co/Mo

Co/Mo multilayers provide an opportunity to study the effects of spacer layers which
have a completely different structure from the Co layers. Not surprisingly, this system
exhibits signiﬁcantly different magnetic behavior than the other two Co/X systems.
Unfortunately, comparison of two published studies of sputtered Co/Mo multilayers
reveals limited agreement and many signiﬁcant differences in both magnetic behavior and
structure. Both studies ﬁnd highly disordered layers and a near loss of ferromagretism

when the Co layer is about 10A or less in thickness. Sato attributes this loss to a "dead

 

87

layer", i.e., Co atoms near the Mo layers have no moment or a reduced moment.19 Wang,
et al. report the presence of a non-magnetic compound——e-Co7Mo(5.20 For thicker Co
layers, these studies report different structures and different magnetic behavior; however,
it should be noted that Sato fabricated his samples using magnetron sputtering while
Wang, et al. used focused ion sputtering.

In each study, XRD produces low angle peaks that are consistent with a layered
structure. For bilayer thicknesses less than 40A, Sato'sl9 higher angle XRD data show a
single dominant peak whose location is dependent upon the relative portions of Mo and
Co in the bilayer unit. For multilayers having equal amounts of Mo and Co, this peak
location is constant. For samples with A = 60A, this single peak has split into Bragg
peaks characteristic of the Mo and Co forming the bilayer. Wang, et a1.20 ﬁnd isolated
Mo<110> and Co<111> peaks for all of the samples that were not disordered. In
addition, a line from e-Co7Mo6 is observed for many samples, and the <002> peak for
hcp Co is observed for thicker Co layers. Their TED data reveal lines consistent with bcc
Mo and 3 lines associated with e-Co7Mo6.

The dependence upon layer thickness for the room temperature saturation
magnetizations of the two studies is also different. For samples with equal amounts of
Co and M0 in the bilayer, the studies agree that 10A Co layers have a saturation
magnetization less than 10% that of bulk Co; however, Sato19 reports a slow rise with
increasing Co layer thickness, still less than 40% of bulk for 30A Co layers, while Wang,
et al.20 report a rapid rise that reaches > 80% for 20A Co layers and 2 95% for 30A Co
layers. The results for samples with differing amounts of Co and M0 in the bilayer vary

somewhat in details but produce similar differences.

 

88

In the remainder of this section, the results of XRD, TED, XAF S, and magnetic
studies of CofMo multilayers fabricated for the present study will be presented and

compared to the results from the other previously cited studies.

6.4.1 Samples Fabricated

The Co/Mo multilayers were fabricated using the previously described sputtering
system. Sapphire and cleaved NaCl were used as substrates. The number of Co ML
varied from 2-28, and the number of Mo ML, from 5-14. The same bilayer unit was
made for samples on both substrates, but the total number of repeated cycles differed
resulting in different total thicknesses. Samples on sapphire had a total thickness of about
2000A while that for samples on NaCl substrates was about 500A. Samples having the
same bilayer dimensions were prepared consecutively. Individual layer thicknesses were
chosen to match an integral number of monolayers (ML) for the metals: 2.25A and 2.05A

were used as the nominal ML thickness for Mo and Co, respectively.

6.4.2 Magnetic Studies

Portions of the sapphire substrate samples were used for magnetization
measurements in a DC SQUID magnetometer. The ﬁeld was typically applied parallel to
the multilayer ﬁlm. The measurements were performed at 5K to determine if the loss of
magnetism previously mentioned resulted from a lowering of the Curie temperature.

The magnetization results for Co/Mo samples with equal layer thicknesses from a
number of studies is contained in Figure 6-1 while Figure 6-2 shows the ﬁeld dependence
of the magnetization for two particular samples in the current study. All values have been

normalized to the saturation magnetization at 5K for pure Co (1450 emu/cm3). The

 

bulk Co
sat

Mm/M

1.0

0.9 -

0.8
0.7
0.6
0.5

0.4 ,
0.3 >

0.2
0.1

89

 

 

-
0..
.u
.

Sato 5K
Sato Rm Tmp
Wang Rm Tmp

 

 

0 0 d -—+— Present study 5K

 

,,1 i . . , A, . . ;.___.L—

5'6'7‘8’9 101112131415

Figure 6-1: Normalized saturation magnetization vs. nominal Co layer thickness for
Co/Mo multilayers with tMo = tcO. In addition to data from the present study, the data of
Wang, et al.20 and Sato19 are presented.

points connected by broken lines are the room temperature saturation magnetization data
from Wang, et al.20 and Sato.19 The single triangle datum is 5K data from Sato. The
solid circles are data at 5K for the Co/Mo samples of the present study. The values of
Wang, et al. approach pure bulk values at room temperature while the values in this study
remain substantially below that limit at 5K where the largest values occur. Comparison
with Sato is complicated by the different temperatures for the measurements. The data
from this study have a general dependence upon layer thickness comparable to that
reported by Sato. Since the values would be expected to decrease at higher temperature,
the agreement should improve. However, Sato's single datum at 5K is about 40% smaller
than the corresponding result in the present study; therefore, a believable comparison

requires actual data at similar temperatures.

 

 

 

90

 

0.8 ' I Y I I I r I T I

bulk Co
sat

M/M

 

 

 

 

 

 

 

 

 

60
H (kOe)
b)
o L
O <
:4 3 _
Ea .
o 10 20 30 40 50 60

H (kOe)

Figure 6-2: Field dependence of the normalized magnetization for the a) 14ML/14ML
and b) 2ML/8ML Co/Mo multilayers on A1203 substrates. The diamagnetic contribution
of the substrate is ﬁt with a straight line to determine the y-intercept thus providing the
saturation magnetization of the multilayers.

 

91

In addition to these samples of equal layer thickness, several samples of unequal
layer thickness were examined. The normalized saturation magnetizations for two
samples with very thin Co layers are 0.26 and 0.023 for the 2ML/10ML and the
2ML/8ML samples respectively. This loss of magnetism is even greater than that for the
5ML/5ML sample. Also, the 28ML/14ML sample with a C0 layer at least twice as thick
as that of any other sample studied here has a saturation magnetization equal to that of

bulk Co.

6.4.3 XRD Results

Low angle XRD data for the Co/Mo multilayers in the present study conﬁrm that the
samples are layered with the actual bilayer distances being within i3% of the nominal
values. The locations of all XRD peaks are independent of the substrate, and the thinner
samples give weaker signals as expected. As the bilayers of these Co/Mo samples vary
from SML/SML to 28ML/14ML, the higher angle XRD data have a progression seen for

1 The bilayer unit progresses from being highly

numerous metallic multilayers.2
disordered to being a well-defmed average crystalline unit and ﬁnally to being a
crystalline unit with resolved constituent Bragg lines as seen in Figure 6-3.

The SML/SML sample has a weak and broad line consistent with a d-spacing of
between 2.135 to 2.156A. The 7ML/7ML sample has a well-defmed line with a d-
spacing of 2.145A and four satellite lines, 2 below and 2 above. This d-spacing is
consistent with a weighted composite line from the d-spacings of Co and Mo and is

hereafter denoted as the dominant line <D>. As the bilayer thickness increases, this same

pattern is maintained. For samples with equal amounts of Co and Mo, the location of all

 

92

 

1 04 AVC CO

Mo 5 {002} ?
{110} e.
2 ~ .-'=. 5 =.
o . u: E f:

103
L10MU10ML5 28ML/14ML

  
 
   

102»

Intensity (arb. units)

101 _.

10°e ,
32 34 36 38 40 42 44 46 48 50 52 54
29 (deg)

 

 

 

Figure 6-3: Comparison of the higher-angle XRD data for the 5ML/5ML, lOML/lOML,
and 28ML/14ML Co/Mo multilayers.
<D> lines is consistent with 2.139 i 0.007A, and the satellite line locations shift
consistent with the different bilayer thicknesses. XRD data for the 14ML/14ML sample
have this same pattern of locations although there is a slight change in the progression of
intensities. For this sample, satellite lines are located very near the d—spacings for pure
Co and pure Mo lines, and the presence of pure element lines might account for this slight
intensity change. The higher angle XRD data for the 28ML/14ML sample are clearly
different. Individual lines from Co and Mo are resolved and are ﬂanked by satellites.
The coherence lengths seem to indicate this same progression. For the samples with one
Bragg peak, the coherence is quite large. As the individual layers begin to display
characteristics more typical of a bulk nature, the coherence begins to decrease.

Given the possibility of strain in these multilayers, the preceding d-spacings are

consistent with either a fcc<111> or hcp<002> line for Co and a bcc<110> line for Mo.

 

 

93

Bragg lines having other indices are not observed in the XRD data which is consistent
with the high degree of ﬁbre texture typical of sputtered metallic multilayers. Most of the
samples with bilayer distances of 7ML/7ML or greater show second order XRD effects of
the <D> line and satellites that conﬁrm the previous interpretation. The 14ML/14ML
sample has very poorly resolved second order effects, and the 28ML/14ML sample has
only the two pure element lines as its second order effect.

For the two samples with very thin Co layers (2ML) and relatively thick Mo layers
(8ML and 10 ML), XRD data clearly indicate that the samples are crystalline including
the Co layer. These samples likewise show second order effects of the <D> line and

satellites. See Table 6—4 for a summary of the XRD results.

Table 6-4: XRD structural results for Co/Mo multilayers. <D> denotes a single line
interpreted as a composite line composed of the Mo<110> line and a C0 line. The
relative error for these d-spacings is $0.003 A. The * denotes a broad, weak line which is
more likely an indication of the nearest neighbor distances in an amorphous sample.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Co/Mo A (A) d-spacing of # peaks from bilayer Coherence
(in ML) Nom. Meas. <D> (A) satellites harmonics Length (A)
2/8 22.1 21.8 2.169 1 3 130

2/10 26.6 25.9 2.180 2 2 230
5/5 21.4 21.8 2.135 to 2156* 0 0 15?
7/5 25.6 25.8 2.126 3 3 290
7/7 30.2 30.1 2.145 4 3 310

10/10 43.0 42.0 2.135 4 2 260

14/14 60.2 61.4 2.132 4 3 180

28/14 88.9 87.5 Mo<110> 2.208 2 4 100
C0<l 11> 2.045 1 140
or Co<002>

 

 

 

94

6.4.4 TED Results

The TED studies were performed with the VG H8501 FESTEM previously described.
The TED data are consistent with the structural progression suggested by the XRD data.
All the TED patterns are dominated by rings. Figure 6-4 shows that for the SML/SML
sample, the pattern consists of one intense but broad ring and two weak, diffuse rings
indicative of an amorphous structure. The 7ML/5ML sample reveals some interesting
features. A TEM image of the 7ML/5ML sample shown in Figure 6-5 and the two
diffraction patterns given in Figure 6-6 indicate a mixture of crystalline and amorphous
structures. Figure 6-7 shows that the TED patterns yield a sequence of strong Bragg lines
that are consistent with a bee structure for all samples with a bilayer distance of
7ML/7ML or greater. Typically 56 lines in the sequence are evident and attributed to the
Mo layers. TED patterns for the samples with thin Co layers (2ML/8ML and
2ML/10ML) indicate that these samples are crystalline with 5 and 6 Bragg lines observed
respectively that are consistent with a bcc structure. These results are again consistent
with the XRD data. Also, none of the TED data exhibit non—bcc lines so TED provides

no direct evidence for the presence of Co-Mo compounds.

6.4.5 XAFS Results

XAF S data for the Co K edge were collected at the NSLS on beam line X23A2 using a
Lytle detector operated in ﬂuorescence mode. The samples were mounted at 45° to the
beam and a ux = 3 Mn ﬁlter was used. The detector which monitored the incoming beam

(10) was ﬁlled with a mixture of ﬂowing N2 and He, and the Lytle detector was ﬁlled with

ﬂowing Ar. A harmonic check was performed as described in section 6.3.2. Typically 5

 

: t - .‘1"n..-.‘.lh£u- 25:51

 

95

 

 

Figure 6—4: TED line scan for Co/Mo (5 ML/SML).

 

Figure 6-5: TEM image of Co/Mo (7 ML/SML). The nominal magniﬁcation is 50 K.

Figure 6-6: TED line scans from different regions of the same Co/Mo (7ML/5ML)
sample illustrating the varying degree of crystallinity.

21)

b)

97
a) jIII \k
b)

I I

 

 

 

 

Figure 6-7: a) TED line scan for Co/Mo (7ML/7ML) and b) TED line scan for Co/Mo
(10ML/10ML).

98

 

5 I I l I T l 1 I l l I Tf
4” M ‘
3t _

:3

2

>4

 

 

,_J

O _ I I 1 i l 1 1 1 l 1 l 1 l i 1 A 1 r l I 1 4 1 A T
7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7
Energy (keV)

 

 

 

Figure 6-8: Combined raw data from 5 ﬂuorescence scans of the 7ML/7ML multilayer.

scans were done with 2-4 more scans done for those samples with thin Co layers. Results
from different scans were combined during the analysis using MacXAFS v. 3.6. Data
from a sputtered 2000A Co ﬁlm was used as the standard in the analysis. Sample raw
data for the 7ML/7ML sample is given in Figure 6-8.

Qualitatively these data reinforce the validity of the structure development with
increasing bilayer thickness as described in section 6.4.3. The XAFS data for the
SML/SML sample consist of a single decaying oscillation while data for the 7ML/5ML
sample are consistent with a mixture of amorphous and crystalline Co. Data for the
7ML/7ML sample and those samples with thicker Co layers have oscillations
characteristic of hcp or fcc Co or a mixture of the two. These data indicate the local
structure as well as the average long range structure changes from amorphous to

crystalline as the bilayer thickness is increased from 5ML/5ML to 7ML/7ML in Co/Mo.

 

 

 

 

99

 

0.06
0.05 e
0.04 —
0.03 »
0.02
0.01
0.00 ~ ~ P , ~ ~. .r‘----"’4“ I ' “
-0.01
-0.02 1" ;
003 ~ ' 7 Tn
-004 »—
-0.05

CHI

 

 

 

3 4 5 6 7 8 9 10 ll 12 l3 l4

 

{Fr-'1 " '

b)

 

12
11
10~

 

RSP

 

OHNUJ-hLIIO‘QOOC

 

 

Figure 6-9: Comparison of the CHI and RSP data for the 5ML/5ML and 7ML/7ML
samples clearly shows the transition from an amorphous to a crystalline structure.

 

100

 

 

 

 

 

1800 ' I T 7 I I ’ l I I ‘ 12
. D .
1600 - ' I r 11
’ ~ 10
1400 - .
a? . I 9
E 1200 h j 8
o I I .
3 1000 — I _. 7
8 ~ 2
v 800 r I 1 6
‘5 .
E 600 ~ I If M5,, 7 5
. . 4 4
400 h . o N j 3 .,
200 — _‘ E
0 1* 1 , 1 r l r l 1 l 1 3',
0 5 10 15 20 25 30 '
tCo (ML)
Figure 6-10: Saturation magnetization and number of nearest neighbors as a function of 0

nominal Co layer thickness. The solid data points are for samples of equal layer
thickness. The unﬁlled data points are for the 28ML/14ML and 2ML/8ML multilayers.

A direct comparison of the CHI data and its transform for the 5ML/5ML and the
7ML/7ML multilayers in Figure 6-9 clearly denotes this transition.

A correlation between structure and magnetization is shown in Figure 6-10. Both
the coordination number N as measured relative to the Co standard and the saturation
magnetization M5,, are shown as functions of Co thickness. The scaling of N and M53, are
very similar indicating a clear correlation between the local structure and the loss of
magnetism. Ignoring the 2ML/8ML multilayer for now, it is clear that the development
of hcp or fcc Co coincides with the increase in saturation magnetization.

Figure 6—11 shows the Fourier transforms, i.e., the pseudo-RDF's, of all the samples
included in the XAFS study. It clearly reveals the different structure of the 2ML/8ML
sample. The other structural studies as well as the XAFS data indicate that the Co layers

are crystalline in this sample even though it has the greatest loss of magnetism.

 

b)

Figure 6-11: Comparison of the CHI and RSP data for the Co standard and all of the

CHI

RSP

0.10

0.08 ~

0.06

0.04 ~
0.02 ‘
0.00 '.

-0.02
-0.04
-0.06
-0.08

101

 

—- Co STD ‘
--------- 28 ML/14 ML ‘
—- 10 ML/lO ML;
--------- 7 ML/7 ML
—— 7 ML/S ML
--------- 5 ML/S ML
2 ML/8 ML

 

    

 

 

 

 

 

‘3‘4'5 6‘7'8‘9‘10‘1'11‘2V‘l‘3'1'4

 

 

 
  
 
 
 
 
   

— Co STD
------ 28 ML/l 4 ML
— 10 ML/l 0 ML
------- 7 ML/7 ML
——- 7 ML/S ML
------- 5 ML/S ML
2 ML/8 ML

 

 

Co/Mo multilayers included in the XAFS study.

 

 

 

 

102

Unfortunately, the structure of these Co layers is not known. FEFF models of pure hcp,
fcc, and bcc Co do not produce results that even vaguely resemble the data. Another
FEFF model substituting Mo atoms for Co atoms in an hep-Co structure also failed to
match the data. However, attempting to model data for only one sample is an extremely
difficult task at best. Additional data for samples with x ML Co/y ML Mo with x = 2-5
and y 2 7 are needed to establish experimental trends so that FEFF may be effectively

used to determine the structure of Co in thin layers.

 

lC.L. Foiles and J .M. Slaughter, J. Appl. Phys. 63, 3209 (1988).

2s.s.P. Parkin, et a1., Phys. Rev. Lett. 64, 2304 (1990).

3s. Pizzini, et al., Phys. Rev. B 46, 1253 (1992).

4S.F. Cheng, et al., Phys Rev. B 47, 206 (1993).

5CL. Foiles, R. Loloee, and T.I. Morrison, Mat. Res. Soc. Symp. Proc. 307, 149 (1993).
6RA. Schroeder, private communication with the authors listed in reference 5.

7MA. Howson, 13.1. Hickey, J. Xu, and D. Greig, J. Magn. Magn. Mater. 126, 416
(1993)

8D.H. Mosca, F. Petroff, A. Fert, P.A. Schroeder, W.P. Pratt and R. Loloee, J. Magn.
Magn. Mater. 94, 1 (1991).

9F.J. Lamelas, C.H. Lee, Hui He, W. Vavra, and Roy Clarke, Phys. Rev. B 40, 5837
(1989)

10K. Le Dang, P. Veillet, Hui He, F .J . Lamelas, C.H. Lee, and Roy Clarke, Phys. Rev. B
41, 12902 (1991); K. Le Dang, P. Veillet, P. Beauvillian, C. Chappert, Hui He, F.J.
Lamelas, C.H. Lee, and Roy Clarke, Phys. Rev. B 43, 13228 (1991).

llH.A.M. de Gronckel, K. Kopinga, W.J.M. de Jonge, P. Panissod, J.P. Schille, and
F.J.A. den Broeder, Phys. Rev. B 44, 9100 (1991).

12C. Meny, P. Panissod and R. Loloee, Phys. Rev. B 45, 12269 (1992).

l3T. Valet, P. Galtier, J.C. Jacquet, C. Meny, and P. Panissod, J. Magn. Magn. Mater.

 

 

 

 

103

 

121, 402 (1993); C. Meny, P. Panissod, P. Humbert, J .P. Nozieres, V.S. Speriosu, B.A.
Gurney and R. Zehringer, ibid., 406 (1993).

14P. Panissod and C. Meny, J. Magn. Magn. Mater. 126, 16 (1993); Y. Saito, K. Inomata,
A. Goto, and H. Yasuoka, ibid, 466 (1993); M. Suzuki, Y. Taga, A. Goto, and H.
Yasuoka, ibid, 495 (1993).

15 S. Pizzini, F. Baudelet, A. Fontaine, M. Galtier, D. Renard, and C. Marliere, Phys. Rev.
B 47, 8754 (1993).

16CL. Foiles, R. Loloee, and T.I. Morrison, Mat. Res. Soc. Symp. Proc. 307, 149 (1993). RF“-
l7C.L. Foiles, private communication.
”Ac. Larson and RB. Von Dreele, Los Alamos Natl. Lab. LAUR86-748.

l9Nohoru Sato, J. Appl. Phys. 63, 3476 (1988).

 

20Y. Wang, F.Z. Cui, w.z. Li and Y.D. Fan, J. Magn. Magn. Mater. 102, 121 (1991).

”BY. Jin and 1.13. Ketterson, Adv. in Phys. 38, 189 (1989).

 

 

CHAPTER 7
FE/SI AND F E/ {FESI} MULTILAYERS

7.1 Introduction

During the 1980's and early 1990's, Fe-Si multilayers (Fe/Si) with thick Si layers,
typically 35A or greater, were studied extensively and seemed to be well understood. In
one study using Mossbauer spectroscopy, an amorphous alloy was found separating
crystalline Fe and amorphous Si (a—Si) layers. This study also determined that Fe layers
less than 20A were not crystalline.l Polarized neutron-scattering studies indicated results
consistent with an amorphous alloy interface having a 16A thickness. Cross-sectional
TEM showed that these same samples also had well-deﬁned and continuous layers.2
Another study determined that the Fe layers were not coupled and that approximately 8-
10A of each Fe layer was nonmagnetic.3 Later studies further evolved the picture by
indicating that the Fe-Si interface was 18A thick with a compositional gradient consisting
of Si-substituted crystalline Fe, magnetic amorphous, and non-magnetic amorphous
layers.4 All of the interfacial thicknesses listed above are totals for the entire bilayer, i.e.,
the thickness of each of the two interfaces associated with each bilayer unit is half the
listed interfacial thickness.

More recent studies of F e-Si systems with thin Si layers, however, have indicated
that the above picture is incomplete. Toscano, et al. discovered an oscillatory magnetic
coupling in Fe-Si trilayers while studying the spin polarization of secondary electron

emission.5 They claimed that the magnetic coupling is mediated through semiconducting

a-Si even though no supporting structural data was provided. Such a spacer could be a

104

 

 

 

105

source of the conduction electrons required in the spacer layer for an exchange type
coupling. This coupling discovered by Griinberg6 in Fe/Cr/Fe trilayer sandwiches was
ﬁrst used to explain the coupling of magnetic layers separated by a nonmagnetic metallic

spacer. It is characterized by an energy per unit area of the form:
Ec = —2A12(M1-M2)—2B12(M1-M2)2 (Eqn. 7-1)

where Ec is the exchange coupling energy, M1 and M2 are unit vectors along the magnetic
moments of the two magnetic layers, and A12 and B12 are the respective bilinear and
biquadratic exchange coupling constants. The biquadratic term7 was found necessary
subsequent to the initial ﬁnding and is required only in certain cases.

Further support for exchange coupling came from a series of studies performed by a
group at Argonne. For sputtered F e/Si multilayers with 30A thick Fe layers and nominal
Si spacer layer thicknesses (tSi) between 10 and 40A, they reported ferromagnetic (FM)
behavior for ts, < 13A, antiferromagnetically (AF) coupled Fe layers for 13A < ts, <17A,
and no coupling between Fe layers for ts, > 17A.8 These magnetic properties were
studied using superconducting quantum interference device (SQUID) magnetometry,
longitudinal Kerr rotation, conversion-electron Mossbauer spectroscopy (CEMS), and
polarized neutron diffraction. Using XRD, they determined that the Fe layers were
structurally coherent for ts, < 17A. Both the magnetic coupling and the structural
coherence were explained by the presence of an Fe silicide inferred from the CEMS
which was reported to most likely be s-FeSi. This semiconductor would be a much better
source of the required conduction electrons since its band gap energy is 0.05eV compared

to the 1.12eV of a-Si. The Argonne group later indicated ﬁnding AF coupling and

 

 

”.111" “I
i' ‘

 

106

structural coherence up to spacer layer thicknesses of 40A when the spacer was {FeSi} .9
This spacer was made by depositing approximately one monolayer (ML) of Fe followed
by approximately one ML of Si and repeated to the required thickness. Independent
studies found that the magnetic coupling could be modiﬁed optically and further
supported the case for exchange couplingm‘” Recently, an electron transport study of
sputtered Fe/ Si multilayers by Inomata, et al. revealed a negative magnetoresistance (MR)
with a signiﬁcant change in its temperature dependence as the Si layer thickness exceeds
15A.12 From the temperature dependence of magnetic properties, they also inferred that
the spacer layers consisted solely of s-FeSi for ts, < 15A and a combination of s-FeSi and
a-Si when ts, > 15A. Nonetheless, this seemingly strong support for exchange coupling is
lessened by the fact that the presence of e-FeSi was never directly conﬁrmed and by
recent questions of the validity of the optical studies.l3

Moreover, a group at Lawrence Livermore National Laboratory (LLNL) shared the
results of their study prior to its publication which seemed to indicate that the magnetic
coupling was dominated either by dipolar coupling related to interfacial roughness or by

4 In multilayers comprised of

superparamagnetism of weakly-coupled Fe particles.l
magnetic layers separated by nonmagnetic metallic spacer layers, the work of Hill, et al.
also indicates that dipolar coupling energies originating from interfacial roughness can
explain both FM- and AF-like coupling.”

Though single Fe-Si interfaces have been studies extensively, the ﬁndings are highly
dependent upon grth method and conditions. '6'” Consequently, reliable extrapolation

of these results to the interfaces found in sputtered multilayers is questionable. Clearly,

direct structural information of these multilayers is required to determine the nature of the

 

 

 

107

spacer layer and possibly the mechanism of magnetic coupling between Fe layers. In this
chapter, the results of magnetic studies, XRD, TED, and XAFS of both Fe/Si and

Fe/{FeSi} multilayers will be presented.

7.2 Samples Fabricated

Using the sputtering system described in Chapter 2, F e/Si and F e/{FeSi} multilayers
were fabricated with all Fe layers being nominally 28.7A (14ML) thick. For the Fe/Si
samples, 10A 3 ts, 3 30A. The Fe/{FeSi} spacer layers were made by alternately
depositing nominally 2A of Si and 2A of Fe repeatedly to obtain total spacer thicknesses
(ti-85,) of 12-40A. Sapphire, crystalline Si, and cleaved NaCl and KC] were used as
substrates. All of the total multilayer thicknesses were around 500A except for the Fe/Si

multilayers on sapphire and Si substrates which were around 2000A in total thickness.

7.3 Magnetic Studies

Portions of the sapphire and Si substrate samples were used for magnetization
measurements in a DC SQUID magnetometer. The magnetization as a function of the
ﬁeld applied both parallel and perpendicular to the multilayers was determined at 5K.
Additional measurements were made using an AC SQUID magnetometer to determine
remanent magnetizations (M,) for further evidence of coupling. At low ﬁelds, the
magnetic ﬁeld of the AC SQUID is closer to an actual value of zero thus providing more
accurate determinations of M,.

For all of the Fe/Si multilayers, the saturation magnetization (Mm/V) was about
70% that of bulk Fe essentially independent of the spacer thickness. Also, the large

parallel ﬁelds required to achieve saturation and the ﬁeld in excess of the demagnetizing

 

 

 

108

Table 7-1: Magnetic properties of Fe/{FeSi} multilayers as a function of spacer layer
thickness. The Msat data were obtained with the DC SQUID, and the Hsat and MrlMsm
data, with the AC SQUID.

 

 

 

 

 

 

 

 

Cycles 0f Msat/V pure Fe Msat/V all Fe Hsat (parallel) Mr/Msat
(Fez/8180A} (103 emu/cm?) (103 emu/cm3) (kOe)

3 1.8 1.5

4 1.8 1.4 0.3 0.95
5 1.7 1.3 1.2 0.93
6 1.8 1.2 1.4 0.95
7 1.8 1.2 5.0 0.81
8 1.8 1.2 3.7 0.83
10 1.7 1.0

 

 

 

 

 

 

 

ﬁeld required for saturation in the perpendicular geometry were consistent with the results
of the previously mentioned studiess’lz.

Likewise, the coupling evidenced by the Fe/ {FeSi} samples was consistent with the
Argonne group's fmdings.9 A summary of the magnetic properties is shown as a function
of spacer thickness in Table 7-1. For the thinner spacer layers, the results are consistent
with FM coupled or uncoupled Fe layers. As the spacer thickness increases, the results
are consistent with AF coupling with a gradually decreasing strength. Ifit is assumed that
the Fe in the {FeSi} spacer is non-magnetic such that the saturation magnetization is
normalized to the volume of the nominally pure Fe layers (V pure Fe) only, then the
measured value for all spacer thicknesses is approximately equal to that of bulk Fe
(1.71x103 emu/cm3) within the i 5% error in these measurements resulting from the
uncertainty in the bilayer distance. Normalizing the magnetization to the total volume of
Fe (V all Fe) results in a saturation magnetization which varies with spacer thickness as

shown in Table 7-1. The saturation magnetizations determined from the AC SQUID data

are slightly larger than those obtained from the DC SQUID data. The AC SQUID data in

 

 

. ' ~
.QI‘...

109

 

1.14 . T 1 . . . . , , I ‘
1.13 i

1.12 a
1“ 1H HI €

1.10 g'
1.09 F' T .
1.08 i "a I -
1.07 T ;
1.06
1.05 l i
1.04 l i
1.03 -
1.02 _ . . . . . . .

M/MWc Fe
sat

I" Fl

1

 

 

 

b)

 

1.14 a
1.12
1.10r
1.08’
1.06’
1.04.
1.02"
1.00.
0.98
0.96h
094*
0.92
0.90

F
M/Mg;::re e

 

 

 

 

H (kOe)

Figure 7-1: Field dependence of the magnetization normalized to the volume of the
nominally pure Fe layers for the a) {F e2ASi2A} X 4 and b) {F e2ASi2A} X 7 spacer layer
samples on A1203 substrates. These AC SQUID data give slightly larger saturation
magnetizations than the DC SQUID data (see Table 7-1).

 

'17

 

110

Figure 7-1 shows this slight discrepancy as well as the ﬁeld dependence of the
magnetization for two of the multilayers. Regardless, either of these normalizations
yields different results from the F e/ Si multilayers and shows that further experiments are
required to determine whether or not the Fe in the {FeSi} spacer is magnetic and if it

affects the magnetization reduction for the nominally pure Fe layer.

7 .4 XRD Results

The x-ray data were taken using the Rigaku system described in section 3.3.2. No
differences in d-spacings greater than experimental errors were observed for the same

sample on different substrates, but differences in intensities were seen.

7.4.1 Low-angleXRD

Low-angle harmonics provide evidence of layer formation for both Fe/Si and
Fe/{FeSi}. The number of harmonics varies from 3-8 for Fe/Si and from 2-5 for
Fe/{FeSi}. The bilayer distances A were determined as discussed in section 3.5.2.
However, the two systems differ markedly with regards to the agreement between the
measured and nominal values of A.

For the Fe/Si multilayers, the measured values of A are substantially lower than the
nominal values. Figure 7-2 shows this variation of A as a function of ts, for those
samples on sapphire substrates—those on Si substrates behaved similarly. This result
was also observed by the Argonne group18 which they interpreted as evidence of
interdiffusion. Yet, for the F e/ {FeSi} multilayers, the measured A agrees fairly well with

the only differences attributable to random error.

 

 

IE.

 

O

Bilayer Spacing (A)

L (A)

 

59 r

57

55*

53
51
49
47

45 y.

43
41
39
37
35

 

 

240

220 .

200
180

160a
140*

120
100
80
60
40

20s

26 28

Figure 7-2: Measured bilayer spacing as a function of nominal Si layer thickness for
F e/Si multilayers. The solid line indicates nominal bilayer spacings.

 

 

‘—O—.—.——o——o—o

tspacer (A)

Si spacer
{FeSi} spacer

35

Figure 7-3’: Coherence length vs. nominal Si layer thickness for both Fe/Si and Fe/{FeSi}
multilayers on A1203 substrates. The horizontal line indicates a constant value.

 

A. .

 

 

112

7.4.2 Higher-angle XRD

A single Bragg peak consistent with the <110> line of Fe is observed for all samples. For
the Fe/Si multilayers with thin Si layers, this line is narrow indicating a structural
coherence greater than one bilayer. In addition, weak satellites are observed. For ts, >
14A, the Bragg peak broadens, and the coherence length becomes comparable to that of a
single Fe layer. No satellites are seen for these samples as well. In contrast, the
Fe/{FeSi} samples exhibit structural coherence over two or more bilayers for all spacer
thicknesses studied and typically have at least one satellite. Two satellites are seen for the
two thickest spacer layers. Figure 7-3 shows the coherence lengths as a function of
spacer thickness for all samples.

The variation in planar spacing for the <110> line as a function of spacer thickness
is shown in Figure 7-4 and Figure 7-5. For comparison, the accepted d-spacing for the
<110> line of bulk bcc Fe is 2.027A, and a measured value using the Rigaku
diffractometer for a 450A Fe ﬁlm sputtered onto a NaCl substrate is 2.025A.

For the Fe/ Si samples, the d-spacing is essentially constant with the exception of the
thinnest Si layers which have a much greater coherence length. Simple step models used
to predict XRD intensities show that not only do the maximum intensities and peak
widths change when the structural coherence is increased, but the peak positions change
as well. The observed change in d-spacing for the Fe/Si multilayers and the
accompanying change in coherence are consistent with step model predictions.

The F e/ {FeSi} multilayers do not exhibit this change in coherence; however, the
planar spacings decrease with increasing spacer thickness. As stated previously in the

XRD chapter, when two diﬁerent crystalline materials with similar d-spacings comprise

 

 

Tr

 

113

 

‘r r v v y r I Y Y Y T
2.03 7 i r

 

2.02

d-spacing (A)

2.01

 

0 A1203 substrate
D A1203 substrate

 

 

 

 

 

 

 

 

 

 

 

2'00 (different run) I
1 .99 l L l 1 l L l 1 l i l I l I l i l L J 4 l
10 12 l4 16 18 20 22 24 26 28 3O
tspacer (A)
b)
l 40
120
A
3
.a 100 a}. —— t31=10A
: :. ,’ 1: ......... tSi = 20 A
e 80 , .3 '1' ' .
a! 3.3137 "' 1:; ,
v :2; s ‘ =-.-'=.-'. s:
>3 60 4:.5'25 35 ‘-
H _ ,.'---. . ' . 2:
S 40 i" ‘ ,
:3 :5 5:.
bl! ' 5 ~
20 . a”.
0 f 1 ‘

41 42 43 44 45 46 47 48 49
20 (deg)

Figure 7-4: a) Planar spacing as a function of spacer layer thickness for the Fe/Si samples
and b) a comparison of the higher-angle XRD data for the ts, = 10A and ts, = 20A
multilayers.

 

 

114

 

2.026 ~ ~
2.024 : T i
2.022 L «4
2.020 r 1 1
2.018 P i i
2.016 P —«

d-spacing (A)

2014 L *
ZIHZ * r
2.010 " :1

 

 

 

2008 I i 1' 1 l 1 1 I l 1 l
10 15 20 25 30 35 40

tspacer (181)

 

b)

 

800

700

  

600*

500

 
 
 

{FeZASiZA} x 10
400

300

 
 
 

{FeZASiA} x 6
200

 

Intensity (arb. units)

100~
{Fe2ASiZA} x 3

  

 

 

;_ i l

42 43 44 45 46 A 47 48
20 (deg)

 

Figure 7-5: a) Planar spacing as a function of spacer layer thickness for the Fe/{FeSi}
samples and b) a comparison of the higher-angle XRD data for the {Fe2ASi2A} X 3, X 6,
and X 10 multilayers.

115

a bilayer unit in a multilayer then one Bragg line is observed with a d-spacing that is the
weighted average of the constituent components for a certain thickness range of the
individual layers. Alloying Si into Fe causes a decrease in planar spacing proportional to
the Si content.‘9 The observed decrease in d-spacing with increased spacer thickness is
consistent with an Fe-Si alloy constituting an increasing portion of the spacer layer. It
should be noted that the entire range of d-spacings in Figure 7-4 and Figure 7-5 lies
within the limits of pure Fe and the F e-Si alloy with greatest Si content which are 2.027A

and 2.006A respectively.

7 .5 TED Results

All measurements were made using the VG HB501 FESTEM described in Chapter 5.
The number of lines seen in the F e/Si multilayers vary from 14 for those samples with the
thinnest Si layers to as few as 8 for the thicker Si layers as shown in Figure 7-6. All of
these lines are consistent with a bcc structure. A summary of these observed Bragg lines
is presented in Table 7-2 along with the results for a 450A Fe ﬁlm included for
comparison. The presence of the <400> and <521> lines in many of the Fe/Si samples
which are missing from the pure Fe ﬁlm may indicate that alloying has taken place since
substitution of Si atoms for Fe atoms changes the atomic form factor for the planes
containing Si. This substitution can produce stronger <400> and <521> lines than those
observed in pure Fe.

The number of Bragg peaks for the Fe/ {F eSi} samples do not show the same trend
as the Fe/Si samples—instead the number seems more nearly constant with random

differences. Given the lack of change in the coherence for the thickness range examined,

 

 

 

116

6!)

 

 

 

b)

 

 

J

Figure 7-6: TED line scans for Fe/Si samples with nominal Si layer thicknesses of a)
12A and b) 3021.

 

117

Table 7-2: TED Bragg lines observed in F e/Si samples. The lines are identiﬁed by their
Miller indices. Y indicates that the line is observed, and N that it is not.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

28.7 A Fe/x A Si
<hkl> x=0 10 12 14 16 18 23 26 30
<110> Y Y Y Y Y Y Y Y Y
<200> Y Y Y Y Y Y Y Y Y
<21 1> Y Y Y Y Y Y Y Y Y
<220> Y Y Y Y Y Y Y Y Y
<310> Y Y Y Y Y Y Y Y Y
<222> Y Y Y Y Y Y Y Y Y
<321> Y Y Y Y Y Y Y Y Y
<400> N Y Y Y Y Y N N N
<411;330> Y Y Y Y Y Y Y Y Y
<420> Y Y Y Y Y Y N N N
<332> Y Y Y Y N Y N N N
<422> Y Y Y Y N ' N N N N
<510;431> Y Y Y Y N N N N N
<521> N N Y Y N N N N N

 

 

 

 

 

 

 

 

 

 

this result is not surprising. All of the Fe/{FeSi} samples have 10 or more lines
consistent with a bcc structure. "Most" samples have at least one additional non-bcc line.
If a very weak line in only one out of the three regions examined is accepted as evidence,
then "most" becomes all. Two of the samples have two non-bcc lines as shown in Figure
7-7. Neither the number of these lines nor their strengths reveal any discemible
correlation with the {FeSi} layer thickness. For instance, the 16A and 40A spacer layer
samples are the multilayers having 2 non-bcc lines. These lines have d-spacings of 3.08A
and 2.51A if the identiﬁed bcc lines are assumed to have the planar spacings of bulk Fe.
The identiﬁcation of the material producing these two extra lines is difﬁcult at best.
Since it seems likely that they might indicate the presence of an Fe silicide, the listings
for d-spacings of known equilibrium Fe silicides from the Powder Diffraction File were

compared to the preceding values. By far the best match was for that of e-FeSi—the

 

 

 

118

    

1

Figure 7-7: TED line scan for the {Fe2ASi2A} X 10 spacer layer sample with the two
non-bcc lines indicated by the arrows.

Tl

 

same silicide cited in the studies mentioned previously. The <110> and <111> lines of s-
FeSi have respective planar spacings of 3.16A and 2.59A. In addition, the next several
lines which have signiﬁcantly greater intensities in XRD powder patterns have d-spacings
such that they would be hidden by the observed bcc lines. Consequently, these ﬁndings
are consistent with the presence of s-FeSi although the non-equilibrium conditions
associated with sputtering could result in the formation of non-equilibrium compounds
for which no comparison can presently be made.

TEM images show some unusual aspects. Normally, the sputtered multilayers
investigated in this study appear to be quite homogeneous when observed with the
FESTEM. This result is also the case for all of the Fe/Si samples and for the Fe/{FeSi}
samples with tires, 3 24A. The remaining samples, however, have BF images consisting

of mostly dark regions with small inclusions of signiﬁcantly lighter regions. The dark

 

 

119

regions are crystalline and have the characteristics noted above. The lighter regions are
amorphous and probably consist of mostly Si though this was never conﬁrmed.
Unfortunately, the x-ray detector was not working during these measurements, so EDX
(energy dispersive x-ray analysis) of the composition could not be used. Later, when
EDX was again available, the samples on salt substrates were observed to have suffered
signiﬁcant oxidation even though kept in a vacuum dessicator. Since positive
identiﬁcation of these regions would not provide any more information regarding the

magnetic coupling, additional samples were not made.

7.6 XAFS Results

A limited analysis of the XAFS data reveals several qualitative features. For Fe/Si
multilayers, the EXAF S region has oscillations quite similar to that of pure Fe indicating
a bcc structure but with a reduced number of Fe ﬁrst and second shell neighbors which
far exceeds that expected for sharp Fe-Si interfaces. In the XANES region comprised of
about 40 eV above the edge, some Fe/Si samples with thicker spacer layers are missing a
broad hump seen for pure Fe. For the Fe/{FeSi} multilayers, the EXAF S data appears to
be the same as that for pure Fe with a decreased amplitude indicating a reduction of
neighbors in the ﬁrst two shells of about one-half.

A variety of structural models have been used to generate theoretical XAF S data
using FEFF. So far, none of these models—including sharply interfaced multilayers, Fe-
Si alloys of varying composition, Fe silicides, and plausible weighted combinations of

these models—have produced the observed XAFS data.

 

 

'1

 

120

 

1C. Dufour, A. Bruson, B. George, G. Marchal, and Ph. Mangin, J. Phys. (Paris) Colloq.
49, C8-1781 (1988).

2C. Dufour, A. Bruson, B. George, G. Marchal, Ph. Mangin, C. Vettier, J .J . Rhyne, and
R.W. Erwin, Solid State Commun. 69, 963 (1989).

3C.L. Foiles and J.M. Slaughter, J. Appl. Phys. 63, 3209 (1988).

4C. Dufour, A. Bruson, G. Marchal, B. George, and Ph. Mangin, J. Magn. Magn. Mater.
93, 545 (1991).

5S. Toscano, B. Briner, H. Hopster, and M. Landolt, J. Magn. Magn. Mater. 114, L6
(1992)

6P. Griinberg, R. Schreiber, Y. Pang, M.B. Brodsky, and H. Sowers, Phys. Rev. Lett. 57,
2442 (1986).

7M. Ruhrig, R. Schafer, A. Hubert, R. Mosler, J .A. Wolf, S. Demokritov, and P.
Grl'inberg, Phys. Stat. Sol. (a) 125, 635 (1991).

8Eric E. Fullerton, J .E. Mattson, S.R. Lee, C.H. Sowers, Y.Y. Huang, G. Felcher, S.D.
Bader, and RT. Parker, J. Appl. Phys. 73 (10), 6335 (1993).

91E. Mattson, Eric E. Fullerton, Sudha Kumar, S.R. Lee, C.H. Sowers, M. Grimsditch,
S.D. Bader, and RT. Parker, J. Appl. Phys. 75, 6169 (1994).

loJ.E. Mattson, Sudha Kumar, Eric E. Fullerton, S.R. Lee, C.H. Sowers, M. Grimsditch,
S.D. Bader, and F .T. Parker, Phys. Rev. Lett. 71, 185 (1993).

“B. Briner and M. Landolt, z. Phys. B92, 137 (1993).

12K. Inomata, K. Yusu, and Y. Saito, Phys. Rev. Lett. 74, 1863 (1995).
13Eric E. Fullerton, private communication.

l4Alison Chaiken, private communication.

15E.W. Hill, S.L. Tomlinson, J .P. Li, J. Appl. Phys. 73 (10), 5978 (1993).

l6J. Alvarez, A.L. Vazquez de Parga, J.J. Hinarejos, J. de la Figurera, E.G. Michel, C.
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(1993).

17Papers in Silicides, Germanides, and Their Interfaces, Mater. Res. Soc. Proc. 320,
(1994)

 

 

Il—

 

 

121

 

18Eric E. Fullerton, J.E. Mattson, S.R. Lee, C.H. Sowers, Y.Y. Huang, G. Felcher, S.D.
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19W.B. Pearson, Handbook of Lattice Spacings and Structure of Metals and Alloys, Vol.
2, Pergamon Press (1967).

 

 

CHAPTER 8
SUMMARY AND CONCLUSIONS

8.1 Co/Cu Multilayers

XAFS data for sputtered Cu/Co multilayers give nearest neighbor distances and
measures of layer disorder which are consistent with the earlier results of Pizzini, et al.
for evaporated multilayers. The use of anomalous dispersion to enhance the x-ray
contrast between Cu and Co supplement the XAF S data in two respects. First, the actual
bilayer distances of the sputtered samples have been measured and conﬁrm the use of
nominal bilayer spacings in describing experimental trends in behavior. Second, both the
Bragg lines and their general intensity patterns suggest that the XAF S data are free of any
complications associated with signiﬁcant deviations from either sharp interfaces or strong

<111> ﬁbre texture.

8.2 Co/Mo Multilayers

The saturation magnetization shows a systematic decrease from bulk value for thick
Co layers to a nearly complete loss of magnetism for thin Co layers. This loss occurs for
both crystalline as well as disordered samples. These results conﬂict with those of Wang,
et al., but are generally consistent with those of Sato. Using XRD and TED, a structural
progression is observed for the multilayers. For equal layer samples, a transition from
amorphous, to crystalline with a dominant composite Bragg line <D>, and ﬁnally to
Bragg lines for the individual elements is seen as the bilayer thickness increases. XAF S

data document that this transition from disorder to crystalline order occurs rapidly as layer

122

 

,. J

 

 

123

thickness increases from SML to 7ML. TED data provide no evidence for the presence of
Co-Mo compounds. These structural ﬁndings are consistent with those of Satol for
Co/Mo prepared by dc magnetron sputtering and are completely inconsistent with the
structural features reported by Wang, et al.2 for Co/Mo prepared by focused ion
sputtering. These observations seem to indicate that magnetron sputtering and focused ion
sputtering form Co/Mo multilayers with different structures.

XAFS data show a clear correlation between local structure and magnetic behavior.
For equal layer samples, XAF S data clearly show that the development of crystalline Co
into an hcp or fee structure or a mixture of these coincides with an increase in saturation
magnetization. For the one crystalline sample (2ML/8ML) with thin Co layers, XAF S
data reveal that the Co layers have a different structure from that of the other Co/Mo
multilayers. Though several plausible structures for this sample were modeled using

FEFF, none of the modeled results were consistent with experiment.

8.3 Fe/Si and Fe/{FeSi} Multilayers

XRD data establish a consistent pattern of structural coherence in Fe/Si and
Fe/{FeSi} multilayers. This coherence occurs for a limited range of nominal Si layer
thicknesses (ts, S 15A) and for a much larger range of {FeSi} thicknesses “{FeSi} 2 40A).
XRD data provide no direct evidence of F e—silicides, but TED data exhibit non-bcc lines
that are such evidence. These lines occur in Fe/{FeSi} multilayers, do not occur in Fe/Si
multilayers, and give a plausible match to the Bragg lines of one equilibrium silicide.
TEM images of the F e/ {F eSi} multilayers indicate that a two phase material is formed for

thicker {FeSi} spacer layers.

 

 

 

124

These results suggest that inferring the presence of silicides from detailed features in
XRD data or macroscopic properties has limited value. For samples having structural
coherence over more than one bilayer, the coherence lengths determined from XRD data
are comparable for Fe/Si and Fe/{FeSi} multilayers but Fe-silicide lines are only
observed in the latter samples. Systematic changes in the position of the <110> Bragg
line are consistent with structural coherence but give no evidence for either silicides or a
change at the {FeSi} spacer layer thicknesses for which TEM images show evidence of
two phases with different structures.

XAFS data indicate a reduction in the Fe coordination numbers for either Si or
{F eSi} spacer layers. The results of saturation magnetization measurements indicate that
the Fe in the {FeSi} spacer layers exhibits different magnetic behavior from that of the
nominally pure Fe layers. The underlying cause of these differences has not yet been

identiﬁed.

8.4 Future Investigations

8.4.1 Co/X Multilayers

With the exception of Co/Mo, the studies of Co/X were largely unsuccessful in
determining any simple correlations between structure and magnetic behavior. In the case
of Co/Mo, more samples with thin Co layers (2ML—5ML) are needed to establish
experimental trends. FEFF modeling of these samples is a promising possibility for
determining the structure of the Co layers. As a general trend, however, further efforts to
study structure and magnetic behavior should perhaps focus more on sample fabrication.

If sample structure can be more easily controlled during sample manufacture, then

 

 

IF

 

125

relationships between the structure and magnetic behavior may be more easily

determined.

8.4.2 Fe/Si and Fe/{FeSi} Multilayers

Further information is needed about both the structure and the magnetic state of the
Fe in the {FeSi} spacer layers. By using isotopically-enriched Fe in the {FeSi} spacer
layers, Mossbauer spectroscopy studies could be used to determine the magnetic state of
Fe in the spacer and to infer its local structural environment since non-magnetic Fe and
magnetic Fe have very different Mossbauer spectra. Since these spectra are sums of
individual contributions, the measured data could be ﬁtted using well-documented results
for silicides and Fe—Si alloys to perhaps determine the actual composition of the spacer

layer.

 

lNoboru Sato, J. Appl. Phys. 63, 3476 (1988).

2Y. Wang, F.Z. Cui, W.Z. Li, and Y.D. Fan, J. Magn. Magn. Mater. 102, 121 (1991).

 

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